Ⅱ-2. Nuclear Physics (Theory)

RIKEN Accel. Prog. Rep. 48 (2015)

Systematic calculation of T = 1 triplets with proton–neutron mixed
energy density functionals
K. Sato,∗1 J. Dobaczewski,∗2,∗3,∗4 T. Nakatsukasa,∗1,∗5 and W. Satu�la∗2,∗4

∗1
∗2
∗3
∗4
∗5

RIKEN Nishina Center
Institute of Theoretical Physics, Faculty of Physics,Universityof Warsaw
Department of Physics, University of Jyväskylä
Helsinki Institute of Physics, University of Helsinki
Center for Computational Sciences, University of Tsukuba

formed a systematic calculation of the T = 1 triplets inA = 4n + 2 nuclei. We calculated the triple energy difference (TED)4) 2E(Tz = 0)−E(Tz = 1)−E(Tz = −1)
with several Skyrme parameter sets. In this model,
while the Tz = ±1 IASs are obtained with the standard Hartree-Fock calculation without p-n mixing, theTz = 0 IAS is calculated using the isocranking modeland is described by a single time-even Slater determinant consisting of p-n mixed single particles.
Figure 1 shows examples of the results of the calculation. We plot the deviation of the calculated TEDs
from the experimental data in the A = 14 − 58 region.
The TEDs in the T = 1 triplets calculated with theSLy4, SIII, and SkM* parameter sets are shown. One
can see a systematic underestimation of the TEDs inFig. 1. In this calculation, we used isoscalar EDFs,
which are invariant under rotation in isospin space,plus the Coulomb energy functional. This systematicdeviation may imply that we need to extend functionals further to include isospin breaking terms. We already started performing a calculation including theisospin breaking interaction, which will be reportedelsewhere.
TED(calc.)-TED(exp.) (MeV)

We performed a systematic calculation for T = 1
isobaric analog states (IASs) based on energy density functionals (EDFs) including proton-neutron (p-n)
mixing. Recently, we developed a new model to calculate IASs on the basis of the Skyrme EDFs that include
arbitrary mixing between protons and neutrons1) . In
this framework, single-particle states are generalized assuperpositions of proton and neutron components. In
connection with this extension of single particles, density functionals are also extened to those with mixing
between protons and neutrons2) . In this work, we consider an extension of EDFs including p-n mixing onlyin the particle-hole (p-h) channel, with both the rotational and isospin symmetries conserved. Our ultimate
goal, however, is to develop a consistent symmetryunrestricted EDF approach including p-n mixing bothin the p-h and pairing channels.
We developed a code for the p-n mixing calculation
by extending the code “HFODD,”3) which solves thenuclear Skyrme–Hartree–Fock(–Bogolyubov) problem
by using the Cartesian deformed harmonic-oscillator
basis. In this p-n mixing calculation, we perform
isocranking calculation by adding the isocranking term
to the Hamiltonian: ĥ� = ĥ − �λ · ˆ�t. Here, ˆ�t is the isospin
operator. The isocranking term is analogous to thatused in the standard tilted-axis-cranking calculations
for high-spin states. By adjusting the isocranking frequency �λ, we can control the size and direction of theisospin of the system.
In Ref. 1), we developed an eﬃcient method for determining the isocranking frequency and successfully
applied the isocranking model to the IASs in eveneven A = 40 − 56 and odd-odd A = 14 isobars. Thus,
we demonstrated that the p-n mixed single-reference
EDF approach is capable of quantitatively describing
the isobaric analog excited states. Among the resultsin Ref. 1), that of odd-odd T = 1 IASs is of particular interest (See Fig. 4 in Ref. 1)). We calculated
the energies of the I = 0+ , T = 1 triplet of statesin the A = 14 isobars, 14 C, 14 N, and 14 O by using
the SkM* EDF. We found that there is asymmetry between the energy diﬀerences |E(Tz = 0)− E(Tz = −1)|and |E(Tz = 0) − E(Tz = 1)|, which may be related tocharge asymmetry and independence of the NN interaction. To investigate this point, in this study, we per-

0.4
0.2
0

SLy4SIII
SkM*

-0.2
-0.4
-0.6
-0.8

10 15 20 25 30 35 40 45 50 55 60
AFig. 1. Deviation of the calculated triple energy diﬀerence
from the experimental data5) , TED(calc.)-TED(exp.),
for the T = 1 triplets in A = 14 − 58 nuclei. The TEDs
calculated with SLy4, SIII, and SkM* are plotted.

References
1) K. Sato et al.: Phys. Rev. C 86, 061301(R) (2013).
2) E. Perlińska et al.: Phys. Rev. C 69, 014316 (2004).
3) N. Schunck et al.: Comput. Phys. Commun. 183, 166(2012); J. Dobaczewski et al. (unpublished).
4) W. Satu�la et al.: Acta. Phys. Pol. B 45 167 (2014).
5) National Nuclear Data Center, Brookhaven National
Laboratory, http://www.nndc.bnl.gov/.

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