---

Prog. Theor. Phys. Vol. 48 No. 6 (1972) pp. 1934-1959

Generalized Eikonal Approximation and Multiple-Scattering Formalism at High Energies

Mitsuaki Obu

Department of Physics, College of Science and Engineering, Nihon University, Chiyoda-ku, Tokyo

(Received April 17, 1972)

Abstract:

A formalism for high-energy multiple-scattering is developed, which is similar to the Glauber formalism but does not assume the eikonal approximation. The time-dependent scattering theory is adopted to generalize this approximation. In the eikonal approximation together with the adiabatic one, the time-dependent interaction Hamiltonian in the interaction representation turns out to be commutative. This commutative nature of the eikonal approximation enables us to propose a generalized approximation which assumes the commutativity itself. The extended approximation is called the generalized eikonal approximation (GEA) and is used to develop the extended multiple-scattering formalism. In the GEA the trajectory of the incident particle may deviate from the straight line, the trajectory adopted in the Glauber theory. Therefore, the extended formalism can be considered to be more reliable at large angles than the Glauber formalism.

URL : http://ptp.ipap.jp/link?PTP/48/1934/
DOI : 10.1143/PTP.48.1934

[ Full Text PDF : FREE ACCESS (2244K) ] Citation: Plain Text BiBTeX EndNote(RIS) RSS

---

References:

1. H. Palevsky, J. L. Friedes, R. J. Sutter, G. W. Bannett, G. J. Igo, W. D. Simpson, G. C. Phillips, D. M. Corley, N. S. Wall, R. L. Stearns and B. Gottshalk, Phys. Rev. Lett. 18 (1967), 1200[APS].
2. G. J. Igo, J. L. Friedes, H. Palevsky, R. Sutter, G. W. Bannett, W. D. Simpson, D. M. Corley and R. L. Stearns, Nucl. Phys. B 3 (1967), 181[CrossRef].
3. E. T. Boschitz, W. K. Roberts, J. S. Vincent, K. Gotow, P. C. Gugelot, C. F. Perdrisat and L. W. Swenson, Phys. Rev. Lett. 20 (1968), 1116[APS].
4. W. Czyż and L. Leśniak, Phys. Lett. B 24 (1967), 227[CrossRef].
5. R. H. Bassel and C. Wilkin, Phys. Rev. 174 (1968), 1179[APS].
6. W. Czyż and L. C. Maximon, Ann. of Phys. 52 (1969), 59[CrossRef].
7. H. Feshbach and J. Hüfner, Ann. of Phys. 56 (1970), 268[CrossRef].
   H. Feshbach, A. Gal and J. Hüfner, Ann. of Phys. 66 (1971), 20[CrossRef].
8. J. Formanek and J. S. Trefile, Nucl. Phys. B 3 (1967), 155[CrossRef].
9. R. J. Glauber, in High-Energy Physics and Nuclear Structure, edited by S. Devons (Plenum Press, New York-London, 1970), p. 207.
10. R. J. Glauber, in Lectures in Theoretical Physics, edited by W. E. Brittin and L. G. Dunham (Interscience Publisher's Inc., New York, 1959), Vol. 1, p. 315.
11. L. I. Schiff, Phys. Rev. 109 (1956), 443[APS].
12. D. S. Saxon and L. I. Schiff, Nuovo Cim. 6 (1957), 614.
13. M. Lévy and J. Sucher, Phys. Rev. 186 (1969), 1656[APS].
14. R. L. Sugar and R. Blankenbecler, Phys. Rev. 183 (1969), 1387[APS].
15. J. J. Tiemann, Phys. Rev. 103 (1958), 183[APS].
16. Y. Hahn, Phys. Rev. 184 (1969), 1022[APS]; Phys. Rev. C 2 (1970), 775[APS].
17. D. K. Ross, Phys. Rev. 173 (1968), 1695[APS].
18. L. I. Schiff, Phys. Rev. 176 (1968), 1390[APS].
19. M. L. Goldberger and K. M. Watson, Collision Theory (Wiley, New York, 1964).
20. S. I. Drozdov, J. Exptl. Theor. Phys. (USSR) 28 (1955), 734; ibid. 28 (1955), 736 [translation: Sov. Phys. -JETP 1 (1955), 588; ibid. 1 (1955), 591].
21. E. V. Inopin, J. Exptl. Theor. Phys. (USSR) 31 (1955), 901 [translation: Sov. Phys. -JETP 4 (1955), 764].
22. R. J. Glauber, in High-Energy Physics and Nuclear Structure, edited by G. Alexander (North-Holland Publishing Co., Amsterdam, 1967), p. 310.
23. R. Blankenbecler and M. L. Goldberger, Phys. Rev. 126 (1962), 766[APS].
24. R. J. Moore, Phys. Rev. D 2 (1970), 313[APS].
25. N. F. Mott and H. S. W. Massey, The Theory of Atomic Collisions (Clarendon Press, Oxford, 1961).
26. Y. Tikochinsky, Phys. Lett. B 29 (1969), 270[CrossRef].
27. J. McDougal, Proc. Roy. Soc. A 136 (1932), 549.
28. F. Bradamante, G. Fidecaro, M. Fidecaro, M. Giorgi, P. Palazzi, A. Penzo, L. Piemonteses, F. Sauli, P. Schiavon and A. Vascotto, Phys. Lett. B 31 (1970), 87[CrossRef]; ibid. 32 (1970), 303[CrossRef].
29. K. M. Watson, Phys. Rev. 89 (1953), 575[APS]; ibid. 105 (1957), 1334[APS].
30. D. R. Harrington, Phys. Rev. 184 (1969), 1745[APS].
31. E. A. Remler, Phys. Rev. 176 (1968), 2108[APS].
32. M. Yamazaki, Prog. Theor. Phys. 47 (1972), 1593[PTP].
33. H. Feshbach, Overlapping Potentials and Multiple-Scattering Theory, in In Honor of Philip M. Morse, edited by H. Feshbach and K. U. Ingard (M. I. T. Press, Cambridge, Mass., 1969), p. 190.
34. S. J. Chang and S. K. Ma, Phys. Rev. Lett. 22 (1969), 1334[APS].
35. H. D. I. Abarbanel and C. Itzykson, Phys. Rev. Lett. 23 (1969), 53[APS].

