Deuteron Magnetic Moment and Momentum Dependence of Two-Nucleon Potential

The correction to the deuteron magnetic moment [${\mu }_d$] is calculated, in the manner pointed out by Feshbach, for the potential derived recently by Sugawara and Okubo from pion field theory. This potential includes, besides an L·S potential, a quadratic term, $-V_2\left(\mathrm{r}\right)\left(\frac{p^2}{2{\kappa }^2}\right)+\mathrm{H}.\mathrm{c}.\mathrm{}$ [$V_2\left(\mathrm{r}\right)$ being the second-order static potential, $p$ and $\kappa$ the nucleon (relative) momentum and rest mass, respectively]. It is shown in particular that this new term gives a positive correction to ${\mu }_d$. Numerical magnitudes are estimated using phenomenological deuteron wave functions fitted to all known deuteron data, the hard-core radius [$r_C$] and the $D$-state probability [$P_D$] being adjustable parameters. Results are shown graphically as functions of $P_D$ for two values of $r_C$. It is seen that the corrections depend sensitively on these two parameters. If there were no other appreciable corrections to ${\mu }_d$ than those discussed here, $ps-ps$ theory would lead to 6% for $P_D$, while ${\mu }_d$ would not be fitted in the $ps-pv$ case as well as for the Gammel-Thaler potential, since the correction due to the quadratic term is not large enough to cancel the correction due to the L·S potential.