E. E. Nikitin

Recovery of the Landau matrix elements from the classical Fourier components: The one‐dimensional dissociating oscillator

The recently suggested method of recovering the Landau exponent of the quasiclassical matrix elements from the attributes of classical motion is illustrated by way of an example of dissociating anharmonic oscillators. For a Morse oscillator, in which case the exact analytical results are available, the so‐called improved semiclassical approximation that incorporates the Landau exponential yields quite accurate matrix elements for classically strongly forbidden events. This provides a firm support for the method of estimation of quasiclassical matrix elements between distant states from the information on the motion of system in the classically allowed region.

Adiabatic and postadiabatic channel description of atom–diatom long‐range half‐collision dynamics: Interchannel radial coupling for P1 and P2 anisotropy

It is shown that the adiabatic channel states of an atom–diatom system with a low‐rank interaction anisotropy (proportional to cos γ and cos2 γ) exhibit a nonlocalized nonadiabatic coupling which persists into the strong coupling region. This feature of adiabatic channel states restricts application of the statistical adiabatic channel model (SACM) for processes of complex decomposition and complex formation to low energies. The change of the representation from adiabatic into the postadiabatic (dynamic) one transforms the coupling to a localized form and makes it possible to find conditions for description of the half‐collision dynamics in terms of uncoupled dynamic states. This result can be regarded as the extension of the statistical adiabatic channel model beyond its formal limits of applicability provided the adiabatic channel potentials are replaced by the postadiabatic (dynamic) potentials. The obtained results are exemplified by calculation of the capture cross section in the approximation of unc...

Collision induced absorption in mercury–rare-gas collisions

The far-wing excitation and probe technique is applied to observe quasimolecular absorption bands on the blue side of the Hg 6 1S0–6 3P2 atomic line for the Hg–Ar, Hg–Kr, and Hg–Xe mixtures. It is found that the excitation of this band is followed predominantly by a rapid elastic half-collision scattering on the excited state potential yielding the nascent product state Hg(3P2). This gives direct evidence of the assignment of the absorption to the c 31→X 10 collision induced dipole transition of the Hg–rare-gas quasimolecules. A chance of nonadiabatic transition from the c state is negligibly small compared to the elastic scattering. Analytical procedures are presented to deduce the c–X transition dipole moment from the relevant potential energy curves by making use of the Hund’s coupling schemes of the molecular electronic states. The c–X transition dipole moment is estimated as a function of the internuclear distance and is incorporated into the analysis of the observed band profiles. The potential ener...

Far‐wing excitation study on the transit region of Hg 3P1→3P0 intramultiplet process in collisions with N2 and CO

Laser‐pump and probe approach has been applied to the far wings of Hg 3P1−1S0 resonance line broadened by collisions with N2 and CO to measure excitation spectra for the formation of Hg(6 3P0) and Hg(6 3P1). The excitation spectra are highly asymmetric with the red wing being much more extended than the blue wing. The absolute ratio of nascent yields of Hg 3P0 to 3P1 is determined as a function of the excitation wave number. From these measurements, it is found, commonly for Hg–N2 and Hg–CO systems, that (a) the nascent product ratio, Hg(3P0)/Hg(3P1), grows on the red‐wing surface (the A state) with increasing shift, Δν, of the excitation wave number from the line center and finally surpasses unity; (b) the blue‐wing surface (the B state) gives mostly Hg(3P1) but has a small chance to give Hg(3P0). Time constant τ0 for the A→3P0 process of Hg–N2 is found to change from 17 to 35 ns as the absorption distance Rc between Hg and N2 changes from 3.6 to 4.7 A. From these values of τ0, the transition probabil...

c←X laser excitation spectrum of the Hg–Ar vdW complex

We have measured the c(v′=0−8)–X(v″=0) laser excitation spectrum of the Hg–Ar van der Waals complex. This corresponds to the first observation of the bound Hg–rare-gas complex in the dark c state. In this measurement, we employ the sequence of two laser pulses; the complex is excited by the first one to the dark bound level in the c state and then successively excited by the second one to another bright state for the optical detection. The Birge–Sponer (BS) plot of the v′ progression is well fitted by a straight line, suggesting that the c-state potential curve of Hg–Ar is well approximated by the Morse function. The linear fitting of this BS plot gives the potential parameters for the c state.

