An universal algorithm of calculating terms of atomic many-body perturbation theory

Abstract An algorithm, based on numerical description of the terms of many-body perturbation theory (Goldstone diagrams), is presented. The algorithm allows the use of the same piece of computer code to evaluate any particular diagram in any specific order of the perturbation theory or to calculate similar terms in other areas of the many-body theory, like, e.g., terms in the coupled-cluster equations. The use of the algorithm is illustrated by calculating the second- and third-order correlation corrections to the removal energies of electrons from the ground state of sodium, copper and gallium and by calculating the hyperfine structure constants of sodium in the linearized single–double coupled cluster approximation.

[1]  O. Sushkov,et al.  Relativistic many-body calculations of energy levels and of fine-structure intervals in the caesium atom , 1983 .

[2]  Andrei Derevianko,et al.  Application of the dual-kinetic-balance sets in the relativistic many-body problem of atomic structure , 2007, Comput. Phys. Commun..

[3]  Ingvar Lindgren,et al.  Atomic Many-Body Theory , 1982 .

[4]  Han,et al.  Supersymmetrization of N=1 ten-dimensional supergravity with Lorentz Chern-Simons term. , 1986, Physical review. D, Particles and fields.

[5]  Johnson,et al.  Relativistic all-order calculations of energies and matrix elements in cesium. , 1991, Physical review. A, Atomic, molecular, and optical physics.

[6]  L. Bartolotti.  Atomic Energy Levels , 1982 .

[7]  G. Breit.  The Effect of Retardation on the Interaction of Two Electrons , 1929 .

[8]  Johnson,et al.  Finite basis sets for the Dirac equation constructed from B splines. , 1988, Physical review. A, General physics.

[9]  J. Pipek,et al.  An effective recursive algorithm for generating many-body Hugenholtz and Goldstone diagrams , 1988 .

[10]  Stephen Wilson.  Diagrammatic many-body perturbation theory of atomic and molecular electronic structure , 1985 .

[11]  J. Paldus,et al.  Computer generation of Feynman diagrams for perturbation theory I. General algorithm , 1973 .

[12]  Relativistic coupled-cluster single-double method applied to alkali-metal atoms , 2007, physics/0702090.

[13]  J. Bearden,et al.  Atomic energy levels , 1965 .

[14]  A. Derevianko.  Fourth-order perturbative extension of the single-double excitation coupled-cluster method , 2002, physics/0204056.

[15]  W. Johnson,et al.  RELATIVISTIC MANY-BODY CALCULATIONS OF ENERGY LEVELS, HYPERFINE CONSTANTS,AND TRANSITION RATES FOR SODIUMLIKE IONS, Z=11-16 , 1998 .

[16]  W. Johnson,et al.  Relativistic many-body calculations of energy levels, hyperfine constants, electric-dipole matrix elements, and static polarizabilities for alkali-metal atoms , 1999, physics/9906044.

[17]  Johnson,et al.  Relativistic all-order calculations of energies and matrix elements for Li and Be+ , 1989, Physical review. A, General physics.

[18]  Johnson,et al.  Second-order energies and third-order matrix elements of alkali-metal atoms. , 1987, Physical review. A, General physics.

[19]  Stephen Wilson,et al.  Diagrammatic many-body perturbation expansion for atoms and molecules: X. Automatic generation and analysis of fifth-order Hugenholtz energy diagrams☆ , 1994 .

[20]  Johnson,et al.  Computation of second-order many-body corrections in relativistic atomic systems. , 1986, Physical review letters.

[21]  W. A. Wijngaarden,et al.  Measurement of hyperfine structure of sodium 3P1/2,3/2 states using optical spectroscopy , 1994 .

[22]  O. Sushkov,et al.  Summation of the perturbation theory high order contributions to the correlation correction for the energy levels of the caesium atom , 1989 .

[23]  R. Mathar.  Table of Feynman diagrams of the interacting Fermion Green's function , 2005, physics/0512022.