A model study of the influence of the properties of the quasicontinuum on MPA and MPD spectra of SF₆at different rotational temperatures

Abstract

The influence of assumed properties of the quasicontinuum on the frequency and temperature dependence of the MPA and M P D of SF, as determined by the lower discrete region has been studied using a simple interfacing model. Here the discrete region is interfaced with the quasicontinuum at v = 3 of the u3 mode using the time averaged population of u3 ( U = 3) level P 3 , as the ground-state population of the quasicontinuum. The dependence of P3 on the laser frequency (henceforth called the P3 spectrum) at different rotational temperatures has been obtained using different levels of approximation for the molecular Hamiltonian, i.e. by ignoring (case I), and incorporating the anharmonic splitting of the degenerate v3 vibrational mode (case 11). These spectra obtained in the two cases differ greatly, the latter showing more structure in the mid-frequency region. The temperature dependence in the wing is large as observed in different experimental studies. But contrary to experimental observation there is no drop in the M P D in the peak of the spectrum with increasing temperature. The cross section of the first excitation step, the anharmonicity in the quasicontinuum and the nature of growth of linewidth with energy have strong influences on the ultimate nature of the MPA and M P D spectra and modify the nature of the thermal dependence of the spectra also. The relative importance of rotational and vibrational temperature in the results obtained in cell experiments is discussed in the light of the above mentioned investigation. It is indicated that the vibrational temperature change must be responsible for the large drop in M P D obtained near and beyond 944.2 cm-' by various experimental studies.

Effect of laser pulse shape on multiphoton excitation of a polyatomic molecule

“…The time-dependent populations at different vibrational energy regions in the QC for laser pulses of frequency 948 cm −1 , obtained from the solution of the rate equations (2.12)- As discussed earlier, a constant time grid has been used here instead of free time generated by a random number. The latter method was used by the authors previously for the constant intensity pulse [21][22][23]. The results obtained using either the constant time grid (ctg) or random mean free time agree for a laser pulse of constant intensity.…”

“…where K n,n+1 and K n+1,n are related to the corresponding absorption (emission) cross sections (σ a(e) n ) as given in [20][21][22]26]. Here the v = 4 level is assumed to be the ground state of the QC (n = 0).…”

“…The time-dependent leakage rates are obtained for a 100 ns laser pulse of both constant and variable intensity profile from the solution of the Bloch equations and used in the rate equations as inputs. The rate equations are solved using the Monte Carlo technique discussed in [19][20][21][22]. Since the intensity profile of the laser pulse and hence the cross section for excitation etc are time dependent now, one should, in general, solve an integral equation as discussed in [25].…”

“…In some cases the optical Bloch equations describing the excitation in the discrete region are solved together with the rate equations describing the excitation in the QC using a natural and direct interfacing of the form given in [12]. But as shown in our previous studies [20][21][22][23], the backflow from the QC to the discrete region (DL) is really negligible when the intensity of the laser pulse is not too low and the principle of detailed balance is assumed to be valid in the region of the interface. The spectral response of MPA is also unchanged if irreversible leakage from the topmost discrete state is assumed instead of the rigorous coupling to the QC [12].…”