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Scaling analyses have been successfully applied to study the inclusiveelectron scattering $(\textit{e}, \textit{e}^{\prime})$ over the past fewdecades. In this paper, we utilize the $\psi^{\prime}$ scaling function inmomentum space to analyze the $(\textit{e}, \textit{e}^{\prime})$ crosssections, where the nucleon momentum distributions are derived fromself-consistent mean-field calculations. By further introducing the energy andmomentum conservation in the scaling analysis, an improved $\psi^{\prime}$scaling function is proposed to investigate the high-momentum part of themomentum distributions. Using the proposed scaling function, we systematicallyexplore the effects of the nucleon-nucleon short-range correlation($\textit{NN}$-SRC) on the $(\textit{e}, \textit{e}^{\prime})$ cross sections.From the experimental $(\textit{e}, \textit{e}^{\prime})$ data, the\textit{NN}-SRC strength is further extracted within the framework of theimproved $\psi^{\prime}$ scaling function. The studies in this paper offer anew method to investigate the nucleon momentum distributions and the$\textit{NN}$-SRC effects in nuclei.

New extended method for $\psi^{\prime}$ scaling function of inclusive electron scattering