Ⅱ-2. Nuclear Physics (Theory)

RIKEN Accel. Prog. Rep. 51 (2018)

Testing constant-temperature approach for nuclear level density†
N. Dinh Dang,∗1 N. Quang Hung,∗2 and L. T. Quynh Huong∗3
According to thermodynamics, the nuclear temperature is a parameter, which is deﬁned from the nuclear
level density (NLD) ρ(E) as[]−1∂ ln ρ(E)
T =.
(1)
∂E

ρ(E*) (MeV -1)

106

In the ﬁrst model for NLD proposed by√Bethe, theNLD is approximately described as exp(2 aE ∗ ) withthe level-density parameter a. The nuclear temperature T , deﬁned from Eq. (1), is then proportional
to the √square root of the excitation energy E ∗ , vizT ≃E ∗ /a, i.e. it increases with E ∗ . However
this model fails to describe the NLD at low excitation energies below the particle separation threshold.
The constant-temperature (CT) model, suggested byGilbert and Cameron,1) assumes that the NLD at lowexcitation energies (E ∗ ≤ 10 MeV) can be describedby a constant temperature T , namely
ρ(E ∗ ) =∗1 (E ∗ −E0 )/Te≡ B(T )eE /T ,T∗1∗2∗3102

T = 1.3 MeV, B = 0.8 MeV -1
1.4
1.5
1.5
3.0

100

Ref. [2]Ref. [3]0510E* (MeV)

1520Fig. 1. Comparison of NLDs obtained from the CT model(2) and experimental NLDs for 60 Ni.

(2)with B(T ) = [T eE0 /T ]−1 , where T and E0 are obtainedby ﬁtting to the experimental NLD. This model has become increasingly popular in the study of NLD in recent years, where it has been suggested that its validity
can be extended to much higher excitation energies up
to E ∗ around 20 MeV for 60 Ni and 60 Co isotopes.2)
Therefore, it is highly desirable to analyze the validityof this phenomenological model by using a microscopicmodel, which is able to describe the NLD in both low
as well as resonance energies. Recently a uniﬁed approach has been proposed to simultaneously describe
both the NLD and radiative strength function (RSF)
based on the solution of exact pairing (EP) problem
in combination with the independent-particle model(IPM), which is referred to as EP+IPM hereafter.4)
In the present work, by using the NLD predictedwithin the EP+IPM method, which agrees well withthe experimental data, the nuclear temperature T iscalculated from the derivative of logarithm of NLD (1).
This temperature T increases almost linearly with theexcitation energy E ∗ . However this increase is relatively slow so that T can be considered as a constantof around 0.5 MeV at 0 < E ∗ ≤ 10 MeV. Meanwhile, in60
Ni, the CT model can describe rather well the experimentally extracted NLD with a constant temperature†104

between 1.3 ≤ T ≤ 1.5 MeV up to E ∗ = 20 MeV, i.e.
much higher than the particle separation threshold, inexcellent agreement with the experimental ﬁnding ofRef. 2) (Fig. 1). It is also shown that pairing plays
an important role in maintaining this nearly-constantvalue of temperature at low excitation energy. In thisway, the EP+IPM oﬀers a consistent description ofthe NLD, which goes smoothly from the low-energy
region E ∗ ≤ 5 MeV to the higher one (up to 20 MeVfor Ni isotopes and 10 MeV for Yb isotopes) without
the need of matching the CT model at low energy andthe Fermi-gas one at high energy, as often done byusing the composite level-density formula.1) Last but
not least, the fact that the NLD at low excitation energy, even at E ∗ = 0, can be well described by the CT
model at a constant nonzero temperature also supports
the suggestion of introducing a ground-state’s eﬀective
temperature.5)
References
1) A. Gilbert, A. G. W. Cameron, Can. J. Phys. 43, 1446
(1965).
2) A. V. Voinov et al., Phys. Rev. C 79, 031301(R) (2009);EPJ Web of Conferences 21, 05001 (2012).
3) https://www-nds.iaea.org/RIPL-3/.
4) N. Quang Hung, N. Dinh Dang, L. T. Quynh Huong,Phys. Rev. Lett. 118, 022502 (2017).
5) V. Zelevisnky, Proc. of 12th Int’l Spring Seminar on
Nuclear Physics, Sant’Angelo d’Ischia, May 15-19, 2017(to be published).

Condensed from the article in Phys. Rev. C 96, 054321(2017)RIKEN Nishina Center
Institute of Fundamental and Applied Sciences, Duy Tan
University
Faculty of Physics and Engineering Physics, Viet Nam National University Ho Chi Minh City- 92 -