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

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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 Chankova et al. (Phys Rev C 73:034311, 2006) and Kaneko et al. (Phys Rev C 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 Kaneko et al. (Phys Rev C 74:024325, 2006) should be re-investigated. The present work also suggests that to 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.

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Data Availability Statement

This manuscript has associated data in a data repository. [Authors’ comment: All data generated in this work are contained in this published article.]


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The authors wish to thank University of Khanh Hoa for supporting through the research project No. KHTN-20.01. This work is funded by the National Foundation for Science and Technology Development (NAFOSTED) of Vietnam under Grant no. 103.04-2019.371.

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Correspondence to Thi Quynh Huong Le or Quang Hung Nguyen.

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Communicated by Jerome Margueron

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Le, T.Q.H., Tran, D.X., Nguyen, N.A. et al. Re-investigation of heat capacity and paring phase transition in hot \(^{93-98}\)Mo nuclei. Eur. Phys. J. A 57, 109 (2021).

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