II-1. Nuclear Physics

RIKEN Accel. Prog. Rep. 55 (2022)

RIKEN Accel. Prog. Rep. 55 (2022)

Proton entropy excess and possible signature of pairing reentrance inhot nuclei†
B. Dey,∗1 S. Bhattacharya,∗2 D. Pandit,∗3,∗4 N. D. Dang,∗5 N. N. Anh,∗6 L. T. Phuc,∗7,∗8 and N. Q. Hung∗7,∗8We conducted a systematic study to understand theproton entropy excess ΔSp obtained for diﬀerent pairsof odd-even and odd-odd nuclei ranging from A = 90 to238 (90 Y and 91 Zr, 196 Pt and 197 Au, 211 Po and 212 At,231
Th and 232 Pa, 237 U and 238 Np). The proton entropy
excess determined from the existing experimental nuclear level density (NLD) data was compared with themicroscopic calculation obtained within the exact pairing plus independent particle model (EP+IPM). The
latter has predicted an enhanced peak of ΔSp at anexcitation energy E ∗ 1 MeV in near spherical nuclei(90 Y and 91 Zr, 211 Po and 212 At), indicating a possible signature of pairing reentrance in hot nuclei. In
the cases under consideration, pairing reentrance occurs because of the weakening of the blocking eﬀectcaused by the odd nucleon in odd nuclei. As a result,the pairing gap of odd nuclei, which is ﬁnite at T = 0,
slightly increases at low T = 0, and decreases as T
increases further, as explained in Ref. 1).
We found that the experimental value of ΔSp as afunction of E ∗ exhibits a strong ﬂuctuation at E ∗ <1 MeV and reaches saturation at high E ∗ > 3–6 MeV.
The analysis using the microscopic EP+IPM calculations shows that the proton entropy excess is approximately 0.1–0.5 kB for spherical systems and approximately 1.0–1.2 kB for the deformed ones, which is ingood agreement with the experimental data, as shownin Figs. 1(a) and 1(b). These values of proton entropy excess are smaller than the neutron ones owing
to the eﬀect of the Coulomb interaction and proton
single-particle level density, which is less than the theneutron one. Moreover, the peak-like structure, which
is seen in the proton entropy excess obtained within
the EP+IPM at low energy E ∗ < 1 MeV, is explainedby the pairing reentrance phenomenon caused by theweakening of the blocking eﬀect of an odd nucleon [SeeFigs. 1(c) and 1(d)].
This peak-like structure is found to be more pronounced in the spherical systems than in the deformed
ones because the pairing reentrance is stronger inspherical nuclei than in deformed ones. However, thistheoretical peak-like structure is not well supported
†
∗1
∗2
∗3
∗4
∗5
∗6
∗7
∗8Fig. 1. [(a) and (b)] Proton entropy excesses ΔSp as functions of excitation energy E ∗ along with the results ofEP+IPM calculations for 211 Po–212 At and 90 Y–91 Zr.
[(c) and (d)] Exact proton Δp and neutron Δn pairing
gaps as functions of temperature T for diﬀerent nuclei.
Exp. data1 and Exp. data2 in (a) are obtained by using the associated NLD data from Refs. 2) and 3), respectively, whereas RIPL-data are calculated by using
the low-energy data taken from RIPL-34) averaged over
the angular-momentum distribution as in Ref. 2). Exp.
data in (b) are obtained by using the NLD data fromRefs. 5) and, 6).

by the experimental observation owing to the strong
ﬂuctuations in the measured data. Therefore, more
precise and direct experimental measurements in thelow-energy region (E ∗ < 1 MeV) are required in order
to conﬁrm our theoretical predictions.
References
1) N. Q. Hung et al., Phys. Rev. C 94, 024341 (2016).
2) B. Dey et al., Phys. Lett. B 789, 634 (2019).
3) P. Roy et al., Phys. Rev. C 94, 064607 (2016).
4) www-nds.iaea.org/RIPL-3/ .
5) M. Guttormsen et al., Phys. Rev. C 90, 044309 (2014).
6) M. Guttormsen et al., Phys. Rev. C 96, 024313 (2017).

Condensed from the article in Phys. Lett. B 819, 136445(2021)
Department of Physics, Bankura University
Department of Physics, Barasat Government College
Variable Energy Cyclotron Centre
Homi Bhabha National Institute
RIKEN Nishina Center
Dalat Nuclear Research Institute
Institute of Fundamental and Applied Sciences, Duy Tan
University
Faculty of Natural Sciences, Duy Tan University- 28 -1