Abstract
The present paper revisits the determination of the semi-classical limit of the Feshbach resonances which play a role in electron impact broadening (the so-called “Stark“ broadening) of isolated spectral lines of ionized atoms. The Gailitis approximation will be used. A few examples of results will be provided, showing the importance of the role of the Feshbach resonances.
Highlights
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The same result was obtained by means of the quantum defect theory [14], and Gailitis resonances could be included automatically in the quantum close-coupling calculations of cross-sections and line broadening since the 1970s, Several publications followed, first based the Schr’odinger equation and relativistic effects treated by perturbations (R-Matrix theory), and more recently based on the Dirac equation
The Feshbach resonances play a role for energies E below the threshold of the transition and are equal to zero above
Summary
The same result was obtained by means of the quantum defect theory [14], and Gailitis resonances could be included automatically in the quantum close-coupling calculations of cross-sections and line broadening since the 1970s, Several publications followed, first based the Schr’odinger equation and relativistic effects treated by perturbations (R-Matrix theory), and more recently based on the Dirac equation This was not the case for the weak coupling methods of calculations of ion-electron cross-sections (distorted wave or semi-classical in particular): the increase of the cross-sections due to the Gailitis resonances needed to be calculated and added independently. A few examples will be provided, showing the importance of the inclusion of the Feshbach resonances in the line width
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