Atomic kinetic energies in bcc 3He.

Helium atoms interact via a pair potential having a steeply repulsive core. ' Since atoms in quantum crystals are not highly localized, two atoms can approach closely enough to be strongly repelled from each other by the repulsive core. This strong repulsion introduces highenergy components into the dynamics and high-energy tails into the dynamical response functions. ~ In a previous Letter, 3 we showed that these high-frequency tails, for example in the one-phonon response function A(q, k;to), contribute significantly to the kinetic energy, Ek, of atoms in solid He. For example, in a harmonic approximation such as the self-consistent harmonic (SCH) approximation, the A(q, &;to) is a b function at the SCH frequency taqz. Thus the SCH A(q, k:,ta) does not have high-frequency tails. Similarly, in an empirical Debye model the density of phonon states is cut off at to taD, where taD is the Debye frequency. Tails are introduced into A(q, k;to) when cubic and higher-order anharmonic terms are included in the dynamics. 2 For solid "He we showed these tails double the Ek beyond that predicted by an empirical Debye model using the observed Debye temperature eD htaD/k and bring Ek close to the observed value. Thus the large Ek observed in solid He may be regarded as a direct manifestation of the highly anharmonic nature of solid helium. Sokol, Skold, Price, and Kleb and Carlson et al. have come to similar conclusions in liquid He. They show that the high-momentum (high-energy) components in the momentum distribution n(p) contribute significantly to the kinetic energy of atoms in liquid He. Indeed, the tail of n(p) for momentum values p~ 2pF, where pF is the Fermi momentum, contributes s approximately one-half of Ek. The existence of high-frequency tails in the dynamic structure factor S(g, to) of liquid helium and the relation of these tails to the repulsive core of the potential has been discussed by several authors. In this note we evaluate Ek in bcc He at T 0 K and four volumes using the self-consistent phonon (SCP) theory. The calculations show that high-energy tails are again most important and that including them leads to Ek values close to those obtained using Monte Carlo (MC) methods. The Et, values obtained using T-matrix shortrange correlation functions2 3 are significantly higher than those obtained using the Nosanow-Jastrow short-range correlation function. '0 Measurement of Ek could be used to distinguish between these two functions.