Ⅱ-1. Nuclear Physics

RIKEN Accel. Prog. Rep. 47 (2014)

Study of proton and neutron density distributions observed via
proton elastic scattering at 200 and 300 MeV
J. Zenihiro,∗1 H. Sakaguchi,∗2 S. Terashima,∗4 Y. Matsuda,∗2 S. Adachi,∗3 T. Baba,∗3 T. Furuno,∗3T. Hashimoto,∗2 T. Kawabata,∗2 J. Lee,∗1 Y. Maeda,∗5 K. Miki,∗2 T. Murakami,∗3 H. J. Ong,∗2A. Tamii,∗2 J. Tanaka,∗2 M. Tsumura,∗3 T. Yamamoto,∗2 and L. Yu,∗4proton and neutron densities can be separately and simultaneously determined by the new method. The extracted proton and neutron radii of 90 Zr are 4.210(20)and 4.300(17) fm, respectively. The extracted proton radius is very consistent with that of 4.198(1) fm,
which is derived from the charge radius determined via
the combined analysis of electron elastic scattering andmuonic atom X-rays data.7)

∗1
∗2
∗3
∗4
∗5dσ/dΩ (mb/sr)

90

10 2

101090Ay

Zr 200-1
1

Ni 200-2x 1030

4050

Zr 2001020304050

20304050

0-0.5 58-410200.558-3

100-0.5 90-1-2Zr 300

0.5

Ay

10-11

Zr 3003x 109010100-0.5

410 3

10.5

Best Fit

10 5
101RIA+RH

10 6

AyA systematic study of the nucleon density distributions of ﬁnite nuclei is important for understanding theisospin dependence of the nuclear many-body system.
For example, the neutron skin thicknesses are known tobe strongly correlated with the density-dependent termof the symmetry energy, and the isospin-dependent
term of the nuclear equation of state.
In previous works,1,2) we have succeeded in extracting the neutron density distributions of stable nuclei
such as Sn and Pb isotopes via proton elastic scattering. At the same time we have launched a new project
aimed at measuring the Elastic Scattering of Protons
with RI beams (ESPRI) with the purpose of the extraction of proton and neutron density distributions ofunstable nuclei. We have newly developed and tested
unique devices for the ESPRI measurements at NIRSHIMAC in Chiba and GSI in Germany.3,4) Finally, we
have successfully performed the ESPRI experiment atRIBF in April, 2013.5)
Unlike the case of stable nuclei, however, we haveno information on the nuclear charge densities of unstable nuclei. Thus, we have proposed a new method
to extract proton and neutron densities via two-energy
proton elastic scattering. This method is based on thelarge diﬀerence between the energy dependences of thep-p and p-n interactions. Recently, we performed anexperiment to demonstrate this new method using real
data of Zr isotopes. In this report, we show the preliminary results of 90 Zr only. For other isotopes (92,94 Zr),
the analysis is still ongoing.
The experiment was performed at RCNP, OsakaUniversity. Polarized proton elastic scattering from90,92,94
Zr and 58 Ni at 200 and 300 MeV was measured by using the Grand Raiden magnetic spectrometer.6) Figure 1 shows the angular distributions of crosssections (dσ/dΩ) and the analyzing powers (Ay ) of90
Zr(⃗p,p) at 200 and 300 MeV and of 58 Ni(⃗p,p) at200 MeV. The red lines denote the result of relativistic
impulse approximation (RIA) with relativistic-Hartree(RH) densities. The 58 Ni data was used to determine
the eﬀective interaction at 200 MeV (solid lines). Using
the eﬀective interaction, the proton and neutron densities of 90 Zr were simultaneously searched and the results are denoted by the solid lines in Fig. 1 and 2. The

203040-150

Θc.m.(degree)

Ni 20010Θc.m.(degree)

Fig. 1. Obtained data of dσ/dΩ and Ay of 90 Zr at 200 and300 MeV and of 58 Ni at 200 MeV. The black solid lines
show the ﬁtting results while the red dashed lines are
RIA calculations with RH densities.

3density (1/fm )0.14

900.120.1

NeutronZr

extracted
RH modelProton

0.08
0.06

0.02
001

2

extracted
unfolded

ilim

Pre

0.04

ynar

345radius (fm)

678Fig. 2. Extracted proton and neutron densities, denoted bysolid red and blue lines, respectively. While upper andlower lines show the error envelopes due to the experimental errors, middle lines are the best-ﬁt results. The
red dashed line shows the proton density by unfolding
the nuclear charge density. Blue dashed line shows thesame by the RH model calculation.

References
1) S. Terashima et al.: Phys. Rev. C 77, 024317 (2008).
2) J. Zenihiro et al.: Phys. Rev. C 82, 044611 (2010).
3) Y. Matsuda et al.: Phys. Rev. C 87, 034614 (2013).
4) S. Terashima et al.: GSI Scientiﬁc Report, 148 (2010).
5) S. Terashima et al.: in this report.
6) M. Fujiwara et al.: Nucl. Instr. Meth. A 422, 484(1999).
7) I. Angeli: At. Data Nucl. Data Tables 87, 185 (2004).

RIKEN Nishina Center
RCNP, Osaka University
Department of Physics, Kyoto University
School of Physics and Nuclear Energy Engineering, Beihang
University
Department of Applied Physics, University of Miyazaki- 16 -