II-2. Nuclear Physics (Theory)

RIKEN Accel. Prog. Rep. 54 (2021)

RIKEN Accel. Prog. Rep. 54 (2021)

Role of exact treatment of thermal pairing in radiative strength
functions of 161, 163 Dy nuclei†
L. Tan Phuc,∗1,∗2 N. Quang Hung,∗1,∗2 N. Dinh Dang,∗3 L. T. Quynh Huong,∗4 N. Ngoc Anh,∗5 N. Ngoc Duy,∗6
L. Ngoc Uyen,∗7 and N. Nhu Le,∗8

where σE1 is the GDR cross section which is obtained microscopically within the PDM, ΓE1 is the temperaturedependent GDR width, and SE1 is the GDR strengthfunction.
Figure 1 depicts the total RSFs obtained within
the PDM with and without EP the experimental
data5) as well as those obtained within the microscopic
D1M+QRPA (E1 and E1 + M 1) and phenomenological GLO-SLO models. The results obtained show that,
due to the eﬀect of EP, the EP+PDM can describe reasonably well the RSF data in both low and high-energy
regions without adding any extra strength function. As aresult, at least eight free parameters have been reduced
within the EP+PDM calculations as compared to thedescription by the phenomenological GLO-SLO model.
†∗1∗2∗2∗3∗4∗5∗6∗7Condensed from the article in Phys. Rev. C 102, 061302(R)(2020)
Institute of Fundamental and Applied Sciences, Duy Tan University
Faculty of Natural Sciences, Duy Tan University
RIKEN Nishina Center
Department of Natural Science and Technology, University ofKhanh Hoa
Dalat Nuclear Research Institute, Vietnam Atomic Energy InstituteDepartment of Physics, Sungkyunkwan University
Department of Engineering Science, University of ElectroCommunications
University of Education, Hue University

fRSF (Eγ ) (MeV -3 )10-510-6a) 161Dy

EP+PDM T=0.59 MeV
PDM T=0.59 MeV

10-7161

10-8fRSF (Eγ ) (MeV -3 ) fRSF (Eγ ) (MeV -3 )The photon or radiative strength function (RSF), deﬁned as the average electromagnetic transition probability per unit of γ-ray energy Eγ ,1) has an importantrole in the study of nuclear reaction properties such as
γ-ray emission rate, reaction cross section, and/or nuclear astrophysical processes.2) Very recently, we haveproposed a microscopic model to simultaneously describe
the nuclear level density and RSF.3) For the RSF, weemployed the phonon damping model (PDM),4) which
consistently includes the exact thermal pairing (EP), inorder to take into account both temperature-dependent
giant dipole resonance (GDR) width (within the PDM)
and thermal pairing (within the EP). The goal of thecurrent work is to shed a light on the microscopic nature of the low-energy enhancement in the RSF datacaused by the PDR (Pygmy Dipole Resonance). Three
dysprosium isotopes 161, 162, 163 Dy are selected to do
the calculations within the EP+PDM. The results will
be compared with the phenomenological models (standard Lorentzian-SLO and generalized Lorentzian-GLO)
and the other microscopic model (Quasiparticle randomphase approximation-QRPA). The RSF at each energy
Eγ and temperature T is deﬁned as follow
fE1 (Eγ , T ) =)((1)
π σE1 ΓE1 (Eγ , T )SE1 (Eγ , T )1,222
3π ℏ c2Eγ10-6Dy( 3He,3 He)
Dy( 3He,α )162
Dy(γ, n)163
Dy(γ, n)162

E1QRPA(E1+M1)QRPA

EP+PDM T=0.56 MeV
PDM T=0.56 MeVb) 162Dy

10-710-810-6

162

E1QRPA(E1+M1)QRPAc) 163Dy

Dy( 3He,3 He)
Dy( 3He,α )162
Dy(γ, n)163

EP+PDM T=0.59 MeV
PDM T=0.59 MeV

10-7
10-8
0

E1QRPA(E1+M1)QRPA

2164

Dy( 3He,α )Dy(γ, n)163

4 6 8 10 12Eγ (MeV)

Fig. 1. Total RSFs obtained within the PDM (thin solidlines), EP+PDM (thick solid lines) versus the QRPA
RSFs for the E1 and E1 + M 1 excitations and the experimental data5) for 161–163 Dy. The dashed, dash-dotted,
and dotted lines stand for the RSFs obtained within
the phenomenological GLO-SLO models with 2 PDRs,
1 PDR, and without PDR, respectively.

Temperature is found to have a signiﬁcant eﬀect on theRSF at the low energy Eγ ≤ Sn , whereas it does notchange much the RSF in the high-energy one Eγ > Sn ,questioning the validity of the Brink-Axel hypothesis.
In addition, due to the eﬀects of EP and couplings of
all ph, pp, and hh conﬁgurations within the PDM, theEP+PDM can also partially reproduce the scissors resonance in 161–163 Dy nucleus at low Eγ without adding aSR strength function in the RSF. These ﬁndings indicate
the importance of EP and couplings to non-collective pp
and hh conﬁgurations at ﬁnite temperature in the microscopic description of total RSF in excited nuclei.
References

1) J. M. Blatt, V. F. Weisskopf, Theoretical Nuclear Physics(Wiley, New York, 1952).
2) J. Kopecky, M. Uhl, Phys. Rev. C 41, 1941 (1990).
3) N. Q. Hung, N. D. Dang, L. T. Q. Huong, Phys. Rev. Lett
118, 022502 (2017).
4) N. D. Dang, A. Arima, Phys. Rev. Lett. 80, 4145 (1998).
5) https://www.mn.uio.no/fysikk/english/research/about/infrastructure/ocl/nuclear-physics-researc
h/compilation/ .

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