Y-scaling analysis of quasielastic electron scattering and nucleon momentum distributions in few-body systems, complex nuclei, and nuclear matter.

Abstract

The approach to y scaling previously adopted to obtain the nucleon momentum distribution in the two- and three-nucleon systems is extended to the case of complex nuclei and nuclear matter. The basic elements of this approach, which takes properly into account nucleon binding and momentum, are reviewed. A new method of analysis, which allows one to obtain the experimental asymptotic scaling function from inclusive cross sections even if these data are affected by final-state interactions, is proposed and illustrated. By such a method, the asymptotic scaling functions of $^{3}\mathrm{He}$, $^{4}\mathrm{He}$, $^{12}\mathrm{C}$, $^{56}\mathrm{Fe}$, and nuclear matter are obtained from recent experimental data and it is demonstrated that, particularly at high negative values of the scaling variable, the available data points at the highest value of the momentum transfer are affected by final-state interaction and cannot therefore be considered to represent the asymptotic scaling function. It is shown that, unlike what is commonly stated, the nucleon momentum distribution is not simply defined in terms of the derivative of the asymptotic scaling function, but as a sum of such a derivative plus the derivative of a quantity, the binding correction, generated by the removal energy distribution of nucleons embedded in the nuclear medium.The binding correction and its derivative are evaluated with various types of spectral functions, and the nucleon momentum distributions in $^{3}\mathrm{He}$, $^{4}\mathrm{He}$, $^{12}\mathrm{C}$, $^{56}\mathrm{Fe}$, and nuclear matter are obtained up to nucleon momenta k\ensuremath{\approxeq}500 MeV/c. For few-body systems the obtained momentum distributions satisfactorily agree with the ones extracted from (e,e'p) reactions and with theoretical calculations performed within Faddeev or variational approaches, whereas for complex nuclei they qualitatively agree with predictions of theoretical many-body approaches which take nucleon-nucleon correlations into account and, at the same time, at k\ensuremath{\ge}350 MeV/c they are larger by orders of magnitude than the ones predicted by mean field approaches. Such a result does represent unambiguous evidence of correlation effects in nuclei.