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Prog. Theor. Phys. Vol. 76 No. 1 (1986) pp. 143-156
Study of the High-Energy Scattering Approximation
Yoshihiko Nishida and
Masaaki Shimauchi
Department of Physics, Saga University, Saga 840
(Received March 17, 1986)
Abstract:
The high-energy scattering approximation proposed long before by the present authors is reformulated so that both the wave function and the scattering amplitude may be given in manageable forms and its properties are elucidated for Gaussian, Woods-Saxon and double-Yukawa potentials. The wave function which has a form similar to that in the second Born approximation is transformed into an infinite series which converges rapidly or exhibits similar behaviour at high energies. It is shown that for the double-Yukawa potential the related series can be summed up to a closed form and the scattering amplitude is the first few terms of the series. It is indicated from numerical tests that in the weak and intermediate coupling cases the present approach can give the scattering amplitude as well as the differential cross section far beyond the conventional angular range of validity of Glauber's formula and satisfies the optical theorem with good accuracy. Finally, discussion is made on its applicability to nuclear collision problems where departures from non-relativistic kinematics become appreciable.
URL :
http://ptp.ipap.jp/link?PTP/76/143/
DOI : 10.1143/PTP.76.143
References:
-
Y. Nishida, M. Shimauchi and H. Tanaka, Nucl. Phys. 50 (1964), 403[CrossRef].
- R. J. Glauber, in Lectures in Theoretical Physics, ed. W. E. Brittin and L. G. Dunham (Interscience, New York, 1959), vol. 1, p. 315.
-
S. J. Wallace, Phys. Rev. Lett. 27 (1971), 622[APS];
Ann. of Phys. 78 (1973), 190[CrossRef];
Phys. Rev. D8 (1973), 1846[APS].
-
A. Baker, Phys. Rev. D6 (1973), 3462[APS];
Phys. Rev. D8 (1973), 1937[APS].
-
F. W. Byron, Jr. and C. J. Joachain, Physica 66 (1973), 33[CrossRef].
-
F. W. Byron, Jr., C. J. Joachain and E. H. Mund, Phys. Rev. D8 (1973), 2622[APS];
Phys. Rev. D11 (1975), 1662[APS];
Phys. Rev. C20 (1979), 2325[APS].
- C. J. Joachain, Quantum Collision Theory (North-Holland, Amsterdam, 1975), chap. 9.
-
A. C. Williams, Ann. of Phys. 129 (1980), 22[CrossRef].
-
Y. Nishida, Nucl. Phys. 82 (1966), 385[CrossRef].
- D. F. Jackson, Nuclear Reactions (Methuen, London, 1970), chap. 10.
-
H. O. Meyer, P. Schwandt, W. W. Jacobs and J. R. Hall, Phys. Rev. C27 (1983), 459[APS].
- R. H. Dalitz, Proc. Roy. Soc. A206 (1951), 509.
- C. J. Joachain, in Ref. 7), Appendix D.
-
C. J. Batty, Nucl. Phys. 23 (1961), 562[CrossRef].
Citing Article(s) :
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Progress of Theoretical Physics Vol. 81 No. 2 (1989) pp. 260-265
:
-
A High-Energy Scattering Approximation
-
Yoshihiko Nishida, Tadashi Takemasa and Masaaki Shimauchi
