Bound and quasibound states

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. 

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... 

FIGURE 1.3 The different types of bound and quasibound states and scattering resonances. For the purpose of illustration only two potential curves are shown, corresponding to the lowest... 

In deciding the scope of this paper in relation to the title of the Workshop, I made a very broad interpretation of what constitutes the "HF dimer". In particular HF-HF collision processes are considered to be relevant since the wave functions describing these processes are the continuum solutions of the same Hamiltonian whose discrete solutions describe the bound van der Waals dimer. I even prefer to turn this around in my own mind, one of the most intriguing aspects of van der Waals chemistry is that it provides information on the bound and quasibound states of potentials that describe interesting collision systems ... 

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

A simple case is the portrayal of the ground state of the OH radical, see Figure 2.14. For simplicity, we show a part of the Morse potential energy curve with the highest bound and quasibound vibrational levels indicated by solid lines and dashed line, respectively, Figure 2.14a. The spectral density is... 

Uin(p) may have wells and these wells support bound or quasibound states which correspond to the resonances. 

Gao, B., Zero-energy bound or quasibound states and their implications for diatomic systems with an asymptotic van der Waals interaction, Phys. Rev. A, 62, 050702, 2000. 

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-... 

Model quantum-mechanical calculations were carried out on the basis of formulas (11.43) and (11.47), and functions V,(R) and T(7 ) were determined by comparison with the distribution shown in Fig. 15.51 As can be seen from Fig. 15, the measured distribution extends considerably into the region of associative Pgl characterized by condition (II.4a). In this region formula (11.47) was used, and in the Pgl region, characterized by (11.4b), formula (11.43) was used, except for those special values of e and / where, for a certain collision energy, the final state of nuclear motion corresponds to a temporarily bound—or quasibound—HeH+ system. 

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... 

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 =... 

The initial and final states are bound (or quasibound) and the absorption spectrum consists of sharp (or slightly broadened, but in principle resolvable) lines, as described in Section 6.1.1. 

True bound states can exist only at energies below the lowest threshold of the same symmetry as the state concerned. However, quasibound states can exist at energies above threshold, as shown in Figure 1.3. These are (relatively) long-lived states that can be seen in spectroscopy in much the same way as true bound states, but are coupled to a continuum and decay (dissociate) spontaneously. As a quasibound state has a finite lifetime t, it has a width in energy Te rather than a precisely defined eigenvalue,... 

The cross-sections in Figure 3.14 do not show a peak corresponding to the metastable state A. This is because the state A is too deeply bound and it is not accessible through scattering in the v = 1, y = 0 channel. Figure 3.14 also shows that the quasibound states preferentially undergo prereaction than predissociation. This... 

The rate constants and averages in Figs. 4-9 and Table 7 all refer to bound rearranged products. Only two of the initial states considered lead to any quasiboundrearranged products these are the 5,24 state, which is itself quasibound, and the 10,12 state, which is barely bound. The 5,24 state has only a small rate constant, 1.0 0.7 X 10 cm molecule"" s"", for producing rearranged quasibound products the 12,10 state has a larger rate constant for quasibound-state production, 1.3 0.4 x 10" cm molecule " s, most of which corresponds to final state (12,11). 

We show how one can image the amplitude and phase of bound, quasibound and continuum wavefunctions, using time-resolved and frequency-resolved fluorescence. The case of unpolarized rotating molecules is considered. Explicit formulae for the extraction of the angular and radial dependence of the excited-state wavepackets are developed. The procedure is demonstrated in Na2 for excited-state wavepackets created by ultra-short pulse excitations. 

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