Abstract
A perturbative semiclassical approximation for the elastics-matrix is used to derive simple and accurate formulae describing the effects of a nuclear quadrupole deformation on the elastic scattering of aligned nuclei. Expressions are derived for the second rank tensor components of the analysing power, the ratios of which turn out to be simple trigonometric functions of the scattering angle in agreement with experimental observations. The approximations are discussed in some detail and higher order corrections are derived. In an appendix we derive a semiclassical first-order perturbation formula describing the effect of a non-central complex perturbation in the presence of a non-perturbatively treated central term. Our formula is in disagreement with some earlier published formulae which fail to treat the real part of the perturbation correctly.
Similar content being viewed by others
References
Austern, N., Direct Nuclear Reaction Theories. New York: Wiley-Interscience 1970
Frahn, W.E., Hill, T.F.: Z. Phys. A — Atoms and Nuclei285, 315 (1978)
Frahn, W.E., Gross, D.H.E.: Ann. Phys. (NY)101, 520 (1976)
Morse, P.H., Feshbach, H.: Methods of Theoretical Physics Vol. 1, p. 466; New York: McGraw-Hill 1953; B.J.B. Crowley, J. Phys. A: Math. Gen.12, 1951 (1979);13, 1901 (1980)
Matthews, J., Walker, R.L.: Mathematical Methods of Physics, 2nd ed. New York: Benjamin 1970
Berry, M.V., Mount, K.E.: Rep. Prog. Phys.35, 315, §6 (1972);
Ford, K.W., Wheeler, J.A.: Ann. Phys. (NY)7, 259, 287 (1959)
Alder, K., Roesel, F., Smilansky, U.: Ann. Phys. (NY)78, 518 (1973)
Zupranski, P., Dreves, W., Egelhof, P., Mobius, K.H., Steffens, E., Tungate, G., Fick, D.: Phys. Lett.91B, 358 (1980)
Crowley, B.J.B.: Phys. Rep.57, 47, §4.2 and Appendix D (1980)
Crowley, B.J.B.: Phys. Lett.71A, 186 (1979); Phys. Rep.57, 47, part I, §§ 1–2 (1980)
Crowley, B.J.B.: Phys. Lett75A, 183 (1980)
Chester, C., Friedman, B., Ursell, F.: Proc. Camb. Phil. Soc. Math. Phys. Sci.,53, 599 (1957)
Connor, J.N.L.: Mol. Phys.31, 33 (1976);
Poston, T., Stewart, I.M.: Catastrophe Theory and its Applications (Pitman, London, 1978) Chap. 4 & 12
Alder, K., Bohr, A., Huus, T., Mottelson, B., Winther, A.: Rev. Mod. Phys.28, 432 (1956)
Löbner, K., Vetter, M., Honig, U.: Nucl. Data Tables A7, 495 (1970)
Fuller, G.H., Cohen, V.W.: Nucl. Data Tables A5, 433 (1969)
Dreves, W., Zupranski, P., Egelhof, P., Kassen, D., Steffens, E., Weiss, W., Fick, D.: Phys. Lett.78B, 36 (1978)
Egelhof, P., Dreves, W., Möbius, K.H., Steffens, E., Tungate, G., Zupranski, P., Fick, D.: Phys. Rev. Lett.44, 1380 (1980)
Szegö, G.: Proc. London Math. Soc. [2],36, 426 (1934)
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Crowley, B.J.B., Hill, T.F. Semiclassical treatment of quadrupole shape effects in the elastic scattering of heavy ions below the Coulomb barrier. Z Physik A 300, 299–312 (1981). https://doi.org/10.1007/BF01419860
Received:
Revised:
Issue Date:
DOI: https://doi.org/10.1007/BF01419860