Summary
A study of the rearrangement collision matrix, under certain asymptotic assumptions is made. It is found that although the «asymptotic states» are non-orthogonal, by a proper choice an orthogonal and complete set of physical states with prescribed asymptotic properties can be constructed. Identity of different expressions of the collision matrix is re-derived. Finally, by the help of the collision matrix the state vector itself is expressed in a form where the incoming and outgoing waves into various channels are explicitly separated without putting any configuration space restrictions.
Riassunto
Si studia la matrice di collisione di riordinamento, in determinate condizioni asintotiche. Si trova che, benchè gli «stati asintotici» non siano ortogonali, con una scelta appropriata si può costruire un sistema completo di stati fisici con proprietà asintotiche assegnate. Si rideriva l’identità di differenti espressioni della matrice di collisione. Infine, con l’ausilio della matrice di collisione, il vettore di stato si esprime in una forma in cui le onde entranti e uscenti da vari canali sono separate esplicitamente senza porre alcuna restrizione allo spazio delle configurazioni.
Similar content being viewed by others
References
For some of the recent developments in this subject seeR. C. Newton:Ann. Phys.,4, 29 (1958);E. Gerjouy:Ann. Phys.,5, 58 (1958). The last mentioned contains a good list of references to earlier work.
CompareA. M. Lane andR. G. Thomas:Rev. Mod. Phys.,30, 257 (1958).
B. A. Lippmann andJ. Schwinger:Phys. Rev.,79, 469 (1950).
B. A. Lippmann:Phys. Rev.,102, 264 (1956).
L. L. Foldy andW. Tobocman:Phys. Rev.,105, 1099 (1957).
S. T. Epstein:Phys. Rev.,106, 598 (1957).
A vector denoted by the form |〉− or |〉 −+ will always be regarded η-dependent. See references (5) and (6).
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Mohan, G. Re-arrangement collision matrix. Nuovo Cim 13, 1065–1073 (1959). https://doi.org/10.1007/BF02725117
Received:
Published:
Issue Date:
DOI: https://doi.org/10.1007/BF02725117