Charge-changing interactions probing point-proton radii of nuclei

Abstract

The question of whether charge-changing interactions can be used to probe point-proton radii of nuclei remains unanswered. Charge-changing cross sections, σcc, were systematically investigated using stable and unstable nuclear beams of intermediateenergy. The ratios of the experimental σcc values to the calculated ones obtained from a phenomenological Glauber-type model analysis are found to be nearly constant in a broad range of Z/N for light neutron-rich nuclei. This enables the determination of density distributions, i.e., the radii of protons tightly bound in nuclei. To test the applicability of the present method to all nuclei in the nuclear chart, extensive measurements were performed for medium-mass nuclei ranging from Z = 18 to 32. The present study suggests the potential capability of a new experimental approach for exploring exotic nuclei.

Full text

Charge-changing interactions probing point-proton radii of nu-
clei
S. Yamaki1, J. Kouno1, D. Nishimura2, M. Nagashima3, M. Takechi4, K. Sato1, K. Abe3, Y. Abe5,
M. Fukuda6, H. Furuki1, I. Hachiuma1, A. Homma3, N. Ichihashi1, C. Ichikawa1, N. Inaba5, T. Ito3,
K. Iwamoto6, T. Izumikawa8, Y. Kamisho6, N. Kikuchi3, S. Kinno2, A. Kitagawa7, T. Kojima2,
T. Kuboki1, M. Mihara6, S. Miyazawa1, S. Momota9, Y. Morita6, D. Nagae5, Y. Nakamura3,
K. Namihira1, R. Nishikiori5, I. Nishizuka1, T. Niwa5, M. Ogura3, Y. Ohkuma3, T. Ohtsubo3,
S. Okada5, J. Ohno6, A. Ozawa5, Y. Saito5, T. Sakai3, S. Sato7, D. Sera3, F. Suzaki1, S. Suzuki1,
S. Suzuki3, T. Suzuki1, M. Taguchi2, H. Uenishi6, M. Wakabayashi6, D. Watanabe2, M. Yaguchi6,
S. Yasumoto1, and T. Yamaguchi1,a
1
Department of Physics, Saitama University, Saitama 338-8570, Japan
2
Department of Physics, Tokyo University of Science, Noda 278-8510, Japan
3
Department of Physics, Niigata University, Niigata 950-2181, Japan
4
GSI Helmholtzzentrum für Schwerionenforschung GmbH, 64291 Darmstadt, Germany
5
Institute of Physics, University of Tsukuba, Ibaraki 305-8571, Japan
6
Department of Physics, Osaka University, Toyonaka 560-0043, Japan
7
National Institute of Radiological Sciences, Chiba 263-8555, Japan
8
RI Center, Niigata University, Niigata 951-8510, Japan
9
School of Environmental Science and Engineering, Kochi University of Technology, Kochi 782-8502, Japan
Abstract. The question of whether charge-changing interactions can be used to probe
point-proton radii of nuclei remains unanswered. Charge-changing cross sections, σcc,
were systematically investigated using stable and unstable nuclear beams of intermediate-
energy. The ratios of the experimental σcc values to the calculated ones obtained from
a phenomenological Glauber-type model analysis are found to be nearly constant in a
broad range of Z/Nfor light neutron-rich nuclei. This enables the determination of den-
sity distributions, i.e., the radii of protons tightly bound in nuclei. To test the applicability
of the present method to all nuclei in the nuclear chart, extensive measurements were per-
formed for medium-mass nuclei ranging from Z=18 to 32. The present study suggests
the potential capability of a new experimental approach for exploring exotic nuclei.
1 Nuclear radii – introduction
Charge radii are the basic ground-state properties of nuclides, reflecting a variety of structures of
point-proton distributions in nuclei. Today, nuclear shell evolution far from the stability line is con-
sidered an intriguing and challenging topic in radioactive-isotope (RI) beam science. Protons and neu-
trons develop differently in a neutron-rich region, resulting in a large difference between the proton-
distribution and neutron-distribution radii, also known as the neutron skin [1]. Such studies have so
ae-mail: yamaguti@phy.saitama-u.ac.jp
DOI: 10.1051/
C
Owned by the authors, published by EDP Sciences, 2014
,
/
03099 (2014)
201
66
epjconf
EPJ Web of Conferences
4 6 60 30 99
This is an Open Access article distributed under the terms of Creative Commons Attribution License 2.0, which permits
unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
the
Article available at http://www.epj-conferences.org or http://dx.doi.org/10.1051/epjconf/20146603099

