{"title":"A semi-analytic approximation for a single-particle continuum wavefunction","authors":"Robin Shakeshaft","doi":"10.1139/cjp-2023-0276","DOIUrl":null,"url":null,"abstract":"A moderately simple approximation to the radial wavefunction of an unbound particle which carries arbitrary angular momentum l( l + 1) and which scatters from any physical potential, including one with a Coulomb tail, is presented. The approximate wavefunction has the form of a linear combination of short- and long-range analytical functions that satisfies the correct boundary conditions at both the origin and at large distances. The coefficients of the short-range functions are determined by solving a matrix equation whose elements are highly suited to numerical quadrature, and which are hardly more difficult to evaluate for l ≫ 1 than for l = 0. The coefficients of the long-range functions are determined by both the nature of the interaction at large distances and the cusp condition on the wavefunction at the origin. This wavefunction has been tested by application to pure Coulomb scattering and to electron scattering from hydrogen within the 1s–2s–2p close coupling framework.","PeriodicalId":9413,"journal":{"name":"Canadian Journal of Physics","volume":null,"pages":null},"PeriodicalIF":1.1000,"publicationDate":"2024-05-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Canadian Journal of Physics","FirstCategoryId":"101","ListUrlMain":"https://doi.org/10.1139/cjp-2023-0276","RegionNum":4,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"PHYSICS, MULTIDISCIPLINARY","Score":null,"Total":0}
引用次数: 0
Abstract
A moderately simple approximation to the radial wavefunction of an unbound particle which carries arbitrary angular momentum l( l + 1) and which scatters from any physical potential, including one with a Coulomb tail, is presented. The approximate wavefunction has the form of a linear combination of short- and long-range analytical functions that satisfies the correct boundary conditions at both the origin and at large distances. The coefficients of the short-range functions are determined by solving a matrix equation whose elements are highly suited to numerical quadrature, and which are hardly more difficult to evaluate for l ≫ 1 than for l = 0. The coefficients of the long-range functions are determined by both the nature of the interaction at large distances and the cusp condition on the wavefunction at the origin. This wavefunction has been tested by application to pure Coulomb scattering and to electron scattering from hydrogen within the 1s–2s–2p close coupling framework.
本文介绍了一个非束缚粒子径向波函数的适度简单近似,该粒子携带任意角动量 l( l + 1),并从任何物理势(包括库仑尾)散射。近似波函数的形式是短程和长程分析函数的线性组合,在原点和大距离处都满足正确的边界条件。短程函数的系数是通过求解一个矩阵方程来确定的,该方程的元素非常适合数值二次方程,而且在 l ≫ 1 时的求值难度并不比 l = 0 时大。该波函数已通过应用于纯库仑散射和氢在 1s-2s-2p 紧密耦合框架内的电子散射进行了检验。
期刊介绍:
The Canadian Journal of Physics publishes research articles, rapid communications, and review articles that report significant advances in research in physics, including atomic and molecular physics; condensed matter; elementary particles and fields; nuclear physics; gases, fluid dynamics, and plasmas; electromagnetism and optics; mathematical physics; interdisciplinary, classical, and applied physics; relativity and cosmology; physics education research; statistical mechanics and thermodynamics; quantum physics and quantum computing; gravitation and string theory; biophysics; aeronomy and space physics; and astrophysics.