National Science Foundation Proposal

C.) PROJECT DESCRIPTION

C.1 Overview

This proposal is for a three-year grant of $4,290,000 to support a program of research in nuclear physics and related subjects at the W. K. Kellogg Radiation Laboratory of the California Institute of Technology. This program includes experimental and theoretical research on the fundamental structure of nuclear and hadronic systems and the interactions responsible for their properties. The proposal is for renewed support of a group of faculty, postdoctoral researchers, students, and support staff that form a dynamic community engaged in research and education in nuclear physics and related subjects.

The proposed research program includes several exciting new initiatives which are generally based on work that was started during our previous grant period:

\item{$\bullet$} The G0 experiment at Jefferson Laboratory is presently under construction and scheduled to begin during 2001. This project represents the definitive study of parity-violating electron scattering at medium energies, the exploration of the neutral weak form factors of the nucleon and the related issue of the role of strange quark-antiquark pairs. It follows directly from our pioneering work at Bates on the SAMPLE experiment and relies on the expertise and knowledge that we gained during that previous effort.

\item{$\bullet$} The E158 experiment at SLAC is also under construction and scheduled to begin in 2001. This project will push the state of the art in parity-violating electron scattering to perform high-precision measurements of Moller scattering that will be sensitive to new weak forces or possible internal structure of the electron.

\item{$\bullet$} The development of a new ultra-cold neutron source in collaboration with physicists at Los Alamos National Laboratory and the proposed high-precision measurement of the asymmetry in neutron beta decay will test the unitarity of the Cabibbo-Kobayashi- Maskawa matrix and provide a sensitive test for right-handed weak interactions. This project requires the development of novel low-energy beta detector technology which is underway in the Kellogg Laboratory.

\item{$\bullet$} A theory of nuclear matter is under development that correctly accounts for the structure of the nucleon and for the structure of light nuclei as constrained by chiral symmetry.

These projects, along with our other proposed activities, are described in more detail in C.2 below.

This proposal includes the research activities of professorial faculty R. McKeown, B. Filippone, and S. Koonin along with research faculty C. Jones and B. van Kolck. (Professor Hughes will seek separate funding for his future activities.) Although Professor S. Koonin has been the Provost and Vice-President of Caltech for the last several years he maintains an active research program and interest in several nuclear physics related subjects; his research plans in this area are outlined in this proposal. Dr. Cathleen Jones was appointed as a Senior Research Associate in 1997, and has played a major role in the development of new research projects in the Laboratory during the last 2 years. Her continued participation is essential to realize the major goals of the proposed experimental research program. Dr. B. van Kolck was appointed as a Senior Research Fellow in 1997 and he has established an active program in effective field theory and medium energy physics phenomenology related to our experimental research. There are presently 2 postdoctoral scholars (with external financial support) working with Dr. van Kolck, and Professor R. Seki (California State Universty at Northridge) has continued his relationship with Kellogg as a Visiting Associate. The present Kellogg research staff includes a total of 12 postdoctoral scholars and other senior research staff, most of whom are supported by other sources.

In addition, we have been fortunate to attract a number of theorists as regular visitors to our Laboratory. These include H. Bethe (Visiting Associate), G. Brown, D. Riska, K.-F. Liu, R. Schiavilla, and J. Humblet (Visiting Associate). Along with the presence of other theorists (supported by S. Koonin's NSF Theory grant), Dr. P. Vogel (Senior Research Associate, supported by DOE), and Dr. J. Beacom (Prize Postdoctoral Fellow supported by Caltech), we have been able to continue an active theoretical research program and maintain a broad and stimulating intellectual environment in the Laboratory while Professor Koonin has been attending to his administrative duties. The importance and impact of this environment on our ability to attract, train, and mentor high-quality students and postdoctoral researchers can not be understated. We therefore propose to continue this theoretical research program as part of our renewal proposal.

The Kellogg Laboratory provides a unique and highly productive environment for the pursuit of research and education in nuclear physics. Results from prior NSF support (last 5 years) are discussed in section C.3 below, and the first 198 references listed in section D represent the publications resulting from that work. We continue to attract excellent graduate students and postdoctoral scholars to participate in this highly successful program. (One postdoctoral scholar, Dr. T. Ito, won an award for his outstanding Ph.D. thesis in nuclear physics from the Japanese Physical Society. Dr. B. Tipton just joined us from MIT as a Millikan Fellow supported by Caltech.) Three Kellogg graduate students received their Ph.D.'s in the last year (P. Carter, A. Dvoredsky, and M. Mueller) and 10 students received Ph.D.'s during the last five years. One student, B. Mueller, was awarded the Peter Demos Award for his outstanding thesis work at the MIT/Bates Laboratory. Our former students and postdocs are in high demand at top research and academic institutions throughout the world; many of them now hold faculty or research positions in nuclear physics and related fields. In addition, many of these young researchers pursue successful careers in the private sector utilizing the skills and knowledge acquired through their education in the Kellogg Laboratory.

Our experimental research program continues to include a substantial component of instrumentation development. Thus it is essential that we maintain our technical staff in order to satisfy our commitments to our collaborators and achieve our mutual research goals. The major activities in instrumentation development are described in section C.2.III below.

Some of our experimental projects receive some or all of their support from funding sources outside this NSF grant. This project description includes all of these activities, and the nature and degree of external support is explicitly indicated for each item where appropriate. It should be emphasized that the general Laboratory infrastructure provided by this NSF grant is often crucial for the execution and/or development of these activities, even when they are primarily supported from external sources. As in the past, NSF support of the Kellogg Laboratory is often a mechanism for highly-leveraged development of synergistic programs in a wide variety of subjects in nuclear physics and related areas.

C.2 Proposed Research

C.2.I Experimental Research

C.2.I.a G0 - A detailed study of strange vector form factors of the nucleon
[R. Carr, S. Covrig, B. W. Filippone, T. Ito, C. E. Jones and R. D. McKeown]

The neutral weak form factors of the nucleon provide crucial new information on the internal structure of the nucleon. In particular, experimental study of these quantities enables a determination of the strange quark-antiquark contributions to static properties of the nucleon.²¹³ The measurement of parity violation in elastic electron-nucleon scattering can be used to study these form factors.²⁰⁰ In the pioneering SAMPLE experiment at the MIT/Bates Linear Accelerator Center we have recently obtained the first results on the neutral weak magnetic form factor using this method. ^{80, 180}

Analogous to the magnetic form factor measured in the SAMPLE experiment, the charge form factor of the proton may also have a contribution from strange quark-antiquark pairs.²¹⁴ In this case, the effect vanishes at Q²=0 (since there is no net strangeness) but it may be sizeable at finite Q². The ``G0'' experiment is a major approved proposal²⁰² [99-016; D. Beck of Illinois is spokesperson] to study the strange vector (electric and magnetic) form factors of the nucleon at TJNAF. These measurements will be in the range 0.2 < Q² < 1.0 (GeV/ c)}², higher than the SAMPLE experiment at Bates. By performing measurements of the parity violating asymmetry in elastic electron scattering at both forward and backward angles, the electric and magnetic neutral weak form factors will be separated. One can then solve for both the strange electric and magnetic form factors in this Q² range. The projected precision is shown in figure C.2.I.a.

Figure C.2.I.a Projected uncertainties for the G0 experiment along with the previously published SAMPLE result and some theoretical predictions.^{199, 238}}

The experimental design consists of a superconducting toroidal magnetic spectrometer, a liquid hydrogen target, scintillation counters, and high rate electronics. The Caltech group is responsible for the liquid hydrogen target (C. Jones is subsystem manager) which is described in more detail in section C.2.III.a below; construction and design are presently underway.

The forward angle elastic electron scattering will be studied by detecting the recoil protons. The combination of magnetic analysis and time-of-flight measurement will allow separation of elastic events. The backward angle electron scattering measurements will be made by detecting the backward scattered electrons directly. In addition, the backward angle measurements will enable a study of the $N\rightarrow \Delta$ axial form factor; this measurement was approved by the JLAB PAC in 1997. Given the intriguing new results from the SAMPLE experiment (see section C.3.I.a below) the possibility of running the G0 experiment with a deuterium target will be investigated in the near future.

Construction of the magnetic spectrometer is also well underway, and the magnet is scheduled for delivery and test at the University of Illinois in early 2000. At present, installation of the experiment at JLAB is anticipated during 2001, followed by beam commissioning studies.

C.2.I.b Precision Measurement of the Weak Mixing Angle via Parity Violation in M\o ller Scattering
[R. Carr, B. Filippone, J. Gao, C. Jones, R. McKeown]

The goal of SLAC experiment E158²⁰³ is a precision determination of the electroweak mixing angle at low Q² via measurement of the parity violating asymmetry in M\o ller scattering. This measurement is complementary to a recent determination²³⁰ of sin² theta_W in atomic Cs where there seems to be a $2\sigma$ deviation from the standard electroweak prediction. Our proposed experiment at SLAC will provide a low Q² determination of sin² theta_W to a precision of \pm 0.00075, a factor of 3 more precise than the Cs result and competitive with the high-precision measurements at the Z-pole in high energy physics experiments. The experiment was approved by the SLAC Program Advisory Committee in September 1997, and further approval (including release of SLAC construction funds) was granted after a milestone review in March 1999.

The experiment will be performed using the new 50 GeV polarized electron beam facility at SLAC. (The SLAC beam parameters, \sim 5 x 10¹⁰ e^- per pulse at 120 Hz and 75% polarization, were essentially achieved in a test run in January 1999. In addition, the precision of beam monitoring devices was tested during this run and satisfactory preliminary performance was demonstrated.) The unpolarized target electrons are provided by a 1.5 meter long liquid hydrogen target. (This target is a major construction item and is the responsibility of the Kellogg Lab under the direction of C. Jones. See section C.2.III.a below for more details.) The M\o ller scattered electrons are selected at small angles (4.5 - 7.2 mr) with energies 12-25 GeV in a forward angle magnetic spectrometer and then detected in a radiation-resistant calorimeter comprised of Cu radiator and Si fibers. The integrated charge in the calorimeter photomultipliers will be digitized for each beam pulse and the parity-violating asymmetry measured in a manner similar to the SAMPLE experiment performed at Bates.

Figure C.2.I.b Projected statistical uncertainty of the E158 measurement of sin² theta_W along with other determinations. The value at low Q² is evolved using electroweak theory from the measured value at M_Z.

