Abstract
A generalised second-quantised notation is used to re-derive Clement's single-particle sum rules, including centre-of-mass corrections. The effect of the repulsive core of the N-N potential on the sum rules is investigated. The corrections produced by the potential core are found to remove ~5% of the sum rule strength to unobservable high-energy states. The second-quantised notation is then used to derive sum rules for two-particle spectroscopic amplitudes. These generalise the result of Bayman and Clement to cover stripping and pickup or nuclei of any spin. Sum rules are derived which relate sums of spectroscopic amplitudes to two-nucleon multipole moments. Predictions are made about these sum rules for transfer of the even type of nucleon in an odd-mass nucleus. The assumptions which have to be made if sum rules are to be applied to two-nucleon transfer data are discussed. Two of these assumptions are unlikely to be valid: the absence of configuration mixing outside a single major shell and the neglect of sequential transfer. However, it is shown that it should still be possible to apply the sum rules without these two assumptions. An exact finite-range DWBA analysis of two-nucleon transfer, with a realistic triton wavefunction, is used in the sum rule analysis of two-neutron transfer on even zirconium isotopes. The fit to the sum rules is not very good and possible reasons for this are discussed. The multipole-moment sum rules are applied to data on various odd-mass nuclei. The results are in good agreement with predictions. The implications for future applications of sum rules to two-nucleon transfer are discussed.