II-2. Nuclear Physics (Theory)

RIKEN Accel. Prog. Rep. 54 (2021)

RIKEN Accel. Prog. Rep. 54 (2021)

Probing dilute nuclear density by antiproton-nucleus scattering†
K. Makiguchi,∗1 W. Horiuchi,∗1 and A. Kohama∗2

1610TheoryExpt.

141012dσ/dΩ (mb/sr)

1040
8p-- Ca (x10 )

1010
108106164p-- O (x10 )

104
102

10010-210-4

180 MeV01012p-- C

2030

405060Fig. 1. Elastic scattering diﬀerential cross sections forantiproton-nucleus scattering at 180 MeV/nucleonadopted from the original paper.

∗1∗2

1.8
1.7
1.6
1.5

31

F (halo)(nonhalo)
29
F

1.4
100

1000

Incident energy (MeV)
Fig. 2. Ratio of total reaction cross sections of 29, 31 F for
antiproton and proton scattering as a function of the incident energy adopted from the original paper.

cantly consistent with the experimental data without
any adjustable parameter using harmonic-oscillator typedensity distributions that reproduce the observed charge
radii.
We found that strong absorption occurs even beyond
the nuclear radius owing to the large p̄N elementarycross sections, resulting in strong sensitivity in the nuclear tail. This sensitivity is quantiﬁed by taking an
example of a possible halo nucleus 31 F, which is locatedat the ﬂuorine dripline; however, the antiproton scattering on unstable nuclei is still not feasible. According to
the investigations in Ref. 4) the shell gap between 0f7/2
and 1p3/2 orbits is essential and the dominance of the(1p3/2 )2 conﬁguration forms the halo structure in 31 F.
We considered these density distributions of 31 F with(1p3/2 )2 (halo) and (0f7/2 )2 (nonhalo) dominance fromRef. 4) and calculated the ratio of the total reaction crosssections of antiproton and proton scattering. Figure 2
displays the ratios of 31 F as a function of incident energy.
The ratios of 29 F with harmonic-oscillator type density
distributions are also plotted for comparison. 31 F withthe halo tail yielded the largest ratios, while the nonhalo density produced almost the same behavior as 29 F,
which demonstrates the advantage of antiproton scattering in the analysis of dilute density distribution.
Referencesθ (deg)†1.9

Cross section ratio

Nuclear density distributions are the basic propertiesof atomic nuclei. Traditionally, the charge density distributions have been measured using electron-nucleus scattering. Hadronic probes have been used to study matter
density distributions, especially via proton-nucleus scattering. Recently, we proposed a practical approach toextract the nuclear surface diﬀuseness of unstable nuclei using proton-nucleus elastic scattering diﬀerential
cross sections.1,2) As a natural extension of the previous study, we investigated antiproton-nucleus scattering because it could provide a diﬀerent sensitivity to
the nuclear structure than the proton probe because theantiproton-nucleon (p̄N ) total cross sections are typically 3–4 times larger than those of N N at incident energies varying from a few hundreds to thousands MeV.
High-energy antiproton-nucleus reactions can be efﬁciently described by the Glauber model.3) The total
reaction and elastic scattering cross sections can be obtained by evaluating the optical phase-shift functioneiχ(b) as a function of the impact parameter vectorb. ∫ In optical limit approximation, we have iχ(b) =− ρN (r)ΓN̄ N (b − s) dr, where r = (s, z) with z denoting the beam direction, nucleon (N ) one-body density ρN (r), and antinucleon-nucleon N̄ N proﬁle function
ΓN̄ N (b). The parameters of the proﬁle function were determined to reproduce the p̄N and p̄-12 C cross-section
data. The validity of the present model is demonstratedin Fig. 1. The theoretical cross sections were signiﬁ-Condensed from the article in Phys. Rev. C 102, 034614(2020)
Department of Physics, Hokkaido University
RIKEN Nishina Center

1) S. Hatakeyama, W. Horiuchi, A. Kohama, Phys. Rev. C97, 054607 (2018).
2) S. Hatakeyama, W. Horiuchi, A. Kohama, RIKEN Accel.
Prog. Rep. 52, 7 (2019).
3) R. J. Glauber, in Lectures in Theoretical Physics, edited
by W. E. Brittin, L. G. Dunham (Interscience, New York,1959).
4) H. Masui, W. Horiuchi, and M. Kimura, Phys. Rev. C101, 041303(R) (2020).

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