Ris3: A program for relativistic isotope shift calculations

Abstract

An atomic spectral line is characteristic of the element producing the spectrum. The line also depends on the isotope. The program ris3 (Relativistic Isotope Shift) calculates the electron density at the origin and the normal and specific mass shift parameters. Combining these electronic quantities with available nuclear data, isotope-dependent energy level shifts are determined. Program summaryProgram title:ris3Catalogue identifier: ADEK_v2_0Program summary URL:http://cpc.cs.qub.ac.uk/summaries/ADEK_v2_0.htmlProgram obtainable from: CPC Program Library, Queen’s University, Belfast, N. IrelandLicensing provisions: Standard CPC licence, http://cpc.cs.qub.ac.uk/licence/licence.htmlNo. of lines in distributed program, including test data, etc.: 5147No. of bytes in distributed program, including test data, etc.: 32869Distribution format: tar.gzProgramming language: Fortran 77.Computer: HP ProLiant BL465c G7 CTO.Operating system: Centos 5.5, which is a Linux distribution compatible with Red Hat Enterprise Advanced Server.Classification: 2.1.Catalogue identifier of previous version: ADEK_v1_0Journal reference of previous version: Comput. Phys. Comm. 100 (1997) 81Subprograms used:Cat IdTitleReferenceADZL_v1_1grasp2K VERSION 1_1to be publishedDoes the new version supersede the previous version?: YesNature of problem:Prediction of level and transition isotope shifts in atoms using four-component relativistic wave functions.Solution method:The nuclear motion and volume effects are treated in first order perturbation theory. Taking the zero-order wave function in terms of a configuration state expansion |ΨPJMJ〉=∑μcμ|Φ(γμPJMj)〉, where P, J and MJ are, respectively, the parity and angular quantum numbers, the electron density at the nucleus and the normal and specific mass shift parameters may generally be expressed as ∑μ,νcμcν〈γμPJMj|V|γνPJMj〉 where V is the relevant operator. The matrix elements, in turn, can be expressed as sums over radial integrals multiplied by angular coefficients. All the angular coefficients are calculated using routines from the grasp2K version 1_1 package [1].Reasons for new version:This new version takes the nuclear recoil corrections into account within the (αZ)4m2/M approximation [2] and also allows storage of the angular coefficients for a series of calculations within a given isoelectronic sequence. Furthermore, the program JJ2LSJ, a module of the grasp2K version 1_1 toolkit that allows a transformation of ASFs from a jj-coupled CSF basis into an LSJ-coupled CSF basis, has been especially adapted to present ris3 results using LSJ labels of the states. This additional tool is called RIS3_LSJ.Summary of revisions:This version is compatible with the new angular approach of the grasp2K version 1_1 package [1] and can store necessary angular coefficients. According to the formalism of the relativistic nuclear recoil, the “uncorrected” expression of the normal mass shift has been fundamentally modified compared with its expression in [3].Restrictions:The complexity of the cases that can be handled is entirely determined by the grasp2K package [1] used for the generation of the electronic wave functions.Unusual features:Angular data is stored on disk and can be reused. LSJ labels are used for the states.Running time:As an example, we evaluated the isotope shift parameters and the electron density at the origin using the wave functions of Be-like system. We used the MCDHF wave function built on a complete active space (CAS) with n=8 (296 626 CSFs-62 orbitals) that contains 3 non-interacting blocks of given parity and J values involving 6 different eigenvalues in total. Calculations take around 10 h on one AMD Opteron 6100 @ 2.3 GHz CPU with 8 cores (64 GB DDR3 RAM 1.333 GHz). If angular files are available the time is reduced to 20 min. The storage of the angular data takes 139 MB and 7.2 GB for the one-body and the two-body elements, respectively.