I. HIGHLIGHTS OF THE YEARRIKEN Accel. Prog. Rep. 54 (2021)

RIKEN Accel. Prog. Rep. 54 (2021)

Mean-square radius of the neutron distribution and skin thickness
derived from electron scattering†
H. Kurasawa,∗1 T. Suda,∗2,∗3 and T. Suzuki∗2
To the authors’ knowledge, this is the ﬁrst study todeduce the neutron distribution from electron scattering data in the history of nuclear physics.1)
The question how neutrons are distributed in nuclei
has been a longstanding problem. Although it is oneof the most fundamental problems in nuclear physics,
the neutron distribution has not been well determined
yet, because there is no simple and reliable method to
explore it experimentally.2) In contrast to the neutron
distribution, the proton distribution has been widely
investigated through the nuclear charge density deduced from electron scattering.3) Electron scattering
is an unambiguous and unique tool to examine thecharge distribution, because the electromagnetic interaction is well understood and allows reactions that do
not disturb the nuclear ground-state properties.4)
So far, electron scattering has been believed to be
useful for the study of the only proton distribution andhas not been discussed in the context of the neutron
distribution in nuclei.4) The SCRIT in RIKEN5) also
constructed with the primary objective of exploring
the proton distribution in unstable nuclei, although theneutron distribution plays a crucial role in the stabilityof neutron-rich nuclei. Such dogma is based on thefact that the neutron charge density is approximately
1% of the total nuclear charge density and oscillates
as a function of the nuclear coordinate, yielding zero
integrated charge.
Recently, the precise expressions for the moments of
the nuclear charge density were derived according torelativistic quantum mechanics.6) It has been shownthat the second-order moment of the nuclear charge
density(Rc2 ) is dominated by the mean-square radius(msr) of the point proton distribution (Rp2 ), while thenth (≥ 4)-order moment depends on the (n-2)th-ordermoment of the point neutron distribution also. For
example, the fourth-order moment (Q4c ) of the charge
density depends on the msr of the point neutron distribution (Rn2 ). The contribution of Rn2 to Q4c is dominated by the number of excess neutrons.
The present authors have analyzed experimental
data of Rc2 and Q4c deduced from the electron scattering oﬀ 40 Ca, 48 Ca, and 208 Pb, which are available atpresent.3) First, using relativistic and non-relativistic
mean ﬁeld models accumulated over the last 50 years
in nuclear physics, the linear relationship between the†
∗1
∗2
∗3

various moments are explored with the use of the leastsquares method. Next, from the intersection of thepredicted least-square lines and the lines of the experimental value for Rc2 or Q4c , the values of Rn2 together
with Rp2 of those nuclei have been estimated. They are
obtained within 1% accuracy, including both experimental error and the standard deviation of the leastsquare lines.1)
This paper opens a new possibility of electron scattering as a clean and practical probe to extract neutron
density information. As the contributions from theneutron density to the charge density are expected toincrease in neutron-rich nuclei, the new electron scattering facilities in the world5) which are led by theSCRIT7) would make the forthcoming study of unstable nuclei more eﬃcient and stimulating, both experimentally and theoretically.
References
1) H. Kurasawa, T. Suda, T. Suzuki, Prog. Theor. Exp.
Phys. 2021, 013D02 (2021).
2) M. Thiel et al., J. Phys. G 46, 093003 (2019).
3) H. De Vries, C. W. De Jager, C. De Vries, Atom. Data
Nucl. Data Tables 36, 495 (1987).
4) T. deForest, J. D. Walecka, Adv. Phys. 15, 1 (1966).
5) T. Suda, H. Simon, Prog. Part. Nucl. Phys. 96, 1 (2017).
6) H. Kurasawa, T. Suzuki, Prog. Theor. Exp. Phys. 2019,
113D01 (2019).
7) K. Tsukada et al., Phys. Rev. Lett. 118, 262501 (2017).

Condensed from the article in Prog. Theor. Exp. Phys.
2021, 013D02 (2021)
Department of Physics, Chiba University
Research Center for Electron-Photon Science, Tohoku University
RIKEN Nishina Center- S23 -1