Re-investigation of heat capacity and paring phase transition in hot $^{93-98}$Mo nuclei

TL;DR

This study re-examines the heat capacities and pairing phase transitions in $^{93-98}$Mo nuclei using updated nuclear level density data and an improved BSFG model, revealing more pronounced pairing effects in even isotopes.

Contribution

It introduces a new parameterization of the BSFG model combined with updated NLD data to better analyze heat capacities and pairing transitions in Mo isotopes.

Findings

More pronounced S-shaped heat capacity in even isotopes

Discrepancies with previous studies using older data

Recommends using updated NLD data for accurate analysis

Abstract

The empirical heat capacities of $^{93-98}$Mo nuclei are re-investigated by using the latest updated and recommended nuclear level density (NLD) data below the neutron binding energy $B_n$ combined with the back-shifted Fermi-gas (BSFG) model for the energy region above $B_n$. For the latter, the BSFG formula with energy-dependent level density parameter is used and the new parameterization has been carried out in order to obtain the best fit to the new NLD data in the whole data range. The results obtained show that the S-shaped heat capacity, a fingerprint of the pairing phase transition, is more pronounced in even $^{94,96,98}$Mo nuclei than that in odd $^{93,95,97}$Mo isotopes. This result is different with those obtained in two previous studies by R. Chankova et al., [Phys. Rev. C {\bf 73}, 034311 (2006)] and K. Kaneko et al., [Phys. Rev. C {\bf 74}, 024325 (2006)], in which the old NLD data and the BSFG model with energy-independent level density parameter were used. Moreover, the present work suggests that the very strong S-shape observed in the heat capacities of both even and odd Molybdenum isotopes by K. Kaneko et al., [Phys. Rev. C {\bf 74}, 024325 (2006)] should be re-investigated. The present work also suggests that obtain the correct heat capacity and associated pairing phase transition in excited nuclei, one should use the correct NLD data and the best fitted BSFG NLD in the entire region where the experimental data are available.