ROTATIONAL LINE SHAPES IN THE RABITZ EFFECTIVE POTENTIAL FORMALISM

TL;DRAbstract

A new “semiclassical” theory of rotational line shapes is presented based upon the use of the Rabitz effective potential formalism and an exact treatment of the exponential scattering matrix $S^{ eff}$. The effective potential $(V^{ eff})$ couples the internal rotational states of the molecule regardless of spatial effects associated with the projection quantum numbers M. This method of coupling is therefore valid for conditions where the M states are degenerate, such as in the typical unsaturated microwave experiment where there is zero Stark field. The use of this formalism results in a substantial reduction in the dimensionality of the problem. The effective scattering matrix $S^{eff}$ is derived in an interaction representation so that $$S^{eff} = exp(iA^{eff})$$ where $$ [A^{ eff}]_{i,j}=\\langle i|-\\frac{i}{h}\\int\\nolimits_{-\\infty}^{\\infty} { dt} \\exp(-i H_{o}{^{eff} t/h}) V^{eff}(t) exp(iH_{o}{^{eff} t/h})| j \\rangle $$ The integrals are evaluated using a straight line p

Chat with Paper

AI Agents for this Paper