Magnetic Susceptibility Measurements in Very Dilute Solid Solutions ofHe4inHe3

Abstract

Measurements of the magnetic susceptibility of very dilute solid solutions of He 4 in He 3 as a function both of molar volume and of He 4 concentration in the a phase have been made between 1 and 0.04°K by steady-state nuclear-resonance techniques. The most dilute solution (5xio~7 He 4 ) followed Curie's law over the range in molar volume (23.0-21.0 cc) measured. The less dilute solutions (lxlO" 4 and 3xl0~4 He 4 ) followed a Curie-Weiss law with relatively large, antiferromagnetic Weiss constants.

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

“…." [11][12][13][14][15][16][17][18][19][20][21][22] Part of the page is not clearly legible. In the second line from the bottom, we have "... B = A/8^ page 2 of Add to ref.…”

“…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…”

“…In sum, Herring wants to find a set of localized [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17] functions which span the manifold or the \^\ « He uses a closely related fictitious system in which there is no exchange, the infinitely separated system, as a tool which suggests how the -f^0*} may be combined to yield these localized functions, the home-base functions.…”

“…The N! p points p in configuration space correspond to all possible ways of placing the N atoms on the N lattice [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18] sites, one to a site. It is now possible to divide all of configuration space into Ni sections $r> such that every point in a given o is closer to a particular P one of the p than to any of the others.…”