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

Abstract

We demonstrate to extract $^{88}\mathrm{Y}(n,γ)$ cross sections using the $(p,p'γ)$ surrogate reaction with proper treatment of the spin-parity distribution of the compound nucleus $^{89}\mathrm{Y}$. Experimental data of both $γ$-decay probability and $γ$-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 $(n,γ)$ data uncertainty. The $^{88}\mathrm{Y}(n,γ)$ 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 $^{88}\mathrm{Sr}(p,γ)$ reaction, of which the measured data are available for comparison. This work opens interesting perspectives on the matter of extracting ($n,γ$) reaction cross sections on unstable nuclei as surrogate reaction experiments are becoming widely available.

Figures (6)

• Figure 1: Calculated SP distribution $F^{CN}_\delta(E^\ast,J,\pi)$ of $^{89}\mathrm{Y}^*$ populated by the $^{89}\mathrm{Y}(p,p'\gamma)$ at $E^\ast$=11.5 MeV, with red bars representing positive parities and black ones representing negative parities.
• Figure 2: (a) Decay probability for $\gamma$ emission (black dots) measured for the $^{89}\mathrm{Y}(p,p'\gamma)^{89}\mathrm{Y}^\ast$ reaction as a function of $E^\ast$ of $^{89}\mathrm{Y}^*$. The $P_{\gamma}(E^\ast)$ calculated with \ref{['eq:P']} using the adjusted TALYS parameters from the HCPS are shown in the blue shaded area. The vertical dotted line indicates the $S_n$ of $^{89}\mathrm{Y}$. The inset panel shows the probability density distribution of $\chi^2_{\text{w}}$ calculated with the BO-MCMC framework, where the blue shaded area represents the $\chi^2_{\text{w}}$ values corresponding to the HCPS. (b) The $\gamma$SF for $^{89}\mathrm{Y}$ as a function of $E_\gamma$. The blue shaded area represents the data fitted with the experimental larsenExperimentallyConstrained892016benouaretDipoleStrength892009szeflinskaGammarayStrengthFunctions1979bermanPhotoneutronCrossSections1967lepretreGiantDipoleStates1971 and evaluated varlamov2003photoneutron data, where the same HCPS shown in panel (a) are employed.
• Figure 3: (a) ^88Sr${}^{88}$Sr(p,$\gamma$) cross section as a function of proton energy. Our results (blue shaded area) are compared with experimental data from Harissopulos $et \ al.$harissopulosCrossSectionMeasurements2021 and Galanopoulos $et \ al.$galanopoulos88Sr892003, as well as with the TALYS default calculations and TENDL-2023. (b) Ratio to JINA REACLIB evaluation for ^88Sr${}^{88}$Sr(p,$\gamma$) reaction rates as a function of astrophysical temperature.
• Figure 4: $^{88}\mathrm{Y}(n,\gamma)$ cross sections as a function of neutron energy. The blue shaded area shows the data from joint constraints of both $P_{\gamma}(E^\ast)$ and $\gamma$SF, while the light blue one indicates the data induced by only constraint of $P_{\gamma}(E^\ast)$. Here, the Jeukenne-Lejeune-Mahaux (JLM) microscopic OMP baugeLaneconsistentSemimicroscopicNucleonnucleus2001 and the CTM of the NLD are employed to interpret our data, and a width-fluctuation correction koningTALYSModelingNuclear2023 is taken into account by default. The black squares are the data obtained with the WE approximation. The pink shaded area represents the inferred data of A.C. Larsen $et \ al.$larsenExperimentallyConstrained892016. The black solid, green dashed, yellow dotted and blue dash-dotted lines indicate the available evaluations koningTENDLCompleteNuclear2019iwamotoJapaneseEvaluatedNuclear2023plompenJointEvaluatedFission2020zabrodskaya2007rosfond.
• Figure 5: Ratio to JINA REACLIB evaluation for ^88Y${}^{88}$Y$(n,\gamma)$ reaction rates as a function of astrophysical temperature. The blue shaded area shows the data obtained from joint constraints of both $P_{\gamma}(E^\ast)$ and $\gamma$SF. The pink shaded area shows the calculations by Larsen $et \ al.$larsenExperimentallyConstrained892016.