Tests of time reversal in neutron‐nucleus scattering

13xperiments to test time-reversal invariance are ctisrussed, The experiments are based on observable col~structwl from the momentum and spin vectors of epithermed neutrons and from the spin of an aligned or polarized target, It is shown that the proposed tests are detailed balance testc of ti]ne-reversal invarirmce, The status of the experiments is briefly reviewed. I will report on tests of time-reversal invariance (TRI), which are in the beginning stages of experimental work at the Proton Storage Ring ( PSR) at Los Alamos. I discussed plans for this work two years ago at the Lnke Louise conference,’ A workshop cm Tests of Time-Reversal Invariance in Neutron Physics was held in C~hapel Hill, North C&rol.ina in April 1987, and the reader is referred to the proceedings for a more complete discussion of many points than wiU he presented here. The initial work that will be discussed has been carried out by a collaboration brtween Los Alamos, Harvard, and Princeton. During 1988 colleagues from TUNL, TR.IUMF, Delft, and University of Virginia joined in the work, Figure 1 illustrates the classical meaning of TRI. A system evolves from an initial state i to a final 3tste j. The system is described by momenta p and .—.-. . -—----. ——-— —-— .— ...—— .—-—.—— —.. ——. Fig. 1, fllustr~tes classical trajectories that obey \ + ;, And violate ] i * time-reversal invariance (see text ). coordinates q. A new initial state ~, is formed by time-reversing the state j. The signs ~f the p’s are changed and tile q’s are kept. The system evolves from the state ~ to some stat~ i*. TRI holds if the state i* is tlie sall]e as tile tilnereversecl initial state ~. For a quantum system T131 holds if the amplitude for the systelil to ]nake a transition froln i to J has the property Sinre only the square9 of of ‘J’R1 must be based on S(l f) = S’(f ;) , (1) amplitudes are measurable, Eq. ( 1) im~lies that tests measurements that test whether or not a(i + J)=u(j +;). (~) In order to see a TRI-violating phase chm~e, the anlplitucle S must be a sum of two or more amplitudes whose phazes cl~ange differently under time reversal (TR). Interest in the use of neutron-spin rhervahleo as probes of symm~try violations in nuclehr states waa sparked hy the observatim by V. P. Alfimenkov, ●t al,,’ of a large helicity (u’K) depmdence of the total scattering cross section at ttw energy of a p-wave resonance in ‘30La, Table I summarizes the properties of the neutron spin (a), the neutron nmmmturn ( K), and the target spin ( J ) under parity (P) and TR transformations, The idea of the present work is to use the spin of ●pithermal, 0.1 to 10 keV, neutrons to construct observable with which to test TRI. Using the fluxes available at the PSR, 1014 neutron-scattering events from a p-wave resonance can be detected in 107 seconds. Thus, tranonliasion asymmetries aa small as 10-7 can IM studied. Two types of measurement have been suggestd. P. K. Kabir ,4 L. Stodolsky,s and V. E. Bunakov and V. P. Cudkov 6 suggested the parity-odd observable UJ x K. P. K. Kabir7 proposed the parity-even observable (J K)(uTJ x K),

I will report on tests of time-reversal invariance (TRI), which are in the beginning stages of experimental work at the Proton Storage Ring ( PSR) at Los Alamos. I discussed plans for this work two years ago at the Lnke Louise conference, ' A workshop cm Tests of Time-Reversal Invariance in Neutron Physics was held in C~hapel Hill, North C&rol.ina in April 1987, and the reader is referred to the proceedings for a more complete discussion of many points than wiU he presented here. The initial work that will be discussed has been carried out by a collaboration brtween Los Alamos, Harvard, and Princeton. During 1988 colleagues from TUNL, TR.IUMF, Delft, and University of Virginia joined in the work, Figure 1 illustrates the classical meaning of TRI. A system evolves from an initial state i to a final 3tste j. The system is described by momenta p and  coordinates q. A new initial state~, is formed by time-reversing the state j. The signs~f the p's are changed and tile q's are kept. The system evolves from the state~to some stat~i*. TRI holds if the state i* is tlie sall]e as tile tilnereversecl initial state~. For a quantum system T131 holds if the amplitude for the systelil to ]nake a transition froln i to J has the property Sinre only the square9 of of 'J'R1 must be based on In order to see a TRI-violating phase chm~e, the anlplitucle S must be a sum of two or more amplitudes whose phazes cl~ange differently under time reversal (TR).
