In the present thesis a number of investigations on population inversions in He I and C III in recombining plasmas are reported. Model calculations for laser action in He I are carried out using the Collisional-Radiative model, when helium plasma is rapidly cooled by expansion. In this model 61 excited levels of He I are considered, and excitation, de-excitation, ionization and three-body recombination by electronic collision, spontaneous transition and radiative recombination have been included. The best available rate coefficients for the processes involved are utilized. The quasi-steady state approximation is used in calculating the population densities of 62 discrete levels of He I. Population inversions have been found to occur in many transitions of He I. We have concentrated our attention on transitions between levels with n less than or equal to 4, which give rise to emission lines in the visible region of the spectrum and show large population inversions. Results are presented for four transitions: 3 ^1S to 2 ^1P (7281), 3 ^1D to 2 ^1P (6678), 4 ^1S to 2 ^1P (5047) and 4 ^1D to 2 ^1P (4922). Available observational evidence for possible laser action in the He I 7281, 6678 lines in Wolf-Rayet and emission line stars is summarized and discussed.

A similar model for laser action in C III is carried out. A total of 59 states
of C III are considered in the Collisional-Radiative model. All the elementary
processes mentioned above are included, in addition, we include the
dielectronic recombination. Accurate oscillator strengths for the allowed
electric dipole transitions between 40 lowest terms in C III required in the
calculations have been calculated. The method of calculation and the results
of these oscillator strengths are given and compared with previous results
and experimental values, where available. Also, a modified ionization
equilibrium model for carbon, applicable to high and low electron densities,
is used to calculate the relative concentrations of various ions. Appreciable
population inversion is found to occur only in two lines 2s3p ^3P^0 to
2s3s 3^S (4650) and 2p3p ^3S to 2p3s ^3P^0 (5263) in the visible region.
The results are presented in the form of *ne*-*Te* diagrams. The relevance of these
results in resolving the problem of intensity anomalies in the spectra of
Wolf-Rayet stars is pointed out.

Extending the model calculation for He I, the sudden cooling assumption is removed and the plasma is allowed to expand in finite time. The initial population densities of excited states of He I are calculated using steady-state assumption. The differential equations for the population relaxation, electron density, ion densities and electron temperature are solved jointly using Runge-Kutta-Gill method. The variations of population densities with time are presented and discussed. The effect of initial conditions of the helium plasma on the population inversion is studied. A similar model is applied to carbon plasmas. The evolution of the densities of the levels of C III are investigated in detail. The calculation is carried out for three sets of initial conditions to study the dependence of the population inversion in the C III ion on the initial plasma parameters.

Results of a theoretical model are presented, which describes a stationary
He I plasma brought into contact with cool and dense hydrogen gas. The model
includes elastic collision interaction and the detailed kinetic excited
levels of helium and hydrogen atoms. Atom-atom collision processes are included.
The quasi-steady state approximation is used only for levels *i* lying above a
certain level *i** which is greater of equal to 11 in He I and 5 in H I.
Effective electron cooling is found to occur in a short time. It is found that
the population inversions which occur between the levels of hydrogen atom
are realized only in the quasi-steady state following the transient phase, while
those in helium are realized in the transient phase. The calculations have shown
that the magnitude of the population inversion which occurs between the levels
of helium is much greater than that obtained previously by expansion.