Spectral profiles of certain atomic lines

Abstract

Several calculations have been carried out using the transition operator technique.

The radiative decay in a two-level quantum system with excited state coupled by an external perturbation has been investigated and an expression obtained for P(t), the probability of finding the atom in its excited state at time t. This is seen to possess a steady value for yt >> 1 and a third term which decays at nearly half the rate of its second.

Next radiative decay of an atom with two close-lying excited states is considered and |b_q|2, the spectral density for spontaneous emission from the uppermost level, calculated. This shows that the proximity of the upper two levels makes the line-shape non-Lorentxian.

Heisenberg equations of motion were then derived for the transitions operators of an ℓ-level atom undergoing radiative decay, the possibility of overlapping pairs of levels being ignored. These master equations were then used to obtain the spectral profiles of certain atomic lines, employing the so-far avoided Markoff approximation.

First the spectral density of the scattered radiation was found for transitions between levels 5P_3/2 and 4S (ground state), and 6S and 5P _3/2, in the potassium atom when driving fields of arbitrary strength coupled levels 6S and 4P_3/2, and 4P3/2 and 4S. Triple-peaked profiles were obtained.

Spectral profiles for emission were then derived for transitions between levels 3P and (ground state), and 3P and in the hydrogen atom when a driving field of arbitrary strength coupled levels The former profile was double the latter quadruple-peaked.

Lastly master equations were derived for an atom, with two excited levels undergoing radiative decay, when allowance was made for thepossibility of their overlapping. A driving field of arbitrary magnitude coupled the uppermost and ground states. The spectrum for the scattered light resulting from transitions between the uppermost and ground state was found and graphs computed for various field strengths and separations of the excited states.