The parity-violating asymmetry is expected to be 1.24 x 10^-7 and the projected statistical uncertainty for a 20 week run is \Delta A \simeq 8 x 10^-9, corresponding to the above quoted uncertainty in sin² theta_W. The expected precision of the measurement is displayed in figure C.2.I.b. Systematic uncertainties, in particular, those related to false asymmetries coming from the polarized beam need to be kept down to a level of a few parts per billion. These are very challenging goals, particularly as the helicity correlations in the beam are more difficult to control with the strained GaAs crystals used in the SLAC polarized source. The spectrometer and target system are presently under construction and we expect to begin test and commissioning runs during the fall of 2000. Preliminary data-taking may begin in 2001.

C.2.I.c Precision measurement of the neutron beta-decay asymmetry with ultra-cold neutrons
[B. Filippone, D. Fong, T. Ito, C. Jones, J. Martin, R. McKeown, R. Patterson, B. Tipton, J. Yuan]

We have begun a major collaboration (with Los Alamos, Princeton, and others) to perform a precision measurement of the angular correlation between the neutron spin and electron momentum following neutron beta-decay²⁰⁴. Using an ultra-cold neutron (UCN) source under development at Los Alamos, this measurement would allow a significant reduction in systematic errors compared to previous experiments.

The angular correlation in neutron beta-decay is usually characterized, via angular integration, by a rate asymmetry for detecting electrons along and opposite the neutron spin direction - the so-called A coefficient. Assuming time-reversal invariance, A is directly related to the ratio of the vector to axial-vector weak coupling constants G_A/G_V. When combined with precision measurements of the neutron lifetime, G_A and G_V can be separately determined. Such measurements would allow the most precise extraction of V_ud (originally known as the cosine of the Cabbibo angle), which is a key input in the Cabbibo-Kobayashi-Maskawa (CKM) matrix of standard model electroweak couplings. A violation of the unitarity of this matrix would signal a significant breakdown of the standard model.

Previous determinations of V_ud from nuclear beta-decay indicate a possible violation (\sim 1.4 sigma) in the unitarity of the CKM matrix²⁰⁴. Also previous measurements of A (which has a magnitude of about 0.1) with fractional uncertainties of \sim 1% disagree at the 3-4% level. Our proposed measurement would initially achieve a total uncertainty of \sim 0.2% with significantly different systematics compared to the previous experiments. In addition, by using the free neutron to extract V_ud, the nuclear corrections involved in the 0⁺ - 0⁺ nuclear decays are absent. A comparison of the values of V_ud and \lambda = |G_A/G_V| are shown in Fig. C.2.I.c.1. Also shown in the figure is the projected error from the present experiment. Precision measurement of A also allows a sensitive test for right-handed currents in the weak interaction.

Figure C.2.I.c.1 V_ud vs \lambda = |G_A/G_V|. Constraints based on requiring unitarity, on the neutron lifetime and the previous and proposed measurements of \lambda.

All previous measurements of A have used cold neutrons produced at reactor facilities. Our measurement would use the pulsed 0.8 GeV proton beam from the LANSCE facility at Los Alamos to produce a volume of trapped UCN. The pulsed beam considerably reduces background by allowing beta-decay detection to occur during beam-off periods, something not possible at reactor experiments. Using UCN also allows the production of essentially 100% neutron polarization via a solenoidal magnetic field filter. Background contributions and knowledge of the neutron polarization were dominant systematic uncertainties in previous experiments.

A schematic overview of the experiment is shown in Fig. C.2.I.c.2. Following polarization [and optional spin flip via an Adiabatic Fast Passage (AFP) NMR apparatus], the neutrons are injected into the solenoidal spectrometer where decay electrons spiral towards two detector systems. Decay rates of 20 to >100 Hz are anticipated based on current understanding of the UCN production source. Over the last year we have been vigorously pursuing the development of this new source of UCN that is based on a solid deuterium moderator. Our recent measurements indicate that we can already achieve a UCN density close to that available at the world's most intense UCN source at the ILL reactor in Grenoble. These measurements are discussed in Section C.2.III.c. Detailed Monte Carlo calculations suggest that the potential density available from such a source could exceed 500 UCN/cc compared to the highest density ever achieved at ILL of \sim 100 UCN/cc (typically experiments at ILL run with 5 - 20 UCN/cc). These higher densities could allow the fractional statistical error in the determination of A to eventually fall well below 0.1%.

Figure C.2.I.c.2 Schematic diagram of apparatus used to measure the correlation of the neutron spin with the electron momentum following neutron beta-decay.

Caltech is responsible for developing, constructing and installing the beta-decay detectors for the measurement. We also expect to play leading roles in the electronics and data acquisition systems as well as with the analysis of the data. Presently we are investigating the use of tracking detectors to measure the electron angle and to reject background from backscattered electrons. The angle measurement will allow an important systematic check of the angular correlation (most previous experiments averaged over the distribution). In addition the very small systematic errors that are needed for this new precision measurement require careful calibration of the detector response. For this we have begun a series of measurements using the NASA-JPL dynamitron to produce 0.15 - 1 MeV electrons. We are also constructing a low energy accelerator (0.02 - .15 MeV) in our lab using spare parts from our Pelletron accelerator. To calibrate both of these accelerators we have constructed a novel iron-free electron spectrometer. The detector and calibration efforts are discussed in Section C.2.III.d. Up to now these efforts have been funded primarily through Caltech discretionary funds.

The physics proposal (submitted to DOE) has been favorably reviewed and construction on the experiment is expected to begin following a technical review at LANL, scheduled for Dec. 1999. Construction of the UCN source, initially funded through LANL, is anticipated to begin early next year with funding from DOE. This initial source would be optimized for the neutron asymmetry measurement (discussed in section C.2.III.c), with future upgrades and improvements leading to a production facility for future UCN experiments.

Regarding future opportunities, we are collaborators on a possible next generation search for a neutron electric dipole moment (EDM). Observation of such a moment would indicate clear evidence for Time-Reversal Violation (or CP violation assuming CPT invariance) in a system other than K mesons and seriously constrain theoretical extensions to the standard model. We are also pursuing a possible neutron lifetime measurement using magnetically trapped UCN fed by our SD2 UCN source.

Within the time frame of this proposal we anticipate physics results from the A correlation measurement and initial construction on at least one of the projects (neutron lifetime and EDM) mentioned above.

C.2.I.d Development of a Large Area Array for Ultra-high Energy Cosmic Ray Research
[R. McKeown, V. Savu, and R. Seki]

We propose to collaborate with local high school physics teachers to site an array of particle detectors at high schools in the Los Angeles area. This array will be capable of detecting the very highest energy cosmic rays observed to date. The origin and nature of the primary incident particles that produce these huge air showers is of great current interest.^{225, 226} The project will offer students in local high schools a unique opportunity to collaborate with Caltech researchers and address fundamental issues at the forefront of present-day astrophysics and particle physics. Thus, in addition to establishing a significant experimental facility for high-energy cosmic ray studies this project will provide an exceptional educational experience for high school students in the Los Angeles area. The Caltech Development office is presently engaged in raising funds from private donors for this project, and we presently plan to establish this program without the use of funds from the Kellogg NSF grant. Nevertheless, the existing lab infrastructure and expertise associated with the Kellogg Lab will be essential in this new venture.

C.2.I.e Neutrino Physics at KamLAND
[L. Hoffman, J.-T. Lee, K. B. Lee, R. McKeown, B. Tipton, and P. Vogel]

There has been a strong tradition of low-energy neutrino physics at Caltech in the group of Prof. F. Boehm, funded by DOE. With the recent retirement of Prof. Boehm and the new opportunities provided by the KamLAND experiment, we have proposed to continue the neutrino group with the leadership of Prof. McKeown as Principal Investigator. We expect that the full support for this program will come from DOE as in the past. A brief description of the Caltech activity is presented here for clarification of its relationship to the Kellogg NSF program.

The principal goal of the KamLAND experiment²⁰⁵ is to perform a search for neutrino oscillations at very low mass scale, \Delta m² < 10^-5 ev². The region of sensitivity will completely overlap the large mixing angle solution to the solar neutrino problem; thus KamLAND will provide a test of this solution in a terrestrial experiment. A large (1000 Ton) liquid scintillator detector is being constructed at the site of the old Kamiokande experiment in Japan. This detector is located an average distance of 200 km from a large number of commercial nuclear power stations in Japan that provide an intense source of 1.5-8 MeV electron antineutrinos. The KamLAND detector will detect about 800 events per year in the absence of neutrino oscillations. The background rate is estimated to be negligibly small compared to this signal rate due to the very deep location of the detector.

The Caltech group will provide measurements of the radiopurity of all detector components using an existing low-background counting facility built for the Palo Verde reactor neutrino oscillation experiment. This facility and the existing group provide an opportunity to make an important contribution to this experiment in the early stages of construction. Bryan Tipton will oversee these radioassay activities and will also play a lead role in establishing a simulation working group for the experiment; Petr Vogel's expertise in low-energy neutrino physics will be extremely valuable for this activity as well.

C.2.I.f Electron Scattering from Tritium
[C.E. Jones]

Cathleen Jones helped organized a workshop at TJNAF in September 1999 to discuss experiments that could be done with a tritium target at the energy range accessible to CEBAF. At the workshop, we identified several measurements of significant importance that could be addressed with high-luminosity experiments at TJNAF using a tritium target, including

\item{$\bullet$} determination of the ratio of the deep inelastic structure functions F_2^n/F_2^p from a measurement of the ratio F_2^{³He}}/F_2^{³H},

\item{$\bullet$} determination of the isovector and isoscalar components of the elastic charge and magnetic form factors for the 3N system at higher momentum transfer, which will require measurements of comparable quality of both tritium and ³He elastic separated cross sections.

Other experiments discussed included a measurement of the Drell-Hearn-Gerasimov sum rule and the Coulomb sum rule of tritium. At the end of the workshop, it was decided to work out experimental details for the deep inelastic structure function and elastic form factor measurements for presentation to the PAC soon, while considering presenting other experiments after getting a response from the PAC and the lab to these two experiments.

C.2.I.g SAMPLE II
[S. Covrig, B. Filippone, J. Gao, T. Ito, C. Jones, R. McKeown]

We are investigating the possibility of running the SAMPLE experiment at lower energies during the next year. As discussed in section C.3.I.a below, the SAMPLE results from the 1998/99 runs seem to indicate a surprising contribution from the nucleon anapole moment. A useful check on the previous results would be to measure the asymmetry at different kinematics where the signal/background ratio is more favorable. We are considering the possibility of another measurement at perhaps 100 MeV incident energy, and we expect to submit a proposal to the MIT/Bates PAC this winter.