Interest in the use of neutron-spin rhervahleo as probes of symm~try violations in nuclehr states waa sparked hy the observatim by V. P. Alfimenkov, qt al,,' of a large helicity (u'K) depmdence of the total scattering cross section at ttw energy of a p-wave resonance in '30La, Table I summarizes the properties of the neutron spin (a), the neutron nmmmturn ( K), and the target spin ( J ) under parity (P) and TR transformations, The idea of the present work is to use the spin of q pithermal, 0.1 to 10 keV, neutrons to construct observable with which to test TRI. Using the fluxes available at the PSR, 1014 neutron-scattering events from a p-wave resonance can be detected in 107 seconds. Thus, tranonliasion asymmetries aa small as 10-7 can IM studied. Two types of measurement have been suggestd. P. K. Kabir ,4 L. Stodolsky,s and V. E. Bunakov and V. P. Cudkov 6 suggested the parity-odd observable UJ x K. P. K. Kabir7 proposed the parity-even observable (J K)(uTJ x K), V. E. Bunakov and k'. P. ("llldkovB showed that the large helicitv dePelI -d~nc~of the total cross scctiml could h understood as resulting frmn tlve Inixillg of nearby s-wave resonance into tile p-~ave resonance by the parity-violating weak nucleon-nucleon force. TWO enhauccment factors increase the size of the obervecl effect: 1) the small energy spacing, 10 q V, in the compound nucleus and 2) the large ratio of s-wave to unanlbiguous neutron decay au~plitudes. They argued that the q nhancement of Ihe dependence of the cross section on the TRocici P-odd scalar triple product mJ x K should be the same as that of the helicity. Since the helicity dependence of the cross section has been measured to be as large M 10~o, a 10-7 measuremmt of the dependence of the cross section on the scalar triple product would test for a TR-udri P-odd iut~raction at tile level of 10-s of the weak force Lctween nucleons, a sensitivity competitive with searches for a non-zero electric dipole nlommt of the neutron.
V, E, BunakovO has recently estinkated the nuclear enhancement of the cross-section dependence of the TR-odd P-even five-fold product, which arises from the mixing of p-wave resonances, to be between 10s and 10s. Thug, a 10-7 measurement of the dependence of the cross section on the five-fold product would test for a TR-ocld P-even force with a sensitivity Of 10-'0 of the strong force between nucleons. P. Herczeg 10 has studied the relationships betwem theories of CP violation in the kaon system and TRI violation in AS = O nuclear systems. Figure 2 shows an q xperimmt designed to look for a clcpendence of the total cross section on the scalar triple product. This approach is flawed. The

Fig. 2.
A neutron beam with momentum K passm through a polarizer and energies with a spin u. The target spin J is perpendicular to K. The neutron spin is switched so that the triple product UJ x K changes sign. A change in the neutron transmission upon switching u is not an ambiguous test of TRf (see texi. ) ~eal part of the spin-orbit force (a" J) will cause the neutron spin, which is initially perpendicular to both J anfl 1{, to prccess around J. The vector u will then develop a component along K and the~' K interaction will produce an asymmetry even in the absence Of TR[ violation. The appearance of a fake TR[violating asymmetry in the above geclanken experiment is closely related to the falsification of TRI violation by final-state interactions in scattering experiments. L. Stodolskyl 1 proposed that by adding an analyzer aftm the target, as shown in Fiu. 3, the apparatus could be made TR invariant and that detailed-balance TRI experimen_t9 in the sense of Eq. 2 above would result. In order to test for --. . -.
