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In the compound process of neutron-induced nuclear reactions, the parity symmetry (P-violation) is violated due to the effect of the weak interaction. It has been experimentally found that the helicity dependence of the reaction cross section due to the P-violating nucleon-nucleon interaction is enhanced by up to six orders of magnitude compared to the bare effect observed in few-nucleon reactions[1]. This amplification effect has been explained by using a statistical model based on the Random Matrix Theory. In this model, transition matrix element is expected to be inversely proportional to the square-root of the level density $N$. The accuracy of the existing experimental data of $W$, however, are not sufficient to verify the model, and thus more accurate data are demanded. $W$ is related to the asymmety ${A_{\rm L}}$ of the helicity-dependent reaction cross section as the following equation;
$A_L \approx -\frac{2xW}{E_{\rm p}-E_{\rm s}}\sqrt{\frac{\Gamma^{\rm n}_{\rm s}}{\Gamma^{\rm n}_{\rm p}}}\hspace{1cm} \left(x\equiv\sqrt{\frac{\Gamma^{\rm n}_{\rm p,j=1/2}}{\Gamma^{\rm n}_{\rm p}}}\right),\hspace{3cm} (1)$
where ${E_{\rm s}}$ and ${E_{\rm p}}$ are the resonance energies of the s-wave and the p-wave resonances, respectively. ${\Gamma^{\rm n}_{\rm s}}$ and ${\Gamma^{\rm n}_{\rm p}}$ are the corresponding neutron widths, respectively. $x$ is the ratio of the partial p-wave neutron width to the total neutron width, it can be determined by measuring the angular dependence of the emitted $\gamma$-rays of the (n,$\gamma$) reaction [2]. Therefore, by measuring ${A_{\rm L}}$ and $x$, one can determine $W$ experimentally from Eq. (1).
In this study, we focus on Pd isotopes which have relatively small values of $N$, and consequently $N$ dependences of $W$ are rather significant. To obtain $x$, the angular distributions of the prompt $\gamma$-rays from the p-wave resonance of the Pd isotopes were measured at the J-PARC MLF BL04 in February 2021. As a preliminary result, the following values of $x$ were obtained for $^{108}$Pd;
$x = 0.9986^{+0.0003}_{-0.0099}\hspace{1cm}{\rm or}\hspace{1cm}x = -0.9986^{+0.0099}_{-0.0003}.\hspace{2cm} (2)$
In this contribution, the experimental procedure and the result will be presented.
[1] G. E. Mitchell et al., Phys. Rep. 354, 157 (2001).
[2] V. V. Flambaum et al., Nucl. Phys. A 435, 352 (1985).