C.2.II Theoretical Research

The theoretical component of our research program aims to complement the experimental study of the fundamental structure of hadronic and nuclear systems. At energies of relevance for nuclear physics, the symmetries of the Standard Model provide important constraints on the dynamics; conversely, un understanding of this dynamics is necessary to the determination of the parameters of the Standard Model, such as light quark masses. Although in principle one can solve QCD in the non-perturbative regime with lattice regularization on the computer, at low energies this solution is encompassed by the most general effective field theory (EFT) consistent with the known symmetries of QCD. Chiral Perturbation Theory (\chi PT) has emerged in the last few years as a promising tool to systematically understand hadronic and nuclear features in a framework which is consistent with QCD. Simultaneously, sophisticated computational methods have been developed at Kellogg and elsewhere for the treatment of nuclear systems. We are approaching a stage where these methods can be applied to QCD-based nuclear potentials.

Our theoretical program ranges from the determination of important nucleon parameters to the solution of heavy nuclei, through the study of a variety of reactions studied by Kellogg and other experimentalists at facilities such as Bates, JLab, IUCF, Duke FEL/TUNL, NIF, RHIC, TRIUMF, SAL, Mainz, KVI, Uppsala, Lund, and CERN.

C.2.II.a QCD and Effective Theories
[L. Diaconescu, C. Maekawa, J.S. da Veiga, R. Seki, and U. van Kolck]

In the prior period of NSF support we have made much progress in establishing a connection between QCD and nuclear physics (see section C.3.II.a below). There is now growing evidence that an effective field theory (EFT) approach can summarize hadronic and light-nuclear physics phenomenology to a given accuracy in terms of a finite number of parameters that carry information about the QCD dynamics. The goal of our proposed program of research is three-fold: 1) extend the description to heavier nuclei and make the connection with phenomenological (such as the Walecka and the shell) models; 2) determine the dynamical parameters (such as nucleon polarizabilities) from experiment; 3) attempt to deduce such parameters from QCD.

To accomplish this, we plan to study a number of concrete issues. The EFT without explicit pion fields works well, but its limits of applicability are not known. The extension to explicit pion fields, \chi PT, presents many subtle issues when two or more nucleons are involved.

Two-nucleon systems

A consensus now exists on the correct power counting for the pionless EFT, but it remains unclear what the most efficient way of organizing pion effects is. Although results based on Weinberg's power counting agree well with experiment, arguments^{227, 228} based on perturbation theory question the consistency of the scheme already at the level of iterated one-pion exchange (OPE). Yet, our work on the three-body system^{152, 153, 162} suggests that non-perturbative and perturbative renormalizations can be very different. Our methods could provide insight into the non-perturbative pion problem.

Problems remain in the phenomenological description of isospin violation. We plan to extend our calculation¹⁶¹ of the leading charge-independence-breaking (CIB) two-pion-exchange (TPE) potential to next order. This potential can be used in the Nijmegen phase-shift analyses, and its magnitude might be sufficient to explain a good fraction of the current \sim 1 fm discrepancy between theoretical and experimental estimates of CIB in the nucleon-nucleon (NN) scattering lengths. We also are going to calculate the leading charge-symmetry-breaking (CSB) TPE potential, which has never been obtained consistently with chiral symmetry.

Three-nucleon systems

We recently understood the main aspects of the power counting and renormalization of the pionless EFT in three-body systems, including the infrared enhancement of the three-body force^{152, 153, 162}. We have achieved a good description of S waves in nucleon-deuteron (Nd) scattering in the J=1/2 channel and the triton in leading order¹⁶², and in the J=3/2 channel in sub-subleading order¹¹⁵. We are working on extensions of this theory, including: i) the NN effective range in the J=1/2 S wave, which will give an indication of the convergence radius of this EFT; ii) Coulomb corrections in the bound state, in order to predict ³He properties; iii) higher partial waves, to study other scattering observables such as the vector analyzing power A_y.

The explicit inclusion of pions might dramatically affect the renormalization group running at higher momenta. The question is whether the three-body force conforms to Weinberg's power counting and becomes a sub-leading effect, or remains of leading order. We intend to examine this and the associated issues of the Thomas and Efimov effects; a possible starting point is a toy model of a contact interaction plus a finite-range separable potential.

The most important three-body forces in \chi PT have the same TPE elements as existing phenomenological models when the latter are corrected in regard to chiral symmetry¹⁵⁴. They also involve two OPE/short-range terms with currently undetermined parameters. Power counting suggests that these interactions could be relevant given the current precision of three-nucleon calculations by the Urbana/Argonne, Bochum/Cracow and Pisa groups, and experiments carried out at IUCF, TUNL, and KVI. We are investigating what effects these new forces have under the assumption that the parameters have size given by dimensional analysis. Our preliminary results indicate that the effects are large enough to potentially solve the A_y puzzle.

Other few-body systems

The extension of the pionless EFT to systems with more nucleons is considerably simpler than those of the EFT with pions and of phenomenological models. But for it to be relevant to more typical nuclei two points need to be understood. Since ⁴He is a reasonable representative of heavier nuclei, we have to determine i) whether ⁴He is within this EFT, and ii) whether a four-body force is present in leading order. We plan to study the renormalization group flow of the four-body interaction following the approach we used in the three-body system^{152, 153, 162}. If the four-body force is enhanced, it can be determined from low-energy neutron-³He scattering, and then the binding energy of ⁴He predicted, which will give an indication of the range of applicability of this EFT. Since we expect five- and more-body forces to be all sub-leading (because the Pauli principle demands they contain one or more derivatives), more-body systems could then be predicted.

Strangeness

The extension of the theory to SU(3) will open a range of applications of astrophysical interest.

We are developing an EFT for the description of kaon and eta interactions in the non-relativistic regime where these mesons behave as heavy particles. After matching with SU(3) x SU(3) \chi PT, the new EFT can be used to investigate the dynamics that might give rise to shallow bound states in \bar{K} K and \bar{K} N systems. This can be done along the lines used in the applications of \chi PT to the two-nucleon system¹⁵¹.

Another possible extension regards interactions of hyperons and nucleons. In leading order in the EFT with explicit pseudoscalar mesons, the new elements in the two-body potential are one-kaon exchange and four contact terms that could be fitted to hyperon-nucleon data. Hypertriton constitutes a new challenge, as its very small binding energy is not immediately identified with the other mass scales in the problem.

Reactions on few-body systems

For the first time, reactions involving external probes with momenta of O(m_\pi), where m_\pi is the pion mass, can be calculated with consistent nucleon and nuclear inputs. These reactions fulfill a dual role. First, they can test the consistency of the approach. Second, they can be used to extract nucleon parameters; in particular, neutron parameters can be obtained from deuteron, triton and/or ³He data. Processes to be investigated include real photons, electron scattering, and pion production.

We are working on an extension of our previous O(Q³) \chi PT calculation of coherent Compton scattering on the deuteron¹⁵⁸ to next order. We expect to constrain the isoscalar combination of neutron and proton polarizabilities from the recently published SAL data²³⁴ and from forthcoming data from Lund.

Electron disintegration of the deuteron is being investigated in the quasi-elastic regime at JLab²⁰⁸, with the purpose of extracting the neutron form factor. The total disintegration cross section is also important for a test of the Drell-Hearn-Gerasimov (DHG) sum rule for light nuclei. The latter is subject to large cancellations between regions below and above the pion production threshold, which we would like to understand in the EFT. There is some indication that the DHG sum rule for real photons might not be satisfied for the proton. Experiments on the deuteron have been proposed at JLab²⁰⁹ for various transfered momenta and at Duke FEL²¹⁰ for real photons and low energies, in order to infer the DHG sum rule for the neutron. We intend to calculate this process in \chi PT and determine the extent to which these inferences are possible.

We have made²²³ a prediction for neutron pion photoproduction on the deuteron at threshold in O(Q⁴) \chi PT that differed significantly from conventional model predictions. Recent SAL data²²⁴ supported our result and ruled out conventional tree-level models. Data are under analysis at Mainz²¹¹ of a similar electroproduction experiment. We plan to extend our calculation to virtual photons to further test the EFT.

The transverse electron asymmetry in scattering on an unpolarized target vanishes in the one-photon approximation. Such an asymmetry could arise from the interference between one- and two-photon exchanges. We are investigating if precise measurements of this asymmetry could constrain the target polarizability.

Extraction of the nucleon strange magnetic form factor from the longitudinal asymmetry in parity-violating electron scattering on the proton at backward angles is limited by the uncertainty in radiative corrections to the axial-vector coupling form factor. These contributions can be disentangled with scattering on a deuteron target. The experiments have been carried out by the Kellogg group at Bates (see section C.3.I.a). We are examining the effects of meson-exchange currents in the observable asymmetry.

Part of the contribution to parity-violating electron scattering comes from the nucleon anapole form factor. The anapole moment cannot be calculated in \chi PT because it involves an undetermined counterterm²¹⁶. We plan to investigate the momentum-transfer dependence of the anapole form factor that is determined from one-loop diagrams. We also hope to study models for the undetermined counterterm.

S-wave pion production in NN collisions has already been studied within a \chi PT-inspired approach^{159, 221, 222}. The higher momenta involved in this process (O(\sqrt{m_\pi m_N}), where m_N is the nucleon mass) introduce some subtleties in the separation of scales necessary to decompose the amplitude into wavefunction and kernel, and to apply \chi PT to each of these elements. These subtleties are important because of (apparently accidental) cancellations that happen in the pion S waves. These subtleties are being analyzed in a toy model where two-meson exchange can be calculated explicitly. The pion P waves do not share the same cancellations and should be under better theoretical control. They do receive low-order contributions from the same pion/four-fermion parameters that contribute to the OPE/short-range three-body force. We are investigating whether these parameters can be determined from recent IUCF pion production data^{235, 236}.

Algebraic realizations of chiral symmetry

As the energy increases, higher-order terms in the EFT become progressively more important and amplitudes approach unitarity constraints. New degrees of freedom need to be added to the theory to control this growth. Under the assumption that amplitudes in the limit of large number of colors do not grow faster than in Regge theory, the new degrees of freedom have, in the chiral limit, to be in reducible representations of the chiral group²¹². We plan to investigate the constraints on pionic and electromagnetic couplings among nucleon and delta resonances that come from the simplest reducible representations, and compare to values inferred from JLab experiments.