far been performed on the interaction (σI) and/or reaction (σR) cross sections using relativistic-energy
RI beams, owing to the development of radioactive nuclear beam facilities worldwide. Nuclear mat-
ter radii have been determined through the Glauber model analysis of the measured cross sections,
while charge radii have predominantly been obtained from precision isotope-shift measurements. The
systematics of matter radii has led to, for example, the discovery of a typical neutron-halo nucleus
11Li [2] and a new magic number N=16 in light neutron-rich nuclei [3]. Recent highlights of σI
measurements can be found in Ref. [4].
In order to experimentally determine the neutron skin of exotic nuclei, a new methodology to dis-
tinguish point-proton and neutron radii is required. Isotope-shift and electron-scattering experiments
have so far provided the highest precision in charge radius measurements; however, they suffer from
a certain limitation with regard to the luminosity of rare species close to the drip line. Since the
charge-changing cross sections, σcc, of intermediate-energy heavy ions are sensitive to their proton
distributions, the point-proton radii could feasibly be extracted [5], facilitating the fastest access to
the drip line. Thus, point-proton radii are determined from σcc measurements, whereas matter radii
are determined from σRmeasurements. Both measurements can be simultaneously performed in a
single experiment, and the same theoretical framework, namely, the Glauber-type model analysis, can
be reliably employed for both reaction channels.
2 Charge-changing cross sections – a new approach
To describe charge-changing cross sections using the Glauber-type approach, we modified the zero-
range optical-limit Glauber model formula (see Ref. [5] in detail). Figures 1(a–f) show the applica-
bility of the present method for stable nuclei with known charge radii. The experimental data for 12C,
20Ne, 27 Al, 24Mg, 36,40 Ar, and 56Fe on C were taken from Refs. [6–10], and the curves were calculated
with the developed formula. The calculated cross sections are mostly greater than the experimental
σ
cc
(mb)
E
(MeV/nucleon)
1900
1800
1700
1600
1500
1400
1000800600400200
(f)
1400
1300
1200
1100
1000
900 1000800600400200
(d)
1300
1200
1100
1000
900
800 1000800600400200
(b)
1200
900
800
700
600
500
8006004002000
(a)
1300
1200
1100
1000
900
8006004002000
(c)
1600
1500
1400
1300
1200
8006004002000
(e)
1000
1300
900
1000
1800
1700
1600
1500
1100
1100
1200
1.3
1.2
1.1
1.0
0.9
0.8
1.00.90.80.70.60.5
Z/N
(g)
Ratio
Figure 1. Left panel: Comparison of the calculated and experimental values of σcc taken from [5]: (a) 12C on C
(open squares [6], crosses [7], open circles [8], and solid circles [9]); (b) 20 Ne on C [6]; (c) 27Al on C [6]; (d) 24 Mg
on C [6]; (e) 36Ar (solid circle [10]) and 40 Ar (open circle [10] and open squares [6]) on C, where corresponding
calculations are indicated by the dashed and solid curves, respectively; and (f) 56Fe on C [6]. Right panel: (g)
The ratios of experimental to calculated values of σcc as a function of Z/Nfor stable and unstable light nuclei
with known charge radii. The solid line and the shaded band show the results of the least-squares fitting of the
experimental data and the corresponding standard deviations, respectively (taken from [11]).
EPJ Web of Conferences
03099-p.2

