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Parity-violating electron scattering (PVES) offers an important and model-independent method for probing the nuclear neutron density distributions. In this paper, a deformed PVES model is constructed, and detailed analyses of parity-violating asymmetry Aₕ are presented for ^208Pb and ^27Al. The impacts of the deformation of neutron and proton distributions (₍ and ) on Aₕ are revealed by the plane- and distorted-wave Born approximations, respectively. It is demonstrated that ₍ mainly affects the depth of the diffraction minima of Aₕ, while influences the width of the diffraction minima of Aₕ. Furthermore, we combine the deformed mean-field model and deformed PVES calculations to modify the linear relation between the neutron skin thickness R₍ and Aₕ that accommodates the correlation between the weak charge radius Rₖ and Aₕ. Based on the latest PVES experimental measurements, R₍ and Rₖ are extracted from the improved linear correlations. The studies in this paper provide new insights into determining ₍ and can serve as a useful guide for future PVES experiments.
Wang et al. (Mon,) studied this question.