C.2.II.b Nuclear Matter and Structure
[H.-M. M\"uller, S.E. Koonin, R. Seki, and U. van Kolck]

One of the longstanding goals of nuclear physics is to solve the nuclear many-body problem with realistic interactions determined from few-nucleon systems. The group at Kellogg has convincingly demonstrated the virtues of the Shell Model Monte Carlo (SMMC) method for the solution of finite nuclei. Infinite nuclear matter affords the simplest many-body arena where this solution might be achieved starting from microscopic interactions. We aim to investigate nuclear matter through a Monte Carlo calculation with realistic interactions. We will also continue to study pion interferometry as a source of information about high-energy nuclear collisions, such as those expected in RHIC, and neutrino interactions with nuclei as input to neutrino detectors and astrophysical processes.

Nuclear matter on a coordinate-space lattice

The first step in the application of SMMC methods to nuclear matter has been taken during the previous period of NSF support (see section C.3.II.b). We are considering a number of ways in which this calculation could be improved.

Our current lattice spacing is about 1.8 fm, which is longer than the inverse Fermi momentum, 0.75 fm. The spacing should be reduced in order to describe the physics of saturation reliably. Moreover, although we have seen evidence for a liquid-gas phase transition, the determination of the order of the transition is obscured by the small size of our lattice. This issue has been studied in the condensed matter field for some years, and techniques developed there should be applied here, including the method of finite scaling²²⁹. This all suggests that our lattice volume be increased by an order of magnitude or more. We will search for ways to run our code more effectively by developing numerically efficient algorithms and securing more suitable computers. Note that the code is already parallelized.

We would like to use an interaction determined from few-nucleon systems. The simplest of such interactions are the ones appearing in leading order in EFT. If nuclear matter is within the range of the pionless EFT, they are two-, three-, and perhaps four-body contact interactions (see section C.2.II.a). However, we naively expect that a lattice spacing of \sim 0.75 fm would require the explicit inclusion of pions. Eventually, a realistic set of interactions should be used. In any case, i) the interaction parameters have to be fitted to few-body data with the few-body system solved on a lattice; and ii) our nuclear matter method, which at present handles only two-body contact forces, would have to be generalized. The pion, for example, might be included in links, similarly to gluons in lattice QCD. Once we use such interactions, the calculation will include full quantum-mechanical effects and thus involve no approximations other than the lattice formulation.

The use of more microscopic interactions might require other algorithm developments. At present we have restricted our parameters to values free of the sign problem in the exponential of the path integral. Should the sign problem become an issue, we would have to face the use of a constraint on the fermion determinant²³⁷. Moreover, we expect that some efficient computational formalism will have to be developed if pions are included, since a large cancellation of pion effects presumably occurs in nuclear matter. Though useful, the Hubbard-Stratonovich transformation requires a separate external field for each part of the N N interaction and rapidly increases the computation time. We plan to examine other computational formalisms, such as those used in lattice quantum chromodynamics²¹⁷: heat-bath and hybrid Monte Carlo algorithms, and algorithms developed specifically for heavy quark systems.

In addition to symmetric nuclear matter, we plan to continue the examination of the thermal properties of neutron matter. We will also investigate various applications of astrophysical interest, such as neutrino interaction with nuclear matter. Effects of nuclear correlations on neutrino opacities in dense matter appear to be significant²³³. We can address the issue more solidly, since our calculation will include all many-body correlations. This calculation could serve as a part of the proposed ``TeraScale Models of Core Collapse Supernovae for Computational Nuclear Astrophysics'' Strategic Simulations Initiative.

Two- and three-pion interferometry in relativistic nuclear collisions

The NA44 collaboration at CERN has recently reported²³² a puzzling result from the first three-pion interferometry experiment. Both two- and the three-pion correlations are weak, with the three-pion correlation nearly vanishing. We have shown that this data can be explained with an intermittent, domain-structured source, or by a disoriented chiral condensate (see section C.3.II.b.

We plan to continue the investigation of two- and three-pion interferometry, so as to identify dynamical phenomena that occur as consequence of color deconfinement in relativistic nuclear collisions. As we continue the investigation of the above two types of sources, new data from three-pion interferometry will become available. We expect that a close comparison of the data and our calculation will be needed. In addition to this, we plan to work on other problems regarding the possibility of using pion interferometry for identifying phase-transition-related dynamics. For example, we have the formal question of how and under what conditions a group of coherent regions exhibits intermittent, domain-structured coherence. At the same time, there is also a question of what features of phenomena related to the QCD phase transition could yield observable consequences in pion interferometry. We plan to identify and investigate such problems.

C.2.II.c Astrophysics Studies at the National Ignition Facility
[S. Koonin, B. Filippone]

The National Ignition Facility (NIF) is being constructed at Lawrence Livermore National Laboratory. While the primary scientific goal of this facility is fusion ignition through inertial confinement fusion, a number of other basic science opportunities are under study. In particular, laser irradiation will create unique plasma conditions in the hohlraum, with temperatures and densities comparable to those important in stellar evolution and nucleosynthesis. We plan to investigate the feasibility of performing measurements of key nuclear reactions of importance to astrophysics at the NIF. Such a study includes simulations of the thermodynamic environment within the hohlraum and identifying techniques to both calibrate and measure the reactions of interest. Important problems to be addressed include how to extract the astrophysical information (eg. resonance strengths or S-factors) from the time varying environment of the laser-induced plasmas and identifying and limiting possible background processes.

We expect that this research will be carried out in collaboration with R. Petrasso (MIT), E. Cecil, and P. B. Radha (Rochester).

C.2.III Facilities and Instrumentation

C.2.III.a G0 Liquid Hydrogen Target Development
[R. Carr, S. Covrig, T. Ito, C. E. Jones and R. D. McKeown]

Caltech is responsible (C. Jones is subsystem manager) for designing and constructing the liquid hydrogen target for the G0 experiment, which will have a 20 cm long target region capable of handling 40 microamps of beam current. The acceptable level for density fluctuations in the liquid hydrogen that are not correlated with the beam helicity is < 0.1% during 1/30 second, set by the requirement that fluctuations in the experimental asymmetry due to density changes not exceed statistical fluctuations over the duration of a single asymmetry measurement.

The G0 liquid hydrogen target underwent a Preliminary Design Review at TJNAF in December 1998 where all design aspects of the target system were reviewed by a committee composed of technical experts, with particular emphasis on the safety aspects of the system. All elements of the system to be built by Caltech were approved and the design was approved specifically in terms of its safe handling of hydrogen. This is a major milestone for the target, which was the first of the G0 subsystems to undergo such a review by the lab.

Figure C.2.III.a G0 liquid hydrogen cryogenic target loop

The cryogenic target loop, shown in Figure C.2.III.a, is being constructed at Kellogg Radiation Laboratory at Caltech. The AutoCAD drawings of the target loop are complete and construction of the loop is in progress. We are currently constructing the hydrogen gas handling system and are on schedule to deliver the target to UIUC for testing next summer and fall. There we will assemble the target system and fully test it before delivery to TJNAF for commissioning with beam in 2001. The construction of the target loop and motion mechanism is funded by $98K from the NSF supplemental grant to Univ. of Illinois and $66K from the Kellogg NSF grant.

Because TJNAF would not continue to assume responsibility for providing the vacuum vessel to house the target, Caltech has taken over that part of the project, which couples closely to the design of the target support and positioning mechanism for which Caltech was already responsible. We have been working with Thermionics Northwest on the design of this major component, have obtained a quote from them for its construction, and now are awaiting a transfer of funds from TJNAF to go forward with the detailed design and construction. At Caltech, in addition to overseeing the work done by Thermionics, we will design and construct the can to house the cryogenic connections to the target. We will get $68K of DOE funds for the support structure.

C.2.III.b E158 Liquid Hydrogen Target Development
[R. Carr, J. Gao, C. E. Jones, and R. McKeown]

Our group in Kellogg (C. Jones is subsystem manager) has responsibility for providing the liquid hydrogen target for SLAC experiment E158. The cryogenic loop design for this target is shown in figure C.2.III.b. The target cell, which is one side of the cryogenic loop, is a cylinder 150 cm long by 7.6 cm diameter through which the hydrogen moves at a velocity of \sim 7-10 m/s. Such a long liquid hydrogen target has never before been used in a high current electron beam where the beam heat load to the fluid is \sim 500 W.

Figure C.2.III.b E158 liquid hydrogen cryogenic target loop

In April 1999, the entire E158 experiment underwent a Milestone Review by an internal committee at SLAC at which all subsystems were reviewed with regard to their technical feasibility. For this review the issues to be addressed by our group were 1) finalizing a conceptual design of the target and 2) presenting a quantitative estimate of the size of density fluctuations due to beam heating that we can expect for the target, including an assessment of how best to keep the fluctuations below the level where they degrade the statistical precision of the experiment. We proposed inserting mesh screens along the length of the target cell to reduce density fluctuations by promoting mixing and transverse flow in the target region. We also calculated the density fluctuations we can expect for this target by modeling heating of the fluid during the beam pulse and how well the fluid would mix between pulses.

The Milestone Review Committee was pleased with the progress on the target design and recommended that funding for the target construction be approved by SLAC. The budget for the E158 target is $192.4K, of which we have received $116K from SLAC already. The balance of the funding will be available during FY00. We expect to deliver the target to SLAC for testing off the beamline sometime next summer and to begin commissioning tests with beam in Fall 2000.

This is a very tight schedule and we must expend considerable effort to meet it. At this point, the conceptual designs for all major elements of the cryogenic loop - the target cell, hydrogen pump and gaseous helium heat exchanger - have been finalized. We are in the process of specifying the details of the elements of the cryogenic loop and have begun to generate AutoCAD drawings of the cryoloop. Construction will be done at Kellogg and can begin shortly, when the G0 cryogenic loop construction in the shop here is completed. The final design of all other components of the target system are also now underway; we will rely heavily upon our experience in designing and operating the SAMPLE target and designing the G0 target for the E158 hydrogen target gas handling system and target control/monitoring hardware and software. Work has begun on writing LabView software for the control system.

To test how well the mesh screens mix the fluid before taking the target to SLAC, Cathleen Jones has been working with two Caltech undergraduates to construct a model of the hydrogen target using high flow rates of water, plexiglass tubing, and a scaled version of the mesh screens that we intend to use in the E158 target. By matching the Reynolds number of the model system to that which we expect for the hydrogen target, we can simulate and study the flow of liquid hydrogen in the beam path. We are imaging the flow by photographing the path of dye injected into the fluid stream to see how well the fluid in the beam path mixes. This project is ongoing and will allow us to optimize the design of the baffles to introduce transverse flow.

