Ⅱ-2. Nuclear Physics (Theory)

RIKEN Accel. Prog. Rep. 47 (2014)

Shell-model description of low-lying states in Rn isotopes
N. Yoshinaga∗1 and K. Higashiyama∗2
Polonium and radon isotopes below the neutron
closed shell at N = 126 provide an important region
for testing shell-model structure. The isomeric 8+
1states in 206−214 Rn were experimentally conﬁrmed tobe based on a proton (0h9/2 )4 conﬁguration1) . The
low-lying near-yrast states were analyzed in terms of
the interacting boson model plus two quasiparticles
model2) , where one of the bosons is replaced by a pairof nucleons at high spin. A good agreement with experiment was achieved for both the energy spectra andelectromagnetic transitions.
In this work, the band structure of the Rn isotopes isstudied in terms of the full-ﬂedged shell model. As for
single-particle levels, all the six orbitals, 0h9/2 , 1f1/2 ,0i13/2 , 1f5/2 , 2p3/2 , and 2p1/2 , in the major shell between the magic numbers 82 and 126 are considered
for both neutrons and protons. The eﬀective interactions comprise single-particle energies and monopoleand quadrupole pairing plus quadrupole-quadrupole
interactions, whose strengths are adjusted to ﬁt experimental data. The interaction strengths adopted in
the present calculations are assumed to be the samefor all the nuclei.
In Fig. 1, the measured spectra for even-even Rn
isotopes are compared with the shell model results.
The even-spin yrast sequences are well reproduced
except for the 8+
1 states, which are lower in energy
than the experimental data. For better reproductionof the 8+
1 states, multipole pairing interactions morethan quadrupole might be necessary. Concerning otherstates, good agreements between theory and experiment are achieved.
In order to investigate the collective behavior at low
energies and the eﬀect of the single particle excitations
at high spins, the energy spectra in the shell model arecompared with those in a pair-truncated shell model(PTSM)3,4) . The building blocks of this model are angular momenta zero (S) and two (D) collective pairs
together with non-collective pairs. The Hamiltonian inthis truncated space (PTSM space) is set identical tothat used in the shell model. In Fig. 2, the energy levels obtained by the PTSM for 208 Rn are compared withthose of the shell model. There is a good correspondence between the energy levels of the shell model andthose in the PTSM. This means that the model spacespanned by the PTSM is suﬃcient for describing theshell model results.
In search for the microscopic structure of the yrast
band, we analyze the expectation values of the numbers of pairs (not shown). It is found that the valence∗1∗210+10+9+10++ +5 8+ +
7 6+5+ +8+7+ +3 4 6+ +0 1+ +
4 1+22+ ++8 6(6 )+(4 )+E(MeV)(4 )+41028+6+

66
40+5+

1++ +4+2+

6 5+ + +++6+++

46 8 7+ ++8+++

7++

382+2+

3 0+
3+ +0 4+ +
1 41210+00++2+22208

Rnexpt.

0+RnSM0+expt.

+0SM

Fig. 1. Comparison of the experimental energy levels(expt.) with those of the shell model (SM) for 208 Rnand 210 Rn.

3E (MeV)

2208

Rn1SM
PTSM
0024681012I (h)Fig. 2. Comparison of the calculated energy levels in thePTSM (PTSM) and the shell model results (SM) for208Rn.

neutron excitation plays an essential role in describing
the low-lying states, and the pair of 0h9/2 protons isindispensable for the states above spin 8.
References
1) K. H. Maier et al.: Hyperfine Interact. 9, 87 (1981).
2) A. Zemel and J. Dobes: Phys. Rev. C 27, 2311 (1983).
3) N. Yoshinaga and K. Higashiyama: Phys. Rev. C 83,054309 (2004).
4) K. Higashiyama and N. Yoshinaga: Phys. Rev. C 83,034321 (2011).

Department of Physics, Saitama University
Department of Physics, Chiba Institute of Technology- 63 -