Relation between (e, e′) sum rules in ^{6, 7}Li and ⁴He nuclei: Experiment and cluster model

Abstract.

The sums over (e, e′) spectra of ⁶Li and ⁷Li nuclei which correspond to the longitudinal sum rule are studied. It is suggested that due to the cluster structure of the lithium isotopes these sums may approximately be expressed in terms of such a sum pertaining to the $\alpha$-particle. Calculation of these sums is performed in the framework of cluster models with antisymmetrization done with respect to all the nucleons. At momentum transfers higher than 0.8 fm^-1 the relations expressing the A = 6 or 7 sum in terms of the A = 4 sum prove to be valid with rather high accuracy. In the region of momentum transfers around 1 fm^-1 the longitudinal correlation functions of ⁶Li and ⁷Li nuclei are found to be close to that of the $\alpha$-particle. Basing on this, the difference between the q values at which the high-q limit of the inelastic sum rule is reached in the ^{6, 7}Li cases and the ⁴He case is explained. The experimental longitudinal sums in the range between 0.450 and 1.625 fm^-1 are employed to perform comparison with the theoretical sum rule calculated in the framework of cluster models. Out of the experimental sums, those in the range between 0.750 and 1.000 fm^-1 in the ⁶Li case and between 0.750 and 1.125 fm^-1 in the ⁷Li case are obtained in the present work. In the ⁶ Li case a complete agreement between experiment and the calculated sum rule is found while in the ⁷Li case an agreement only at a qualitative level is observed.