Exploring the statistical properties of the neutron-deficient $^{109}$In isotope with the Oslo method

TL;DR

This study delivers the first Oslo-method extraction of the nuclear level density (NLD) and gamma-ray strength function (GSF) for the neutron-deficient isotope $^{109}$In, using the $^{106}$Cd$(\alpha,p\gamma)^{109}$In reaction. Anchored by low-lying levels and neutron-resonance data, the NLD follows a pronounced BSFG trend, while the GSF lacks a pronounced low-energy $E1$ enhancement and a near-threshold PDR, instead displaying a small low-lying $E1$ component of about $0.53(13)\%$ of the TRK sum rule; a decomposition suggests this strength is proton-dominated. The authors augment the experimental inputs with REOM$^2$/RQTBA calculations to interpret the low-energy dipole response, finding fragmentation and a suppressed neutron contribution below $S_n$ in $^{109}$In. Using the measured NLD and GSF in TALYS, they constrain $^{108}$In$(n,\gamma)^{109}$In and $^{108}$Cd$(p,\gamma)^{109}$In cross sections, achieving excellent agreement for the $(p,\gamma)$ data but revealing notable deviations from JINA REACLIB for the $(n,\gamma)$ rate, which has implications for p-process modeling. Overall, the work provides valuable benchmarks for NLD/GSF models in neutron-deficient nuclei and demonstrates how experimental constraints reduce uncertainties in astrophysical reaction-rate calculations.

Abstract

The nuclear level density (NLD) and the $γ$-ray strength function (GSF) of the neutron-deficient $^{109}$In isotope were extracted for the first time with data from the $^{106}$Cd$(α,pγ)^{109}$In reaction using a combination of the Oslo and the shape methods. Both quantities are consistent with those of neighboring Cd and Sn nuclei, but show substantial discrepancies with currently available model predictions. In contrast to earlier observations in the neighboring isotopic chains, $^{109}$In does not exhibit any significant enhancement of the dipole strength near the neutron separation energy. To interpret this feature, random-phase time-blocking approximation calculations have been performed for $^{109}$In and the neighboring $^{110,112}$Sn nuclei. The experimental data were also employed to estimate cross sections and rates of the radiative neutron- and proton-capture reactions, $^{108}$In($n,γ)$$^{109}$In and $^{108}$Cd($p,γ)$$^{109}$In, respectively, with the reaction code TALYS. Our ($p,γ)$ cross section is in excellent agreement with direct measurements over a wide range of proton energies, while the ($n,γ)$ cross section demonstrates notable deviations from predictions in the JINA REACLIB library. The new results on the statistical properties of $^{109}$In provide valuable constraints that may help address the problem of large model uncertainties compromising the accuracy of astrophysical $p$-process simulations.

Figures (14)

• Figure 1: (a) Experimental $p-\gamma$ coincidence data, (b) unfolded, and (c) primary matrices for $^{109}$In. Yellow dashed lines mark the neutron separation energy. The ranges of excitation and $\gamma$-ray energies used for the analysis with the Oslo method are shown with solid blue lines in (c). The gates on the ground state with spin-parity $9/2^+$ (D1) and a cluster of states with spin-parities $3/2^-$, $11/2^+$, $5/2^+$, $1/2^+$ (D2) used for the shape method are shown with red dashed lines in (c). Excitation-energy and $\gamma$-ray-energy bins are 124-keV wide.
• Figure 2: Experimental systematics of the average total radiative widths $\langle\Gamma_{\gamma}\rangle$ for Cd, In, and Sn isotopes. The experimental values are taken from Ref. Mughabghab18. The quadratic fit to the experimental data for the odd Cd and Sn isotopes and the corresponding 95% confidence interval are shown as a light-blue dashed line and a light-blue shaded area. The $\langle\Gamma_{\gamma}\rangle$ value used for the normalization of the $^{109}$In data, extracted from the fit, is indicated with a light-blue cross.
• Figure 3: Scaling factor applied to $\langle \Gamma_{\gamma}\rangle$ versus the spin-cutoff parameter. A quadratic fit to the data is shown with the dashed red line. The horizontal light-blue area corresponds to the 95% confidence interval for the $\langle \Gamma_{\gamma}\rangle$ value from the systematics, shown also in Fig. \ref{['fig 2: Systematics Gg']}. The vertical orange area shows the corresponding range of spin-cutoff values.
• Figure 4: Spin distribution at the neutron separation energy estimated with the spin-cutoff provided by Eq. (16) from Ref. Egidy2009, Eq. (\ref{['eq:8']}) (G&C) and Eq. (\ref{['eq:7']}) (RMI) with the parameters $a$ and $E1$ taken from Ref. Egidy05. The spin-distribution based on the recommended $\sigma(S_n)$ value is presented by a hatched histogram. The spin-distributions from microscopic calculations with the Skyrme-HF-BCS plus statistical model based on the MSk7 Skyrme interaction Demetriou2001, BSk14 Skyrme- and D1M Gogny-HFB plus combinatorial models (Goriely2008 and Hilaire2012, respectively) are depicted with triangular, squared, and round markers.
• Figure 5: Experimental NLD of $^{109}$In, plotted together with the NLDs of $^{105,111}$Cd Larsen2013_Cd and $^{111}$Sn Markova2023Markova2024. Known low-lying states ensdf are shown as a shaded hatched area. Dashed and dash-dotted lines indicate the BSFG and constant-temperature (CT) interpolations, respectively. Large open circles correspond to the $\rho(S_n)$ values extracted from the systematics of neutron resonance data. The open square and the cross correspond to $\rho(S_n)$ values from neutron resonance data and from the procedure described in Sec.\ref{['subsec 2.3: Normalization 109In']}, respectively.