Measurement of the angular distribution of γ-rays after neutron capture by 139La for a T-violation search

Parity violating effects enhanced by up to 106 times compared to proton-proton scattering have been observed in several neutron capture induced compound nuclei. This enhancement is explained as an interference between an s-wave and a p-wave amplitude (s-p mixing). Theory predicts that this mechanism can also enhance T-violating effects. For estimation of this enhancement in a promising candidate nucleus, we measured the angular distribution of γ-rays in the (n,γ) reaction induced in a 139La target. Experiments were performed at J-PARC, using a germanium detector array at an intense neutron beam. Analysis of the observed angular dependence around the 0.74 eV p-wave resonance allowed us to determine the ratio of the partial p-wave neutron width to the total neutron width in the entrance channel of the compound nucleus. We also report our development of a 3He spin filter needed as an epithermal-neutron polarizer for the T-violation search.


Strategy to search for T-violation in compound nuclei
It is well known that the weak interaction violates parity symmetry. Tiny parity violation caused by the hadronic weak interaction is observed as a helicity dependence of the cross section of p-p scattering in experiments using a polarized proton beam and an unpolarized proton target, and the size of this fundamental parity violating asymmetry is approximately 10 −7 [1][2][3].
Very large parity violating asymmetries with a size of 10 −1 at maximum have been observed in several compound nuclei formed after neutron capture by stable nuclides such as 139 La, 131 Xe, and 81 Br (Fig. 1). The parity violation was measured as a longitudinal asymmetry of the neutron capture cross section, A L . This parity violation occurs in a p-wave resonance (neutron orbital angular momentum l = 1) located at the tail of an s-wave resonance (l = 0). It is theoretically understood a e-mail: okudaira@post.j-parc.jp that fundamental parity violation enhancement by up to 10 6 is a result of an interference between the s-wave and thee p-wave amplitudes, called "s-p mixing".
There is a theoretical prediction that fundamental CP-violation can be also enhanced in these nuclei under the assumption of being due to the s-p mixing as for the enhancement of P-violation [4]. This implies that, invoking the CPT theorem, time reversal violation is also enhanced in these systems and can be searched for with very sensitive measurements of the compound nucleus system. We are aiming to search for T-violation beyond that predicted by the Standard Model, for which several experiments and developments are in progress at J-PARC.
The forward scattering amplitude of polarized neutrons incident upon polarized nuclei can be written as where σ ,Î andk are unit vectors parallel to the spin of the incident neutron, the spin of the target nucleus The vertical axis is the longitudinal asymmetry of the neutron absorption cross section at a p-wave resonance. The horizontal axis is resonance energy of the p-wave resonance. and the wave vector of the neutron, respectively [5].
Here we assume that the target nucleus is purely vector polarized. A is the spin independent (P-even, T-even) term, the imaginary part of which is related to the total neutron cross section via the optical theorem. B is the spin dependent (P-even, T-even) term corresponding to a "pseudomagnetic" neutron spin rotation through the polarized target. C is the P-violating (P-odd, T-even) term, which is enhanced for the nuclei mentioned before. The imaginary part of the T-violating (T-odd and P-odd) term D gives rise to a difference of total cross sections observed in the transmission of neutrons, polarized parallel and antiparallel to theÎ ×k axis: The expression on the right side relates the T-violating effect to the (enhanced) P-violating cross section difference σ P measured via transmission of the two neutron helicity states through the unpolarized target (due to the C term in Eq. (1)). W T and W are the T-violating and P-violating matrix elements (ranges of values for their ratio as predicted by various models can be found in Ref. [4]). The factor κ(J ) includes amplitudes of the partial neutron widths and depends on the total channel spin J = I + 1/2 or J = I − 1/2 (I being the spin of the target nucleus). The amplitudes can be expressed in terms of two variables x and y which are given by where n p is the neutron width of the p-wave resonance and n p, j= 1 2 and n p, j= 3 2 are its partial neutron widths for the two values of total angular momentum j of the neutron. The variables x and y satisfy  . A mixing angle φ of the j = 1/2 and j = 3/2 components can then be defined as x = cos φ, y = sin φ.
For the two channels of total spin, κ(J ) is given by [6] As examples, φ dependencies are shown in Fig. 2 for the target isotopes 139 La, 131 Xe, 81 Br and 117 Sn. Eq. (2) and Eq. (6) indicate that the T-violation sensitivity strongly depends on the value of φ. Therefore, it is important to determine κ(J ) for an estimate of the experimental sensitivity.
First of all, we need to find suitable nuclei for the T-violation search. Nuclei that have large σ P and large κ(J ) are obviously advantageous. Helpful for a larger statistical sensitivity are a large natural abundance of the nucleus to be employed and a p-wave resonance sitting at low energy where typical neutron sources can provide high beam intensities. Small nuclear spin is also important for the nuclear polarization because nuclei that have large spin are difficult to polarize due to the quadrupole coupling with intra-atomic electric fields, leading to broad lines of magnetic resonance. Unfortunately, the method for the nuclear polarization has not been established for most of the nuclei that otherwise might be suitable. Candidate nuclei for the experiment are 139 La, 131 Xe, 81 Br and 117 Sn and others, whose σ P is large and resonance energy is low. Their properties are shown in Table 1.

PPNS 2018
The isotope 139 La looks particularly promising, also due to its high natural abundance. In addition, an exceptional high nuclear polarization of about 50% has been achieved using a Neodymium doped LaAlO 3 crystal at PSI [7]. However, κ(J ) of these nuclei is still unknown. This can be extracted from measurements of angular distributions of (n,γ ) reactions using unpolarized neutrons (see next section). We have recently performed such measurements at J-PARC for the target nuclei 139 La, 131 Xe, 81 Br, 117 Sn, 115 In, 113 Cd, 127 I, and 103 Rh.
On the other hand, an experiment to verify the compound nuclear model is also ongoing at J-PARC. The enhancement of the P-and T-violation is based on the assumption of the s-p mixing and is derived from the statistical interpretation of the compound nuclear model. It can be tested by measuring the angular distribution of the (n,γ ) reaction using polarized neutrons. We have installed a neutron polarizer at a neutron beam line and confirmed that it delivers polarized epithermal neutrons (see Sect. 3 and Ref. [8]).
This paper reports the result of a measurement of κ(J ) for the target nucleus 139 La and the development of a neutron polarizer for the T-violation search. The results of unpolarized (n,γ ) measurements for the target nuclei 117 Sn and 81 Br are discussed in Refs. [9] and [10], respectively. An experiment to measure the (n,γ ) reaction using polarized neutrons for verification of the compound nuclear model is reported in Ref. [8].

Formalism of the angular distribution of γ -rays
In order to obtain the value of κ(J ), it is necessary to determine φ by measuring the angular distribution of γ -rays in (n, γ ) reactions. The corresponding differential cross section for unpolarized neutrons and unpolarized nuclei can be written as where θ γ is the polar angle of the outgoing γ -ray momentum for the case that only s-and p-wave amplitudes are present [11]. The angular correlation terms a 0 , a 1 and a 3 can be written as Here I is the spin of the target nucleus, J and J are the spin of the compound states, j and j are the total angular momenta of the incident neutrons, m is an integer number, and F is the spin of the final state. z r p j is given as with x and y as defined in Eq. (3). V 1 and V 2 are s-wave and p-wave amplitudes respectively, written as where k is the neutron wave number, E n is its kinetic energy, n r is the neutron width, γ r f is the partial γ width to f -th final state, and E r is the energy of the neutron resonance. The subscript of r in all quantities indicates whether it is an s-or p-wave, and g r is statistical weight factor defined as For further details of this formalism please see Ref. [11]. Since E n dependent functions a 1 and a 3 belonging to specific angular dependences of γ -ray emission depend on x and y, the parameter φ (related to x and y via Eq. (5)) can be determined from measurements of the angular distribution of γ -rays.

Experimental setup
The experiment to measure the angular distribution was conducted at the ANNRI (Accurate Neutron-Nucleus Reaction measurement Instrument) beam line of the Material and Life science experimental Facility (MLF) of the Japan Proton Accelerator Research Complex (J-PARC). A schematic view of the beam line is shown in Fig. 3. The average proton beam power was 150 kW during the experiment. A beam of pulsed neutrons was provided with a repetition rate of 25 Hz and collimated to a 22 mm diameter at the target position. The total measurement time for the 139 La(n,γ ) reaction was about 60 hours (5.4 × 10 6 shots). A nat La target with a dimension of 1 × 40 × 40 mm 3 was used. The angular distribution was measured with a detector array consisting of 22 germanium crystals (Fig. 4), whose angles are 36 • , 71 • , 72 • , 90 • , 108 • , 109 • , and 144 • with respect to the neutron beam    line. The nuclear target was mounted in the center of the spectrometer at a distance of 21.5 m from the neutron source. This length determines the baseline for the neutron spectrum via Time-Of-Flight (TOF, see next section). Characteristics and simulation results for this spectrometer are reported in Ref. [16]. Figure 5 presents a γ -ray energy spectrum displaying intense γ -ray transitions from 139 La(n, γ ) reactions. Figure 6 shows well-resolved resonances obtained from the γ -ray yield as a function of the neutron TOF. Here, a normalization to the intensity of the incident neutron beam was applied using a TOF spectrum with a 10 B target, measuring the 477.6 keV γ -rays from the (resonance-free) 10 B(n,αγ ) 7 Li reaction.

