Ⅱ-2. Nuclear Physics (Theory)

RIKEN Accel. Prog. Rep. 51 (2018)

Level density and thermodynamics in hot rotating 96 Tc nucleus†
B. Dey,∗1 D. Pandit,∗2 S. Bhattacharya,∗3 N. Quang Hung,∗4 N. Dinh Dang,∗5 L. Tan Phuc,∗4 D. Mondal,∗2S. Mukhopadhyay,∗2 S. Pal,∗2 A. De,∗6 and S. R. Banerjee∗2†

∗1
∗2
∗3
∗4
∗5

∗6Condensed from the article in Phys. Rev. C 96, 054326 (2017)
Tata Institute of Fundamental Research, Mumbai
Variable Energy Cyclotron Centre, Kolkata
Barasat Govt. College, Kolkata
Institute of Fundamental and Applied Sciences, Duy Tan University
RIKEN Nishina CenterRaniganj Girls’ College, Raniganj- 94 -108
107
106
105
104
103
102
101
100
10-1
10-2
107
106
105
104
103
102
101
100
10-1
10-2
10-3
10-4

Nuclear level density

J = 12 ∓ 4 �

low-E data [45]High-E data
EP+IPM
HFBC (+ve parity)
HFBC (-ve parity)
HFBCS
Earlier data [52]J = 16 ∓ 4 �

Nuclear level density

One of the basic aims in diverse ﬁelds of science(physics, chemistry, and biology) is understanding thesmall system, which manifests many striking properties
due to its tiny dimension. The study of thermodynamic
properties of such small system like atomic nucleus, inspite of being an arduous task, is highly imperative
as those properties describe how such systems respondto the changes in their environment. In addition, theknowledge of nuclear thermodynamics also enables us
to understand the presence of pairing phase transitionin the nucleus, whose eﬀect was included in the nuclear
theory after the Bardeen-Cooper-Schrieﬀer (BCS) theory. Thus, the study of nuclear thermodynamics hasgained much enthusiasm in the recent past.
Measuring the nuclear level density (NLD) is the starting point to obtain the thermodynamic quantities (TQ)of atomic nuclei. Earlier, the NLD was measured below the particle threshold energy at very low angularmomentum J and extrapolated to the higher energy byusing the functional form of the Fermi-Gas model toestimate the TQs. But, the knowledge of the NLD functional form is not yet satisfactory due to the lack of experimental data at high E ∗ and J. Therefore, it would
be better if one could measure the NLD below and above
the particle threshold, and compare the measured datawith a consistent theoretical calculation to investigate
TQs of atomic nuclei. In the present work,1) the angularmomentum gated NLDs in the excitation energies rangeof E ∗ ∼ 5–15 MeV are extracted by using the evaporated neutron energy spectra in the 4 He+93 Nb reaction
and compared with the results of diﬀerent microscopic
calculations.
The experimental NLD along with the results of different theoretical calculations for J = 12 and 16 h̄ areshown in Fig. 1. It is observed that EP+IPM (exact pairing plus independent particle model) explainsrather well the experimental data and thus it was used toextract the thermodynamic properties of 96 Tc nucleus.
The TQ of 96 Tc have been estimated using EP+IPM
NLDs for J = 12 and 16 h̄ as shown in Fig. 2. It is quite
interesting to note that the free energy, entropy, and average energy show the correct trend as that observed in
the nearby 96 Mo nucleus.2) However, the bump in theheat capacity (signature of pairing phase transition) of96Tc is not as pronounced as that seen in 96 Mo,2) in spiteof being the same mass. This diﬀerence might come from

0510Energy (MeV)

1520

Fig. 1. Angular momentum gated NLD (symbols) along withthe results of diﬀerent theoretical calculations.

Fig. 2. Angular momentum gated TQs as functions of temperature obtained using EP+IPM level densities.

the pairing property of odd-odd 96 Tc nucleus, which is
weaker than that in even-even 96 Mo. It is also observedthat the angular momentum does not have much eﬀect
on the nature of the TQs. However, at low T , there is a
noticeable change in the heat capcity due to the angularmomentum. Therefore, it would be very interesting tostudy the angular momentum eﬀect on the pairing phasetransition in even-even systems in future.
References

1) B. Dey et al., Phys. Rev. C 96, 054326 (2017).
2) K. Kaneko et al., Phys. Rev. C 74, 024325 (2006).