Z. Phys. D -Atoms, Molecules and Clusters 7, 227-232 (1987) Atoms, Molecules and Clusters ~r Physik D © Springer-Verlag 1987 The effect of hyperfine structure on the collisional relaxation of the Thallium atom excited by laser beam J. Filoficzuk, J. Fiutak, and W. Miklaszewski* Institute of Theoretical Physics and Astrophysics, University of Gdafisk, ul. Wita Stwosza 57, 80-952 Gdafisk, Poland Received 19 May 1987 The theoretical analysis of the thallium atom relaxation is presented for various intensities of the incident laser beam tuned to the transition $1/2 - PI/2. We present numerically computed time dependencies of the populations of different states. It is shown that the hyperfine structure affects the relaxation process in non-trivial way, especially for weak and moderate field intensities. PACS: 31.70.Hq; 32.80.Bx; 32.90. + a 1. Introduction The aim of the present paper is to analyze the time evolution of the multi-level atom resonantly coupled to the laser beam with special emphasis on the effect of hyperfine structure. As an example we have chosen the thallium atom so that this paper may be viewed on as an extension of the paper by Czub and Fiutak [1]. The outline of the employed theoretical description is presented in Sect. 2. We start with expanding the density matrix in the proper set of atomic operators, which we shall call the Liouville space vectors. We have considered two sets of these vectors. The first is labelled by the total angular momentum of the atom and nucleus, while the second is formed by some products of electronic and nuclear operators. The second choice is most suitable for the description of relaxation and numerical computations. On the other hand, the first set is more convenient for the presentation of final results. Thus, in effect, we have described the Liouville equation in terms of the second basis, while the results are presented with reference to the first one. In this connection we have followed the paper of Baylis [2]. * Supported by the Polish Ministry of Science and Technology under Project CPBP 01.03 1.3 Our calculations correspond to the cw-laser exci- tation of the thallium atom perturbed by the collisions with the argon gas atoms. The laser is assumed to be turned on instantaneously at a given time. The whole description is phenomenological, i.e. we have taken the values of the radiative and collisional relaxation constants and optical cross-sections from some experimental results. The obtained results are discussed in the Sect. 3. The essential feature of the relaxation process is the existence of three time regions. The first one is the initial one which corresponds to a time interval of the order of 10-8 s in which the Rabi oscillations are visible for sufficiently intense fields. In the intermediate time region, for times of the order of 10-7-10-rs from the switching on of the laser field, the relaxation is very complex and sensible to the tuning of the laser frequency to different transition frequencies, density of the perturbers and laser fight intensity. In the third region, which extends up to hundreds of microseconds, we observe a relatively smooth approach to the stationary state. When Rabi frequencies are comparable to hyper- fine structure splitting or when the detunings from the atomic resonance transition frequencies are sufficiently large then the relaxation process does not depend on the hyperfine structure.