Impulse Approximation in Solid Helium

The incoherent dynamic form factor S/Q , to) is evaluated in solid helium for comparison with the impulse approximation (IA). The purpose is to determine the Q values for which the IA is valid for systems such as helium where the atoms interact via a potential having a steeply repulsive but not infinite hard core. For 3He, Si(Q, to) is evaluated from first principles, beginning with the pair potential. The density of states g (to) is evaluated using the self-consistent phonon theory and Si(Q, o~) is expressed in terms of g(to). For solid 4He reasonable models of g(to) using observed input parameters are used to evaluate Si(Q, to). In both cases Si(Q, to) is found to approach the impulse approximation SIA(Q, to) closely for wave vector transfers Q ~> 20 ~ -1. The difference between S~ and SIA, which is due to final state interactions of the scattering atom with the remainder of the atoms in the solid, is also predominantly antisymmetric in (to -ton), where toR is the recoil frequency. This suggests that the symmetrization procedure proposed by Sears to eliminate final state contributions should work well in solid helium.