On the neutron-proton correlations and deuteron production

Stamstaw Mr6wczyriskl
1992 Physics Letters B   unpublished
The neutron-proton correlations and deuteron formation m nuclear colhslons both appear due to the final state interactions Thus, we suggest simultaneous measurements of the neutron-proton correlation function and the deuteron formation rate We calculate in parallel the two quantmes and express them through the space-rime parameters of the particle source created in nucleus-nucleus colhslons The measurements of two-particle correlations are well known to provide reformation about space-time
more » ... cteristics of particle sources m nuclear colh-slons for bombarding energies from tens of MeV [ 1 ] to hundreds of GeV [ 2 ] One usually deals with pairs of ldent~cal particles, protons at lower energies and plons at h~gher ones However, the correlations of non-identical particles [ 3 ] and the probabilmes of bound state formations [ 4 ] (see also ref [ 5 ]) determine the space-time size of particle sources as well The neutron and proton are of particular interest here since one can study the two-particle correlation and bound state formation with the same particles It is important to stress that the correlation between neutron and proton with small relative momentum and the deuteron formation both appear due to the final state interaction [ 6-8 ] The recent successful measurements of the neutron neutron correlations [ 9 ] and the very first data on the neutron-proton (n-p) correlations [ 10] show that the n-p correlation function can be precisely measured We suggest to study this quantity simultaneously with the probablhty of the deuteron production , which can be easily measured at present The analysis of such data would prowde, m particular, a valuable test of the method which uses the two-particle correlations to determine the space-time structure of particle sources If the method ~s indeed accurate the n-p pair in a scattering state and the E-mall address MROW@PLEARN bltnet deuteron should provide exactly the same space-time size of a source The derivation of the main formula of the method shows that it holds under rather restrictive condmons, which might be not always fulfilled in nuclear colhslons (see e g ref [8]) The aim of this paper is to derive simple formulas, which can be used m the analysis of simultaneous measurements of the n-p correlatton and deuteron production ~ The n-p correlation function and the deuteron formation rate, which relates the deuteron production cross section to the cross section of the n-p pair production, were calculated in ref [ 3 ] and refs [ 4-7 ], respecUvely The calculations [ 4-7 ] assumed the simultaneous emission of the neutron and proton which further form a deuteron, while the analysis of two-particle correlations usually takes into account nonlnstantaneous particle emission Thus, we derive here the deuteron formation rate for nonlnstanta-neous emission to make the two processes comparable The authors of ref [ 3 ], where the n-p correla-tton functton was calculated were interested m relativistic systems and for this reason they used a rather comphcated formahsm of the Bethe-Salpeter amphtudes instead of wave functions. However, the n-p correlation function can be measured at present only for nonrelatlvlst~c neutrons Thus, we calculate the n-p correlation function using the familiar language ofnonrelat~v~st~c wave functions We then find #1 The CHIC Collaboration led by Bo Jakobsson indeed plans such measurements 0370-2693/92/$ 05 00