Experimental results
The angular distribution described by Eq. (7) is measured as a function of neutron energy E n . In our analysis we focus on the 5161 keV γ -rays of the transition to the ground state of 140 La. While a 0 is the ordinary, symmetric Breit-Wigner function, a 1 is asymmetric around the energy of the p-wave resonance and thus leads, for cos θ γ = 0, to a distortion of the resonance. The sizes of the a 1 and a 3 terms in Eq. (7) depend on the value of φ. Accordingly, we can determine φ from measurements of the angular distribution of γ -rays as a function of neutron energy in the vicinity of the p-wave resonance. In order to quantify the asymmetric contribution to the shape of the p-wave resonance, we define an asymmetry where N L and N H are the number of events in the regions of E p − 2 p ≤ E n ≤ E p and E p ≤ E n ≤ E p + 2 p of the neutron spectrum, respectively. The peak energy E p and the peak width p of the resonance are obtained from a fit of a Breit-Wigner function convoluted with the pulse structure of the neutron beam and the Doppler broadening due to the thermal motion of target nuclei. The pulse structure of the ANNRI beamline was evaluated in Ref. [13], which to reproduce we adopted an Ikeda-Carpenter function [14]. The thermal motion of the target nuclei has been taken into account using the free-gas model. Figure 7 shows the p-wave resonance gated with the full absorption peak at 5161 keV at the 36 • detectors to visualize its asymmetric shape and the definition of N L and N H . The angular distribution of A LH is shown in Fig. 8, and it was fitted with a function A cos θ γ + B. The fitting results of the parameters A and B were A = −0.388 ± 0.024, B = −0.075 ± 0.011. (14) We thus found a clear angular distribution of the γ -rays in the transition from the 0.74 eV p-wave resonance of 139 La+n to the ground state of 140 La. From the results, φ can be obtained from where the left side is the experimental value of A from Eq. (14), and the right side was obtained from theoretical calculations of a 0 and a 1 . Here, the effect of a 3 is neglected. This is justified since a 3 is derived from the pwave amplitudes which are small compared to the s-wave amplitude. Two solutions were obtained as PPNS 2018 as visualized in Fig. 9. This result implies that for 139 La target nuclei any fundamental T-violation will be enhanced at a similar or slightly larger level than the P-violation. The details of this experiment and analysis are reported in Ref. [15].

Development of 3 He spin filters at JAEA
As discussed in the previous section, the enhancement of T-violation in the 0.74 eV p-wave resonance in 139 La+n can be expected to be of similar size as the P-violation. It is however also important to validate the underlying compound nucleus model at this neutron energy, which requires a polarizer for epithermal neutrons. Here the current status of a development of the 3 He spin filters at J-PARC is reported.
Polarized 3 He has previously been used for polarization of epithermal neutrons at 0.74 eV experiments on P-violation in neutron transmission through a 139 La target [17]. The isotope 3 He has a very large absorption cross section (10666 barn at thermal energy) for neutrons with spin antiparallel to the 3 He spin, while the absorption cross section for parallel neutrons is approximately zero. The neutron beam is polarized passing through a glass cell into which polarized 3 He is encapsulated. A figure of merit (FOM) used to describe the polarization efficiency of the   3 He spin filter is defined as where P and T are neutron polarization and neutron transmission, respectively. As shown in Fig. 10, P, T and thus the FOM depends on the thickness of the 3 He, given by the product of the pressure of 3 He gas and the length of the 3 He spin filter. For a 3 He polarization of 70% and 0.74 eV neutrons, the FOM has a maximum at 79 atm · cm, for which P = 87% and T = 30%. A development of a large spin filter for epithermal neutrons is ongoing at J-PARC, KEK and Nagoya University. The glass cell of the 3 He spin filter is made from the special, boron-free glass GE180. The cell contains, besides the 3 He, Rb used for the spin exchange optical pumping (SEOP) method [18]. The polarization of 3 He is maintained by a uniform magnetic field. It relaxes, however, due to the inhomogeneity of the magnetic field, impurities inside the glass cell, and other effects. To avoid contamination from impurities, the cell must be evacuated and filled using a clean gas handling system. Such a system was recently constructed at J-PARC as shown in Fig. 11. The glassware and the stainless steel tubing were baked out for one week at 400 • C and 200 • C, respectively, and the ultimate achieved vacuum was approximately 2 × 10 −7 Pa after the baking. A first 3 He spin filter fabricated at J-PARC using this vacuum system is shown in Fig. 12. The laser system developed at J-PARC is shown in Fig. 13. It can be installed on the neutron beam line and maintain the 3 He polarization during experiments. The laser power is 40 W. A Volume Holographic Grating (VHG) is used for preparation of a narrow range of wavelengths about 795 nm for resonant absorption by the Rb atoms. Since a magnetic field homogeneity at the order of 10 −4 cm −1 is required to prevent decay of the 3 He polarization, a homogeneous magnetic field (2 mT) is applied to the 3 He spin filter using a coil and a double magnetic shielding. The amount of 3 He gas is 15 atm · cm, and 70% 3 He polarization are achieved. Larger 3 He spin filters and a laser system with a higher power of 100 W are currently being developed.