Structure of 31 Na studied by the Monte-Carlo shell model†
I. Suzuki,∗1 T. Yamada,∗2 T. Yamato,∗3 K. Yamada,∗4 and S. Sato∗1,∗2
Since anomalous properties of 31 Na concerning themass1) and the ground-state spin and magnetic moment2) were observed in the 1970’s, the structure ofneutron-rich nuclei around N = 20 has attracted
much interest, particularly concerning vanishing of theN = 20 magic number. Based on the Monte-Carloshell model (MCSM),3) we performed a systematic
shell-model calculation for even-even N ∼ 20 exotic
nuclei with full mixing between the normal, intruder,and higher intruder conﬁgurations for the ﬁrst time,4)
and gave a comprehensive picture of the region. As for
odd-A nuclei, since we should adopt the J-compressedbases,3) which require much computational time in theMCSM calculation, such a calculation was unfeasible
until the Alphleet computer system5) was introduced
at RIKEN. In this report, the structure of a neutronrich odd-A nucleus 31 Na, which is expected to be in
the “island of inversion”,6) is studied by the MCSM
with the Alphleet computer system.
Since anomalous properties of 31 Na concerning themass1) and the ground-state spin and magnetic moment2) were observed in the 1970’s, the structure ofneutron-rich nuclei around N = 20 has attracted
much interest, particularly concerning vanishing of theN = 20 magic number. Based on the Monte-Carloshell model (MCSM),3) we performed a systematic
shell-model calculation for even-even N ∼ 20 exotic
nuclei with full mixing between the normal, intruder,and higher intruder conﬁgurations for the ﬁrst time,4)
and gave a comprehensive picture of the region. As forodd-A nuclei, since we should adopt the J-compressedbases,3) which require much computational time in theMCSM calculation, such a calculation was unfeasible
until the Alphleet computer system5) was introduced
at RIKEN. In this report, the structure of a neutronrich odd-A nucleus 31 Na, which is expected to be in
the “island of inversion”,6) is studied by the MCSM
with the Alphleet computer system.
In this report, the structure of a neutron-rich oddA nucleus 31 Na, which is expected to be in the “island of inversion”,6) is studied by the MCSM with theAlphleet computer system.
In this report, the structure of a neutron-rich oddA nucleus 31 Na, which is expected to be in the “island of inversion”,6) is studied by the MCSM with theAlphleet computer system.
Y =a+b+c+d+e+f +g
†
∗1
∗2
∗3
∗4

In this report, the structure of a neutron-rich oddA nucleus 31 Na, which is expected to be in the “island of inversion”,6) is studied by the MCSM with theAlphleet computer system.
In this report, the structure of a neutron-rich oddA nucleus 31 Na, which is expected to be in the “island of inversion”,6) is studied by the MCSM with theAlphleet computer system.
∑Y =ai + h + i + j + k + l + m(2)i=∞The energy levels of 31 Na are shown in Fig. 1. The
ground-state spin 3/2+ agrees with an experiment, incontrast to the sd-shell model prediction of 5/2+ . The
calculated magnetic moment of the ground state is
2.17 µN with free-nucleon g factors being consistent
with the experimental value of 2.283 (38) µN .2) The
present study shows that, while the ground state isdominated by the 2-particle 2-hole (2p2h) excitations
from the N = 20 core, 4p4h and higher excited conﬁgurations are mixed and lower the ground-state energy
by more than 700 keV. This energy gain gives rise
to a better two-neutron separation energy. The ﬁrst
excited state obtained by the MCSM calculation is a
5/2+ state located at 310 keV, in good agreement witha recent measurement of 350 ± 20 keV.7) On the otherhand, this level was calculated to lie around 200 keV
in the 0p0h + 2p2h truncation. A comparison between
the truncated and full calculations clearly indicates theimportance of the higher intruder conﬁgurations (i.e.,
4p4h and higher excited conﬁgurations from N = 20core):a) these conﬁgurations lower the ground state
more than the ﬁrst excited state, giving rise to a better agreement with experiment. The higher intruder(1)

Condensed from the article in Phys. Rev. Lett. 85, 1827
(2000)RIKEN Nishina Center
Department of Physics, University of Tokyo
Atomic Physics Laboratory, RIKEN
Department of Physics, Omsk University

Fig. 1. Experimental energy levels of 31 Na (Exp.) compared with those of the MCSM calculation (MCSM).
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