Nuclear Susceptibility of Solid Helium-3

CRITIQUE OF RECENT THEORIES AND MONTE CARLO CALCULATION OF EXCHANGE IN SOLID $sup 3$He.

“…The exchange energy of a pair is about three orders of magnitude larger than that or the nuclear spin magnetic dipole-dipole 1-2 interaction, though about three orders of magnitude [7][8][9][10][11][12][13][14][15][16][17] smaller than the energy per particle.…”

“…Indeed, only the |& I for P = e occur in IL, so that it describes a fictitious system in which a given atom always remains mainly localized about the same lattice site. We identify H~ as the exchange Hamiltonian, and note that it contains an exchange operator having matrix elements [1][2][3][4][5][6][7][8][9][10][11][12][13] between the presumably phonon-like states of the lattice…”

The heat capacity of solid He3

“…The temperature dependence of the relaxation times is roughly T ^ (25), so that with falling temperature the times soon become pro hibitively long for performing experiments. Moreover, there are indications (21,25) that these equilibrium times are substantially increased at low temperatures by the presence of He^ impurities,…”

“…The value of J in principle can be determined by nuclear magnetic resonance techniques (NMR) as well as specific heat measurements. Recent NMR work (21)(22)(23)(24)(25)(26) indicates that for densities near the melting line, Curie's law is obeyed down to temperatures as low as 0.04°K and that j/k is of the order of a few millidegrees or less. Very recently, Richards e^ a^.…”

“…(25) have determined j/k to be a decreasing function of the density, starting with a value of about 7x10 near the melting line (bcc phase), and falling to as low as 10 for the low pressure hep phase. All of these measurements (21)(22)(23)(24)(25)(26) are complicated by the fact that the thermal equilibrium times between 3 the spin system and the lattice in solid He can become extremely long at low temperatures. These relaxation times are of the order of 15 minutes at 0,5°K for the hep phase, and somewhat smaller for the bcc phase.…”