# Amplitude reconstruction in charged particles scattering

Conference paper

First Online:

## Abstract

It is shown how to obtain, in modulus and phase, the forward short-range amplitude in the elastic channel for a collision between charged particles. The problem The reconstruction ofthe short range or, as often called, the nuclear amplitude f

_{N}(θ) □ f_{N}will be discussed in the following sections and some new data presented. One consider two spinless, non identical, particles with charges Z_{1}e,Z_{2}e (e electron charge).If these charges are localized in points the pure Coulomb amplitude f_{C}(θ) □ f_{c}can be obtained in a closed form /1/ as well as the corresponding Rutherford cross-section dσ_{C}/dω = |f_{C}|^{2}. The amplitude f_{C}is governed by the Sommerfeld parameter n = Z_{1}Z_{2}e^{2}/v,where v is the relative velocity of the two particles. When the long range potential is due to charges spread in space superimposed to short-range interactions, new elastic amplitude f(θ)□ f and cross-section dσ/dω = |f|^{2}are computed. The short range or nuclear amplitude is by definition f_{N}= f − f_{C}. f and f_{C}are not functions but distributions /2/ and it is always assumed here that$$f_N \in c^2 [0,\pi ]$$

(1)

A non-linear equation between f

_{N}and the two above cross-sections is easily derived as$$d\sigma /d\Omega - d\sigma _C /d\Omega = |f_N |^2 + 2\operatorname{Re} f_C^ * f_N$$

(2)

In (2) the LHS can be obtained from measurements in the elastic channel from some angle θ_{0} up to π .Equation (2) is very difficult to analyze and the author is not aware of any formal discussion of it as it is the case for standard amplitude reconstruction /3/. The experimentalists interested by these problems have given methods appropriate to find the solution(s) f_{N} of (2) at a given energy E taking into account errors of measurement (for references see /4/). The new results concerning f_{N} are not obtained from (2) but from an other equation derived from it.

## Keywords

Elastic Channel Forward Zone Sommerfeld Parameter Quantum Scattering Theory Amplitude Reconstruction
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

## Preview

Unable to display preview. Download preview PDF.

## References

- /1/.Messiah, A.M.L.: Mécanique Quantique, p. 359. Paris: Dunod 1959.Google Scholar
- /2/.Taylor, J.R.: Nuovo Cimento
**23B**, 313 (1974).Google Scholar - /3/.Chadan, K., Sabatier, P.E.: Inverse Problems in Quantum Scattering Theory, p.146, New York, Heidelberg, Berlin: Springer-Verlag 1977.Google Scholar
- /4/.Gai, M., Korotky, S.K., Manoyan, J.M., Schloemer, E.C., Schivakumar, B., Sterbenz, S.M., Willett, S.J., Bromley, D.A., Voit, H. Phys. Rev.
**C31**, 1260 (1985).Google Scholar - /5/.Holdeman, J.T., Thaler, R.M.: Phys. Rev.
**139B**, 1186 (1985).Google Scholar - /6/.Wojciechowski, H., Gustfason, D.E., Medsker, L.R., Davis, R.H.: Phys. Lett.
**63B**, 143 (1976).Google Scholar - /7/.Marty, C., Z. Phys.
**A309**, 261 (1983).Google Scholar - /8/.Barrette, J., Alamanos, N.: Phys. Lett.
**153B**, 208 (1985).Google Scholar - /9/.Barrette, J., Alamanos, N.: Nucl. Phys.
**A**: to be published.Google Scholar - /10/.Henning, W., Eisen, Y., Erskine, J.R., Kovar, D.G., Zeidman, B.: Phys. Rev.
**C15**, 292 (1977).Google Scholar

## Copyright information

© Springer-Verlag 1985