Microscopic study of the low-energy enhancement in the gamma-decay strength of \(^{50}\)V

TL;DR

This paper addresses the microscopic origin of the low-energy enhancement (LEE) in the gamma-decay strength of $^{50}$V by performing large-scale shell-model calculations that treat both $E1$ and $M1$ transitions within a unified framework. Using a valence space spanning $sd$-$pf$-$sdg$ and the SDPFSDG-MU interaction in KSHELL, the study demonstrates that the LEE is entirely magnetic dipole in nature and arises from a constructive interference between orbital and spin components of the $M1$ operator, with the diagonal $0f_{7/2} ightarrow 0f_{7/2}$ proton transitions providing the dominant contribution. The calculations reproduce the low-lying discrete levels and the nuclear level density up to about $E_x oughly 7.5$ MeV, and the dipole gamma strength function matches the Oslo data in shape, offering a microscopic link between shell-model configurations and statistical gamma decay properties. The work lays the groundwork for systematic studies across nearby nuclei and for incorporating Porter–Thomas fluctuations and generalized Brink–Axel hypotheses, with potential implications for astrophysical reaction rates and nucleosynthesis modeling. **Key result:** the LEE in $^{50}$V is driven by $M1$ transitions, amplified by interference, and rooted in $0f_{7/2} ightarrow 0f_{7/2}$ diagonal proton channels.

Abstract

We address the microscopic origin of the low-energy enhancement (LEE) in \(^{50}\)V with large-scale shell-model calculations to obtain $E1$ and $M1$ transitions within the same theoretical framework. The valence space spans the three major shells $sd$, $pf$ and $sdg$ and is treated with the SDPFSDG-MU interaction using the KSHELL code. With a \(1 \hbar ω\) truncation, 3600 energy eigenstates and a basis of $7.02\times10^{6}$ positive and $5.94\times10^{8}$ negative parity states, the calculations yield nearly two million individual dipole transitions. The fourteen lowest experimental levels are reproduced within $0.30$~MeV, the calculated total level density excellently reproduces Oslo-method data up to $E \approx 7.5$~MeV, and the calculated dipole gamma strength function follows the experimental shape -- including the LEE -- for the full gamma-energy range covered by the Oslo experiment. The LEE is shown to be entirely magnetic dipole in origin. Both spin and orbital parts of the \(\hat{M}1\) operator are required to reproduce the LEE, with constructive interference between the spin and orbital parts giving an extra enhancement to the LEE. Reduced one-body transition densities identify $0f_{7/2} \rightarrow 0f_{7/2}$ proton transitions as the principal driver of the LEE.

Figures (16)

• Figure 1: Approximate energy spacings of the orbitals in the nuclear shell model. The model spaces of SDPF-MU and SDPFSDG-MU are indicated in blue and purple respectively.
• Figure 2: The expectation value of the CM Hamiltonian as a function of excitation energy for each of the 3600 levels calculated with the SDPFSDG-MU interaction (purple) and the SDPF-MU interaction (orange).
• Figure 3: The 14 lowest experimental levels of $^{50}$V bnl_50v (black) compared to the corresponding calculated levels (green).
• Figure 4: A level scheme of all the calculated levels of this work. The negative and positive levels are in the left and right column for each $j$ respectively.
• Figure 5: Comparing the experimental level density of $^{50}$V PhysRevC.73.064301 with the calculated level density from this work.