σcc obtained for 12C and 20 Ne in the present energy range, but the calculations underestimate the data
for 27Al, 24 Mg, 36,40Ar, and 56 Fe. A typical difference between the experimental and predicted σcc
values is ∼4%.
To extend the present method to unstable nuclei, σcc values of neutron-rich Be, C, and O isotopes
on a carbon target were measured at 300 MeV/nucleon [11]. A series of experiments were carried out
using the fragment separator at the Heavy Ion Medical Accelerator in Chiba (HIMAC) synchrotron
facility at the National Institute of Radiological Sciences (NIRS) [12]. Since the charge radii of some
of these unstable nuclei are precisely known already, the ratios of the experimental σcc values to the
calculated ones are obtained as a function of Z/N, as shown in Fig. 1(g) (see also Fig. 2 of Ref. [11])
in which the data measured at high energies are also included [13]. We find that the ratios are nearly
constant, over a broad range of Z/N, with a standard deviation of ±3%, as shown by the shaded
area in Fig. 1(g). The constant ratio suggests that the direct proton removal channel dominates the
charge-changing process at intermediate energies. This fact enables the determination of the density
distributions, i.e., the radii of protons bound in neutron-rich nuclei. A successful application is seen
in 15,16C [11].
3 Towards medium-mass nuclei
As an extension of previous studies on light nuclei, we systematically measured σcc of medium-mass
nuclei on a carbon target at 300 MeV/nucleon. The measured nuclei ranged from Z=18 to 32, and
their partial charge-changing cross sections were also measured [14]. Figure 2 shows preliminary
results for the measurements of the σcc values of Ca, Ti, Cr, and Fe isotopes as a function of the
neutron number N. For comparison, σcc values of light neutron-rich nuclei, B, C, N, O, and F isotopes
measured at approximately 1 GeV/nucleon are plotted as well [13].
In general, the charge-changing cross section is, by definition, sensitive to the Znumber of the
projectile. Figure 2 clearly shows that the measured σcc values increase with Zbut are less sensitive
to N. The data stay constant within a relative variance of approximately ±5%. A careful observation
of the variance of the present data reveals that the σcc values often increase toward the neutron-
deficient side. Here, it should be noted that the high-energy data lie in the neutron-rich unstable
region, whereas the present data, some of which are even located at the neutron-deficient side, lie in
the stable region. For such nuclei, there might be a correlation between the σcc values and the proton
separation energies, Sp, which monotonically decrease toward the neutron-deficient side.
Figure 3 shows correlations between the values of σcc and Spfor (a) Ca, Ti, (b) Cr, and Fe isotopes.
The σcc values of Ca and Ti isotopes mostly increase as Spdecreases, as shown in Fig. 3(a), while σcc
1600
1400
1200
1000
800
cc
(mb)
3530252015105
N
BC
NO
F
Ca
Ti
Cr Fe
Figure 2. Preliminary results for the σcc values of Ca
(solid circles), Ti (open circles), Cr (solid triangles), and
Fe (open triangles) isotopes as a function of N. The data
for B, C, N, O, and F isotopes measured at high energies
are taken from Ref. [13].
INPC 2013
03099-p.3

1500
1450
1400
1350
1300
1250
cc
(mb)
1412108
S
p
(MeV)
(a)
1600
1550
1500
1450
1400
1350
cc
(mb)
1412108
S
p
(MeV)
(b)
Figure 3. Correlations of preliminary σcc versus proton separation energy, Sp, for (a) Ca (solid circles), Ti (open
circles), (b) Cr (solid triangles), and Fe isotopes (open triangles).
of Cr and Fe isotopes stay nearly constant as shown in Fig. 3(b). The present behavior in the stable
and neutron-deficient region is apparently different from that in the light neutron-rich region. Using
nuclei with known charge radii, the systematic behavior of the ratios of the experimental σcc values to
the calculated ones should be carefully calibrated. The modified Glauber-type approach would then
provide the point-proton radii of medium-mass unstable nuclei for which charge radii are yet to be
determined. The results will be presented in a forthcoming publication.
Acknowledgments
These experiments were supported by the Research Project with Heavy Ions at NIRS-HIMAC. The
present study was partly supported by JSPS KAKENHI Grant Numbers 23600002 and 24244024.
References
[1] T. Suzuki et al., Phys. Rev. Lett. 75, 3241 (1995).
[2] I. Tanihata et al., Phys. Rev. Lett. 55, 2676 (1985).
[3] A. Ozawa et al., Phys. Rev. Lett. 84, 5493 (2000).
[4] M. Takechi et al., Phys. Lett. B 707, 357 (2012).
[5] T. Yamaguchi et al., Phys. Rev. C 82, 014609 (2010).
[6] W.R. Webber, J.C. Kish, and D.A. Schrier, Phys. Rev. C 41, 520 (1990).
[7] A. N. Golovchenko et al., Phys. Rev. C 66, 014609 (2002).
[8] I. Schall et al., Nucl. Instrum. Methods Phys. Res. B 117, 221 (1996).
[9] C. Zeitlin at al., Phys. Rev. C 76, 014911 (2007).
[10] G. Iancu, F. Flesch, and W. Heinrich, Radiat. Meas. 39, 525 (2005).
[11] T. Yamaguchi et al., Phys. Rev. Lett. 107, 032502 (2011).
[12] M. Kanazawa et al., Nucl. Phys. A 746, 393c (2004).
[13] L.V. Chulkov et al., Nucl. Phys. A 674, 330 (2000).
[14] S. Yamaki et al., Nucl. Instrum. Methods Phys. Res. B, (2013) in press.
doi:10.1016/j.nimb.2013.05.057
EPJ Web of Conferences
03099-p.4