The Okamoto-Nolen-Schiffer anomaly without rho-omega mixing

Abstract

We examine the effect of isospin-violating meson-nucleon coupling constants and of $\pi$-$\eta$ mixing on the binding-energy differences of mirror nuclei in a model that possesses no contribution from $\rho$-$\omega$ mixing. The ${}^3$He-${}^3$H binding-energy difference is computed in a nonrelativistic approach using a realistic wave function. We find the ${}^3$He-${}^3$H binding-energy difference very sensitive to the short-distance behavior of the nucleon-nucleon potential. We conclude that for the typically hard Bonn form factors such models can not account for the observed binding-energy difference in the three-nucleon system. For the medium-mass region (A=15--41) the binding-energy differences of mirror nuclei are computed using a relativistic mean-field approximation to the Walecka model. We obtain large binding-energy differences---of the order of several hundred keV---arising from the pseudoscalar sector. Two effects are primarily responsible for this new finding: a) the inclusion of isospin breaking in the pion-nucleon coupling constant, and b) the in-medium enhancement of the small components of the bound-state wave functions. We look for off-shell ambiguities in these results and find them to be large.

19 LaTeX pages and 2 postscript figures. Revisions/additions: Manuscript now includes a treatment of the binding-energy difference in the three-nucleon system as well as a study of possible off-shell ambiguities in the binding-energy differences of (A=15-41) mirror nuclei

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