Multipair excitations in liquid ${}_{}{}^3{}_{}{}^{}\mathrm{He}$ at low temperature are investigated using a sum-rule approach. The ${\mathit{m}}_3$=FS(q,ω)${\mathrm{\omega }}^3$ dω sum rule is calculated microscopically by properly accounting for short-range correlations. The average spin multipair (mp) energy ${\mathrm{\omega }}_{31}^{\mathit{i}}$[${\mathit{m}}_3^{\mathit{i}}$(mp)/${\mathit{m}}_1^{\mathit{i}}$(mp)${]}^{1/2}$ is found to be ∼50 K in the low-q limit. A rigorous lower bound for the multipair contribution to the static form factor in the low-q limit is derived. The relative importance of coherent and spin-dependent multipair excitations is also discussed.

• Received 11 April 1988

DOI:https://doi.org/10.1103/PhysRevLett.63.532