VIBRATIONAL PREDISSOCIATION RATE FROM DYNAMICS OF A FULL COLLISION : A TEST OF THE LANDAU METHOD AGAINST THE EXACT RESULTS

We applied the Landau method of calculating the coupling matrix element for a bound–free transition to the evaluation of the vibrational predissociation rate constant of the van der Waals complex ICl*–Ne. Use of the adiabatic separation of the radial and angular motion of the van der Waals modes complemented with the angular averaging with the help of the dominant natural expansion wave function of the bending mode, calculated by Lipkin, Moiseyev, and Leforestier [J. Chem. Phys. 98, 1888 (1993)], yields the rate constant which is about 10%–15% lower compared to the best theoretical estimates. This disagreement is ascribed to the true dynamical interaction between the stretching and bending modes which cannot be incorporated into the adiabatic separation of motion of these modes. Different approximations for treating bending motion are discussed and the sensitivity of the rate constant to the variation of principle parameters of the potential energy surface is studied.

Two-channel vibrational relaxation of H2 by He: A bridge between the Landau–Teller and Bethe–Wigner limits

We present a two-channel model of the vibrational relaxation (VR) of H2 molecule, ν=1, j=0→ν=0, j=0, in collisions with a He atom over a broad energy range, bridging the gap between the Landau–Teller and Bethe–Wigner limits. The model is based on the generalized Landau approach for calculating the VR transition matrix element. The analytical expression for the VR cross section qualitatively reproduces the energy dependence of the numerically calculated cross section and identify the key parameters that determine this energy dependence: the steepness of the repulsive part of the potential, the depth of the potential well, and the s-wave elastic scattering length. On the basis of our findings and available data from the literature, we discuss the manifestation of the attractive interaction on the qualitative features of the VR cross sections and rate constants over a wide range of energies and temperatures.

Classical diffusion model of vibrational predissociation of van der Waals complexes

The quantum and classical expressions for the vibrational predissociation rates of two-degree-of-freedom triatomic van der Waals complexes are compared. The classical rate is approximated by its diffusional counterparts (Parts I and II of this series), while the expression for the quantum rate is based on the generalization of the Landau method (E. E. Nikitin and L. Pitaevski, Phys. Rev. A, 1994, 49, 695). The ratio of the classical to quantum rates is expressed by an analytical formula which shows the reason for the difference between the classical and quantum rates and which explains a similar trend of both rates with the change of the key parameters of the vibrational predissociation event. We conclude that the occasional numerical closeness of classical and quantum rates results from the delicate interplay between the classical diffusion through a narrow energy layer and quantum tunneling through the broad energy range.

Double-cone problem revisited: Effect of the geometric phase on the broad semiclassical resonances

We present a semiclassical analysis of resonance states supported by a conical potential well coupled to a conical peak. The positions of the energy levels are calculated by Wentzel–Kramers–Brillouin (WKB) procedures, which are applied to an adiabatic Hamiltonian with the contribution from the geometric phase taken into account. The probability of escape from the well is calculated by resorting to a comparison equation of the Zener–Dykhne–Chaplik type. The widths of the energy levels are calculated via the escape probability by using a general relation derived recently by Zhu, Nikitin, and Nakamura [J. Chem. Phys. 104, 7059 (1996)]. It is shown that the present calculations are in excellent agreement with accurate numerical data for the positions and widths as recovered from an analysis of the scattering matrix and from a direct calculation of the complex-valued energy levels. The results obtained explain the very fast decay of the low-lying states and the good performance of the surface-hopping approxima...

Classical diffusion model of vibrational predissociation of van der Waals complexes: truncated mean first passage time approximation.

A classical diffusion theory of the vibrational predissociation for a triatomic van der Waals (vdW) complex A–BC is presented under the condition that the mean square energy transferred to the low-frequency oscillator per one ‘‘ encounter’’ with the repulsive part of the A–BC potential is small compared with the square of its dissociation energy. Unlike the case of a thermal dissociation of diatomic molecules in a heat bath, or from the case of fission of a strong bond in an isolated polyatomic molecule when the dissociation rate is given by the inverse of the mean first passage time, in the considered case of vibrational predissociation the dissociation energy is lower than the ‘‘ thermal’’ energy of the heat bath. For the present situation, a truncated first mean time approximation is developed and tested against numerical solutions of the respective diffusion equation. It is shown that the truncated first mean time approximation provides a reasonable approximation to the predissociation rate, provided that the relevant diffusion coefficient depends comparatively strongly on the energy of the vdW oscillator. This approach allows one to relate directly the mean square energy transferred to the vdW bond per one encounter in the initial energy state of the vdW oscillator to the rate of predissociation from this state.