| Three generalized energy weighted sum rules applicable in the long wavelength limit are derived using the double commutator approach. These are an ML sum rule for L (GREATERTHEQ) 2 isovector spin-flip transitions, an EL sum rule for L (GREATERTHEQ) 1 isovector current and spin-flip transitions, and a generalized isospin dependent sum rule which separates isospin components of nuclear electric and magnetic transitions.; These sum rules are validated by demonstrating their reduction to previously known specialized sum rules. The ML sum rule is shown to reduce to equivalence with the results of the Goldhaber-Teller model. The EL sum rule is shown to reduce to an E2 sum rule derived by Uberall(' )et al., while the isospin sum rule is specialized to Kurath's M1 sum rule for self-conjugate nuclei. These sum rules are compared to experimental data for appropriate E1 through M8 transitions in ('7)Li, ('9)Be, ('11)B, ('12)C, ('13)C, ('16)O, ('24)Mg, and ('58)Ni.; In addition, extension of the ML and EL sum rules to the generalized Helm model is shown to provide a sensitive tool for exploration of nuclear surface structure for high multipolarity transitions where the sum rule depends on high order moments of the nuclear charge-matter distribution. As specialized to the M1 transition, the generalized isospin sum rule improves over estimates of isospin separation resulting from modifications of Kurath's sum rule with isospin Clebsch-Gordon coefficients. |
