I. HIGHLIGHTS OF THE YEARRIKEN Accel. Prog. Rep. 55 (2022)

RIKEN Accel. Prog. Rep. 55 (2022)

Total reaction cross sections in the island of inversion near N = 40†
W. Horiuchi,∗1,∗2 T. Inakura,∗3 and S. Michimasa∗40.35
0.3

|β2|

0.25

Ti
Cr
Fe

0.2
0.15
0.1
0.05
00.2

β40.15
0.1
0.05
030

32

3436

38

40

42

Neutron numberFig. 1. Quadrupole (β2 ) and hexadecapole (β4 ) deformation
parameters of Ti, Cr, and Fe isotopes calculated withSkM∗ (closed symbols with solid lines) and SLy4 (opensymbols with dashed lines).
†
∗1
∗2
∗3
∗4

Condensed from the article in Phys. Rev. C 105, 014316(2022)
Department of Physics, Hokkaido University
Department of Physics and NITEP, Osaka Metropolitan University
Laboratory for Zero-Carbon Energy, Tokyo Institute of Technology
Center for Nuclear Study, University of Tokyo

1950
Ti

1900
1850

σR (mb)A systematic analysis of the deformation phenomena of Ti, Cr, and Fe isotopes is performed to understand the nuclear structure in the “island of inversion”1)near the neutron number N = 40. As large nuclear
deformations are expected in this mass region, we describe various nuclear deformations using the SkyrmeHartree-Fock method in the three-dimensional coordinate space.2) A detailed analysis of the obtained nuclear
structure information not only the quadrupole deformation but also the hexadecapole deformation increases signiﬁcantly in the island of inversion. This is because of
the excess neutrons occupying elongated intruder orbits.
This characteristic is manifested as a change in the density distribution at the nuclear surface and can be observed as a signiﬁcant increase in the total reaction crosssection (σR ).
Figure 1 plots the quadrupole (β2 ) and hexadecapole(β4 ) deformation parameters of Ti, Cr, and Fe isotopes
as a function of the neutron number N . The results withCrFe

1800
1750
1700

240 AMeV

1650
1600
30323436384042Neutron numberFig. 2. Total reaction cross sections of Ti, Cr, and Fe isotopes
calculated with SkM∗ (closed symbols with solid lines)
and SLy4 (open symbols with dashed lines).

two Skyrme density functionals, SkM∗3) and SLy4,4)
are shown. SkM∗ predicts large quadrupole deformation for N > 34, which is consistent with empirical |β2 |values found in Ref. 5), while the SLy4 results showless deformed ground states for those isotopes. We
ﬁnd that the hexadecapole deformation also enhances
for N > 34 with SkM∗ owing to the occupation of the[nnz Λ]Ω = [330]1/2 Nillson orbit, where the hexadecapole moment becomes the largest for the most prolately elongated orbitals among the orbits belonging to
the same n, i.e., for n = nz and Λ = 0.
These diﬀerent deformations are well reﬂected in thedensity proﬁles near the nuclear surface and can be distinguished by total reaction or interaction cross section
measurements. Figure 2 displays the calculated σR on acarbon target at 240 MeV/nucleon of these nuclei. Thecross sections with SkM∗ are signiﬁcantly larger thanthose obtained with SLy4 for N = 36–40, where themagnitudes of the nuclear deformations are quite diﬀerent. The diﬀerence is at most approximately 2%, which
is signiﬁcant considering the precision of recent interaction cross section measurements was  1%.6) Such asystematic cross section measurement is desired to clarify the nuclear properties in the island of inversion nearN = 40.
References
1) E. K. Warburton et al., Phys. Rev. C 41, 1147 (1990).
2) T. Inakura et al., Nucl. Phys. A 768, 61 (2006).
3) J. Bartel et al., Nucl. Phys. A 386, 79 (1982).
4) E. Chanbanat et al., Nucl. Phys. A 627, 710 (1997).
5) B. Pritychenko et al., At. Data Nucl. Data Tables 107, 1(2016).
6) M. Tanaka et al., Phys. Rev. Lett. 124, 102501 (2020).

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