C.2.III.c Development of a Solid Deuterium source for Ultra-Cold Neutrons
[B. W. Filippone, T. Ito, J. Martin, B. Tipton, J. Yuan]

In collaboration with Los Alamos National Laboratory (LANL) and Princeton University we are developing a source of high density ultra-cold neutrons (UCN) based on a solid deuterium (SD₂) moderator coupled to a spallation target. Because of the phonon structure of the solid, a cold (\sim 40 K) flux of neutrons incident on SD₂ cooled to 4 - 6 K can be efficiently converted into the ultra-cold regime. UCN are neutrons with velocities less than \sim 8 m/s. Below this velocity neutrons can be totally reflected from the surface of some materials due to an effectively repulsive nuclear interation and thus become trapped.

The combination of the pulsed nature of spallation induced neutrons (generated by directing the 800 MeV proton beam at LANSCE onto a W target) and the non-thermal cooling properties of SD₂ lead to a predicted high production rate for UCN. Detailed Monte Carlo calculations suggest that the ultimate density achievable with such a source could be orders of magnitude higher than those available at present reactor UCN sources. We have constructed a prototype source to explore the optimal characteristics for production of high densities of UCN.

In the prototype source the proton beam strikes a W spallation target to produce an intense burst of high energy neutrons. These neutrons are contained by Be reflectors and cooled with plastic moderators at both LN2 and LHe temperatures. This flux of cold neutrons is then incident on a volume of SD₂ located in the bottom of a UCN neutron guide tube. The guide tube is then connected to a ³He neutron detector, to measure the time dependence of the neutrons.

With the geometry of the neutron guide tube (about 2 m from the SD₂ to the ³He detector), any neutrons detected \sim 0.3 sec after the proton beam burst should be UCN. A typical time spectrum obtained with and without 50 cc of solid deuterium is shown in Fig. C.2.III.c.2. A very significant increase in the yield of neutrons more than 0.3 sec after the beam burst is observed with the SD₂ in place. Based on the present results, a measurement of the neutron beta-decay asymmetry (as discussed in Section C.2.I.c) with the present prototype SD₂ source, run at higher proton beam currents is clearly feasible. Presently we restrict the proton beam currents to limit the activation of the source in order to facilitate simple and rapid modifications to the system during optimization.

At present, the observed flux of UCN is somewhat below the predicted flux. We are actively pursuing the optimization of the source to try to understand the difference between the calculations and the measurements and hopefully produce a significant improvement in the output of the source. If such an increase in intensity can be realized, the beta-decay asymmetry can be measured in days instead of months allowing many systematic checks on the experiment and greatly improving the statistical precision.

Fig. C.2.III.c.2 Neutron yield vs. time for 50 cc of solid deuterium. The hatched histogram is the neutron yield with an empty neutron guide.

Following additional measurements this winter and demonstration of significant densities of {\it stored} UCN, we will begin construction on an optimized UCN source. This source would most likely be located in Area B of the old LAMPF endstation area, and would allow reasonably high average proton beam currents (3 - 10 \mu A) on the spallation target.

C.2.III.d Detector development and calibration for measurement of neutron beta decay
[B. Carr, B. Filippone, D. Fong, T. Ito, J. Martin, R. Patterson, B. Tipton, J. Yuan]

The high precision measurement of the beta-decay asymmetry in polarized neutron decay (see Section C.2.I.c) requires careful calibration of the electron detection system. In addition an optimized detector system can allow additional measurements to aid in reducing systematic errors. In fact in our proposal to measure A with UCN at Los Alamos, detector systematics are one of the largest remaining systematic errors. Improvements in detector design and calibration are thus crucial in providing the highest precision for the experiment.

We have begun an extensive calibration program in order to test prototype detectors and to allow detailed measurements of detector response for the final experiment. For the ``high'' energy regime (E > 0.15 MeV) we are using the 1 MV dynamitron accelerator at NASA-JPL. This electron accelerator is used to study radiation damage in electronic chips and solar cells. We have demonstrated that the accelerator can be run as low as 0.15 MeV and produce a momentum analyzed beam with only 100 - 1000 particles/sec. Initial measurements of scintillator detector response have been made under these conditions.

For the low energy regime (E < 0.15 MeV) we have constructed a small electron accelerator in Kellogg using spare power supplies and beam line components from the Kellogg Pelletron accelerator. Following extraction from a W filament and initial focusing the beam is accelerated and measured with a beam profile monitor and Faraday cup. Extracted beams of up to 30 keV have been obtained and studies of beam optics and higher energy are underway.

In order to provide an absolute calibration and to allow off-line measurements with momentum analyzed radioactive sources we have constructed a novel iron-free electron spectrometer. The spectrometer is based on a simple Helmholtz coil geometry that is easy to model and can be carefully mapped. Based on detailed Monte Carlo studies we have discovered (apparently for the first time) a geometry that allows double focusing using only the field from the Helmholtz coil. Measurements with a ¹¹³Sn source have confirmed the focusing properties of the spectrometer and demonstrated a momentum resolution of \sim 0.3%. This device will be used at JPL in order to calibrate the accelerator/magnetic analysis system to \sim 0.1% (the present calibration is only good to \sim 5%). We will also couple the spectrometer to the low energy Kellogg accelerator to provide high quality, continuous beams of low energy electrons for detailed measurements of detector response. It is anticipated that this device will be shipped to LANL for detector calibrations during the beta-decay asymmetry measurements.

Figure C.2.III.d Schematic diagram of TPC prototype beta detector.

We are also preparing prototype detectors for the beta-decay experiment. A small Time-Projection-Chamber (TPC) is being assembled in order to compare its response to Monte Carlo predictions. A diagram of the TPC prototype is shown in Fig. C.2.III.d. The use of such a detector in the beta-decay asymmetry measurements would provide direct information on the angular correlation in the decay, a very useful systematic check. Total energy measurement of the decay electrons via plastic scintillator detectors and Si detectors are also being investigated. If there is sufficient intensity from the ultra-cold neutron source we anticipate constructing several independent detector geometries (eg. Si vs. scintillator) to further constrain possible systematic errors from uncertainties in detector response. We also plan to use our calibration accelerators to produce monochromatic beams of electrons in order to study electron backscattering from the detectors - a common systematic problem in previous measurements of the neutron beta-decay asymmetry.

As part of the detector development, we are also developing advanced electronics read-out and investigation modern PC-based data-acquisition systems for use in the full A correlation measurement.

C.3 Results from Prior NSF Support

C.3.I Experimental Research

C.3.I.a SAMPLE
[A. Blake, R. Carr, S. Covrig, B. Filippone, P.Frazier, J. Gao, T. Ito C. Jones, P. Lee, E. Maneva, K. McCarty, R. McKeown, V. Savu, and M. Sullivan]

The SAMPLE experiment was a major part of the Kellogg experimental program during the last 5 years. This important high-priority experiment was successfully completed during the summer of 1999. Physics results were reported in one published Letter⁸⁰ and another recently submitted Letter¹⁸⁰. In addition, many conference proceedings resulted from this work and further publications are anticipated pending the analysis of the 1999 data, which is currently still in progress. One Caltech Ph.D. student, Bryon Mueller, wrote his thesis on this experiment.

The major goal of the SAMPLE experiment was to determine the strange quark-antiquark contribution to the proton's magnetic moment via parity-violating elastic electron scattering.²⁰⁰ The parity-violating amplitude arises from the neutral weak interaction; the main interest here is in the neutral weak magnetic form factor G_M^Z and its static limit \mu^Z \equiv G_M^Z (Q² = 0).

The SAMPLE collaboration includes the University of Illinois, University of Maryland, Virginia Tech, Louisiana Tech, University of Kentucky, College of William and Mary, and MIT-Bates. The experiment measures parity violating electron-proton and electron-deuteron scattering at low Q². The parity violating asymmetry (i.e., the asymmetry between cross sections for right- and left-handed incident electrons) depends upon two weak form factors: the magnetic form factor G_M^Z and the axial form factor G_A^Z. The combined measurements on the proton and deuteron can be used to determine both of these form factors.

The experiment was performed using a 200 MeV longitudinally polarized electron beam incident on a liquid hydrogen target. (The hydrogen target was a major piece of equipment constructed in the Kellogg Lab for this experiment; see section C.3.III.a.) The scattered electrons were detected in a large solid angle (\sim 1.5 sr) air Cerenkov detector at backward angles (130^\circ < \theta < 170^\circ), giving an average Q² \approx 0.1 (GeV/c)².

Figure C.3.I.a Error band for the allowed region (shaded) from the 1998 SAMPLE Hydrogen data. the vertical dashed line is from ^{215, 218}.

The results of the 1998 experimental run with a LH target are described in detail in the manuscript submitted to PRL¹⁸⁰. This experiment determines a linear combination of G_M^s and G_A^Z as shown in figure C.3.I.a. The 1999 experimental run with a LD target will provide a determination of G_A^Z (T=1) which is expected to be the dominant contribution to G_A^Z. Based on the on-line analysis of the 1999 deuteron data, the measured value of G_A^Z is substantially different than the calculated values in the literature^{215, 218}. Further analysis is in progress to determine a final numerical result, but it appears from the preliminary analysis that G_A^Z is positive and that (as can be seen from figure C.3.I.a) G_M^s is close to zero.

The surprising result for G_A^Z may be interpreted as a rather sizeable value for the anapole moment of the nucleon. This quantity would be a new and interesting form factor, corresponding to the axial vector coupling of the photon to the nucleon (via the electroweak interaction). Clearly, further experimental and theoretical studies are necessary to verify and explore the ramifications of this interesting experimental result.

C.3.I.b HERMES
[B. Bray, J. Briceno, P. Carter, A. Dvoredsky, B. W. Filippone, D. Guskin, W. Korsch, A. Lung, R. D. McKeown, M. Pitt]

The HERMES experiment at DESY (originated in our group in collaboration with groups in Germany) was constructed to make precision measurements of the spin structure of the proton and neutron. By combining a large acceptance spectrometer¹³¹ with high intensity e^{\pm} beams and highly polarized pure internal targets^{135, 171} HERMES is capable of determining inclusive and semi-inclusive asymmetries from polarized H, D, and ³He targets. These measurements provide new information on the flavor, valence, and sea contributions of the quarks' spin to the spin of the nucleon. Our group has been responsible for the development of a number of innovative components (see sec. C.3.III) in the HERMES experiment and has also played a significant role in the analysis of the data.

