Effects of the n-n potential core on the spectroscopic sum rules for one-nucleon transfer

Previously derived sum rules are shown to have corrections if the potential contains a hard core. The corrections represent a total loss of single-particle strength which also occurs from the low-energy observable region in the soft-core case. Estimates give a reduction of at least 5 % in the total sum rules, but negligible additional spin-dependent corrections to the partial or spin-dependent sum rules. Important consequences of this lack of spin dependence are pointed out for existing and future sum-rule analyses of spectroscopic data.