Constraining Neutron Capture Cross Sections for $^{88}\mathrm{Y}$ with Gamma-ray Strength Function in $(p,p^\prime\gamma)$ Surrogate Reaction

TL;DR

This paper introduces a Bayesian and MCMC-based method to accurately extract neutron capture cross sections for $^{88}$Y using surrogate $(p,p'\gamma)$ reactions, significantly reducing uncertainties where direct data are unavailable.

Contribution

The study presents a novel approach combining experimental gamma-ray data with advanced statistical methods to determine neutron capture cross sections on unstable nuclei.

Findings

Achieved cross section uncertainties of 7.6%-23.1%.

Validated method with $^{88}$Sr(p,γ) reaction data.

First-time extraction of $^{88}$Y(n,γ) cross sections in the 0.01-3.0 MeV range.

Abstract

We demonstrate to extract $^{88}\mathrm{Y}(n,\gamma)$ cross sections using the $(p,p'\gamma)$ surrogate reaction with proper treatment of the spin-parity distribution of the compound nucleus $^{89}\mathrm{Y}$. Experimental data of both $\gamma$-decay probability and $\gamma$-ray strength function are used to constrain the nuclear model parameters within a computational framework combining the Bayesian optimization and Markov chain Monte Carlo method, which helps to significantly reduce the $(n,\gamma)$ data uncertainty. The $^{88}\mathrm{Y}(n,\gamma)$ cross sections are then extracted with a narrow uncertainty of 7.6\%-23.1\% within neutron energy range of 0.01 to 3.0 MeV for the first time, where no experimental data are available. Moreover, our method is verified with the $^{88}\mathrm{Sr}(p,\gamma)$ reaction, of which the measured data are available for comparison. This work opens interesting perspectives on the matter of extracting ($n,\gamma$) reaction cross sections on unstable nuclei as surrogate reaction experiments are becoming widely available.