Observation of Nuclear Scaling in the $A(e,e^{\prime})$ Reaction at $x_B>$1

Abstract

The ratios of inclusive electron scattering cross sections of $^4$He, $^{12}$C, and $^{56}$Fe to $^3$He have been measured for the first time. It is shown that these ratios are independent of $x_B$ at Q$^2>$1.4 (GeV/c)$^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 and $x_B >$1.5 is consistent with the kinematical expectation that two nucleon short range correlations (SRC) are dominate the nuclear wave function at $p_m\gtrsim$ 300 MeV/c. The values of these ratios in the scaling region can be related to the relative probabilities of SRC in nuclei with A$\ge$3. Our data demonstrate that for nuclei with A$\geq$12 these probabilities are 5-5.5 times larger than in deuterium, while for $^4$He it is larger by a factor of about 3.5.