Abstract
The problem of exchange energy in solid3He is investigated, and the exchange integral for bcc3He is calculated. Results are obtained from reaction-matrix elements calculated by means of a modified Brueckner theory developed earlier, and the calculations are repeated for several values of the molar volume and the parameter α2 defining the unperturbed wave functions. The final results indicate an antiferromagnetic and strongly density-dependent exchange integral with the absolute value decreasing rapidly with increasing density or decreasing molar volume. The calculations are made for two different two-body potentials, an Yntema-Schneider potential given by Brueckner and Gammel, and a Frost-Musulin potential given by Bruch and McGee. Theoretical results for the exchange integral are approximately −0.13 to −0.16 mK at a molar volume of 22 cm3/mole, and −0.44 to −0.57 mK at a molar volume of 24 cm3/mole. The corresponding experimental results are approximately −0.135 and −0.655 mK, respectively, i.e., the difference is generally within a factor of 1.5. The agreement with experimental results is reasonably good since the theoretical value is given by a small difference between several large terms of opposite sign almost canceling each other, and the results are also very sensitive to the choice of the parameter value α2 for each molar volume.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
N. Bernardes and H. Primakoff,Phys. Rev. Letters 2, 290 (1959);3, 144 (1959);Phys. Rev. 119, 968 (1960).
E. M. Saunders,Phys. Rev. 126, 1724 (1962).
S. R. Hartmann,Phys. Rev. 133, A17 (1964).
L. H. Nosanow,Phys. Rev. Letters 13, 270 (1964).
L. H. Nosanow and W. J. Mullin,Phys. Rev. Letters 14, 133 (1965).
R. L. Garwin and A. Landesman,Physics 2, 107 (1965).
D. J. Thouless,Proc. Phys. Soc. (London)86, 893 (1965).
J. H. Hetherington, W. J. Mullin, and L. H. Nosanow,Phys. Rev. 154, 175 (1967).
W. J. Mullin,Phys. Rev. 166, 142 (1968).
L. H. Nosanow and C. M. Varma,Phys. Rev. Letters 20, 912 (1968);Phys. Rev. 187, 660 (1969).
H. R. Glyde,Phys. Rev. 177, 262 (1969);A1, 296 (1970).
W. J. Mullin, L. H. Nosanow, and P. M. Steinback,Phys. Rev. 188, 410 (1969).
R. A. Guyer and L. I. Zane,Phys. Rev. 188, 445 (1969);Phys. Rev. Letters 24, 660, 1325 (1970).
C. M. Varma and L. H. Nosanow,Phys. Rev. A1, 133 (1970).
C. Ebner and C. C. Sung,Phys. Rev. A4, 1099 (1971).
B. H. Brandow,Phys. Rev. A4, 422 (1971);Ann. Phys., to be published.
D. O. Edwards, A. S. McWilliams, and J. G. Daunt,Phys. Letters 1, 218 (1962).
R. L. Garwin and H. A. Reich,Phys. Rev. Letters 12, 354 (1964).
A. L. Thomson, H. Meyer, and P. N. Dheer,Phys. Rev. 132, 1455 (1963).
H. D. Cohen, P. B. Pipes, K. L. Verosub, and W. M. Fairbank,Phys. Rev. Letters 21, 677 (1968).
P. B. Pipes and W. M. Fairbank,Phys. Rev. Letters 23, 520 (1969).
W. P. Kirk, E. Osgood, and M. Garber,Phys. Rev. Letters 23, 833 (1969).
J. R. Sites, D. D. Osheroff, R. C. Richardson, and D. M. Lee,Phys. Rev. Letters 23, 836 (1969).
R. T. Johnson and J. C. Wheatley,Phys. Rev. A1, 1836 (1970).
M. F. Panczyk, R. A. Scribner, G. C. Straty, and E. D. Adams,Phys. Rev. Letters 19, 1102 (1967).
R. T. Johnson, R. Rosenbaum, O. G. Symko, and J. C. Wheatley,Phys. Rev. Letters 22, 449 (1969).
M. F. Panczyk and E. D. Adams,Phys. Rev. 187, 321 (1969);A1, 1356 (1970).
H. A. Reich,Phys. Rev. 129, 630 (1963).
R. L. Garwin and A. Landesman,Phys. Rev. 133, A1503 (1964).
B. T. Beal, R. P. Giffard, J. Hatton, M. G. Richards, and P. M. Richards,Phys. Rev. Letters 12, 393 (1964).
R. C. Richardson, E. Hunt, and H. Meyer,Phys. Rev. 138, A1326 (1965).
M. G. Richards, J. Hatton, and R. P. Giffard,Phys. Rev. 139, A91 (1965).
R. P. Giffard and J. Hatton,Phys. Rev. Letters 18, 1106 (1967).
E. R. Hunt, R. C. Richardson, J. R. Thompson, R. A. Guyer, and H. Meyer,Phys. Rev. 163, 181 (1967).
J. R. Thompson, E. R. Hunt, and H. Meyer,Phys. Letters 25A, 313 (1967).
H. Meyer,J. Appl. Phys. 39, 390 (1968).
M. Bernier and A. Landesman,Solid State Commun. 7, 529 (1969).
W. N. Yu and H. A. Reich,Solid State Commun. 7, 1521 (1969).
M. Bernier,J. Low Temp. Phys. 3, 29 (1970).
E. Østgaard,J. Low Temp. Phys. 5, 237 (1971).
K. A. Brueckner and J. L. Gammel,Phys. Rev. 109, 1040 (1958).
L. M. Bruch and I. J. McGee,J. Chem. Phys. 46, 2959 (1967);52, 5884 (1970).
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Østgaard, E. Solid helium. II. Exchange energy in solid3He. J Low Temp Phys 7, 471–489 (1972). https://doi.org/10.1007/BF00628258
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF00628258