Observation of nuclear scaling in the ${A(e,e}^{\prime })$ reaction at $x_B>1\mathrm{}$

The ratios of inclusive electron scattering cross sections of ${}^4\mathrm{He},$ ${}^{12}\mathrm{C},$ and ${}^{56}\mathrm{Fe}$ to ${}^3\mathrm{He}$ have been measured for the first time. It is shown that these ratios are independent of $x_B$ at $Q^2>1.4\mathrm{}{\mathrm{GeV}}^2$ for $x_B>1.5,$ where the inclusive cross section depends primarily on the high momentum components of the nuclear wave function. The observed scaling shows that the momentum distributions at high-momenta have the same shape for all nuclei and differ only by a scale factor. The observed onset of the scaling at $Q^2>1.4\mathrm{}{\mathrm{GeV}}^2$ and $x_B>1.5\mathrm{}$ is consistent with the kinematical expectation that two-nucleon short range correlations (SRC) dominate the nuclear wave function at $p_m\gtrsim 300\mathrm{MeV}/c.\mathrm{}$ The values of these ratios in the scaling region can be related to the relative probabilities of SRC in nuclei with $A>~3.$ Our data, combined with calculations and other measurements of the ${}^3\mathrm{H}\mathrm{e}/\mathrm{d}\mathrm{e}\mathrm{u}\mathrm{t}\mathrm{e}\mathrm{r}\mathrm{i}\mathrm{u}\mathrm{m}$ ratio, demonstrate that for nuclei with $A>~12$ these probabilities are 4.9–5.9 times larger than in deuterium, while for ${}^4\mathrm{He}$ it is larger by a factor of about 3.8.

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