Ⅱ-2. Nuclear Physics (Theory)

RIKEN Accel. Prog. Rep. 51 (2018)

Role of deformation in odd-even staggering in reaction cross sectionsfor 30,31,32 Ne and 36,37,38 Mg isotopes†
Y. Urata,∗1 K. Hagino,∗1,∗2 and H. Sagawa∗3,∗4

1.5
σR (b)We discuss the role of the pairing anti-halo eﬀect
in the observed odd-even staggering in reaction crosssections for 30,31,32 Ne and 36,37,38 Mg isotopes by taking into account the ground state deformation of thesenuclei. We construct the ground state density forthe 30,31 Ne and 36,37 Mg nuclei based on a deformed
Woods-Saxon potential, while for the 32 Ne and 38 Mg
nuclei we also take into account the pairing correlation
using the Hartree-Fock-Bogoliubov (HFB) method.
We consider the collision of a deformed projectile
nucleus with a spherical target nucleus and computethe reaction cross sections, σR . To this end, we employ the Glauber theory, which is based on the eikonal
approximation and the adiabatic approximation to therotational motion of a deformed nucleus. That is, weﬁrst ﬁx the orientation angle of the deformed nucleus
and then take an average of the resultant cross section
over all the orientation angles:1)∫1dΩ σR (Ω),(1)
σR =4π∗1∗2∗3∗412Ne + C (240 MeV/A)
31Sn ( Ne) = 0.3 MeV

1.4
Deformed (β2 = 0.3)
Spherical (Ref. [5])

1.3
30

31A

32

Fig. 1. Reaction cross sections for the 30,31,32 Ne + 12 C reaction at E = 240 MeV/nucleon evaluated at the one
neutron separation energy of 31 Ne of Sn = 0.3 MeV.
The filled circles with error bars indicate the experimental interaction cross sections taken from Ref. 4).
For comparison, the result of the previous analysis inRef. 5) based on the spherical density distributions is
also shown by the dashed line.

where Ω is the angle of the symmetric axis of the deformed nucleus in the laboratory frame, and σR (Ω) is
the reaction cross section for a ﬁxed Ω.
We analyze the experimental data at an incident energy E = 240 MeV/nucleon with a 12 C target. We use
the same density for 12 C as that given in Ref. 2), while
we use the same parameters given in Ref. 3) for theproﬁle function, ΓN N in the Glauber model calculations.
The reaction cross sections for the 30,31,32 Ne nuclei
evaluated at Sn (31 Ne) = 0.3 MeV are shown in Fig. 1,
along with a comparison to the experimental interaction cross sections.4) We also show the result of a previous analysis based on the spherical density distributions at a similar one neutron separation energy.5) One
can see that the odd-even staggering can still be reproduced by taking into account the nuclear deformation.
Notice that the degree of the staggering is lower in thepresent calculation compared to the previous sphericalcalculation because the valence neutron in 31 Ne fully
occupies the 1p3/2 level in the spherical case, while theoccupation probability for the p3/2 level decreases fromunity in the deformed case. We also checked the eﬀectof pairing correlations on the odd-even staggering with†A

the deformed wave functions. We found that the reaction cross section for 32 Ne is not sensitive to the valueof the average pairing gap as long as it is large enough.
We have also investigated the role of nuclear deformation in the odd-even staggering observed in reaction
cross sections for Mg isotopes. We have shown that thedeformation mainly decreases the degree of odd-evenstaggering, as in the Ne isotopes, because of the admixture of several angular momentum states in a deformed single-particle wave function. Despite this, theodd-even staggering persists even with ﬁnite deformation when the one neutron separation energy is smallenough. These results strongly indicate that the pairing anti-halo eﬀect indeed contributes to the observed
odd-even staggering in reaction cross sections.
References1) J. A. Christley, J. A. Tostevin, Phys. Rev. C 59, 2309(1999); K. Hagino, N. Takigawa, Prog. Theor. Phys.
128, 1061 (2012).
2) Y. Ogawa, K. Yabana, Y. Suzuki, Nucl. Phys. A 543,722 (1992).
3) B. Abu-Ibrahim, W. Horiuchi, A. Kohama, Y. Suzuki,
Phys. Rev. C 77, 034607 (2008).
4) M. Takechi et al., Phys. Lett. B 707, 357 (2012).
5) K. Hagino, H. Sagawa, Phys. Rev. C 84, 011303(R)(2011).

Condensed from the article in Phys. Rev. C 96, 064311(2017)
Department of Physics, Tohoku University
Research Center for Electron Photon Science, Tohoku University
RIKEN Nishina Center
Center for Mathematics and Physics, University of Aizu

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