On the Space Exchange Magnetic Moments of Light Nuclei

Abstract

The calculations were based on Sachs' phenomenological theory and on the independent particle model. Spin exchange moments were not included. Uncertainties in the parameters required to characterize the shell dimensions and the neutron-proton interaction, which was assumed to be of an entirely exchange nature, cause the calculated values to be uncertain by a factor of about 3; they are probably too large. For $L-S$ coupling, the values found in the $1p$ shell for ${}_{}{}^2{}_{}{}^{}P$ states for ${\mathrm{Li}}^7$, ${\mathrm{Be}}^9$, ${\mathrm{B}}^{11}$, ${\mathrm{C}}^{13}$, and ${\mathrm{N}}^{15}$, and in the $1d$ shell for ${}_{}{}^2{}_{}{}^{}D$ states for ${\mathrm{Ne}}^{21}$, ${\mathrm{Na}}^{23}$, ${\mathrm{Cl}}^{37}$, and ${\mathrm{K}}^{39}$ were -0.04, -0.01, 0.1, 0.05, 0.1, -0.4, -0.1, 0.4, and 0.4 nuclear Bohr magnetons, respectively. For $j-j$ coupling, the values found for ${\mathrm{B}}^{11}{\left(p_{\frac{3}{2}}\right)}^{-1\mathrm{}}$, ${\mathrm{C}}^{13}\left(p_{\frac{1}{2}}\right)$, and ${\mathrm{N}}^{15}\left(p_{\frac{1}{2}}\right)$ were 0.2, -0.09, and 0.1, respectively. The signs and ratios of these values are such as to lead to the conclusion that the simple models used here cannot be brought into agreement with the data by the addition of space exchange contributions alone. The magnitudes are nevertheless reasonably large in some cases, and indicate that they must be included in any consistent theory of nuclear magnetic moments.