Ⅱ-2. Nuclear Physics (Theory)

RIKEN Accel. Prog. Rep. 47 (2014)

Deformed nuclei in the black-sphere approximation
A. Kohama, ∗1 K. Iida,∗1,∗2 K. Oyamatsu,∗1,∗3 and H. Koura∗1,∗4
The size of an atomic nucleus is one of the most fundamental quantities that characterize the bulk properties of the nucleus. It is well known for β stable nuclei in the ground state thanks to systematic measurements of electron and proton elastic differential crosssections. This helps clarify the equation of state of nuclear matter near the saturation point.1) When studying the density derivative L of the symmetry energyof nearly symmetric nuclear matter, the total reaction
cross section, σR , of neutron-rich nuclei is one of themost important observables.
In this work, in order to obtain the value of L, we
focus on the empirical data of the interaction crosssection, σI , measured at ∼900 MeV per nucleon,2,3) asa first step. Since the data of Ne and Mg isotopes at∼240 MeV per nucleon have already been obtained at
the RI Beam Factory of RIKEN,4) systematic analyses
are necessary. For the analyses, we adopt the blacksphere (BS) model of nuclei.
We have so far systematically analyzed the proton
elastic scattering and σR data for stable nuclei at a proton incident energy of Tp ∼ 800–1000 MeV on the basisof a “black-sphere picture” of nuclei.5) We showed thatfor proton beams incident on stable nuclei, the crosssection of a black sphere of radius a, which is determined by fitting the angle of the first elastic diffraction peak calculated for proton diffraction by a circular black disk of radius a to the measured value, isconsistent with the measured σR .5) This finding is also
observed for σR of nucleus-nucleus reactions down toapproximately 100 MeV per nucleon.6)
In the model, the absorption cross section is written
2by σBS = π (a0 (proj.) + a0 (C)) , where a0 (proj.) is theBS radius of a projectile. a0 (C) is the BS radius of thetarget C nucleus obtained using the method mentioned
above.5,6) For proton incident energies higher than ∼800 MeV, a0 (C) = 2.69 ± 0.07 fm.
According to the systematic analysis based on amacroscopic nuclear model, at large neutron excess,the calculated nuclear matter radius increases with L
via the L dependence of the nuclear matter saturation
density. It is indispensable to duly incorporate suchdependence into the BS model for application to thereactions involving neutron-rich nuclei.
The relatively large neutron excess of the isotopes ofNe and Mg is advantageous for studying the value ofL. However, nuclear deformation occurs in this regionof nuclei. We change the black sphere into a spheroidof the same volume to take nuclear deformation into
∗1
∗2
∗3
∗4Fig. 1. Effect of nuclear deformation on σR as a function ofprojectile mass number, A, indicated by squares withcrosses. The values of β are from SkM*. The spherical cases (◦) are obtained by “BS scaling”, a0 (proj.) ≃1.2135A1/3 fm, in σBS .5) For comparison, we plot theempirical values of σI of A Mg on a carbon target.2,3)

account before discussing the L dependence. The values of the deformation parameter, β, are taken frommicroscopic nuclear structure models.7) Under the adiabatic approximation, the values of σR for deformed
nuclei should be evaluated by angle averaging of thecross section values over the deformation direction ofnuclei.8)
The results are shown in Fig. 1. Although weadopt the values of β given by a mean field calculation with the effective interaction SkM*, which tends
to offer large deformation, the effect on σR is rathersmall. This is consistent with the work of Christley
and Tostevin,8) but inconsistent with the work of Horiuchi et al.9) Before drawing conclusions, we have toexamine the interaction dependence by adopting SLy4,KTUY,7,10) etc. The study is now in progress.
References
1) K. Oyamatsu et al.: Prog. Theor. Phys. 109, 631 (2003).
2) A. Ozawa et al.: Nucl. Phys. A 693, 32 (2001).
3) R. Kanungo et al.: Phys. Rev. C 83, 021302(R) (2011).
4) M. Takechi et al.: Phys. Lett. B 707, 357 (2012).
5) A. Kohama et al.: Phys. Rev. C 72, 024602 (2005).
6) A. Kohama et al.: Phys. Rev. C 78, 0061601(R) (2008).
7) T. Inakura et al.: Nucl. Phys. A710, 261 (2002).
8) J. A. Christley et al.: Phys. Rev. C 59, 2309 (1999).
9) W. Horiuchi et al.: Phys. Rev. C 86, 024614 (2012).
10) H. Koura et al.: Prog. Theo. Phys. 113, 305 (2005).

RIKEN Nishina Center
Depart. of Natural Science, Kochi University
Depart. of Human Informatics, Aichi Shukutoku University
ASRC, JAEA

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