The phonon spectrum of bcc 3 He has been calculated including the leading anharmonic corrections to the self-consistent harmonic approximation. For small wave vectors an anomalous dispersion is found causing a maximum in ^(T) in agreement with experiments .Heat-capacity, 1 ' 2 strain-gauge, 3 and thermalconductivity 4 measurements indicate that B D 0O for 3 He increases for T ^ 0.5 K, goes through a maximum, and shows the usual decrease only for T >0 o 5 K. Varma 5 suggested that this anomaly might be the result of a T ~2 contribution to C v caused by a phonon-induced four-spin interaction. In Ref. 3, however, any such contribution was subtracted but the anomaly persisted, indicating that it might be due to the lattice only. 6 We have calculated the phonon spectrum of bcc 3 He, including the leading correction 7 to the selfconsistent harmonic approximation. 8 This term is almost identical to the expression, quadratic in the third-order coupling parameters, known from standard anharmonic perturbation theory. Only the third-order coupling parameters are replaced by the third derivatives of the averaged potential,
(ViR 1 )) = (Idetr^/Ti 3 )^2 Jd 3 rV(r)xexp[-S«a^aa , (^«-^a < )(ra-/2B < )], (D where the tensor r % is the inverse of the static displacement correlation function. Since Eq. (1) diverges for a Lennard-Jones interaction we have replaced V(r) by a Brueckner scattering matrix. 9 This procedure is debatable since certain correlations are counted twice, but it should be reliable enough for the present -40