Ⅱ-2. Nuclear Physics (Theory)

RIKEN Accel. Prog. Rep. 49 (2016)

Pairing Reentrance in warm rotating 104Pd nucleus†
N. Quang Hung,∗1,∗2 N. Dinh Dang,∗2 B.K. Agrawal,∗3 V.M. Datar,∗4 A. Mitra,∗4 and D.R. Chakrabarty∗4

†
∗1
∗2
∗3
∗4Condensed from the article in Act. Phys. Pol. B 8, 551(2015)
Institute of Research and Development, Duy Tan University
RIKEN Nishina Center
Theory Division, Saha Institute of Nuclear Physics
Nuclear Physics Division, Bhabha Atomic Research Center- 79 -0.2(a)0.1

β20.0-0.1-0.205101520_J (h )1012

ρ (MeV -1 )2530ExpFTBCSFTBCS11010
108
10 6104

β2 = 0.2210210β2 = 0.2__(d) J = 10 h(b) J = 0 h01010

ρ (MeV -1 )The recent series of experiments conducted at theBhabha Atomic Research Center (BARC) for the reaction 12 C + 93 Nb → 105 Ag∗ → 104 Pd∗ +p at the incident
energy of 40 - 45 MeV has observed an anomalous enhancement of the nuclear level density (NLD) of 104 Pd
nucleus at low excitation energy E ∗ and high angularmomentum J 1) . This enhancement is similar to that
previously predicted by the shell-model Monte Carlo(SMMC)2) and FTBCS1 calculations3) for a warm rotating 72 Ge nucleus. Both the SMMC and FTBCS1
have pointed out that the local enhancement of NLDat low T and high J is associated with the pairing
reentrance effect. The latter occurs when the angularmomentum of the system is sufficiently high so that thepairing correlation, which is zero at low T < T1 , reappears at T > T1 . The goal of this work is to apply theFTBCS1 theory including finite angular momentum tostudy if the enhanced NLD observed in 104 Pd can beinterpreted as the first evidence of pairing reentrance
in a warm rotating finite nucleus.
The FTBCS1 theory at finite temperature and angular momentum is obtained based on the conventional finite-temperature Bardeen-Cooper-Schrieffer(FTBCS) theory that takes into account the effect ofquasiparticle-number fluctuations (QNF) on the pairing field3) . The numerical calculations are carried outfor 104 Pd nucleus, whose single-particle spectra aretaken from the axially deformed Woods-Saxon potential including the spin-orbit and Coulomb interactions.
The quadrupole deformation parameter β2 potential isadjusted so that the NLD obtained at different valuesof J fit best the experimental data, especially in the region where the enhancement of NLD is observed. The
variation of β2 with J is plotted in Fig. 1 (a). This
figure clearly shows that 104 Pd nucleus undergoes ashape transition from the prolate shape (β2 > 0) tothe oblate one (β2 < 0) at around J = 20 h̄, whichis reasonable in this mass region because of an alignment of protons in g9/2 and neutrons in h11/2 orbits.
Figs. 1 (d) - (e) depict the NLD as a function of excitation energy E ∗ obtained within the FTBCS1 andthe conventional FTBCS theories.
It is found that due to the QNF, the FTBCS1 gaps
at different J values decrease monotonically with increasing E ∗ and do not collapse at the critical value
E ∗ = Ec∗ as in the case of the FTBCS. As a result,the pairing reentrance takes place only in the pairing

108
10 6104102

β2 = −0.015

β2 = −0.205(d) J = 20 h(e) J = 30 h__10005101520E* (MeV)

25051015202530

E* (MeV)Fig. 1. (Color online) (a) - Quadrupole deformation parameter β2 as functions of the total angular momentum
J obtained within the FTBCS1 theory. [(b) - (e)] - Total NLD as function of excitation energy E ∗ obtained
within the FTBCS (dotted lines) and FTBCS1 (dashedlines) at different values of J and β2 . The solid lines
are the experimental data.

gaps obtained within the FTBCS1 (e.g., for protons
at J = 20h̄ and neutrons and at J = 30h̄), whereas
this effect does not appear in the FTBCS gaps. This
leads to the local enhancements of the NLD obtained
within the FTBCS1 at low E ∗ (2 < E ∗ < 5 MeV) andhigh J, in agreement with the experimental data. Thisagreement indicates that the observed enhancement ofthe NLD might be the first experimental detection of
the pairing reentrance in a finite nucleus.
References
1) A. Mitra et al., J. Phys. G 36, 095103 (2009); A. Mitraet al., EPJ Web of Conf. 2, 04004 (2010); V.M. Datar,A. Mitra, D.R. Chakrabarty, Proceedings of the DAE
Sym. on Nucl. Phys., University of Delhi, Dec 37, 2012,
Vol. 57, p. 184 (2012).
2) D.J. Dean, K. Langanke, H.A. Nam, W. Nazarewicz,
Phys. Rev. Lett. 105, 212504 (2010).
3) N.Q. Hung and N.D. Dang, Phys. Rev. C 78, 064315(2008), Phys. Rev. C 84, 054324 (2011).