Quantum defects

Tlie differences between the KS eigenvalues obtained with the exact potential from Ref. 156. 

To demonstrate the power of QD analysis, we test two common approximations to the ground-state potential, both of which produce asymptotically correct potentials (exact exchange (see the discussion on approximate functionals above and LB94 °). Exact exchange calculations are more CPU demanding than are traditional DFT calculations, but they are becoming pop- 

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From this set of standard size screening constants it is possible to obtain screening constants for any atom or ion for any property dependent mainly on the behaviour of the electrons in the outer parts of their orbits. The constants can probably be trusted to be accurate to within about 10% of the quantum defect, for example, Ss values for M levels to within 1. In case that empirical data are available for some atoms or ions of a sequence it is well to use them to correct the screening constants. 

The fitted value of 8p 8rf is in good agreement with the number calculated from the quantum defects of the atom and the phases of the Coulomb wavefunctions. 

The spectrum of the Sun contains the absorption lines associated with the atomic spectrum of heavier elements such as Fe (Figure 4.2), which indicates that the Sun is a second-generation star formed from a stellar nebula containing many heavy nuclei. The atomic spectra of heavier atoms are more complex. The simple expression for the H atom spectrum needs to be modified to include a quantum defect but this is beyond the scope of this book. Atomic spectra are visible for all other elements in the same way as for H, including transitions in ionised species such as Ca2+ and Fe2+ (Figure 4.2). 

Figure 12.7 Electronic transitions giving rise to the emission spectrum of sodium in the visible, as listed in Table 12.1. The principal series consists of transitions from the 3s level to 3p or a higher p orbital the sharp series from 3p to 4s or a higher s orbital diffuse from 3p to 3d or above and the fundamental from 3d to 4/or higher. The terms below the lines [(R/(3-1.37)2, etc.] are the quantum defect corrections referred to in Section 10.4.

Relativistic Quantum Defect Orbital (RQDO) calculations, with and without explicit account for core-valence correlation, have been performed on several electronic transitions in halogen atoms, for which transition probability data are particularly scarce. For the atomic species iodine, we supply the only available oscillator strengths at the moment. In our calculations of /-values we have followed either the LS or I coupling schemes. 

The relativistic version (RQDO) of the quantum defect orbital formalism has been employed to obtain the wavefunctions required to calculate the radial transition integral. The relativistic quantum defect orbitals corresponding to a state characterized by its experimental energy are the analytical solutions of the quasirelativistic second-order Dirac-like equation [8]... 

The relativistic quantum defect orbitals lead to closed-form analytical expressions for the transition integrals. This allows us to calculate transition probabilities and oscillator strengths by simple algebra and with little computational effort. 

Extension of the Relativistic Quantum Defect Orbital Method to the Treatment of Many-Valence Electron Atoms. Atomic Transitions in Ar II... 

Formulae for calculating transition probabilities in both the LS and Jcl coupling schemes, within the context of the Relativistic Quantum Defect Orbital (RQDO) formalism, which yields one-electron functions, are given and applied to the complex atomic system Ar 11. The application of a given coupling scheme to the different energy levels dealt with is justified. 

Extension of the Relativistic Quantum Defect Orbital Method... 

The Relativistic Quantum Defect Orbital (RQDO) method... 

As in the non-relativistic case [14], the relativistic quantum defect is determined empirically. We have... 

Kwato Njock et al. [15] have presented more recently a relativistic generalisation of the quantum defect orbital method. This formulation has some resemblances with the previous one [1,2] but is, in our view, unnecessarily complicated. 

I. Martin, From The Relativistic Quantum Defect Orbital Method and Some of its Applications, in R. Me Weeny and others (Eds.), Quantum Systems in Chemistry and Physics. Trends in Methods and Applications, Kluwer Academic Publishers, Dordrecht, 51 (1997). 

Extension of the relativistic quantum defect orbital method to the treatment 273 of many-valence electron atoms. Atomic transitions in Ar II... 

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