A new description of the initial states

Abstract

In the sca t t e r ing exper iments one has to consider the in i t ia l ensemble E of two-part ic le s ta tes (1 pa r t i c l e f rom the beam, 1 par t ic le f rom the target ) . I f E is pure, each pair of par t ic les before sca t te r ing has to be in the same two-par t ic le quan tum state. I t was real ized t h a t in most expe r imen t s we deal w i th in i t ia l pairs in different spin states. Thus E is in general not pure and in t he theore t i ca l descr ip t ion of the sca t ter ing one has to describe th is ensemble by a spin dens i ty mat r ix . In spi te of t he fact t h a t the range of the s t rong in te rac t ions is f inite and all the beam and t a rge t par t ic les have some small spread in the i r l inear momen ta , i t was assumed tha t w i th respect to o ther q u a n t u m numbers E is pure . This supposi t ion was suppor ted by the independence of the counting ra tes of t he beam in tens i ty and the g e o m e t r y of the expe r imen t checked in m a n y exper iments . However , in our opinion the usual tests for the pu r i t y (*) of E were insufficient and a careful expe r imen ta l and theore t ica l s tudy of E is needed. Le t us imagine t h a t the p u r i t y tests will show t h a t E is mixed, how we could find tha t i t is not only an effect of spin? The answer is t h a t one believes tha t the to t a l cross-sections, inclusive cross-sections, ra t ios of the d i f ferent -channel to ta l cross-sections and the mul t ipl ic i t ies of the final par t ic les are p rac t i ca l ly spin independent . Thus the change of the init ial m i x t u r e in t he p u r i t y tests should not influence the es t ima ted values of these quanti t ies . On the o ther hand, i f E is mixed , for example , wi th respect to the re la t ive orbitalm o m e n t u m q u a n t u m number , the measured values of t he above-ment ioned quant i t ies should depend s t rongly on the in i t ia l mix tu re . The idea t h a t E is a m ixed ensemble wi th respect to some addi t ional pa ramete rs was expressed in t he papers (1.2). In this paper we want to develop the idea f rom paper (2) w i thou t in t roduc ing new pa ramete r s for the two-par t ic le states. Our hypothes i s is the fol lowing: