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Unitary Pole Approximation and Binding Energy of the Trinucleon

T. Brady*, M. Fuda†, E. Harms‡, J. S. Levinger, and R. Stagat§

  • Rensselaer Polytechnic Institute, Department of Physics and Astronomy, Troy, New York 12181

  • *National Defense Education Act Fellow; present address: Linac Laboratory, University of Saskatchewan, Saskatoon, Sask., Canada.
  • †Present address: State University of New York at Buffalo. Part of this paper is based on part of S. Fuda's Ph.D. dissertation, Rensselaer Polytechnic Institute, 1967 (unpublished).
  • ‡National Science Foundation Trainee; present address: Fairfield University, Fairfield, Conn.
  • §National Science Foundation Trainee; present address: University of Florida, Gainesville. Part of this paper is based on part of R. Stagat's Ph.D. dissertation, Rensselaer Polytechnic Institute, 1968 (unpublished).
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Phys. Rev. 186, 1069 – Published 20 October, 1969

DOI: https://doi.org/10.1103/PhysRev.186.1069

Abstract

The unitary pole approximation (UPA) uses the two-body binding energy and wave function to determine the form factor for the UPA separable t matrix. We develop the UPA for Tabakin's 1965 spin-independent model potential for the trinucleon, and obtain a trinucleon energy within 0.2 MeV of his result. We then develop the UPA for Tabakin's 1964 spin-singlet potential, and for the Schrenk-Mitra singlet. We combine these with Yamaguchi shapes and also a modified Hulthén shape for the spin-triplet central and tensor potentials. These choices give trinucleon energies within 0.3 MeV of the experimental value, provided that we fit the deuteron with 4% D state. We further study the dependence of trinucleon energy on the percent D state in the range 0.78%≤PD≤7%. We also use Tabakin's recent rank-1 separable fit to singlet phase shifts. This separable potential gives a trinucleon energy 1.5 MeV higher than the singlet choices above because of its relatively weak attraction in off-shell t-matrix elements.

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References (39)

  1. B. S. Bhakar and A. N. Mitra, Phys. Rev. Letters 14, 143 (1965)
  2. V. F. Kharchenko, N. M. Petrov, and S. A. Storozhenko, Nucl. Phys. A106, 464 (1968)
  3. A. C. Phillips, Nucl. Phys. A107, 209 (1968)
  4. H. P. Noyes and H. Fiedeldey, in Three-Particle Scattering in Quantum Mechanics, edited by J. Gillespie and J. Nuttall (W. A. Benjamin, Inc., New York), pp. 195-294
  5. L. M. Delves and A. C. Phillips, Rev. Mod. Phys. 41, 497 (1969) L. M. Delves, [4], pp. 369-416
  6. A. N. Mitra, in Advances in Nuclear Physics, edited by M. Baranger and E. Vogt (Plenum Press, Inc., New York, 1969), Vol. 3
  7. Y. Yamaguchi and Y. Yamaguchi, Phys. Rev. 95, 1635 (1954)
  8. V. K. Gupta, B. S. Bhakar, and A. N. Mitra, Phys. Rev. 153, 1114 (1967)
  9. R. Aaron, R. D. Amado, and W. Yam, Phys. Rev. 140, B1291 (1965) R. D. Amado, [4], pp. 325-368
  10. Ian Duck, in Advances in Nuclear Physics, edited by M. Baranger and E. Vogt (Plenum Press, Inc., New York, 1968), Vol. 1, Chap. 5
  11. J. S. Levinger, A. H. Lu, and R. Stagat, Phys. Rev. 179, 926 (1969)
  12. S. Weinberg, Phys. Rev. 131, 440 (1963) M. Rotenberg, Ann. Phys. (N. Y.) 19, 262 (1962)
  13. M. G. Fuda, Phys. Rev. 174, 1134 (1968) ibid.178, 1682 (1969) ibid.186, 1078 (1969)
  14. J. S. Ball and D. Y. Wong, Phys. Rev. 169, 1362 (1968)
  15. A. G. Sitenko, V. F. Kharchenko, and N. M. Petrov, Phys. Letters 28B, 308 (1968) A. H. Lu and H. S. Levinger, Bull. Am. Phys. Soc. 14, 21 (1969) A. H. Lu, Ph.D. thesis, Rensselaer Polytechnic Institute, 1969 (unpublished)
  16. E. Harms, Bull. Am. Phys. Soc. 14, 493 (1969) Ph.D. thesis, Rensselaer Polytechnic Institute, 1969 (unpublished)
  17. R. A. Malfliet and J. A. Tjon, Nucl. Phys. A127, 161 (1969) R. V. Reid, Ann. Phys. (N. Y.) 50, 411 (1968)
  18. L. P. Kok, G. Erens, and R. Van Wageningen, Nucl. Phys. A122, 684 (1968)
  19. G. L. Schrenk and A. N. Mitra, Phys. Rev. Letters 19, 530 (1967)
  20. J. Dabrowski and M. Dworzecka, Phys. Letters 28B, 4 (1968)
  21. R. Stagat, Nucl. Phys. A125, 654 (1969)
  22. T. J. Brady, Bull. Am. Phys. Soc. 14, 512 (1969) Ph.D. thesis, Rensselear Polytechnic Institute, 1969 (unpublished)
  23. F. Tabakin, Ann. Phys. (N. Y.) 30, 51 (1964)
  24. T. R. Mongan, Phys. Rev. 175, 1260 (1968) ibid.178, 1597 (1969)
  25. T. L. Houk and R. Wilson, Rev. Mod. Phys. 39, 546 (1967) ibid.40, 672 (1968)
  26. J. S. Levinger, Phys. Letters 27B, 216 (1969)
  27. C. Lovelace, Phys. Rev. 135, B1225 (1964)
  28. M. G. Fuda, Nucl. Phys. A116, 83 (1968)
  29. F. Tabakin, Phys. Rev. 137, B75 (1965)
  30. F. Tabakin, Phys. Rev. 174, 1208 (1968)
  31. Y. Yamaguchi, Phys. Rev. 95, 1628 (1954)
  32. M. Bolsterli, Phys. Rev. 182, 1095 (1969)
  33. A. Messiah, Quantum Mechanics (Wiley-Interscience, Inc., New York, 1961), Vol. 1, Chap. III, Sec. 12
  34. T. Mongan, Phys. Rev. (to be published)
  35. D. Y. Wong, Phys. Rev. Letters 2, 406 (1959) A. C. Phillips (private communication)
  36. R. D. Purrington and R. W. Peacock [Bull. Am. Phys. Soc. 14, 512 (1969) Tabakin's [30] V. A. Alessandrini and C. A. Garcia Canal, Nucl. Phys. A133, 590 (1969) J. E. Beam, Phys. Letters 30B 67 (1969)
  37. L. M. Delves, J. M. Blatt, C. Pask, and B. Davies, Phys. Letters 28B, 472 (1969)
  38. U. W. Hochstrasser, in Handbook of Mathematical Functions, edited by M. Abramowitz and I. A. Stegun (Dover Publications, Inc., New York, 1965), Chap. 22
  39. R. Stagat, Ph.D. thesis, Rensselaer Polytechnic Institute, 1969 (unpublished)

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Phys. Rev. 186, 1069– Published 20 October, 1969
  • Received 26 May 1969

© 1969 American Physical Society

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