A program to view the relationship between atomic energy levels and Slater parameters

PAGAN CESAR; REYNA ALMANDOS JORGE; RAINERI MÓNICA

Foz de Iguazú

Congreso; Encontro de Física 2011; 2011

Sociedad Brasileña de Física

For a single con¯guration description of an atom, the energy levels can be found as a weighted sum of energy components representing the electrostatic and relativistic interactions, obtained from the atomic hamiltonian. These energy parameters are usually referred to as Slater parameters, and represent the average con¯guration energy Eav, the electrostatic direct Fk and exchange Gk integrals, and spin-orbit parameters ³nl. The same is valid in a multicon¯gurational approach, where we take into account the presence of the con¯guration interaction integrals Rk and eigenvectors components obtained from the matrix diagonalization for each total angular momentum (J) value. One of the most widely used Fortran packages for atomic calculation was developed by R.D. Cowan, and is composed of four codes: RCN, RCN2, RCG, and RCE. Brie°y, RCN calculates the single-con¯guration radial wavefunctions, RCN2 calculates two-con¯guration radial integrals, and RCG uses the previous results to obtain energy levels and weighted oscillator strengths. The RCE code is used is to adjust the values of the energy parameters in order to produce computed atomic energy levels in the best possible agreement with experimentally known level values by a least-squares calculation. Levels whose energies are not known experimentally can be disregarded. The output from these codes are ASCII type ¯les. When large numbers of levels are involved, these ¯les can becomes very large and di±cult to understand. In order to produce a user-friendly interface, we developed a computer program to control input data and produce a graphical output from Cowan's RCE code. This program has two main graphical windows. The ¯rst one shows the Slater energy parameters and controls to select input and output ¯les, \undo", and controls to specify the input parameters for Cowan's RCE code. Controls are provided held any parameter ¯xed, or allow groups of parameters forced to vary in such a way that the ratios of the values within a group remain ¯xed relative to each other. The second window displays the known experimental and the theoretical level values obtained from a least-squares calculation. The main feature of this code is to allow a dynamical variation of the levels, and display them on screen as an energy level diagram, while the user varies the Slater parameters with help of the mouse { all in real time. The code was written in Visual Basic for the Microsoft Windows operational system.Eav, the electrostatic direct Fk and exchange Gk integrals, and spin-orbit parameters ³nl. The same is valid in a multicon¯gurational approach, where we take into account the presence of the con¯guration interaction integrals Rk and eigenvectors components obtained from the matrix diagonalization for each total angular momentum (J) value. One of the most widely used Fortran packages for atomic calculation was developed by R.D. Cowan, and is composed of four codes: RCN, RCN2, RCG, and RCE. Brie°y, RCN calculates the single-con¯guration radial wavefunctions, RCN2 calculates two-con¯guration radial integrals, and RCG uses the previous results to obtain energy levels and weighted oscillator strengths. The RCE code is used is to adjust the values of the energy parameters in order to produce computed atomic energy levels in the best possible agreement with experimentally known level values by a least-squares calculation. Levels whose energies are not known experimentally can be disregarded. The output from these codes are ASCII type ¯les. When large numbers of levels are involved, these ¯les can becomes very large and di±cult to understand. In order to produce a user-friendly interface, we developed a computer program to control input data and produce a graphical output from Cowan's RCE code. This program has two main graphical windows. The ¯rst one shows the Slater energy parameters and controls to select input and output ¯les, \undo", and controls to specify the input parameters for Cowan's RCE code. Controls are provided held any parameter ¯xed, or allow groups of parameters forced to vary in such a way that the ratios of the values within a group remain ¯xed relative to each other. The second window displays the known experimental and the theoretical level values obtained from a least-squares calculation. The main feature of this code is to allow a dynamical variation of the levels, and display them on screen as an energy level diagram, while the user varies the Slater parameters with help of the mouse { all in real time. The code was written in Visual Basic for the Microsoft Windows operational system.Rk and eigenvectors components obtained from the matrix diagonalization for each total angular momentum (J) value. One of the most widely used Fortran packages for atomic calculation was developed by R.D. Cowan, and is composed of four codes: RCN, RCN2, RCG, and RCE. Brie°y, RCN calculates the single-con¯guration radial wavefunctions, RCN2 calculates two-con¯guration radial integrals, and RCG uses the previous results to obtain energy levels and weighted oscillator strengths. The RCE code is used is to adjust the values of the energy parameters in order to produce computed atomic energy levels in the best possible agreement with experimentally known level values by a least-squares calculation. Levels whose energies are not known experimentally can be disregarded. The output from these codes are ASCII type ¯les. When large numbers of levels are involved, these ¯les can becomes very large and di±cult to understand. In order to produce a user-friendly interface, we developed a computer program to control input data and produce a graphical output from Cowan's RCE code. This program has two main graphical windows. The ¯rst one shows the Slater energy parameters and controls to select input and output ¯les, \undo", and controls to specify the input parameters for Cowan's RCE code. Controls are provided held any parameter ¯xed, or allow groups of parameters forced to vary in such a way that the ratios of the values within a group remain ¯xed relative to each other. The second window displays the known experimental and the theoretical level values obtained from a least-squares calculation. The main feature of this code is to allow a dynamical variation of the levels, and display them on screen as an energy level diagram, while the user varies the Slater parameters with help of the mouse { all in real time. The code was written in Visual Basic for the Microsoft Windows operational system.