N. BEDIDA, M. T. MEFTAH 1681
In this formula, neglecting the coupling effect of the
njm with the state 31
, we obtain
By using the properties of the spherical harmonics and
the selection rules for the different terms of order , the
result of this component is :
If we proceed similarly for the other components:
, we show that the odd terms of
vanish, and only even terms contribute, and their results
may be written as:
Summarizing (19) and (20), we can write the formula
(5) for the dipolar auto-correlation function
e and are the electronic collision operators
tions respectively, and the symbol
means as said
earlier the statistical average over the ionic perturbers.
Making the integral over
in (22), leads to express
ht as a function of the time microfield auto-correla-
EE . The latter represents, as known,
the dynamical effect of the electric microfield on the
emitters radiative properties :
where t means the time in the inverse of the electronic
plasma frequency unit .
Equation (21) gives the time dipolar autocorrelation
function regardless of the nature of charged particles, we
can apply it according to different interests, either to ions
or to electrons.
Using the path integral formalism, we derive an expres-
sion for the Lyman alpha line shape retaining the fine
structure and the effect of ion dynamics. Our main ap-
proximation is a reduction to pair correlation functions of
a cluster expansion in the electric microfield.
This allows to sum all the terms appearing in the stan-
dard perturbative solution in the path integral point of
view, and to express the time dipolar autocorrelation
function in a compact expression involving the electric
field autocorrelation function. In particular, we would
like to use the ability of the path integral point of view
for the description of a full quantum emitter-perturber
interaction. Interesting applications of a full quantum
approach exist in high temperature plasmas such as
found in fusion devices, for a modelling of the emission
of multicharged emitters perturbed by electrons.
 H. R. Griem, M. Blaha and P. Kepple, “Stark-Profile Cal-
culations for Resonance Lines of Heliumlike Argon in
Dense Plasmas,” Physical Review A, Vol. 41, 1990, pp.
 M. Baranger, “Atomic and Molecular Processes,” Acade-
mic Press Inc., New York, 1962.
 M. Baranger, “Simplified Quantum-Mechanical Theory
of Pressure Broadening,” Physical Review, Vol. 111, No.
2, 1958, pp. 481-491. doi:10.1103/PhysRev.111.481
 A. C. Kolb and H. R. Griem, “Theory of Line Broadening
in Multiplet Spectra,” Physical Review, Vol. 111, 1958,
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