Within the three-dimensional semiclassical approximation, an analytic expression is obtained for the amplitude of proton-nucleus scattering at intermediate energies of incident protons. The method for deriving this amplitude is based on the use of the high-energy approximation with distorted waves. In view of the short-range character of proton-nucleon interaction, the process of proton-nucleus scattering is represented as a series of single scattering events occurring on each individual nucleon. With the aid of the proposed mathematical formalism, a recursion relation is derived that makes it possible to express the nuclear form factor obtained within the distorted-wave method in terms of the sum of an infinite Born series. Parameters that characterize the distributions of protons and neutrons in the spherical nuclei Ca-40, Ca-48, Zr-90, and Pb-208 and which include the width of the surface layer of nucleons and the root-mean-square radii of the proton-, neutron-, and nucleon-density distributions are determined from an analysis of the measured cross sections for the elastic scattering of 1-GeV protons, a modified Fermi function being employed for the nucleon-density distribution. (C) 2004 MAIK "Nauka/Interperiodica".
展开▼
机译：在三维半经典近似中，获得了在入射质子的中间能量下质子-原子核散射幅度的解析表达式。推导该振幅的方法是基于使用扭曲波的高能近似。考虑到质子-核子相互作用的短距离特性，质子-核子散射的过程表示为发生在每个单个核子上的一系列单个散射事件。借助于所提出的数学形式主义，推导了一个递归关系，该递归关系使得可以利用无限的Born级数之和来表达在畸变波方法中获得的核形状因子。表征球核Ca-40，Ca-48，Zr-90和Pb-208中质子和中子分布的参数，包括核子表面层的宽度和原子核的均方根半径质子，中子和核子密度分布是通过对1-GeV质子的弹性散射的测量横截面的分析确定的，改进的费米函数用于核子密度分布。 （C）2004 MAIK“ Nauka / Interperiodica”。
展开▼
