Numerical Calculation of the Ground-State Properties of Nuclear Matter Using the <span class="aps-inline-formula"><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><msub><mrow><mi>Λ</mi></mrow><mrow><mn>10</mn></mrow></msub></mrow></math></span> Approximation

Theodore C. Foster

doi:10.1103/PhysRev.149.784

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Numerical Calculation of the Ground-State Properties of Nuclear Matter Using the $Λ_{10}$ Approximation

Theodore C. Foster^*

University of Washington, Seattle, Washington

^*Present address: Department of Physics, University of California, San Diego, La Jolla, California.

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Phys. Rev. 149, 784 – Published 23 September, 1966

DOI: https://doi.org/10.1103/PhysRev.149.784

Abstract

This paper investigates numerically for the case of nuclear matter the consequences of one particular method of terminating the infinite chain of coupled Green's-function equations. Of special interest is a comparison of this $Λ_{10}$ theory with the $Λ_{00}$ theory investigated previously. These two approximate theories rely on solution of a $T$ -matrix equation and they differ in the selection of the propagator for intermediate states. Using separable, nonlocal potentials the $T$ -matrix equations are solved and the bulk properties of the system obtained. Results are presented for the energy and number densities, the effective mass, the nuclear compressibility, and the two-particle correlation function. It is found that the two theories give similar results, with $Λ_{10}$ predicting several MeV less binding than $Λ_{00}$ does.

References (16)

P. C. Martin and J. Schwinger, Phys. Rev. 115, 1342 (1959)
K. A. Brueckner and J. L. Gammel, Phys. Rev. 109, 1023 (1958)
R. D. Puff, Ann. Phys. (N. Y.) 13, 317 (1961)
D. S. Falk and L. Wilets, Phys. Rev. 124, 1887 (1961)
R. Puff, A. S. Reiner, and L. Wilets, preceding paper, Phys. Rev. 147, 778 (1966)
G. Baym and L. P. Kadanoff, Phys. Rev. 124, 287 (1961)
R. C. Kennedy, doctoral dissertation, University of Washington, 1964 (unpublished) R. C. Kennedy, L. Wilets, and E. M. Henley, Phys. Rev. 133, B1131 (1964)
M. H. MacGregor, M. J. Moravcsik, and H. P. Stapp, Ann. Rev. Nucl. Sci. 10, 291 (1960)
J. L. Gammel, R. S. Christian, and R. M. Thaler, Phys. Rev. 105, 311 (1957)
M. H. Hull, Jr., K. E. Lassila, H. M. Ruppel, F. A. McDonald, and G. Breit, Phys. Rev. 122, 1606 (1961)
J. C. Reynolds and R. D. Puff, Phys. Rev. 130, 1877 (1963)
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C. T. DeDominicis, Ph.D. thesis, University of Birmingham, 1957 (unpublished)

[c1] P. C. Martin and J. Schwinger, Phys. Rev. 115, 1342 (1959)

[c2] K. A. Brueckner and J. L. Gammel, Phys. Rev. 109, 1023 (1958)

[c3] R. D. Puff, Ann. Phys. (N. Y.) 13, 317 (1961)

[c4] D. S. Falk and L. Wilets, Phys. Rev. 124, 1887 (1961)

[c5] R. Puff, A. S. Reiner, and L. Wilets, preceding paper, Phys. Rev. 147, 778 (1966)

[c6] G. Baym and L. P. Kadanoff, Phys. Rev. 124, 287 (1961)

[c7] R. C. Kennedy, doctoral dissertation, University of Washington, 1964 (unpublished) R. C. Kennedy, L. Wilets, and E. M. Henley, Phys. Rev. 133, B1131 (1964)

[c8] M. H. MacGregor, M. J. Moravcsik, and H. P. Stapp, Ann. Rev. Nucl. Sci. 10, 291 (1960)

[c9] J. L. Gammel, R. S. Christian, and R. M. Thaler, Phys. Rev. 105, 311 (1957)

[c10] M. H. Hull, Jr., K. E. Lassila, H. M. Ruppel, F. A. McDonald, and G. Breit, Phys. Rev. 122, 1606 (1961)

[c11] J. C. Reynolds and R. D. Puff, Phys. Rev. 130, 1877 (1963)

[c12] K. A. Brueckner and K. S. Masterson, Jr., Phys. Rev. 128, 2267 (1962)

[c13] C. W. Wong, Nucl. Phys. 56, 213 (1964)

[c14] H. A. Bethe, Phys. Rev. 138, B804 (1965)

[c15] S. A. Moszkowski, Phys. Rev. 140, B283 (1965)

[c16] C. T. DeDominicis, Ph.D. thesis, University of Birmingham, 1957 (unpublished)

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Numerical Calculation of the Ground-State Properties of Nuclear Matter Using the $Λ_{10}$ Approximation

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Numerical Calculation of the Ground-State Properties of Nuclear Matter Using the Λ10 Approximation

Abstract

References (16)

Numerical Calculation of the Ground-State Properties of Nuclear Matter Using the $Λ_{10}$ Approximation