High-temperature series expansions to fourth order with a multiple-exchange Hamiltonian for both bcc and hcp phases of solidHe3

The high-temperature series expansions with a multiple-exchange Hamiltonian including the most important two, three, and four-particle exchange processes for the bcc and hcp phases of solid ${}_{}{}^3{}_{}{}^{}\mathrm{He}$ are calculated up to fourth order in β=1/$k_B$T, with arbitrary magnetic field. The series for the susceptibility are derived and compared to the experimental results. For bcc ${}_{}{}^3{}_{}{}^{}\mathrm{He}$ an excellent agreement is obtained with the third- and fourth-order Padé approximants, using the phenomenological parameters formerly published. For hcp ${}_{}{}^3{}_{}{}^{}\mathrm{He}$, we show that the Curie-Weiss temperature Θ has been underestimated for the largest molar volumes and propose more accurate fits in better agreement with earlier nuclear-magnetic-resonance estimates.