Calculation of Transition Strengthof Nuclei
J. Terasaki
Center for Computational Science
Univ. of Tsukuba

Dec. 5, 2011
Shima１．Motivation and purpose
One of the goals of nuclear physics：
to establish theoretical methods to describe all properties of
all nuclei
To establish capability to supply other fields including
nuclear astrophysics with the nuclear data they need.
My basic idea：application is very important.
The purpose of my research：
to calculate as many transition strengths and energies ofnuclei as possible using density functional theory andSearch reliable nuclear density functional

2．Density functional theory (DFT)Energy density functional
Dynamical equation⟶ technically mean-field eq.

Dynamical eq. of random-phase approximation（RPA）.
Solutions are stationary states.
Add pairing energy density (contact interaction, volume type)

Quasiparticle RPA（QRPA）

３. Spherical Nuclei
Strength functionJ

SJ ( E ) = ∑ ∑k M =− JΨk Fˆ JM Ψ02

Lk ( E )Transition operator
IsoscalarZ
f J ( ri )YJM (Ω i )e∑
A i:nucleonsIsovectoreZN−()()
f J ( ri )YJM ( Ωi )
frY
Ωe∑
∑
J iJMiA i:neutron
A i:protonf J ( ri ) ∝ rin

Isoscalar 1− strength functions

SkM*
Threshold energy

J.T. et al. Phys. Rev. C 74, 044301 (2006)

Isoscalar 1− strength functions

Isoscalar 1− strength functions

Isoscalar 1− strength functions

Isoscalar 1− strength functions

Isoscalar 1− strength functions

Isoscalar 1− strength functions

Isoscalar 1− strength functions

Isoscalar 1− strength functions

Isoscalar 1− strength functions

Isoscalar 1− strength functions

Isoscalar 1− strength functions

Isoscalar 1− strength functions

Isoscalar 1− strength functions

Isoscalar 1− strength functions

Isoscalar 1− strength functions

Isoscalar 1− strength functions

Isoscalar 1− strength functions

Isoscalar 1− strength functions

Isoscalar 1− strength functions

Isoscalar 1− strength functions

Isoscalar 1− strength functions

Isoscalar 1− strength functions

Isoscalar 1− strength functions

Isoscalar 0+ strength functions

SkM*

Isoscalar 0+ strength functions

Isoscalar 0+ strength functions

Isoscalar 0+ strength functions

Isoscalar 0+ strength functions

Isoscalar 0+ strength functions

Isoscalar 0+ strength functions

Isoscalar 0+ strength functions

Isoscalar 0+ strength functions

Isoscalar 0+ strength functions

Isoscalar 0+ strength functions

Isoscalar 0+ strength functions

Isoscalar 0+ strength functions

Isoscalar 0+ strength functions

Isoscalar 0+ strength functions

Isoscalar 0+ strength functions

Isoscalar 0+ strength functions

Isoscalar 0+ strength functions

Isoscalar 0+ strength functions

Isoscalar 0+ strength functions

Isoscalar 0+ strength functions

Isoscalar 0+ strength functions

Isoscalar 0+ strength functions

Isoscalar 0+ strength functions

Isoscalar 0+ strength functions

Isoscalar 0+ strength functions

Isoscalar 0+ strength functions

At A = 154 - 162 (N = 104 - 112)
ground states : deformed

Isoscalar 0+ strength functions

Isoscalar 0+ strength functions

Isoscalar 0+ strength functions

Isoscalar 0+ strength functions

Isoscalar 0+ strength functions

Isoscalar 0+ strength functions

Isoscalar 0+ strength functions

J.T. et al. Phys. Rev. C 74, 044301 (2006)

４．Deformed nuclei
DFT breaks rotational symmetry in deformed nuclei.
Another code for deformed nuclei developed
assuming axial symmetry and parity.

Deformed nuclei calculated

β > 0.3,(SkM*)

Gamma-vibrational states
measuredEnergy of Gamma-vibrational states

Nucl. Phys. 65, 1(1965)
QRPA, P+QQ

J. T. and J. Engel, Phys. Rev. C 84, 014332 (2011)

B(E2)↑ of Gamma-vibrational states

N-dependence of the gamma-vib. states (SkM*)

Two-quasiparticle energy of thecomp. having the largest forward
amp. of neutronsNeutron unperturbed energy

Z-dependence of the gamma-vib. states (SkM*)

Two-quasiparticle energy of thecomp. having the largest forward
amp. of protons

Proton unperturbed energy

5．Summary
1．It is coming possible to calculate not only ground but also
excited states of a much larger number of nuclear species
than before thanks to powerful parallel computers.
The remarkable enhancement of the transition strength
is found in the low-energy region of nuclei near the neutron
drip line in a variety of isotopic chains and Jπ.
2．Calculated results of γ-vibrational states have been
compared with the exp. data systematically. They are notbad, but more many-body correlations are seen in the data.