Power considerations in the collision-induced double resonance

Thekkumthala, Jose (1978) Power considerations in the collision-induced double resonance. Masters thesis, Memorial University of Newfoundland.

[English] PDF (Migrated (PDF/A Conversion) from original format: (application/pdf)) - Accepted Version Available under License - The author retains copyright ownership and moral rights in this thesis. Neither the thesis nor substantial extracts from it may be printed or otherwise reproduced without the author's permission. Download (12MB) [English] PDF - Accepted Version Available under License - The author retains copyright ownership and moral rights in this thesis. Neither the thesis nor substantial extracts from it may be printed or otherwise reproduced without the author's permission. (Original Version)

Abstract

Two pairs of energy levels of a molecule are considered. Optical transitions among each of these two pairs are coupled by the molecular binary collision. The case where the collision keeps the velocity of the molecule constant while reorienting it and maintaining the rotational energy is considered. Since the velocity is maintained constant, the molecules undergoing both the optical transitions belong to the same velocity group. This condition may be satisfied by tuning the molecular level structure by a varying Stark field. In short, we are considering coupling of two optical transitions due to the velocity-maintaining collisions. -- An expression for the energy absorbed in the molecular system when the collision - induced double resonance occurs is found. This leads to the expression for the signal absorption in any molecular system in general. The treatment begins with the phenomenological equation of motion for the velocity - dependent density matrix of the two level molecular system. This is obtained by adding the phenomenological terms to the usual equation of motion in the Heisenberg picture. A two level molecular system can be represented by a 2X2 density matrix. Since the system under consideration consists of two pairs of levels, two 2X2 density matrices are dealt with. The effect of collisions is taken care of by introducing the collision kernel in the equation of motion. The equation of motion for the diagonal and the off-diagonal elements are obtained from the equation of motion for the general density matrix. The expression for the difference in the diagonal elements is obtained in terms of the difference in the off - diagonal elements and vice versa. From these two equations, an expression for the difference in the off - diagonal elements is obtained in terms of measurable quantities. This difference along with the expectation value of the component of the dipole moment between the molecular energy states of interest is introduced in an expression for the energy absorbed in the molecular system. This expression involves the time derivative of the polarisation induced in the molecules by the field. Since the molecular system exhibits dynamic behaviour, the energy expression is time averaged. Also, since different molecular velocity groups of the Maxwell velocity distribution curve are involved in the collision, the energy expression is velocity averaged over the Maxwellian velocity range. -- Two cases are considered. First, energy expression is found in the general case, i.e., when the velocity changes during the collision. Secondly, energy is calculated when the velocity is maintained constant during the collision. This expression shows that the energy depends linearly and quadratically upon the collision constants. This is shown to be a general expression for the particular energy expression obtained by Shoemaker et al. -- Numerical evaluation for the signal absorption in the molecule methyl fluoride is done. The value is found to be ∆I = 1.323 X 10⁻² ergs/sec cm². The contribution due to the linear terms in the collision constants is 1.15 X 10⁻² ergs/sec cm² and the contribution due to the quadratic terms is 1.73 X 10⁻³ ergs/sec cm². The meaning of this is that the quadratic contribution is 13.1% of the total contribution, which is a considerable proportion. This contribution will be larger for a molecule with larger collision constants. This fact argues in favour of the general expression obtained.

Actions (login required)

View Item