- Access by Xinjiang University
Treatment of the Three- and Four-Nucleon Systems by a Generalized Separable-Potential Model
Phys. Rev. C 1, 85 – Published 1 January, 1970
DOI: https://doi.org/10.1103/PhysRevC.1.85
Abstract
A formalism, proposed previously, which represents a generalization of the separable-potential model is applied to the four-nucleon system. It consists essentially in approximating the off-shell nucleon-deuteron scattering amplitude—as obtained in the separable-potential model—again by separable expressions. We arrive thereby at effective two-particle equations which are solvable by standard methods. The determination of the required separable terms is studied in detail. A first attempt to solve approximately our final integral equations is made. The results demonstrate the applicability of the method.
Comments & Replies
Inelastic Effects in Approximate Three-Body Amplitudes
References (40)
- Y. Yamaguchi, Phys. Rev. 95, 1628 (1954) Y. Yamaguchi and Y. Yamaguchi, ibid. 95, 1635 (1954)
- A. N. Mitra, Nucl. Phys. 32, 529 (1962) A. N. Mitra and V. S. Bhasin, Phys. Rev. 131, 1265 (1963)
- R. D. Amado, Phys. Rev. 132, 485 (1963) R. Aaron, R. D. Amado, and Y. Y. Yam, ibid. 136, B650 (1964)
- R. Aaron, R. D. Amado, and Y. Y. Yam, Phys. Rev. 140, B1291 (1965) Phys. Rev. Letters 13, 574 (1964) R. Aaron and R. D. Amado, Phys. Rev. 150, 857 (1966)
- A. G. Sitenko and V. F. Kharchenko, Nucl. Phys. 49, 15 (1963) V. F. Kharchenko, Ukr. Fiz. Zh. 7, 573 (1962) ibid.7, 582 (1962)
- C. Lovelace, Phys. Rev. 135, B1225 (1964)
- P. Grassberger and W. Sandhas, Nucl. Phys. B2, 181 (1967) [Z. Physik 217, 9 (1968)]
- L. D. Faddeev, Zh. Eksperim. i Teor. Fiz. 39, 1459 (1960) [English transl.: Soviet Phys.—JETP 12, 1014 (1961)] L. D. FaddeevDokl. Akad. Nauk SSSR 138, 565 (1961) ibid.145, 301 (1962) [English transls.: Soviet Phys.—Doklady 6, 384 (1961) Soviet Phys.—Doklady 7, 600 (1963)] L. D. FaddeevMathematical Aspects of the Three-Body Problem in the Quantum Scattering Theory (Israel Program for Scientific Translations, Jerusalem, 1965)
- S. Weinberg, Phys. Rev. 130, 776 (1963) ibid.131, 440 (1963) M. Scadron, S. Weinberg, and J. Wright, ibid. 135, B202 (1964) J. V. Noble, ibid. 148, 1527 (1966) E. O. Alt, P. Grassberger, and W. Sandhas, Nucl. Phys. B2, 167 (1967) [7]
- L. Rosenberg, Phys. Rev. 138, B1343 (1965) ibid.168, 1756 (1968) R. Yaes, ibid. 170, 1236 (1968) M. G. Fuda, ibid. 166, 1064 (1968) F. Riordan, Nuovo Cimento 54, 552 (1968)
- K. Meetz, J. Math. Phys. 3, 690 (1962) [6,9,7]
- E. A. Harms and L. Laroze, Bull. Am. Phys. Soc. 14, 21 (1969)
- A. C. Phillips. Phys. Rev. 142, 984 (1966) ibid.145, 733 (1966)
- J. Wright and M. Scadron, Nuovo Cimento 34, 1571 (1964)
- V. V. Komarov and A. M. Popova, Nucl. Phys. 69, 253 (1965) ibid.A90, 635 (1967)
- J. Weyers, Phys. Rev. 145, 1236 (1966)
- J. H. Naqui [Nucl. Phys. 58, 289 (1964)] K. M. Watson and J. Nuttall [Topics in Several Particle Dynamics (Holden-Day, San Francisco, 1967)]
- F. Tabakin, Ann. Phys. (N.Y.) 30, 51 (1964) R. D. Puff, ibid. 13, 317 (1961) J. H. Naqui, Nucl. Phys. A103, 565 (1967) G. L. Strobel, ibid. A116, 465 (1968)
- V. S. Bhasin, G. L. Schrenk, and A. N. Mitra, Phys. Rev. 137, B398 (1965) B. S. Bhakar and A. N. Mitra, Phys. Rev. Letters 14, 143 (1965) G. L. Schrenk and A. N. Mitra, ibid. 19, 530 (1967) A. G. Sitenko and V. F. Kharchenko, Yadern. Fiz. 1, 994 (1965) [English transl.: Soviet J. Nucl. Phys. 1, 708 (1965)] A. G. Sitenko, V. F. Kharchenko, and N. M. Petrov, Phys. Letters 21, 54 (1966) J. Borysowicz and J. Dabrowski, ibid. 24B, 125 (1967) N. M. Petrov, S. A. Storozhenko, and V. F. Kharchenko, Yadern Fiz. 6, 466 (1967) [English transl.: Soviet J. Nucl. Phys. 6, 340 (1968)] F. Tabakin, Phys. Rev. 137, B75 (1965)
- S. Weinberg, [9]
Omitted endnote
Omitted endnote
- H. P. Noyes [Phys. Rev. Letters 15, 538 (1965)] K. L. Kowalski [ibid. 15, 798 (1965)] Weinberg ([9])
- [3]
- [6]
Omitted endnote
- M. Golderger and K. M. Watson, Collision Theory (John Wiley & Sons, Inc., New York, 1964)
Omitted endnote
Omitted endnote
- [7]
Omitted endnote
- W. E. Meyerhof and T. A. Tombrello, Nucl. Phys. A109, 1 (1968)
- D. Fick and H. W. Franz, Phys. Letters 27B, 541 (1968)
- J. H. Sloan, Phys. Rev. 165, 1587 (1968)
- J. E. Brolley, Jr., T. M. Putnam, and L. Rosen, Phys. Rev. 107, 820 (1957)
- W. T. H. Van Oers and K. W. Brockmann, Nucl. Phys. 48, 625 (1963)
- H. Brückmann, E. L. Haase, W. Kluge, and L. Schänzler, Z. Physik 230, 383 (1970)
- R. H. Lovberg, Phys. Rev. 103, 1393 (1957)
- Wright and Scadron ([14])
- M. Scadron and S. Weinberg, Phys. Rev. 133, B1589 (1964)