文摘
The program MTRXCOUL [1] calculates the matrix elements of the Coulomb interaction between a charged particle and an atomic electron, ∫ψf∗(r)|R−r|−1ψi(r)dr. Bound-free transitions are considered, and non-relativistic hydrogenic wave functions are used. In this revised version a bug discovered in the F3Y CPC Program Library (PL) subprogram [2] is fixed. Furthermore, the COULCC CPC PL subprogram [3] applied for the calculations of the radial wave functions of the free states and the Bessel functions is replaced by the CPC PL subprogram DCOUL [4].New version program summaryProgram Title: MTRXCOULProgram Files doi:http://dx.doi.org/10.17632/xyg9zrmzz2.1Licensing provisions: GNU GPL v3Programming language: Fortran 77Journal reference of previous version: Comput. Phys. Commun. 133 (2000) 119.Does the new version supersede the previous version?: YesReasons for the new version:1.In some applications MTRXCOUL led to unexpected results that were traced back to the erroneous execution of the subprogram F3Y [2]. For example, in some cases F3Y yielded completely different values for the inputs (l,m1,l,m2,l′,m′)(l,m1,l,m2,l′,m′) and (l,m2,l,m1,l′,m′)(l,m2,l,m1,l′,m′), while, for symmetry reason, one expects equal results. In the new version this error in F3Y was corrected.2.In MTRXCOUL the COULCC subprogram [3] is applied for the calculations of the radial wave functions of the free states RE,l(r)RE,l(r) and the Bessel functions Jn(x)Jn(x). Since the publication of MTRXCOUL a relativistic version of the program, MTRDCOUL has also been developed and published [5]. In MTRDCOUL RE,l(r)RE,l(r) and Jn(x)Jn(x) are calculated by the subprogram DCOUL written by Salvat et al. [4]. Since the latter program is suitable also for calculations of non-relativistic wave functions, to ensure consistency between MTRXCOUL and MTRDCOUL, in the revised program the COULCC [3] was replaced by DCOUL. Furthermore, in some applications DCOUL turned out to be more efficient than COULCC.Summary of revisions:1.In the line AAQQ0036 of the original F3Y program [2] the incorrect assignment A2=L1−M1−N2 was replaced by A2=L1−M1−N1. The corrected F3Y was tested by comparing its results with those obtained by a program written for the integral of the product of three spherical harmonics using the 369j program [6]. An agreement within 10−1410−14 was found between the two calculations for all possible arguments of the function belonging to the values of lili up to 10.2.In the RFINAL function of the revised MTRXCOUL the regular Coulomb function Fl(η,x)Fl(η,x) is calculated using the code DCOUL [4]. For E≠0E≠0Fl(η,x)Fl(η,x) is obtained using the SCOUL subroutine. For E=0E=0RE,l(r)RE,l(r) is expressed in terms of the Bessel function Jn(x)Jn(x). The latter is obtained calling the FCOUL subroutine of DCOUL in a separate program unit, BESSJ(N,X).Nature of problem: The theoretical description of the excitation and ionization of atoms by charged particle impact often requires the knowledge of the matrix elements of the Coulomb interaction. Considering that the program can easily be extended to the calculations of matrix elements between wave functions other than the hydrogenic ones, it may find a broad application including the treatment of the electron–electron correlation problems.Solution method: The algorithm is based on the multipole series expansion of the Coulomb potential.Additional comments including Restrictions and Unusual features: The matrix elements can be calculated with the following restrictions. The initial bound states are limited to 1s, 2s, 2p, 3s, 3p, 3d. The quantum number ll in the final state has a maximum value of 10.AcknowledgmentsThis work was supported by the National Scientific Research Foundation (OTKA, Grant No. K109440). [1]L. Sarkadi, Comput. Phys. Commun. 133 (2000) 119.[2]A. Liberato de Brito, Comput. Phys. Commun. 25 (1982) 81.[3]I.J. Thompson and A.R. Barnett, Comput. Phys. Commun. 36 (1985) 363.[4]F. Salvat, J.M. Fernández-Varea and W. Williamson Jr., Comput. Phys. Commun. 90 (1995) 151.[5]L. Lugosi and L. Sarkadi, Comput. Phys. Commun. 141 (2001) 73.[6]L. Wei, Comput. Phys. Commun. 120 (1999) 222; Erratum: 182 (2011) 1199.AppendixTEST RUN OUTPUTFigure options