Citing Article(s) :

1. Progress of Theoretical Physics Vol. 50 No. 1 (1973) pp. 147-167 :

   Linked Cluster Decomposition of an S Matrix

   Mitsuaki Obu

2. Progress of Theoretical Physics Vol. 50 No. 6 (1973) pp. 1958-1964 :

   Comments on the Ordering Problem in the Application of the Glauber Multiple-Scattering Theory

   Mitsuaki Obu

3. Progress of Theoretical Physics Vol. 51 No. 2 (1974) pp. 518-527 :

   New Description of Nuclear Scattering at Intermediate Energies and Permissibility of Glauber Expression to Large-Angle Elastic Scattering

   Toshitake Kohmura and Tsunejiro Negishi

4. Progress of Theoretical Physics Vol. 52 No. 1 (1974) pp. 170-183 :

   Geometrical Corrections to the Glauber Multiple-Scattering Theory

   Mitsuaki Obu

5. Progress of Theoretical Physics Vol. 56 No. 1 (1976) pp. 135-150 :

   Cluster Decomposition of the S Matrix and Density Expansion of Nuclear Phase Shifts

   Mitsuaki Obu

6. Progress of Theoretical Physics Vol. 56 No. 5 (1976) pp. 1521-1534 :

   Potential Scattering in Three Dimension

   Takaomi Ishihara

---

[PTP HOME] [BROWSE] [SEARCH] [SUBSCRIPTION] [SUBMISSION] [REGISTRATION]

Copyright © Progress of Theoretical Physics 2013 All rights reserved.