Absorptive Separable Potentials Constructed from <span class="aps-inline-formula"><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>π</mi><mi>N</mi></math></span> Data

Rubin H. Landau; Frank Tabakin

doi:10.1103/PhysRevD.5.2746

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Absorptive Separable Potentials Constructed from $π N$ Data

Rubin H. Landau and Frank Tabakin

Physics Department, University of Pittsburgh, Pittsburgh, Pennsylvania 15213

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Phys. Rev. D 5, 2746 – Published 1 June, 1972

DOI: https://doi.org/10.1103/PhysRevD.5.2746

Abstract

A simple method for constructing an absorptive (complex) separable potential directly from the $π N$ phase shifts and absorption parameters is presented. This permits the transition matrix to be calculated both on and off the energy shell as required in the calculation of the $π$ -nucleus optical potential. The solution of the inverse scattering problem presented here is an extension of a previous solution to include absorption, when the phase shifts are complex, and relativistic kinematics. The potentials for all $S$ - and $P$ -wave $π N$ eigenchannels are constructed and displayed. The construction of a complex separable potential is also applicable to other systems such as $NN$ , $Λ N$ , and $KN$ .

References (16)

D. S. Koltun, Advan. Nucl. Phys. 3, 71 (1969)
L. A. Charlton and J. M. Eisenberg, Ann. Phys. (N.Y.) 63, 286 (1971)
M. M. Sternheim and E. H. Auerbach, Phys. Rev. Letters 25, 1550 (1970) H. K. Lee and H. McManus, Nucl. Phys. A167, 257 (1971) R. Seki, Phys. Rev. C 3, 454 (1971) R. H. Landau, Phys. Rev. D 3, 81 (1971) M. Krell and S. Barmo, Nucl. Phys. B20, 461 (1970) C. Schmit, Lett. Nuovo Cimento 1, 454 (1970)
F. Tabakin, Phys. Rev. 177, 1443 (1969)
R. L. Mills and J. F. Reading, J. Math. Phys. 10, 321 (1969) M. Bolsterli and J. MacKenzie, Physics 2, 141 (1965) H. Fiedeldey, Nucl. Phys. A135, 353 (1969)
M. Bawin, Nucl. Phys. B28, 109 (1971)
J. Boguta and H. W. Wyld, Jr., Phys. Rev. 164, 1996 (1967) ibid.179, 1330 (1969)
M. Goldberger and K. Watson, Collision Theory (Wiley, New York, 1964), p. 231
([6])
D. H. Herndon, A. Barbaro-Galtieri, and A. H. Rosenfeld, LRL Report No. UCRL-20030πN, 1970 (unpublished)
W. Rarita, R. J. Riddell, Jr., C. B. Chiu, and R. J. N. Phillips, Phys. Rev. 165, 1615 (1968)
S. S. Schweber, An Introduction to Relativistic Quantum Field Theory (Harper and Row, New York, 1962), p. 372
W. M. Layson, Nuovo Cimento 20, 1207 (1961)
R. H. Landau, S. Phatak, and F. Tabakin (unpublished)
J. P. Dedonder, Nucl. Phys. A174, 251 (1971) T. E. O. Ericson and J. Hüfner, Phys. Letters 33B, 601 (1970) R. H. Landau, Nucl. Phys. B35, 390 (1971)
L. L. Foldy and J. D. Walecka, Ann. Phys. (N.Y.) 54, 447 (1969)

[c1] D. S. Koltun, Advan. Nucl. Phys. 3, 71 (1969)

[c2] L. A. Charlton and J. M. Eisenberg, Ann. Phys. (N.Y.) 63, 286 (1971)

[c3] M. M. Sternheim and E. H. Auerbach, Phys. Rev. Letters 25, 1550 (1970) H. K. Lee and H. McManus, Nucl. Phys. A167, 257 (1971) R. Seki, Phys. Rev. C 3, 454 (1971) R. H. Landau, Phys. Rev. D 3, 81 (1971) M. Krell and S. Barmo, Nucl. Phys. B20, 461 (1970) C. Schmit, Lett. Nuovo Cimento 1, 454 (1970)

[c4] F. Tabakin, Phys. Rev. 177, 1443 (1969)

[c5] R. L. Mills and J. F. Reading, J. Math. Phys. 10, 321 (1969) M. Bolsterli and J. MacKenzie, Physics 2, 141 (1965) H. Fiedeldey, Nucl. Phys. A135, 353 (1969)

[c6] M. Bawin, Nucl. Phys. B28, 109 (1971)

[c7] J. Boguta and H. W. Wyld, Jr., Phys. Rev. 164, 1996 (1967) ibid.179, 1330 (1969)

[c8] M. Goldberger and K. Watson, Collision Theory (Wiley, New York, 1964), p. 231

[c9] ([6])

[c10] D. H. Herndon, A. Barbaro-Galtieri, and A. H. Rosenfeld, LRL Report No. UCRL-20030πN, 1970 (unpublished)

[c11] W. Rarita, R. J. Riddell, Jr., C. B. Chiu, and R. J. N. Phillips, Phys. Rev. 165, 1615 (1968)

[c12] S. S. Schweber, An Introduction to Relativistic Quantum Field Theory (Harper and Row, New York, 1962), p. 372

[c13] W. M. Layson, Nuovo Cimento 20, 1207 (1961)

[c14] R. H. Landau, S. Phatak, and F. Tabakin (unpublished)

[c15] J. P. Dedonder, Nucl. Phys. A174, 251 (1971) T. E. O. Ericson and J. Hüfner, Phys. Letters 33B, 601 (1970) R. H. Landau, Nucl. Phys. B35, 390 (1971)

[c16] L. L. Foldy and J. D. Walecka, Ann. Phys. (N.Y.) 54, 447 (1969)

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Absorptive Separable Potentials Constructed from $π N$ Data

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Absorptive Separable Potentials Constructed from πN Data

Abstract

References (16)

Absorptive Separable Potentials Constructed from $π N$ Data