The experiment has been running in production mode since 1995, and many physics results have been obtained and reported in the literature. These include

\item{$\bullet$} Determination of the spin structure function of the neutron g_1^n from inclusive deep inelastic scattering from polarized ³He.⁸⁴

\item{$\bullet$} Precision measurement of the spin structure function of the proton g_1^p from inclusive deep inelastic scattering from polarized Hydrogen.¹³³

\item{$\bullet$} First demonstration of coherence length effects via a study of nuclear transparency in diffractive rho producion.¹⁷²

\item{$\bullet$} Determination of flavor-separated polarized quark distribution functions from semi-inclusive \pi^\pm spin dependent deep inelastic scattering.¹⁸⁵

\item{$\bullet$} First intriguing data indicating polarized gluons in high p_T photoproduced hadron pairs.¹⁸⁴

\item{$\bullet$} First evidence for a single-spin asymmetry in electroproduction, suggesting a method to determine the third leading-order quark distribution (after F₁ and g₁) called transversity.¹⁹⁸ \item{$\bullet$} First indication that the ratio R \equiv sigma_L / sigma_T in unpolarized deep inelastic scattering depends upon the nuclear target A at low x and low Q².¹⁸⁸ This phenomenon represents a new and unexpected nuclear effect in deep inelastic scattering.

HERMES will continue to acquire data until summer 2000 with a polarized deuteron target. Further analysis of these and other existing data will produce many new results from HERMES, including semi-inclusive K asymmetries (sensitive to polarized strange quarks and accessed via the recently installed RICH detector), high-precision inclusive asymmetries on deuterons, azimuthal distributions of electroproduced hadrons, and other novel effects in deep inelastic scattering.

After the 2000 shutdown, we will reduce our activity on HERMES to analysis and reporting of the existing data set. Due to our other commitments (see C.2.I) we do not intend to participate in further data acquisition beyond spring 2000, and will phase out our HERMES activity over the next few years. HERMES has been the subject of Ph.D. theses for three of our graduate students: B. Bray, P. Carter, and A. Dvoredsky.

C.3.I.c Nucleon Spin Structure Studies at SLAC
[T. Averett, E.W. Hughes, Y. G. Kolomensky]

Over the past several years SLAC has performed a series of experiments aimed at studying the spin structure of the proton and neutron. These experiments use inclusive deep inelastic scattering of polarized electrons off polarized targets and have provided definitive data on g_1^p, g_1^n, g_2^p, and g_2^n. The early experiments E142 and E143 led to a substantial series of publications^{219, 220, 73, 77, 121, 69} on these quantities.

In 1995, SLAC upgraded the electron beam transport line so that experiments could be performed with energies up to 50 GeV. The Kellogg Lab was actively involved in the two recent experiments (SLAC experiment E154 and E155) that study the proton and neutron spin structure function with expanded kinematic range (particularly lower x) using the new beam transport line. The E154 data on a polarized ³He target were published in a set of three Letters^{81, 85, 110}.

In spring of 1997, SLAC Experiment E155 collected a large data sample using polarized proton and deuteron targets. The E155 experiment used a new dedicated 10 degree spectrometer to measure the proton and deuteron spin structure functions at mid and high x at high Q². The Kellogg group assembled, tested and installed the lead glass calorimeter used in this spectrometer. Publications of the results of E155 are still in progress.^{182, 174, 173}

In March and April of 1999, SLAC collected the last data sample on nucleon spin structure functions in Experiment E155x. This experiment was dedicated to measuring the proton and deuteron spin structure functions g₂. Preliminary results on g₂ for the proton and deuteron have already been presented at 1999 conferences.

C.3.I.d Polarized ³He Target Experiments at Jefferson Lab
[B. Filippone, S.Jensen, C. Jones, E. W. Hughes, R. McKeown, D. Pripstein]

We have particiated in two experiments during 1998-99 to study spin dependent electron scattering from polarized ³He. Experiment 94-010 (Cates and Meziani, spokespersons)²⁰⁶ was a study of the spin dependent inelastic structure function of the neutron as a function of Q² using polarized ³He. The physics goal is to connect the high-Q² deep inelastic structure function to the low-Q² inelastic structure governed by the resonance region and explore the connection of the Ellis-Jaffe sum rule to the Drell-Hearn-Gerasimov sum rule. The experiment collected data over a wide kinematic range in the autumn of 1998, essentially achieving the proposal goals of kinematic coverage.

The second polarized ³He experiment (95-001 - Gao, spokesperson)²⁰⁷ was a measurement of the quasi-elastic transverse asymmetry, A_T, and extraction of precision values of the neutron magnetic form factor G_M^n as a function of Q² in the range 0.1 - 0.6 GeV². This method was developed in our lab as part of H. Gao's Ph.D. thesis work²⁰¹. The experiment was successfully completed in early 1999.

Our group was responsible for implementing the laser optics and the target support/motion mechanism for these experiments. A Kellogg graduate student, S. Jensen, has worked on 94-010 for his Ph.D. thesis. Data analysis is in progress for both of these experiments and results should be available in the near future.

C.3.I.e Inclusive scattering from nuclei at Bjorken x > 1
[J. Arrington, J. S. Jensen, B. W. Filippone, E. W. Hughes, and R. D. McKeown]

High energy electron scattering from nuclei can provide important information on the structure of nucleons in the nucleus, as well as on the quark structure of the nucleus. In particular, with simple assumptions about the reaction mechanism, scaling functions can be defined that provide information on the momentum distribution of the constituents (eg. nucleons or quarks).

Figure C.3.I.e Nuclear structure function nu W₂ for an Fe target as a function of the Nachtmann scaling variable xi. The different symbols correspond to different four-momentum transfers.

The first results of experiment 89-008 at Jefferson Lab [B. W. Filippone - cospokesperson] have been published in Physical Review Letters¹⁵⁶. These results explored the scaling in terms of the y-scaling variable which is the correct variable to probe electron nucleon ``elastic'' scattering in the nucleus. These data showed that y-scaling for nucleons with momentum larger than the Fermi momentum (\sim 250 MeV/c) persists at higher momentum transfer than previous data. In addition, when the Jefferson Lab results from 89-008 are analyzed in terms of the Nachtmann scaling variable \xi an improved scaling behavior is observed (see Fig. C.3.I.e). Comparison of these data with higher energy muon and neutrino scattering at CERN and Fermilab will allow an investigation of the momentum transfer dependence (Q²) of the nuclear structure function.

Our group was responsible for the design, assembly and testing of the trigger electronics for the two spectrometers in Hall C. We have also led the analysis effort for the experiment. This analysis has been a critical component in providing a detailed understanding of the two spectrometers in Hall C. This experiment was the Ph.D. thesis work of Caltech graduate student J. Arrington.

C.3.I.f Photodisintegration of the deuteron at high energies
[J. Arrington, B. W. Filippone, and R. D. McKeown]

We were also collaborators on experiment 89-012 at Jefferson Lab; a measurement of the two-body photodisintegration of the deuteron up to E_gamma = 4 GeV. These data provide an important testing ground for comparison of nuclear models that incorporate QCD vs. meson-nucleon based models. This was an extension (to higher energies and new scattering angles) of a previous experiment NE17 at SLAC (on which we were major collaborators). The new JLAB data have been published¹³⁶ and indicate that the scaling behavior at \theta_CM = 90^\circ observed at SLAC persists to higher energies with higher precision. However this scaling is clearly not observed in the more forward angle data. Both the energy and angular dependence of the cross section should help identify the basic reaction mechanism and relevant degrees-of-freedom for this fundamental nuclear reaction.

C.3.I.g A Measurement of \vec{p}-\vec{d} Spin Observables using a Laser-Driven Polarized Deuterium Internal Target in the IUCF Cooler Ring
[C. E. Jones]

The final run of IUCF experiment CE68, a measurement of the spin observables in the scattering of 197 MeV polarized protons from a laser-driven vector-polarized deuterium internal target, was completed in November 1998. The \vec{d}(\vec{p},pd) data from that measurement has been analyzed and the polarization observables extracted. The results for the deuteron vector analyzing power iT₁₁ significantly improve upon the previous measurement at Saclay. In addition, we have measured for the first time the vector-vector spin-correlation of this reaction. Both of the measured spin observables are sensitive to 3--body forces. The data from this experiment are in much better agreement with calculations using the CD-Bonn potential that include 3--body forces using the Tucson-Melbourne model than with those that have no 3--body interaction. These data may be the first to show the 3--body force in a dynamical interaction. A manuscript reporting these results has been submitted to Science.¹⁷⁰.

C.3.II Theoretical Research

The theory component of the Kellogg program has dealt with a variety of theoretical and phenomenological problems. Many of these were motivated by interactions with the experimental component of the program. As the experimental emphasis has shifted throughout the years from nuclear structure problems of astrophysical interest to nucleon properties of relevance for the Standard Model, the theoretical research has added a stronger QCD component. The following is a summary of the theoretical research carried out during the previous period of NSF support.

C.3.II.a QCD and Effective Theories
[M.C. Chu, L. Diaconescu, H.-M. M\"uller, R. Seki, and U. van Kolck]

Our effort in this area has involved lattice QCD studies and effective field theory (EFT). In the past the EFT description of strong interactions at low energies based on chiral symmetry has been developed for processes involving at most one nucleon, under the name of chiral perturbation theory (\chi PT). We have been working to extend EFT ideas to systems of two or more nucleons. The application of EFT to nuclear physics involves a novel interplay of perturbative and non-perturbative physics, mixing subtle issues of regularization, renormalization, fine-tuning, power counting, and role of potentials. We have made considerable progress in understanding the two- and three-nucleon dynamics, including several reactions involving two nucleons, as reviewed in ^{151, 168, 149, 189} and described below.

$\bullet$ The temperature dependence of the instanton content of gluon fields was investigated using quenched¹ and unquenched¹⁹⁶ lattice QCD and the cooling method. It has been found that the topological susceptibility arising from instantons decreases rapidly below the phase-transition temperature T_c\approx 150 MeV.

$\bullet$ The two-nucleon problem has been further studied within EFT^{150, 155}. In the pionless theory, it was shown explicitly that despite the existence of fine-tuning, a controlled expansion in momentum exists for the full two-body amplitude in any regularization scheme, and that for particular regulators one can, alternatively, expand the potential. This supports earlier studies of the two-nucleon potential in \chi PT. Moreover, the NN interaction was solved to sub-subleading order with lattice regularization¹¹⁹.

$\bullet$ Within the \chi PT approach, we have investigated¹⁶¹ one mechanism that contributes to the observed charge-independence breaking in the NN system: the pion-mass difference in the (chiral) TPE two-nucleon force. We derived a general formula, and applied it in leading order, recovering a known term from box diagrams, but also obtaining new, non-negligible terms required by chiral symmetry.

