Comparative study of Gamow-Teller strength distributions in the odd-odd nucleus 50V and its impact on electron capture rates in astrophysical environments

Gamow-Teller (GT) strength transitions are an ideal probe for testing nuclear structure models. In addition to nuclear structure, GT transitions in nuclei directly affect the early phases of Type Ia and Type-II supernovae core collapse since the electron capture rates are partly determined by these GT transitions. In astrophysics, GT transitions provide an important input for model calculations and element formation during the explosive phase of a massive star at the end of its life-time. Recent nucleosynthesis calculations show that odd-odd and odd-A nuclei cause the largest contribution in the rate of change of lepton-to-baryon ratio. In the present manuscript, we have calculated the GT strength distributions and electron capture rates for odd-odd nucleus 50V by using the pn-QRPA theory. At present 50V is the first experimentally available odd-odd nucleus in fp-shell nuclei. We also compare our GT strength distribution with the recently measured results of a 50V(d,2He)50Ti experiment, with the earlier work of Fuller, Fowler, and Newman (referred to as FFN) and subsequently with the large-scale shell model calculations. One curious finding of the paper is that the Brink’s hypothesis, usually employed in large-scale shell model calculations, is not a good approximation to use at least in the case of 50V. SNe Ia model calculations performed using FFN rates result in overproduction of 50Ti, and were brought to a much acceptable value by employing shell model results. It might be interesting to study how the composition of the ejecta using presently reported QRPA rates compare with the observed abundances.

💡 Research Summary

The paper presents a comprehensive study of Gamow‑Teller (GT) strength distributions and electron‑capture (EC) rates for the odd‑odd fp‑shell nucleus ^50V, employing the proton‑neutron quasiparticle random‑phase approximation (pn‑QRPA). Using a large model space (seven major harmonic‑oscillator shells) and Nilsson single‑particle energies that incorporate nuclear deformation, the authors calculate GT⁺ transition strengths for the ground state and the first two excited states (0.23 MeV and 0.32 MeV). A standard quenching factor of 0.77 is applied, and experimental excitation energies and log ft values are substituted when they lie within 0.5 MeV of the theoretical levels, enhancing reliability.

The calculated GT strength for the ground state shows a centroid at 8.8 MeV, in excellent agreement with recent (d, 2He) measurements on ^50Ti, and a total strength of 2.51 ± 0.15, which lies near the experimental upper limit and is significantly larger than the large‑scale shell‑model value (≈1.42). For the first two excited states, the centroids remain around 8.8–9.0 MeV, but the total strengths increase to 7.9 and 11.2, respectively. This demonstrates that the Brink hypothesis—assuming identical GT distributions for excited states shifted only by excitation energy—is not valid for ^50V.

Electron‑capture rates are derived from the GT distributions using standard phase‑space integrals, the Fermi‑Dirac electron distribution, and the usual constants (D = 6295 s, g_A/g_V = −1.254). The authors compare their QRPA rates with those from Fuller‑Fowler‑Newman (FFN) and the large‑scale shell model across a grid of densities (log ρY_e = 3, 7, 11) and temperatures (T₉ ≈ 1–10). At low temperature and density (log ρY_e ≈ 3, T₉ ≈ 1) QRPA rates are suppressed by up to three orders of magnitude relative to the shell model, reflecting the slightly higher GT centroid. As temperature rises (T₉ ≈ 3) the QRPA rates converge with the shell‑model values. At high density (log ρY_e ≈ 11) the QRPA rates exceed the shell‑model rates by a factor of ~5, because the electron Fermi energy is large enough that the total GT strength, rather than its detailed distribution, dominates the capture rate, and the QRPA predicts a larger total strength. QRPA rates are comparable to FFN rates at the highest densities, while showing similar trends at lower densities.

The astrophysical implications are discussed in the context of Type Ia and Type II supernova nucleosynthesis. Previous simulations using FFN rates overproduced ^50Ti, whereas those employing shell‑model rates reduced the excess. The QRPA rates, being intermediate—suppressed at low densities but enhanced at high densities—could lead to a more balanced production of ^50Ti, potentially improving agreement with solar abundances. The authors stress that accurate treatment of GT strength from excited states is essential for reliable EC rate tables used in stellar evolution codes.

Finally, the paper outlines ongoing work to extend QRPA calculations to other fp‑shell nuclei using the same extensive model space, aiming to provide a comprehensive set of weak interaction rates that will refine neutronization and nucleosynthesis predictions in future supernova simulations.