Abstract
The effects of the polarization potential serve to model spectra of alkaline atoms. These effects have been known for a long time and notably explained by the physicist Max Born (1926). The experimental knowledge of these alkaline spectra enables us to specify the values of these quantum defects. A simple code is used to calculate two quantum defects for which δl can be distinguished as: δs l = 0 and δp l = 1. On the theoretical part, it is possible to have an analytical expression for these quantum defects δl. A second code gives the correct wave functions modified by the quantum defects δl with the condition for the principal number: n* = n – δl ≥ 1. It is well known that δl → 0 when the kinetic momentum l ≥ 4, and for such momenta the spectra turns out to be hydrogenic. Modern software such as Mathematica, allows us to efficiently generate the polynomes defining wave functions with fractional quantum numbers. This leads to a good theoretical representation of these wave functions. To get numerically the quantum defects, a simple code is given to obtain these quantities when the levels assigned to a transition are known. Then, the quantum defects are inserted into the arguments of the correct modified wave functions for the outer electron of an atom or ion undergoing the short range polarization potential.
Highlights
The quantum defects are inserted into the arguments of the correct modified wave functions for the outer electron of an atom or ion undergoing the short range polarization potential
The author shows how the quantum theory, with the use of wave functions taking into account the modification of the quantum numbers, as explained by Kostelecky and Nieto [3] provides a simple framework for computing atomic and ionic wave functions using current symbolic software
This work shows how to produce, with the help of a modified Schrodinger equation, the probability distribution for the optical electron near the nucleus of alkaline atoms and their ions. Our approach to this problem is self-consistent that is: a simple code is given, this enables to calculate the quantum defects associated with a spectroscopically identified transition of an alkaline atom such as MgI Equation (2), another code is used to construct the quantum wave functions using these set of quantum defects Equation (29), as shown in the figures
Summary
Once the theorical δl is set, a simple code furnishes the numerical quantum defects associated with a spectroscopically identified transition wavelength of an alkaline atom The comparison of these two values enables us an estimate the static polarizability αD for the considered atom species. It is easy to use symbolic software like Mathematica, and solve two equations, if one wants to have two quantum defects: δs and δ p , that requires two identified transitions of any alkaline, for instance for the Na (sodium) atom and Mg (magnesium). This exactly represents the difference between the hydrogen energy levels from the deeper energy levels associated with the effect of the polarization potential This leads to an estimate of the static polarizability αD by solving the following set of equations.
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