$\bullet$ We have developed the first EFT approach to the three-body system. Working in leading order at momenta much smaller than any mass in the problem, we have shown^{153, 152, 162} that, in channels where the Pauli principle does not forbid three-particle overlap, the renormalization of the full, non-perturbative amplitude is strikingly different from that of the truncated perturbative solution. We demonstrated that a large three-body force appears as consequence of the fine-tuning in the two-body force. We have successfully applied this theory to the ³He trimer^{153, 152} and to triton and Nd scattering in the $J=1/2$ channel¹⁶². In the $J=3/2$ Nd channel, where contact three-body forces are suppressed, the EFT prediction for scattering to sub-subleading order (based on two-body input only) was found to work strikingly well¹¹⁵.

$\bullet$ $\chi$PT allows an analysis¹⁵⁴ of the TPE components of three-nucleon forces. We have demonstrated that the short-range c-term of the Tucson-Melbourne force violates chiral symmetry. When this term is dropped, the class of existing of TPE three-nucleon forces becomes rather uniform.

$\bullet$ Coherent Compton scattering on the deuteron was studied¹⁵⁸ to O(Q³), for photon energies of O(m\pi). Results are in good agreement with existing experimental data from the Illinois group, and a prediction was made for higher-energy SAL data.

$\bullet$ We have discussed^{159, 167} the extension of the approach to the higher momenta relevant for $N N \rightarrow d \pi, pn \pi, pp \pi$ reactions at threshold, which are sensitive to some aspects of the intermediate- and short-range nuclear dynamics. The estimated cross sections are considerably smaller than the data.

Progress made in the application of EFT ideas to nuclear physics during the last few years was the subject of a number of workshops organized by our group. A joint Caltech/INT workshop was held at Kellogg in February 1998¹⁴³, and an INT workshop was held at the INT in Seattle in February 1999, to discuss further progress¹⁹⁰. A more general meeting including also other approaches to the nuclear-force problem was organized by U. van Kolck, B. Gibson (Los Alamos National Laboratory), and R.G.E. Timmermans (KVI-Groningen) and held at the ECT* in Trento, Italy, from June 28 to July 9, 1999. All these workshops had a substantial number of young (graduate students and postdocs) participants.

C.3.II.b Nuclear Matter and Structure
[A. Cs\'ot\'o, D.J. Dean, J. Humblet, S.E. Koonin, K. Langanke, G. Mart\'{\i}nez-Pinedo, H.-M. M\"uller, W.E. Ormand, P.B. Radha, M.T. Ressell, R. Seki, U. van Kolck, P. Vogel, and J.A. White]

The exact solution of the nuclear many-body problem is a demanding computational problem. A number of reactions of interest for electroweak interactions and astrophysics require understanding of nuclear structure. Methods for the solution of the nuclear shell model based on Monte Carlo (SMMC) techniques have been developed and implemented at Kellogg. Studies with more conventional diagonalization techniques have been pursued simultaneously. Pion interferometry as a method of extracting information from heavy-ion collisions was also studied. This work on nuclear structure is of importance to present or future neutrino experiments at LAMPF, KARMEN and SuperKamiokande, radioactive beam facilities, CERN, and RHIC.

SMMC methods allow complete $0\hbar\omega$ calculations with realistic interactions for nuclei with masses larger than 50. Reviews can be found in ^{75, 107}. Applications developed during the previous support included:

$\bullet$ Several properties of even-even and N=Z nuclei with A=48-64, such as masses and Gamow-Teller (GT) strengths¹¹, response functions for GT operators¹¹³, pairing correlations⁸⁶, and the isovector part of the pairing interaction^{64, 102}, studied with all $0 \hbar \omega$ configurations in the pf-shell and employing realistic residual interactions.

$\bullet$ The temperature dependence of various observables in ⁵⁴Fe ³ and the isospin and temperature dependence of pair correlations in ^54,56,58Fe and ⁵⁶Cr⁴¹.

$\bullet$ The temperature dependence of binding energies for various isobar chains, with complete $0 \hbar \omega$ model spaces and realistic residual interactions, and the resulting temperature dependence of the symmetry energy⁸.

$\bullet$ Pairing properties and the possible isospin band crossing measured in ⁷⁴Rb, by adding a cranking term to the shell model Hamiltonian⁸³.

$\bullet$ The first calculations of the GT strength for the N=50 isotones in the complete (0g-1d-2s) shell⁴³.

$\bullet$ Both monopole and quadrupole pairing and the collective quadrupole interaction for nuclei with $A\sim 100-140$ within the full 50-82 shell for both protons and neutrons⁴².

$\bullet$ Matrix elements of two-neutrino double beta decay, through the calculation of multi-imaginary time response functions⁴⁴.

$\bullet$ Basic properties, such as energy, deformation, and band crossing, of rare earth nuclei at various temperatures and spin, in a model space that encompasses one major shell ($N=4$) for protons and one major shell ($N=5$) for neutrons¹⁹¹. This work was the subject of the Ph.D. thesis of J. White.

$\bullet$ The study, with controlled contamination from excitations of the center of mass, of a series of unstable neutron-rich nuclei with active nucleons in both the sd and $pf$ major oscillator shells¹⁸⁷.

A number of processes of particle or astrophysical interest involving nuclei were also studied with more conventional methods, including:

$\bullet$ Effects of pairing correlations on the shell structure of very neutron-rich nuclei, particularly for single-particles states with low angular momentum, and on $r$-process abundances¹⁶.

$\bullet$ Matter distributions of neutron-rich nuclei that yield unusually large reaction radii as well as large elastic and charge-exchange cross sections, by the method of model-independent analysis that has been used extensively in the determination of the nuclear charge distributions from high-energy electron scattering and muonic atoms¹⁶³.

$\bullet$ The parity-violating $\alpha + d$ decay of the lowest 0⁺ state of ⁶Li, in a microscopic three-cluster model⁴⁷.

$\bullet$ Nuclear shell model calculations of the neutral current GT strength with a finite strange quark contribution, for a number of nuclei likely to be present during stellar core collapse ⁵¹.

$\bullet$ The double-beta decay of $^{48}$Ca, in the shell model with complete $pf$-shell and a Hamiltonian optimally describing the spectroscopy of the $A=48$ nuclei¹⁹.

$\bullet$ $\beta^+$ and $\beta^-$ decay rates of ⁵⁴Mn and other known unique second forbidden beta decays from the nuclear p and sd shells (¹⁰Be, ²²Na, and two decay branches of ²⁶Al)¹⁴⁵.

$\bullet$ The interference of M1 and E2 multipoles in the gamma-decay of ⁵⁷Fe, used to bound the time-reversal-violating, parity-conserving rho N N vertex⁵⁰.

$\bullet$ The neutrino-¹²C interaction. It was shown that: for currently available neutrino energies, E_\nu \le 300 MeV, calculated exclusive cross sections ¹²C_gs (\nu,l)¹²N_gs for both muon and electron neutrinos are essentially model independent and agree well with experiment⁶¹; the continuum random phase approximation (CRPA) reproduces the muon capture rate on ¹²C and the inclusive ¹²C(\nu_e,e^-)¹²N cross section for Michel spectrum neutrinos, while it overestimates the inclusive ¹²C(\nu_\mu,\mu^-)¹²N cross section for the LAMPF pion decay-in-flight \nu^\mu neutrino beam¹⁸; the CRPA consistently reproduces inelastic electron scattering data at the excitation energies in ¹²C probed by the LAMPF experiment⁸⁹.

$\bullet$ Solar neutrino absorption cross section for ⁴⁰Ar, and its relation to the $\beta$-decay of the mirror nucleus ⁴⁰Ti ².

$\bullet$ Nuclear transparency in high-energy, semi-inclusive $(e,e^{\prime }p)$, by accounting for all orders of Glauber multiple scattering and by using realistic finite-range interactions and correlated wavefunctions⁴⁹.

$\bullet$ Spin-polarization response functions for the high-energy $(\vec{e},e^{\prime }\vec{p})$ reaction, by computing the full 18 response functions for the proton kinetic energies of 0.515 and 3.170 GeV with an ¹⁶O target, and using the Dirac eikonal formalism to account for the final-state interactions⁹².

$\bullet$ Spin-dependent cross sections for the scattering of neutralinos from mica²⁷ and several nuclei in the $A = 127$ region⁷⁹.

$\bullet$ Screening in various molecular fusion reactions: new ³He(d,p)⁴He S-factors were obtained and the electron screening energy was found in agreement with the adiabatic limit employed in electron-screening calculations⁴⁶; a TDHF calculation for the low-energy collision of $Z=1$ nuclei with hydrogen molecules was carried out⁵³; the probability for one electron to be emitted to the continuum during the lifetime of the ⁸Be ground state resonance in the atomic He⁺+He collision was calculated⁸⁷.

$\bullet$ The nonresonant part of the ⁷Be(p, gamma)⁸B reaction, using a three-cluster resonating group model, to investigate the astrophysical S-factor⁷.

$\bullet$ Global R- and K-matrix fits to the combined set of the ¹⁶N decay data and the available angular distributions from radiative $\alpha$-capture and elastic $\alpha$-scattering on ¹²C, to determine the total ¹²C(alpha, gamma)¹⁶O cross section ⁵⁸; and a comparison of the two types of parametrizations in the simpler case of S-wave alpha + alpha elastic scattering¹⁴⁰.

The limit of infinite nuclear matter might afford enough simplification to allow us to build an understanding of nuclear dynamics based on an exact solution consistent with QCD. Two aspects of this program were explored:

$\bullet$ The change in the self-energy of decuplet baryons in nuclear matter was calculated in $\chi$PT⁸².

$\bullet$ Thermal properties of infinite nuclear matter on a 4x4x4 lattice with fixed spacing were studied with SMMC methods^{119, 194}. As an exploratory calculation, the interaction was taken to be of the Skyrme type with central, and spin-spin exchange terms, each of which including on-site and nearest-neighbor interactions. The four parameters were fixed in order to approximately reproduce the empirical shape of the energy as function of density. Evidence of a liquid-gas phase transition was found at T_c\sim 15 MeV. This work was the Ph.D. thesis of H.-M. M\"uller.

Pion interferometry is an important source of information about the space-time extent of heavy ion collisions, which might shed light into the quark structure of nuclear matter:

$\bullet$ The correlations of like-particles emitted from a charged source were studied, and it was discovered that for pairs of pions with low total momentum, where the expected correlations arise almost entirely from the Bose-Einstein symmetry of the emitted particles, the source-pion Coulomb interaction causes an apparent increase in the source size, in agreement with experimental observation¹⁶⁵.

