Short- and Long-Range Charge Independence

Abstract

The difference between the proton-proton ($p-p$) and neutron-proton ($n-p$) ${}_{}{}^1{}_{}{}^{}S_0^{}{}_{}{}^{}$ interactions attributable to effects of other than electromagnetic origin is discussed in connection with evidence concerning long-range charge independence. The latter evidence is based on the adjustment of the amplitude of the one-pion-exchange (OPE) group of phase parameters to secure best agreement with $p-p$ and $n-p$ scattering data. It is concerned mainly with distant collisions and long-range effects. The ${}_{}{}^1{}_{}{}^{}S_0^{}{}_{}{}^{}$ phase shift is appreciably influenced by short-range interactions. Although the pion-mass difference is only $\approx 3.3\%$, an appreciably larger fractional difference of effective $p-p$ and $n-p$ ranges, ${\left({}_{}{}^1{}_{}{}^{}r_0^{}{}_{}{}^{}\right)}_{\mathrm{pp}}-{\left({}_{}{}^1{}_{}{}^{}r_0^{}{}_{}{}^{}\right)}_{\mathrm{np}}$, is shown to be conceivable. In particular, the approximately 10% effect on ${}_{}{}^1{}_{}{}^{}r_0^{}{}_{}{}^{}$ obtained by Noyes in his effective-range-type analysis, employing a literal acceptance of the published low-energy $n-p$ data, is not out of the question. The argument used for these conclusions is only semiquantitative. It differs from other earlier treatments in that the reconciliation of short-range charge dependence with long-range charge independence is not made to depend on the adjustment of the shape of the energy curve of the $N-N$ potential versus distance at a distance comparable to the core radius, such as results from an adjustable cutoff radius for the OPE interaction. The adjustments in the shape of the potential-energy curve are those needed to reproduce the phenomenological phase-parameter fits to $p-p$ scattering data, with some direct guidance from the data. The semiquantitative procedure applied to a hard-core potential of the Hamada-Johnston type then yields a fair, though not an exact, reproduction of the phenomenological requirements on the ${}_{}{}^1{}_{}{}^{}S_0^{}{}_{}{}^{}-(n-p)$ phase shift in the 0-350 MeV incident laboratory energy range. Although the hard-core-potential work makes a 10% difference in the effective ranges conceivable, it favors a smaller effect, such as ${\left({}_{}{}^1{}_{}{}^{}r_0^{}{}_{}{}^{}\right)}_{\mathrm{np}}=2.7\mathrm{}$ F. The same procedure, when applied to a soft-core potential somewhat similar to that of Reid, does not give nearly as satisfactory a reproduction of $n-p$ data. It appears possible, though far from certain, that the soft-core potential does not give as satisfactory results because it does not include sufficiently the effect of the smeared out $\delta$ function of the OPE potential. The procedure used hybridizes the viewpoints of the $S$ matrix and...