Ⅱ-2. Nuclear Physics (Theory)

RIKEN Accel. Prog. Rep. 51 (2018)

Giant dipole resonance and shape transitions in hot and rotating
88Mo†
A. K. Rhine Kumar,∗1 P. Arumugam,∗2 N. Dinh Dang,∗3 and I. Mazumdar∗4
The exploration of extremes of nuclear landscape
has unraveled several interesting phenomena, leading
to a better understanding of the nuclear force. Thegiant dipole resonance (GDR) has been considered asa unique and powerful tool to investigate the nuclear
structure properties at these extreme conditions. The
most important experimental observable for the GDR
is the cross section (σ) as a function of the photon energy, from which one can extract the centroid energies
and the GDR width (Γ ). These observables could effectively reﬂect the structure of the nuclear state on
which the GDR is built.
In a recent work,1) the GDR γ-rays emitted fromhighly excited 88 Mo nucleus which is formed in thereaction 48 Ti + 40 Ca, and a number of daughter nuclei created along the cooling path of the compound
nucleus were measured. The data analysis indicatesthe possibility of Γ saturation at higher angular momentum (I) values. In this article, we study the GDR
properties of the hot and rotating compound nucleus
88
Mo at diﬀerent excitation energies within the thermal shape ﬂuctuation model (TSFM) built on themicroscopic-macroscopic approach for the free energy
calculations and a macroscopic approach for the GDR
calculations.
We calculate the average GDR cross section of anucleus with a given Z and N at a given average T(Tave ) and having
a probability distribution for I, as∑ave ,Ii )C(i)i σ(T∑σave (Tave ) =where Ii is the spin ofC(i)Fig. 1. The GDR width Γ of 88 Mo calculated using TSFM
at two diﬀerent excitation energies are plotted as a function of T . The ﬁlled upward triangles connected withsolid line represent Γ of the ﬁnal σ [Γ (Tave )], where σ ofthe daughter nuclei are obtained by considering the Taveand the angular momentum probability distributions.
The ﬁlled downward triangles connected with dashedline [Γ (Tave , Iave )] and ﬁlled circles connected withdash-dotted line [ΓLDM (Tave , Iave )] represent the Γ ofthe ﬁnal σ, where σ of the daughter nuclei are obtainedby considering the Tave and Iave within the TSFM withfree energies obtained from microscopic-macroscopic
approach and liquid drop model (LDM), respectively.
The experimental results are taken for Ref. 1). The
widths obtained within the (Phonon damping model)
PDM and Lublin-Strasbourg drop (LSD) model takenfrom Ref. 1) are also shown with open circles and open
triangles. The lines are drawn just to guide the eyes.

ithe ith step of the statistical decay of the compoundnucleus and C(i) are the corresponding spin counts. As
the ﬁrst step, it is very important to analyze, whether
the average GDR cross sections σave (Tave ) of a nucleus
obtained by considering the Tave and the probability
distribution of I are similar or not, to the GDR crosssections σ(Tave , Iave ) of a nucleus obtained with theTave and average I (Iave ) values obtained from the same
fromprobability distributions. The Iave is estimated∑i Ii C(i)∑the probability distribution of I as, Iave =.
i C(i)
An important conclusion from these analysis is that
it is not necessary to calculate the theoretical σ at eachvalue of T and I obtained in the probability distribution with their respective weights, instead the σ ob†
∗1
∗2
∗3
∗4

tained at the average values of T and I are good enoughto compare with the experimental data. In Fig. 1
we compare the Γ of 88 Mo calculated using TSFM
at two diﬀerent excitation energies. In the range of2 ≲ T ≲ 3 MeV, the data suggest a slower increase in
the Γ whereas the our results and the PDM suggest alarger increase.
At higher T , as I increases the free energy surfaces
shows a gamma-softness before the nucleus undergoes
a Jacobi shape transition. Considering the role of enhanced ﬂuctuations at higher T and the Coriolis splitting of GDR components at higher I the GDR widthof 88 Mo nucleus will not saturate at high T and I.

Condensed from the article in Phys. Rev. C. 96, 024322(2017)
Department of Physics, Cochin University of Science andTechnology
Department of Physics, Indian Institute of Technology Roorkee
RIKEN Nishina Center
Department of Nuclear and Atomic Physics, Tata Instituteof Fundamental Research

Reference1) M. Ciema�la et al., Phys. Rev. C 91, 054313 (2015).

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