The pair-potentials calculations of McCaffrey and Kerins [J. Chem. Phys. 106, 7885 (1997)] used with success in simulating the emission spectroscopy of the Zn-RG matrix systems are extended to examine the different temporal decay characteristics exhibited at low temperature, T < 13 K, by the singlet emission bands in the Zn-Ar matrix system. The 238 nm band, assigned in the earlier theoretical work to the body mode Q(2), exhibits a 0.1 ns risetime, the 219 nm band assigned to the waist mode Q(3), is prompt. By extracting the gradients and the second derivatives of the Q(3) and Q(2) mode potentials of a Zn . Ar-18 cluster, decay rates of 3 and 2 ps, respectively, are calculated at the Franck-Condon regions of these potentials accessed in absorption, leading to effective competition between the Q(2) and Q(3) modes for relaxation of excited-state population and thereby to the coexistence of the 238 nm emission with the 219 nm band. A quasi-bound region is located at 0.32 Angstrom in the body mode, Q(2), which slows down the relaxation on this mode and is identified as responsible for the recorded risetime on the 238 nm emission. The temperature dependence exhibited in the Zn-Ar system at higher temperatures (T > 14 K) in which the intensity of the 219 nm band can reversibly be put into the 238 nm band, was examined by generating the (PES) potential-energy surface for coupled Q(2) x Q(3) vibronic modes. The theoretically predicted activation energy barrier is 380 cm(-1) which is only in qualitative agreement with the value of 130.6 cm(-1) extracted in the kinetics study. Possible reasons for the overestimation in the theoretical value are discussed.