Abstract
The analytic properties of the partial wave S-matrix and related quantities are studied and numerically investigated. The analysis is carried out by means of integration along paths in the complex k-plane. The domain for the choice of integration contours can be rigorously defined by the use of complex scaling techniques. A generalization of Levinson's theorem incorporating the poles in the lower half k-plane is proved and exemplified. An expansion theorem for the partial wave S-matrix in terms of its poles and residues is derived and analyzed. The connections between poles and associated residues and their relationships with the Breit-Wigner ansatz and the Fano line shape parameters are discussed and numerically realized. Finally, the implications of the present development in connection with the inversion problem are indicated.
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References
M. Rittby, N. Elander and E. Brändas, Phys. Rev. A24, 1636 (1981).
M. Rittby, N. Elander and E. Brändas, Mol. Phys. 45, 553 (1982).
H. J. Korsch and R. Möhlenkamp, J. Phys. B15, L559 (1982).
O. Atabek, R. Lefebvre and M. Jacon, J. Phys. B15, 2689 (1982).
H. J. Korsch, R. Möhlenkamp, J. Phys. B15, L559 (1982).
H. J. Korsch, R. Möhlenkamp and H.-D. Meyer, J. Phys. B17, 2955 (1984).
H.-D. Meyer, J. Phys. B16, 2265 (1983).
H.-D. Meyer, J. Phys. B16, 2785 (1983).
P. L. Kapur and R. E. Peierls, Proc. Roy. Soc. A166, 277 (1938).
R. E. Peierls, Proc. Roy. Soc. A253, 16 (1959).
H. M. Nussenzveig ‘Causality and Dispersion Relations”, Academic Press, New York (1972).
R. E. Peierls, in ‘The Physics of Electronic and Atomic Collisions’ IX ICPEAC (24–30 July 1975) ed. by Risley J. and Geballe R., Univ. of Wash. Press, Seattle London (1976).
R. G. Newton, ‘Scattering Theory of Waves and Particles”, Springer Verlag, New York Heidelberg Berlin (1982).
E. Brändas, M. Rittby and N. Elander, J. Math. Phys. 26, 2648 (1985).
R. Jost, Helv. Phys. Acta 20, 256 (1947).
V. Bargmann, Rev. Mod. Phys. 21, 48 (1949).
K. Kodaira, Am. J. Math. 71, 921 (1949).
P. Krylstedt, N. Elander and E. Brändas, Int. J. Quant. Chem. 31, 755 (1987).
E. Engdahl, E. Brändas, M. Rittby and N. Elander, J. Math. Phys. 27, 2629 (1986).
P. Swan, Proc. Roy. Soc. A228, 10 (1955).
E. Brändas, E. Engdahl, M. Rittby and N. Elander, Int. J. Quant. Chem. 19, 457 (1986).
G. Breit and E. Wigner, Phys Rev. 49, 519 (1936).
A. Böhm, ‘Quantum Mechanics', Springer Verlag, New York (1979).
U. Fano, Phys. Rev. 124, 1866 (1961).
K. Chadan and P.C. Sabatier, “Inverse Problems in Scattering Theory” (Springer-Verlag, New York, Heidelberg, Berlin, 1977).
I.M. Gel'fand and N. Ya. Vilenkin, “Generalized Functions”, volume 4 (Academic Press, New York, 1964).
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Rittby, M., Elander, N., Brändas, E. (1979). On the analytical continuation of the partial wave S-matrix using complex scaling techniques. In: Brändas, E., Elander, N. (eds) Resonances The Unifying Route Towards the Formulation of Dynamical Processes Foundations and Applications in Nuclear, Atomic and Molecular Physics. Lecture Notes in Physics, vol 325. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-50994-1_39
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DOI: https://doi.org/10.1007/3-540-50994-1_39
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