Quick Search:
Prog. Theor. Phys. Supplement No.37 & 38 (1966) pp. 297-305
Unitarity Relation in an Impact Parameter Representation
Toshimi Adachi and
Tsuneyuki Kotani*
The Tokyo Metropolitan Technical College, Shinagawa, Tokyo
*Department of Physics, Tokyo Metropolitan University, Setagaya, Tokyo
(Received August 1, 1966)
Abstract:
The unitarity relation for impact parameter amplitudes can be expressed in a transparent form by using phase functions. There is no essential difference for the theoretical treatment of both partial wave and impact parameter amplitudes, whenever the reaction (or inelastic) channels have to be taken into account. The threshold behaviour of the impact parameter amplitude is shown by using the effective range theory. The imaginary part of the impact parameter phase function is not equal to zero even below the lowest threshold of the reaction channels, while the non-zero value of the imaginary part of the partial wave phase shift corresponds to the existence of the reaction channels. At the higher energies or the large values pf the impact parameter, the impact parameter amplitude becomes to be equal to the partial wave amplitude of the corresponding orbital angular momentum state.
URL :
http://ptp.ipap.jp/link?PTPS/37/297/
DOI : 10.1143/PTPS.37.297
References:
-
W. N. Cottingham and R. F. Peierls, Phys. Rev. 137 (1965), B147[APS].
- T. Adachi and T. Kotani, Prog. Theor. Phys. Suppl. Extra Number (1965), 316[PTP].
- T. Adachi, Prog. Theor. Phys. 35 (1966), 463[PTP].
- T. Adachi and T. Kotani, Prog. Theor. Phys. 35 (1966), 485[PTP].
- Adachi, Kotani and Takeda, Prog. Theor. Phys. 36 (1966), 745[PTP].
- M. M. Islam, preprint, “Shrinking, Non-shrinking, and Expanding Diffraction Peaks” (Brown Univ., May, 1966).
- G. N. Watson, A Treatise on the Theory of Bessel Functions (Cambridge Univ. Press, Cambridge, 1962), 2nd edition, p. 158.
- M. Froissart, Nuovo Cim. 22 (1961), 191.
-
Fernbach, Serber and Taylor, Phys. Rev. 75 (1949), 1352[APS].
- R. J. Glauber, Lectures in Theoretical Physics (Interscience Publishers Inc., New York, 1958), Vol. 1, p. 315.
- R. C. Arnold, preprint, “An Optical Potential for High Energy Physics: Theory and Applications” (Argonne National Laboratory, March, 1966).
