2019/01/01 by Jean-Christophe Pain, Franck Gilleron · 1 citation
Engineering · Physics and Astronomy · #Atomic and Molecular Physics #Bessel function #Collision #Dipole #Dust and Plasma Wave Phenomena #Electron #Formalism (music) #Laser-induced spectroscopy and plasma #Randomness #Recursion (computer science) #Simple (philosophy) #Wave function #physics.atom-ph
paper · pdf · doi:10.1016/j.hedp.2019.01.004
submitted to "High Energy Density Physics"
openalex publication_date 2019/01/01 · openalex created_date 2019/02/21 · arxiv created 2019/05/21 · arxiv updated 2019/05/22 · openalex updated_date 2026/08/05
Spectral lines emitted by plasmas provide information about the thermodynamic conditions, the degree of randomness or the interactions prevailing in the medium. Collisions by plasma electrons penetrating the extent of bound-electron wavefunctions is important at high density, where short-range interactions become dominant. Such collisions are usually not taken into account properly in the standard lineshape theory, assuming long-range dipole approximation. The formalism of penetrating collisions for hydrogen relies on the introduction of a family of integrals calculated using a recursion relation. In this work, we show that such integrals can be expressed analytically, as a finite sum involving binomial coefficients and modified Bessel functions of the third kind. The explicit expression enabled us to obtain a simple approximate analytical form for the collision operator, making numerical implementation and physical interpretation easier. We also propose simple analytical forms of coefficients and integrals important for the modeling of penetrating collisions.