PERTURBATION EXPANSIONS OF THE RESPONSE FUNCTION AND THE ASYMPTOTIC REGIME

Perturbation expansions of the response function S(q, omega) of a many-body system in orders of any chosen component of the Hamiltonian are obtained. The response S(q, omega) describes the inclusive scattering of a projectile interacting weakly with a target, where q and omega are the momentum and energy transfer. Each term of a given order is written as an expectation value of products of paired Green's functions representing each initial- and final-state effects. For several choices of the perturbing operator, close expressions are obtained for the first orders of these expansions. The resulting terms represent partial summations over the Gersch series, whose relation to Green's-function expansions is established. Also, they are finite for singular potentials and are useful in the asymptotic regime of large q. In this regime they can give the dominant contribution to the response and initial- and final-state interactions of the hit particle and other particles in the system may be fully accounted for. Contributions of the n-particle density matrix can be separated for some expansions. In particular, an expression for the complete two-body contribution involving the hit particle is given.