Direct Numerical Solution of the Three-Body Problem

S. Rosati; M. Barbi

doi:10.1103/PhysRev.147.730

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Direct Numerical Solution of the Three-Body Problem

S. Rosati

M. Barbi

Istituto di Fisica dell' Università, Pisa, Italy
Istituto Nazionale di Fisica Nucleare, Sezione di Pisa, Pisa, Italy

Istituto di Fisica dell' Università, Pisa, Italy

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Phys. Rev. 147, 730 – Published 22 July, 1966

DOI: https://doi.org/10.1103/PhysRev.147.730

Abstract

We discuss a numerical method to determine the binding energy and the wave function for a three-body system. Radial wave functions of the form $g_{1} (r_{1}) g_{2} (r_{2}) g_{3} (r_{3})$ are used, $r_{1}$ , $r_{2}$ , and $r_{3}$ being the interparticle distances. The method is applied to ${He}^{3}$ and $H^{3}$ with central forces and hard core to show the accuracy and the speed of the calculation.

References (11)

N. Austern and P. Iano, Nucl. Phys. 18, 672 (1960)
P. H. Wackman and N. Austern, Nucl. Phys. 30, 529 (1962) E. W. Schmid. Y. C. Tang, and R. C. Herndon, Nuovo Cimento 33, 259 (1964)
Y. C. Tang, R. C. Herndon, and E. W. Schmid, Nucl. Phys. 65, 203 (1965) Phys. Rev. 134, B743 (1964)
G. A. Baker, Jr., J. L. Gamel, B. J. Hill, and J. G. Wills, Phys. Rev. 125, 1754 (1962)
M. H. Kalos, Phys. Rev. 128, 1791 (1962)
A. R. Bodmer and S. Ali, Nucl. Phys. 56, 657 (1964)
J. W. Murphy and S. Rosati, Nucl. Phys. 63, 625 (1965)
L. Lovitch and S. Rosati, Nucl. Phys. 73, 648 (1965) S. Ali, J. W. Murphy, and A. R. Bodmer, Phys. Rev. Letters 15, 534 (1965)
Omitted endnote
W. Rarita and R. D. Present, Phys. Rev. 51, 788 (1937)
Handbook of Mathematical Functions, edited by M. Abramowitz and I. A. Stegun (U. S. Department of Commerce, National Bureau of Standards, Washington, D. C., 1965), Appl. Math. Ser

[c1] N. Austern and P. Iano, Nucl. Phys. 18, 672 (1960)

[c2] P. H. Wackman and N. Austern, Nucl. Phys. 30, 529 (1962) E. W. Schmid. Y. C. Tang, and R. C. Herndon, Nuovo Cimento 33, 259 (1964)

[c3] Y. C. Tang, R. C. Herndon, and E. W. Schmid, Nucl. Phys. 65, 203 (1965) Phys. Rev. 134, B743 (1964)

[c4] G. A. Baker, Jr., J. L. Gamel, B. J. Hill, and J. G. Wills, Phys. Rev. 125, 1754 (1962)

[c5] M. H. Kalos, Phys. Rev. 128, 1791 (1962)

[c6] A. R. Bodmer and S. Ali, Nucl. Phys. 56, 657 (1964)

[c7] J. W. Murphy and S. Rosati, Nucl. Phys. 63, 625 (1965)

[c8] L. Lovitch and S. Rosati, Nucl. Phys. 73, 648 (1965) S. Ali, J. W. Murphy, and A. R. Bodmer, Phys. Rev. Letters 15, 534 (1965)

[c9] Omitted endnote

[c10] W. Rarita and R. D. Present, Phys. Rev. 51, 788 (1937)

[c11] Handbook of Mathematical Functions, edited by M. Abramowitz and I. A. Stegun (U. S. Department of Commerce, National Bureau of Standards, Washington, D. C., 1965), Appl. Math. Ser

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Direct Numerical Solution of the Three-Body Problem

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References (11)

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