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Manuscript Title: A program to calculate transverse Breit and QED corrections to energy levels in a multi-configuration Dirac-Fock environment.
Authors: B.J. McKenzie, I.P. Grant, P.H. Norrington
Program title: MCBP/BENA
Catalogue identifier: AAND_v1_0
Distribution format: gz
Journal reference: Comput. Phys. Commun. 21(1980)233
Programming language: Fortran.
Computer: IBM 360/195.
Operating system: OS/360, HASP.
Program overlaid: yes
RAM: 346K words
Word size: 8
Peripherals: magnetic tape, disc.
Keywords: Atomic physics, Racah, Structure, Multiconfiguration, Fractional parentage, Dirac-fock, Recoupling coefficients, Slater integrals, Complex atoms, Relativistic, Dirac equation, Jj-coupling, Methods theoretical, Breit, Transverse, Rydberg, Qed, Vacuum polarization, Self energy.
Classification: 2.1.

Subprograms used:
Cat Id Title Reference
AANC_v1_0 MCDF CPC 21(1980)207

Revision history:
Type Tit le Reference
correction 000A CORRECTION 27/04/81 See below

Nature of problem:
The program is an extension of, and is used in conjunction with, a multiconfigurational Dirac-Fock (MCDF) program already published. This previous program solved the MCDF equations for an atomic system and dumped the solution (i.e. wavefunctions etc.) to tape or direct access device (hereafter referred to as disk). The present program is able to read this dump and supply corrections to the MCDF energy levels that result from including the transverse Breit operator in first order perturbation, the second order vacuum polarization and an approximate estimate of the self-energy operator. The program is designed to be incorporated into the previous program structure so that the present programs are called as subroutines of that system.

Solution method:
Construct atomic state functions (ASF) from a linear combination of configuration state functions (CSF) which are eigenfunctions of J**2, Jz and parity. These in turn are built from single-electron central-field spinors that are solutions of the one-electron Dirac equation. A method of reducing matrix elements of the transverse Breit operator to a sum of products of coefficients and radial integrals is described. Routines to calculate these coefficients were developed within the framework of the coefficient-calculating routines and these coefficients are stored on a tape/disc file. These are later read and multiplied by the relevant radial integrals which are calculated by reasonably straightforward numerical integration techniques. After all the matrix elements for the system have been calculated, they are added in turn to the zero-order Hamiltonian matrix elements and the matrix diagonalized. The difference in the resulting eigenvalues from those of the zero-order matrix gives the Breit correction to the energy levels. The second-order vacuum polarization corrections are obtained using the methods described by Fullerton and Rinker; this provides an analytic potential, which is integrated over the electron density to give corrections to the orbital energies. The self-energy corrections are an approximate estimate based on interpolation among the hydrogenic results for various atomic numbers supplied by Mohr.

Restrictions:
The present version of the program is restricted to 25 orbitals and 30 configurations with up to 350 grid points per orbtial. However, the structure of the program allows these values to be increased by replacement of the relevant common statements.

Unusual features:
The program includes a few system routines for such things as recording the time and the date of run and giving the names of data sets used. These, however, are clearly marked in the source as such and can be easily replaced by equivalent local routines.

Running time:
This varies widely from problem to problem but is usually less than 10 on the IBM 360/195. The four examples in the test deck took 66 s using the G-compiler and 30 s using the H extended plus compiler.

CORRECTION SUMMARY
Manuscript Title: A program to calculate transverse Breit and QED corrections to energy levels in a multi-configuration Dirac-Fock environment. (C.P.C. 21(1980)233).
Authors: B.J. McKenzie, I.P. Grant, P.H. Norrington
Program title: 000A CORRECTION 27/04/81
Catalogue identifier: AAND_v1_0
Distribution format: gz
Journal reference: Comput. Phys. Commun. 23(1981)222
Classification: 2.1.