Least-squares analysis of the moments of the charge distribution in the mean-field models

• Published in: Progress of theoretical and experimental physics Vol. 2024; no. 1
• Main Author: Suzuki, Toshio
• Format: Journal Article
• Language: English
• Published: Oxford Oxford University Press 01.01.2024
• ISSN: 2050-3911; 2050-3911
• DOI: 10.1093/ptep/ptad152

The nth moment, $R^{(n)}_c$, of the charge distribution is composed of not only the m(≤ n)th moments, $R^{(m)}_p$, of the point proton distribution, but also the m(≤ (n − 2))th ones, $R^{(m)}_n$, of the point neutron distribution. The experimental value of $R^{(n)}_c(R^{(n)}_{c,{\rm exp}})$ observed through electromagnetic interaction makes it possible to investigate the point proton and neutron distributions together on the same basis. In order to estimate $R^{(m)}_\tau (\tau =p,n)$ from $R^{(n)}_{c,{\rm exp}}$, however, nuclear models are required. The structure of the least-squares analysis (LSA) between $R^{(n)}_c$ and $R^{(m)}_\tau$ is investigated within the mean-field framework. The LSA reveals constraints inherent in the model framework through the least-squares lines (LSL) and determines the value of $R^{(m)}_\tau$ of $R^{(n)}_{c,{\rm exp}}$ uniquely as a result of the sum rule with respect to the coefficients of the LSL equations. The n-dependence of the values of $R^{(m)}_\tau$ in the LSA is examined numerically by using the moments calculated up to n = 6 for 40Ca, 48Ca, and 208Pb.