Final state effects on superfluid $^{\bf 4}$He in the deep inelastic regime

TL;DR

This paper investigates how final state effects influence the dynamic structure function of superfluid helium-4 at high momentum transfer, using the Gersch-Rodriguez formalism and comparing with experimental data.

Contribution

It applies the Gersch-Rodriguez formalism to superfluid helium-4, analyzing the impact of ground state quantities on final state effects and validating the approach against experimental results.

Findings

Predicted response sensitive to condensate fraction, best fit at n_0=0.082

Gersch-Rodriguez theory yields results comparable to recent FSE models

Sum rules of the FSE broadening function are derived and discussed

Abstract

A study of Final State Effects (FSE) on the dynamic structure function of superfluid $^4$He in the Gersch--Rodriguez formalism is presented. The main ingredients needed in the calculation are the momentum distribution and the semidiagonal two--body density matrix. The influence of these ground state quantities on the FSE is analyzed. A variational form of $\rho_2$ is used, even though simpler forms turn out to give accurate results if properly chosen. Comparison to the experimental response at high momentum transfer is performed. The predicted response is quite sensitive to slight variations on the value of the condensate fraction, the best agreement with experiment being obtained with $n_0=0.082$. Sum rules of the FSE broadening function are also derived and commented. Finally, it is shown that Gersch--Rodriguez theory produces results as accurate as those coming from other more recent FSE theories.