II-2. Nuclear Physics (Theory)

RIKEN Accel. Prog. Rep. 55 (2022)

RIKEN Accel. Prog. Rep. 55 (2022)

Nuclear surface diﬀuseness of Ne and Mg isotopes in the island ofinversion†

Diffuseness parameter (fm)V. Choudhary,∗1 W. Horiuchi,∗2,∗3 M. Kimura,∗2,∗4 and R. Chatterjee∗1
It had been suggested in the literature,1) that theisland of inversion close to N = 20 and 28 arises because of the ν(sd)−2 (f p)2 intruder conﬁgurations. It
was proposed that two neutrons from the sd-shell are
excited to the f p-shell become so low in energy thatthey manifest as the ground state of Z = 10–12 andN = 20–22 nuclei. This proposition was conﬁrmed bymass measurements and reactions involving neutronrich isotopes of Ne, Na and Mg, especially at RIBF.
This change in occupation of nucleons in diﬀerent energy levels not only results in large deformations but
also aﬀects the nuclear density proﬁle, particularly thenuclear surface diﬀuseness. In this work, we attempt tosystematically investigate the connection between thenuclear surface diﬀuseness and various spectroscopic
information of Ne and Mg isotopes (N = 19–28) ator near the island of inversion. We calculate the density and spectroscopic information of Ne and Mg isotopes using the antisymmetrized molecular dynamics(AMD) model.2,3) We then construct a two-parameter
Fermi density distribution (2 pF), with adjustable radius and diﬀuseness parameters. These parameters arethen estimated using two complementary methods one analyzing the static structure and the other dynamical, in which reaction observables involving thesenuclei are analyzed. In the ﬁrst method, the optimizedradius and diﬀuseness parameters of the 2 pF are estimated by minimizing the diﬀerence between densities obtained by AMD and 2 pF density distributions.
In the second, both the AMD and 2 pF densities aretaken as inputs to calculate the proton-nucleus elastic
scattering diﬀerential cross section using the Glaubermodel. We then demand that the ﬁrst peak position
and its magnitude are reproduced for both these densities as prescribed.4) We have veriﬁed that the parameters estimated using these complementary methods
agree within a margin of 1–3%.
The nuclear surface diﬀuseness, i.e., the diﬀusenessparameter of the 2 pF density of Ne and Mg isotopes
extracted from the matter density distribution of AMD
is plotted in Fig. 1. The diﬀuseness parameter has similar dependency on neutron number, illustrating thesimilarity in nuclear deformations for both Ne and Mg
isotopes.2,3) We observe that the neutron occupancy of†
∗1
∗2
∗3
∗4

0.7
0.65
0.6
0.55

Mg
Ne0.5
10 12 14 16 18 20 22 24 26 28

Neutron numberFig. 1. Diﬀuseness parameters of Ne and Mg isotopes asa function of neutron number. The ﬁgure is adopted
from the original article.†

the weakly-bound 1p3/2 orbit has a signiﬁcant impact
on the global behavior of the diﬀuseness parameter.
The absence of intruder orbitals till N = 18 results innormal shell ﬁlling and hence diﬀuseness parameters
are very similar to the standard value of 0.54 fm. The
eﬀect of the intruder orbitals begins to be felt fromN = 19 onwards resulting in strong quadrupole deformation and mixing of p- and f -waves. 29 Ne and31
Mg (N = 19) have predominant 2p3h conﬁgurations
in which two particles are promoted from the sd- topf -shell. The increasing occupation probability of the1p3/2 orbit not only results in a large diﬀuseness but
also the breakdown of the N = 20 and 28 magic numbers in this region. An exception, however, is notedfor 35–37 Mg where the ﬁlling up the holes in the deeply
bound sd-shell somewhat compensates the increase in
diﬀuseness due to ﬁlling up of the 1p3/2 orbit. Noticeably, for N = 22, 34 Mg has predominant 4p2h conﬁguration, whereas 32 Ne has an admixture of 4p2h and
2p0h conﬁgurations. This could be the reason why34
Mg is more diﬀused than 32 Ne.
In conclusion our work shows that information about
the nucleus surface diﬀuseness in exotic neutron richnuclei can be extracted from the ﬁrst diﬀraction peakof nucleon-nucleus elastic scattering diﬀerential crosssection.

Condensed from the article in Phys. Rev. C. 104, 054313(2021)
Department of Physics, Indian Institute of Technology Roorkee
Department of Physics, Hokkaido University
Department of Physics and NITEP, Osaka Metropolitan
University
RIKEN Nishina CenterReferences
1) E. K. Warburton et al., Phys. Rev. C 41, 1147 (1990).
2) T. Sumi et al., Phys. Rev. C 85, 064613 (2012).
3) S. Watanabe et al., Phys. Rev. C 89, 044610 (2014).
4) S. Hatakeyama et al., Phys. Rev. C 97, 054607 (2018).

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