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The absorption spectroscopy of calcium-doped argon clusters is described interms of an effective diatomics molecule Ca-(Ar_n), in the framework ofsemiclassical vertical transitions. We show how, upon choosing a suitablereaction coordinate, the effective finite-temperature equilibrium propertiescan be obtained for the ground- and excited-surfaces from the potential of meanforce (PMF). An extension of the recent multiple range random-walk method isused to calculate the PMF over continuous intervals of distances. Theabsorption spectra calculated using this single-coordinate description arefound to be in good agreement with the spectra obtained from high-statisticsMonte Carlo data, in various situations. For CaAr$_{13}$, we compare theperformances of two different choices of the reaction coordinate. For CaAr_37,the method is seen to be accurate enough to distinguish between differentlow-energy structures. Finally, the idea of casting the initial many-bodyproblem into a single degree of freedom problem is tested on the spectroscopyof calcium in bulk solid argon.Comment: 8 pages, 9 figure

Theoretical study of the finite-temperature spectroscopy in van der Waals clusters. III. Solvated chromophore as an effective diatomics