Study of parity violation in radiative neutron capture reactions

written by Yasuyuki MATSUDA

for PEN collaboration

The neutron-nucleus reaction in resonance region has attracted our attention because of its large enhancement of the weak interaction. The helicity dependence of cross section was measured and found to be 9.7 ± 0.3% on 0.734eV p-resonance of ^{139}La [1][2], which can be compared to (0.24 ± 0.11) × 10^{−6} on p-p scattering at 800MeV [3]. This enhancement is caused by the interference between two resonances, which have same spin but opposite parity, such as s- and p- resonances (s-p mixing). Theorodical approachs based on s-p mixing models predicted that the enhancement appears also in T-violating amplitudes[4]. It gives us unique oppprtunity to test time reversal invariance(TRI) with excellent accuracy, even better than neutron EDM measurements. Various experiments to obsserve TRI have been proposed.

For TRI experiment, it is very important to know the detail of enhancement mechanism. We will report recent experiment at KEK-BSF which have been performed to verify the model of enhancement.

In resonance region, all the experiments which have been done until now are measurements of helicity dependence of the cross section. This is called A_{10} term, corresponding to (vecσ_{n}·veck_{n}), where vecσ_{n} is the spin of the neutron and k_{n} is the momentum of the neutron. If we observe γ-rays from capture reactions at resonances, we can measure other terms like A_{2} and A_{9}, corresponding to (σ⃗_{n} ·(k⃗_{n} ×k⃗_{γ})), (σ⃗_{n} ·k⃗_{γ}), respectively. These correlation terms are different for each γ-ray transitions, therefore we must identify each single γ-rays from compound nuclei. We have measured A_{2} and A_{9} terms. From s-p mixing model, these asymmetry terms for 5.1MeV γ-ray transition are written as [5][6],

A_{2} ≃ η\sqrt{\frac{Γ_{s}^{n}}{Γ_{p}^{n}}} \sqrt{\frac{Γ_{s}^{γ}}{Γ_{p}^{γ}}} \frac{Γ_{p}(E − E_{p})}{(E − E_{s})^{2} + (Γ_{s}/2)^{2}} · (−0.125x − 0.074y),  (1)

A_{9} ≃ \frac{−2W (E − E_{p})}{(E − E_{s})^{2} + (Γ_{s}/2)^{2}} \frac{Γ_{s}^{n}}{Γ_{p}^{n}} \sqrt{\frac{Γ_{s}^{γ}}{Γ_{p}^{γ}}} · (−0.125),  (2)

A_{10} ≃ \frac{2xW}{E_{p} − E_{s}} \sqrt{\frac{Γ_{s}^{n}}{Γ_{p}^{n}}} ,  (3)

where W is the weak matrix element in nulcei, and E_{n} is incident neutron energy. The E_{s(p)} is resonance energy, Γ_{s(p)}, is its width. The x and y are defined as x = \sqrt{Γ_{p \frac{1}{2}} /Γ_{p}}, y = \sqrt{Γ_{p \frac{3}{2}} /Γ_{p}}, and satisfy x^{2} + y^{2} = 1. The Γ_{p \frac{1}{2} ( \frac{3}{2} )} is the partial neutron width for p-wave neutrons with j = 1/2(3/2). Among these factors, we know all the values except W and x and Γ_{s}^{γ}/Γ_{p}^{γ}. In this experiment, we have measured Γ_{s}^{γ}/Γ_{p}^{γ} and asymmetries. Then we can determine the limit for the values of x and y from A_{2} and A_{9} mesurements using known A_{10} values.

Figure 1: Experimental Setup

The experimental setup is shown in Fig 1. Pulsed neutron beam were polarized by a dynamically polarized proton filter, and transported through a coil in which the polarization were kept. Two NaI(Tl) crystals shielded by 5cm Pb and 3cm B_{4}C were used as γ-ray detector. Its energy resolution was 7.7% for 0.662MeV γ-ray from the ^{60}Co, and 4.4% for 4.4MeV γ-ray from ^{12}C*. The direction of the neutron spin were changed through a spin-flipper adiabatically. Then it bombared La target. The field direction of the spin-flipper was reversed every 4sec to reduce systematic errors.

The experimental results for 5.1MeV transition are

\sqrt{Γ_{s}^{γ}/Γ_{p}^{γ}} = 4.07 ± 0.07,
A_{2} = 0.011 ± 0.115,  (4)
A_{9} = 0.068 ± 0.140.

Allowed regions for x and y from individual A_{2} and A_{9} measurements do not conflict each other. It supports s-p mixing model, which predicts the enhancement of T-violating amplitudes. Taking into account the value of xW which were deduced from the previous A_{10} measurement [6], we have obtained x and W values as,

x = 0.86_{−0.25}^{+0.12},
y = 0.51_{−0.33}^{+0.28},  (5)
W = 3.3_{−1.3}^{+6.4} [meV].

The x and y values are of importance for the measurement of a T-violating amplitude in neutron scattering experiments. Gudkov showed [7] a relation between T-violating P-violationg obserbables (Δσ_{T}) and T-conserving P-violating obserbables (Δσ_{P}) based on the s-p mixing model.

\frac{Δσ_{T}}{Δσ_{P}} = ⟨λ⟩κ(J),  (6)
⟨λ⟩ = \frac{1}{1 + 2ξ} \frac{g_{T}}{g_{P}} ,  (7)

where ξ ≃ 1. The g_{T} and g_{P} are the T-violating coupling constant and the P-violating one in the nucleon-nucleon interaction respectively. The κ(J) is related to total angular momentum of compound nucleus. Assuming J = 4 for the 0.734eV p-resonance, κ(J) is given as,

κ(4) = \frac{6}{5} (\frac{−\sqrt{7}x + \sqrt{5}y}{5\sqrt{5}x − \sqrt{7}y} ) .  (8)

The value of κ(J) obtained in this experiment is κ(J) = 0.49_{−0.09}^{+0.20}, which seems to be large enough to enable us to measure T-violating effect in the neutron resonance reaction.

References

[1] V.P. Alfimenkov et al, Nucl. Phys. \underline{A398} (1983) 93.

[2] Y.Masuda et al, Hyperfine Interactions \underline{34} (1987) 143.

[3] V.W. Yuan et al, Phys. Rev. Lett. \underline{57} (1986) 1680.

[4] L. Stodolsky, Phys. Lett. \underline{172B} (1986) 5.

[5] V.V. Flambaum and O.P. Susukov, Nucl. Phys. \underline{A435} (1985) 352.

[6] H.M. Shimizu, PhD thesis, Kyoto University (1992).

H.M. Shimizu et al, Nucl. Phys. \underline{A552} (1993) 293.

[7] V.P. Gudkov, Phys. Rep. \underline{212, No.2} (1992) 77.