Final State Effects in the high q response of ³He-⁴He mixtures

A modified Gersch-Rodriguez formalism describing the leading Final State Effects in the high momentum transfer response of low concentration $^3$He-$^4$He mixtures is presented and discussed. The leading corrections to the Impulse Approximation are expressed in terms of the interatomic potentials and the semidiagonal two-body density matrices of both the mixture and its boson-boson approximation, in which the $^3$He atoms are replaced by bosons of the same mass and at the same partial density. Numerical calculations of the Final State Effects functions of $^3$He and $^4$He are finally presented and discussed.