- TRI in the scalar triple product the polarizer-target-analyzer configuration is necen~ary, In the Chapel HiU workshnp 112 showed that since the five. fo]dproduct q xperiment could be carried out with an aligned target, where the average value of J is zero, the analyzm is not necmary.
We began work on parity and time-reversal experiments at Los Alamos in 1986. In our first experiment we meazurcd the degree of helicity dependence in the totai cross section of the 0.734 qV resonance in lsOLa, The Alfimenkov, et 81,,s experiment, which measured an asymmetry of 7.2 + 0.4Y0, and the A. Maaaike, et al.,ls experiment, which measured an aaymmetry of 10.4 + 0.3%, both used polarized proton filters to prepare a polarized neutron beam. In 1986 no polarized neutron beam was available at LoR Alamos. We carried out an asymmetry measurement as shown in Fig, 4. The helicity clependence in the total cross section was used both to polarize and to analyze the neutron beam. We obtained an asymmetry of 8.2 + 1,7%, To my knowledge, this is the first time the weak interactioli has been used both to polarize and analyze a beanl. The 1986 work was done by counting illdiviciual ,~cutrons using a 'iLi loaded giaas scintiliator.
Pulse-counting techniques limited us to instantaneous rates of M than 108 Hz, The PSR delivers neutron beams into a few micro steradians of 1012 Hz. In order to utilize fully the available neutron fluxes we develop~d and tested neutron-~urrcnt measurillq techniques in 1987. our detecticm apparat us is shown in Fig. 5, U3ing these teclllliqlles, we will be aide to take advantage of tile fldl intensity available from the PSlt without loss of neutrm-enmgy resoluti[m or degradation on the statistical accuracy of the number of neutrons detected. Using this detector we began a sllrvey of p-wave resonances in atoms that a~ow nuclear polarization or alignment.
In 1987, our colleagues from Princeton and Harvard set up a polarized 'He filter, which prepared a po~arizd neutron b~am. About 10-atmosphere-cn~3 of 3He were polarized using optical pumping tcchniquea. This apparatus has been described by K. Coulter14 in the Chapel Hill workshop, IIsing this polarized neutrou beam we repeated the 130La experiment, and searched for new examples of p-wave resonances with helicity-dependent cross sections. One such resonance was identified in lsl Gd. This techniques has the attractive feature that it is modest in scale and is noncryogenic. Furthermore, the s He spin, and, hence, the neutron spin, can be reversed relative to a weak holding field using an adiabatic fast paasag~. Reversing the neutron spin in this way is attractive for symmetrytest q xperiments because the neutron spin i~reversed without changing the magnetic fields used for spin transport.
The weakness of this technique is that since the n-3He cross section decreases u the inverse of the neutron velocity, neutrons can only be polarized up to a few eV, and over a fraction of a square centimeter using a 10-at mosphere-cnls cell. The 'He technique is attractive as a polarization-sensitive detector or as a polarizer/analyzer if thicker cells can be developed.
For 1988, we are developing a dynamically polarized proton filter with which to polnrize the neutron beam up to 10 keV. This project is well under way, with our collaborators from TRIU MF and Detft playing a leading role. We expect to have an area of 10 cmJ with a polarization of 70%, We have developed a sevendetector array, which is suitable for measurements over a 60-m flight path. We will have adequate qnergy resolution up to energies of 100 keV. We have designed and built a spin flipper that can reverse the neutron's spin between energies of 0.01 and 10 keV. A new data acquisition and analysis code has been written by the TUNL team. With this apparatus we plan to continue our search for pwave resonances suitable for TRI tests to higher energies and additiomd targets. The data obtained in this survey wiU determine the distribution and strength of parity violation as a function of atomic mass. [t will be interesting to see whether or not mmon-exchange models of the weak nucleon-nucleon force with experimentally determined couplings combined with theories of the compound nucleus can correctly explain the observed distribution of parity-violating mixing amplitudes.