$\bullet$ Two- and three-pion correlations were numerically computed for incoherent source functions based on the Bjorken hydrodynamical model, over a wide range of the kinematic variables, in order to determine what new information can be obtained from three-pion interferometry¹⁶⁴.

$\bullet$ Two- and three-pion correlation functions were investigated for sources that are not fully chaotic¹⁷⁸, are domain-structured¹⁸¹, or exhibit a disoriented chiral condensate¹⁷⁹.

C.3.II.c Applied Theoretical Physics
[C. Adami, N.J. Cerf, W. Fink, S.E. Koonin, H.-M. M\"uller, and J. White]

The methods developed in nuclear physics frequently find applications in other areas. During the previous period a number of these applications were developed, including various problems in other scientific disciplines, e.g., Biology, Chemistry, and Medical sciences. A sample of the work is:

$\bullet$ A phase transition with increasing magnetic field from a disc or annulus to a spin-polarized Wigner crystal-like structure was shown to exist in a Hartree-Fock calculation of systems of up to twenty electrons moving in two dimensions and confined by a parabolic potential (quantum dots)⁶⁵.

$\bullet$ The application of a Monte Carlo method based on the Hubbard-Stratonovich transformation to the simulation of quantum computers was explored¹⁴¹.

$\bullet$ A quantum information theory was formulated¹⁴² that parallels classical information theory but is based entirely on density matrices for the description of quantum ensembles, and allows for the consistent description of quantum entanglement.

C.3.II.d Evolution of Massive Binaries
[H. Bethe and G. Brown]

Prof.'s Bethe and Brown have continued their annual visits to Kellogg during this grant period. These have been quite productive, leading to two recent publications of wide interest on the subject of the evolution of massive binary objects^157,166. In their most recent work¹⁶⁶, they considered the merging of high-mass black-hole binaries of the Cyg X-1 type, in which the O-star companion becomes a neutron star following a supernova explosion. The estimated rate of mergers, \sim 2 x 10^-5 yr^-1 for the Galaxy, is relatively low because of the paucity of high-mass black holes. Nonetheless, because of their high masses, these black-hole, neutron-star binaries could contribute importantly to the merging sought by LIGO. They estimated the detection rate for LIGO of high-mass black hole neutron-star mergers to be a factor $\sim 40$ greater than that for binary neutron stars. They continue to work on the related subject of gamma-ray bursters and plan to continue their annual visits to Kellogg.

C.3.III Facilities and Instrumentation

C.3.III.a High-power Liquid Hydrogen Target Development
[B. Carr, R. D. McKeown and B. Mueller]

A major project in our laboratory over the last few years has been the development of high-power liquid hydrogen (and deuterium) targets for parity violating electron scattering experiments. This effort began with the design and construction of the target for the SAMPLE experiment at Bates (C.3I.a), and led to the new projects associated with G0 at JLAB (C.2.III.a) and E158 at SLAC (C.2.III.b).

The SAMPLE target was constructed using the supplemental equipment grant from NSF for SAMPLE in collaboration with J. Mark, the (now retired) engineer who developed the targets used at SLAC. This target is a high flow rate circulating LH target cooled by a commercial closed cycle He gas refrigerator. It was designed to handle over 500 Watts of beam power, which was a factor of 2--3 higher than previous experience at SLAC. All of the major components of the target loop were fabricated in our shop at Caltech, including heat exchanger, circulating pump, heater, and target cell. The system was completely assembled and tested at Caltech using He gas rather than LH.

This target set important new standards for high-power liquid hydrogen targets. In particular, for parity violation experiments the boiling due to beam heating must be minimal so as to avoid density fluctuations that could add noise to the experiment signal. We have studied this effect with the Bates electron beam and our SAMPLE target, and determined that the effects are a small contribution under normal SAMPLE conditions. Experience with smaller beam spot sizes has yielded crucial new information for future target designs, particularly the E158 target(C.2.III.b). A paper describing the design and performance of the SAMPLE target was published in NIM⁵⁷.

During the last year, the gas handling system was modified in collaboration with Bates personnel to accommodate running with deuterium rather than hydrogen. This entailed installation of storage tanks on the roof of the North Hall for the (more expensive) deuterium gas. The system ran quite well with only minor maintenance problems during the summer 1999 SAMPLE run.

C.3.III.b A Piezo-electric Optical Beam Position Stabilization System for Polarized Electron Sources
[T. Averett, C. E. Jones, and R. D. McKeown]

When measuring the parity-violating asymmetry in electron scattering, it is extremely important to minimize helicity-correlated variations in the electron beam energy, intensity and position as they give rise to asymmetries in the detector signals that mimic the physics signal to be measured. In particular, small imperfections in the Pockels cell system that generates the helicity of the laser light in the polarized source can cause helicity correlated position shifts (up to several hundred nm) in the electron beam at the target. In order to control the systematic error due to this beam motion, these position shifts need to be kept well below $\pm 100$ nm in the SAMPLE experiment.

In our lab at Caltech we assembled and tested a piezo-electric driven optical feedback system to compensate the helicity-correlated shifts generated by the Pockels cell. The device consisted of an optical flat mounted to a two-axis piezo-electric motor controlled drive, placed after the helicity Pockels cell. A quad photodiode was used to measure the x and y positions of the outgoing light beam, and the signals read by a computer, which calculated the average x and y position shift between the beams of different helicity. A helicity-correlated voltage is then applied to the piezo drive to move the optical flat and compensate for the beam shift measured in the quad diode. Using this system, the optical beam was stabalized to $< 10$ nm.

Figure C.3.III.b Measured helicity correlated shift in the vertical position of the Bates polarized electron beam measured in the SAMPLE beamline during the 1998 run. The piezo driven feedback system was implemented after 12 days of running.

The optical feedback system was incorporated into the optics of the Bates polarized source for the SAMPLE run in Summer 1998. The performance during this run is illustrated in figure C.3.III.b. With the position correction circuit on, the helicity-correlated electron beam position shifts were reduced to Delta x = 6.4 \pm 2.3 nm and Delta y = -3.5 \pm 2.0 nm. The system was also used during the 1999 SAMPLE deuterium run. A NIM paper describing this work has been accepted for publication¹⁶⁰.

C.3.III.c HERMES Trigger Hodoscope
[B. Bray, R. Carr, P. Carter, B. W. Filippone, A. Lung, K. McIlhany]

Good particle identification is essential for HERMES both for the inclusive and semi-inclusive measurements. For the inclusive data the rate of single hadrons can far exceed that of the scattered positrons. Thus, it is important to have high rejection of hadrons both at the trigger level and in the off-line analysis. This is achieved with a trigger hodoscope for discrimination from photons, a Transition Radiation Detector, a Pb-scintillator preshower counter, and a Pb-Glass electromagnetic calorimeter. For the 1995-98 semi-inclusive measurements, a threshold Cerenkov detector was used to identify and separate pions from the below-threshold kaons and protons. (This was replaced by a RICH counter in 1999, see {C.3.III.e.) Also for low-energy hadrons from heavy particle decays, time-of-flight is also being exploited using the fast response of the trigger hodoscope.

The trigger hodoscope and Pb-scintillator preshower detector were designed, assembled, and tested at Caltech prior to installation at DESY. In addition Caltech was involved in the design and testing of the Pb-glass calorimeter.⁵⁹ Caltech has also played a lead role in the analysis algorithms that have been used for particle identification in the HERMES analysis. The particle identification performance of the HERMES spectrometer is described in more detail in ¹³¹.

C.3.III.d Target Optical Monitor (TOM) for HERMES
[A. Dvoredsky, W. Korsch, R. D. McKeown, and M. Pitt]

We have developed a new method for monitoring the polarization of a polarized ³He target in a storage ring. This device, a Target Optical Monitor (TOM), utilizes the excitation of the ³He atoms by the stored beam (in our case protons) to monitor optical transitions for polarization. In this way one can actually monitor the polarization of atoms directly in the path of the beam, and determine if there are any depolarization effects in the target cell. Although the measurement is relative, it is possible to calibrate it with the polarization of the optical pumping cell at high temperatures and low stored beam currents where depolarization effects are negligible.

The method was developed in our laboratory at Caltech and tested using a low energy proton beam generated with our Pelletron accelerator. The device was then installed in the HERA ring for the HERMES experiment. It utilized the 4¹ D \rightarrow 2¹ P transition at 492 nm in Helium. The lifetime of the 4¹ D state is 30 ns which allows observation of the decay photons during the time between beam bunches (96 ns), thus avoiding the intense synchrotron light in time with the beam bunch. We used a narrow (3 nm) interference filter to select the wavelength, and a second photomultiplier monitors the background light in an adjacent band of wavelengths. The signals were very reliable, and the device functioned well during the whole HERMES data run in 1995. The data from the TOM have been used to set limits on depolarization of the atoms due to wall bounces at lower temperatures and due to the beam interaction at high beam currents. In addition, for several weeks the pumping cell polarimeter was inoperative and the TOM was the sole source of target polarization information for the experiment. This work was reported in two NIM publications^{88, 135}.

C.3.III.e Development of a RICH Detector for HERMES
[R. Carr, P. Carter, B. W. Filippone, J. Renes]

A significant upgrade for the HERMES experiment was installed before the present run cycle: a Ring Imaging CHerenkov (RICH) detector for identification of pions, kaons and protons from 2 - 20 GeV. This upgrade allows a significant improvement in the capabilities of the experiment to measure semi-inclusive asymmetries from identified hadronic final states. Aside from providing the first semi-inclusive asymmetries with kaons, this detector will greatly improve the ability to identify decaying particles, eg. $\phi$'s, $\Lambda$'s, and charmed mesons and baryons.

Fig. III-4F.6a HERMES RICH event display. Shown in the upper panel are aerogel and Cherenkov rings for a 4 GeV pion and in the lower panel the aerogel ring for a 8 GeV kaon.

The detector takes advantage of new developments in the production of highly transparent aerogel, wherein a significant fraction of the Cherenkov photons can traverse the material without scattering. By imaging rings both from the aerogel and from a heavy gas (C_4F_{10}), \pi, K, p$ identification is performed over the full energy acceptance of HERMES. This detector is the first RICH detector to use aerogel as a radiator. An example of a two particle event is shown in Fig. III-4F.6a, where the dual rings from a pion and the single aerogel ring from a kaon (the kaon is below threshold for the $C_4F_{10}$ gas) are visible.

Caltech was responsible for design, testing and procurement of the aerogel radiator. This construction was funded through Caltech (about \$ 100k) in order to allow completion of the project on time. An extensive series of tests were conducted at Caltech to characterize the optical properties of this new material. This work formed part of the PhD thesis of Paul Carter.