Dynamic Structure Function in 3he-4he Mixtures

TL;DR

This paper investigates the dynamic structure function of helium-3 and helium-4 mixtures at zero temperature, analyzing contributions from different excitations and the role of cross terms across various momentum ranges.

Contribution

It provides a detailed analysis of the dynamic structure function in helium mixtures, incorporating sum rules to constrain contributions and exploring the role of cross terms.

Findings

Sum rules constrain the contributions to $S(q,)$.

Analysis of low-$q$ excitations includes phonon-roton and 1p-1h excitations.

High-$q$ range analysis relates to deep inelastic scattering.

Abstract

Relevant features of the dynamic structure function $S(q,\omega)$ in $^3$He-$^4$He mixtures at zero temperature are investigated starting from known properties of the ground state. Sum rules are used to fix rigorous constraints to the different contributions to $S(q,\omega)$, coming from $^3$He and $^4$He elementary excitations, as well as to explore the role of the cross term $S^{(3,4)}(q,\omega)$. Both the low-$q$ (phonon-roton $^4$He excitations and 1p-1h $^3$He excitations) and high-$q$ (deep inelastic scattering) ranges are discussed.