Statistical properties of $^{133}$Xe and the $^{132}$Xe$(n,γ)$ cross section

TL;DR

This study reports the first extraction of the nuclear level density and gamma-strength function for $^{133}$Xe below the neutron separation energy using the inverse-Oslo method, enabling a statistically grounded constraint on the $^{132}$Xe$(n,\gamma)$ cross section via Hauser-Feshbach modeling. By combining unfolding, first-generation gamma analysis, and Bayesian normalization, the authors determine a consistent NLD and $ ext{gSF}$ parameterization, including a detailed SMLO-based $E1$ component and a potential pygmy resonance, with an exploration of a low-energy enhancement. Large-scale shell-model calculations support the interpretation of the NLD and $ ext{gSF}$, highlighting parity distributions and a magnetic nature for the low-energy strength. Using the resultant NLD and $ ext{gSF}$ as inputs to TALYS, they obtain a tightly constrained $^{132}$Xe$(n,\gamma)^{133}$Xe cross section and stellar reaction rate, improving upon TENDL predictions, particularly at low energies and low temperatures. The work demonstrates the feasibility of applying inverse-Oslo to noble gases and provides data of immediate relevance to NEEC and plasma-related nuclear processes.

Abstract

$^{133}$Xe is an interesting case for plasma physics to explore nuclear excitation by electron capture, as the process can be studied using statistical properties of $^{133}$Xe. In this work we present results on $^{133}$Xe from the inverse-Oslo method where we extract the nuclear level density and the $γ$-strength function, which is used to calculate the (n,$γ$) cross section on $^{132}$Xe. The $γ$-strength function of $^{133}$Xe can constrain the estimated decay rate from nuclear excitation by electron capture. The $\mathrm{d}(^{132}\mathrm{Xe},\mathrm{p})^{132}\mathrm{Xe}$ reaction was used to create the compound nucleus $^{133}$Xe, which was recorded with an annular particle telescope and a scintillator array consisting of \la and BGO-shielded HPGe Clover detectors. With the inverse-Oslo method, it is possible to study nuclei that are impossible or unable to manufacture targets from, short lived isotopes, or as in this work, noble gases. We present the extracted nuclear level density, and $γ$-strength function for $^{133}$Xe, along with shell-model calculations of the statistical properties of $^{133}$Xe. These are the first statistical properties extracted below 6 MeV for any xenon isotope. We constrain the $^{132}$Xe(n,$γ$) $^{133}$Xe cross section and reaction rate using the TALYS reaction code.

Figures (10)

• Figure 1: (a) Raw, unprocessed excitation--$\gamma$ coincidence matrix and (b) unfolded matrix with $100$ keV/bins (both axes). The first--generation matrix (c) was re-binned from $100$ to $300$ keV to reduce possible fluctuations.
• Figure 2: Model dependent spin distribution, $g(J,E_x)$ plotted together with the shell model spin distribution (blue dots). The solid red line is the rigid moment of inertia (RMI) with a reduction factor of 0.8, the solid black line is the constant temperature model with parameters from Egidy and Bucurescu (E&B CT), the dashed magenta line is the Fermi gas model with parameters from Egidy and Bucurescu (E&B FG) eb2006ebe2006, and the dash-dotted cyan line is the Fermi gas model with parameters from Gilbert and Cameron (G&C FG) Gilbert1965. (a) $g(J, E_x = 2\,\mathrm{ MeV})$, (b) $g (J, E_x = 3.2\,\mathrm{ MeV})$, (c) $g (J, E_x = 4.6\,\mathrm{ MeV})$.
• Figure 3: Experimental NLD for $^{133}$Xe (filled circles), the NLD at $S_n$ (solid diamond), known low-lying levels CAPOTE20093107 (solid black line), the NLD from large-scale shell model calculations with the SN100 and SN100PN (dashed-dotted and dashed lines, respectively), and the extrapolated NLD from the Constant Temperature model (solid blue line). The red shaded bands indicate the credibility intervals for $\sigma$, $2\sigma$ and $3\sigma$ of the model interpolation. The shaded gray areas indicate the energy regions to which the experimental NLD was normalized to discrete level density and the CT model.
• Figure 4: The experimental $\gamma$SF of $^{133}$Xe shown with the filled black circles while the red and blue diamonds shows the nuclear resonance fluorescence results in $^{132}\mathrm{Xe}$ and $^{134}\mathrm{Xe}$, respectively Massarczyk2014. The $M1$ strength function from large--scale shell model calculations are shown by the black line, see Sect. \ref{['sec:shellmodel']} for more details.
• Figure 5: The $\gamma$SF of $^{133}$Xe (filled black circles), with the credibility bands $\pm1\sigma$, $\pm2\sigma$ and $\pm3\sigma$ for the $\gamma$SF model fit. The blue and red diamonds shows the $E1$ and $M1$$\gamma$SF of $^{134}\mathrm{Xe}$ from NRF, respectively massarczyk_magnetic_2014. Photo nuclear data on $^{133}\mathrm{Cs}$ data Berman1969Lepretre1974 are shown in filled purple and orange squares. The $M1$ strength function from large--scale Shell model calculation is included as a solid black line.