Quasibound states

The preceding discussion was limited mostly to VP processes occurring by direct coupling of the quasibound state of the complex to the dissociative continuum, which is the simplest and most commonly observed decay route for the complexes. However, these systems also serve as ideal venues for studying an array of more complicated dynamical processes, including IVR, and electronic predissociation. This brief section will focus on the former, underscoring some of the inherent dynamical differences between Rg XY complexes by discussing the IVR behavior of a few systems. 

Briefly, XANES is associated with the excitation process of a core electron to bound and quasibound states, where the bound states interacting with the continuum are located below the ionization threshold (vacuum level) and the quasibound states interacting with the continuum are located above or near the threshold. Thus, XANES contains information about the electronic state of the x-ray absorbing atom and the local surrounding structure. However, as stated above, unhke EXAES, since the excitation process essentially involves multielectron and multiple scattering interactions, interpretation of XANES data is substantially more complicated than that of EXAFS data. 

Among them, Li-i-HP can be considered a benchmark model system [29, 30] because its low number of electrons makes possible to calculate accurate PES s. Its electronic spectrum has been meassured by Polanyi and coworkers [22], and has been recently very nicely reproduced using purely adiabatic PES s [31]. In the simulation of the spectrum[31], the transition lines were artificially dressed by lorentzians which widths were fitted to better reproduce the experimental envelop. The physical origin of such widths is the decay of the quasibound states of the excited electronic states through electronic predissociation (EP) towards the ground electronic state. This EP process is the result of the non-adiabatic cou-... 

Let s consider an initial quasibound state q/ (r, R)Co , corresponding to a rovi-brational level A in an excited electronic state a, which decays on dissociative states in the electronic state (3, (r, where v, j labels the quantum... 

When there are many (quasi)bound states, healing can occur in an off-diagonal manner in that the (quasibound) state that they come back to need not be the same as the (quasibound) state that they dissociated from. Healing thus provides for an enhanced mixing of the bound phase space. 

V. Engel Let me come back to the distribution of lifetimes of the ZEKE Rydberg states. I wonder if there is a simple picture behind. Consider a much simpler molecule, namely the Nal molecule Prof. Zewail told us about. There you have a bound state coupled to a continuum. It can be shown that in such a system the lifetimes of the quasibound states oscillate as a function of energy. In fact, Prof. Child showed with the help of semiclassical methods that there are lifetimes ranging from almost infinity to zero [1]. That can be understood by the two series (neglecting rotation) of vibrational levels obtained from the adiabatic and diabatic picture. If two energy levels of different series are degen-... 

It can also be noticed in Fig. 1 that spectral features for these three peaks are not symmetrical that is, their spectral shape deviates considerably from a simple Lorentzian line shape. Since the rotational contribution in the peak width in the PHOFEX spectrum is -1 cm-1, which is significantly smaller than the observed peak width, these asymmetrical spectral features are regarded as Fano-type profiles, which can appear in a spectrum for quasibound states. 

Because of the occurrence of quasibound states it was necessary to calculate the lifetimes of these states and to compute the associative Pgl Pgl ratio for times relevant in the actual experiment. For a collision energy of 42 meV, the dependence of the computed quasi associative Pgl cross section on the time (T) elapsed since electron ejection is shown in Fig. 26. Under typical experimental conditions the associative ion is detected at 7 10 5 sec. It is seen that at these times the quasibound states contribute only little to the experimentally determined associative Pgl cross section of 3oq at 42 meV. For comparison with experiment, a computed cross section for 7 = 13 fisec was used. 

The sharp structures above 50 meV are the result of orbiting resonances from the deep attractive well of Vu. All particles can tunnel through the maximum in Vu. The amplitude for finding a particle inside the maximum will be resonantly enhanced if the kinetic energy matches the energy of a quasibound state of Vu. For energies much below the barrier height, the... 

The nuclear wavefunctions and (jp are bound or quasibound states. In the harmonic approximation each can be written as a product... 

However, rather than continuing to extract differential and total cross sections, see Ref. [36], we will return to the precise meaning of m, defined in Eq. (25), remembering that our original task, defined above, is to give a uniform formulation of both bound and so-called quasibound states. In Appendix C, we have explicitly demonstrated the relation between nii(E) and the spectral function lim ph(E) = p E) that gives... 

P. Froelich, E. Brandas, Variational Principle for Quasibound States, Phys. Rev. A12 (1975) 1 P. Froelich, E. Brandas, Calculation of Resonance Widths via Expansion Techniques, Int. J. Quant. Chem. Symp. 10 (1976) 353. 

M.S. Zhao, M. Mladenovic, D.G. Truhlar, D.W. Schwenke, O. Sharafeddin, Y. Yan, D.J. Kouri, Spectroscopic analysis of transition state energy levels Bending-rotational spectrum and lifetime analysis of H3 quasibound states, J. Chem. Phys. 91 (1989) 5302. 

There is a second, alternative approach. One could assume that the unpaired neutron and the unpaired proton form a quasibound state. The total number of components of the angular momenta of this quasi-bound state is given by n n v. Then we introduce a pair of new bosonic creation and annihilation operators associated with each level of this subsystem, cj, Cj, I,J =... 

FIGURE 3a. The effects of a potential barrier (e. g. the centrifugal barrier) on the unbounded electronic wavefunction in the vicinity of a quasi-bound state at E = ER. The potential energy is denoted by a solid curve. The energy of the quasibound state is denoted by the horizontal line ER. The electronic wavefunctions are the dotted curves, the amplitudes of which represent i/re. The electronic coordinate is denoted by r... 

Vissers GWM, Groenenboom GC, van der Avoird A (2003) Spectrum and vibrational predissociation of the HF dimer. I. Bound and quasibound states. J Chem Phys 119 277-285... 

Abstract We show that the slowing down or speeding up of the decay of a quasibound state to the continuum are realizable by current-bias modulation in Josephson junctions (and their analogs in atomic condensates). 

Figure 2. Schematic of the effect of a potential barrier on an unbound wave function In the vicinity of a quasibound state at E E (adapted from Ref. 18). In the present context, the horizontal axis represents the distance of the excited electron from the center of the molecule. Reproduced with permission from Ref. 18. Copyright 1974, Academic Press.

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