Quasibound levels

R. J. Le Roy, 2002, LEVEL 7.5 a Computer Program for Solving the Radial Schrodinger Equations for Bound and Quasibound Levels, University of Waterloo Chemical Physics Research Report CP-655. 

Figure 6.27. Morse potential for J = 0 and J = 10, showing the presence of the centrifugal barrier in the J = 10 case, and a quasibound level, QB.

It should be mentioned that significant variation of the decay rates to the continuum of a JJ as a function of the bias-current rate of modulation has been observed by Silvestrini et al. [Silvestrini 1997]. This observation was made under rather high-temperature conditions, where many (bound or quasibound) levels are populated in the JJ potential and the present picture does not hold. 

ABSTRACT. Previous theoretical and experimental work on the ions H+ and HD+ is reviewed. Earlier work using ion beam techniques to study the uppermost bound levels and quasibound levels of H+ is discussed, and a suitable model for the molecule in these levels is proposed. Earlier work using ion beam techniques to study the vibration-rotation levels of HD+ is reviewed. 

FIGURE 3.16 Adiabatic potential and the wavefunctions of the quasibound levels B and E shown in Figure 3.15 as functions of the atom-molecule separation. Amplitudes of the wavefunctions have been reduced by a factor of 10 for the convenience of plotting. (From Balakrishnan, N., J. Chem. Phys., 121, 5563, 2004. With permission.)... 

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. 

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... 

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-... 

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... 

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 =... 

A vibration rotation level of a diatomic molecule which lies above the lowest dissociation limit may be quasibound and able to undergo spontaneous dissociation into the separate atoms. This process is known as predissociation, and two different cases may be distinguished for diatomic molecules, as we will see shortly. Predissociation does not normally play an important role in rotational spectroscopy but merits a brief discussion here for the sake of completeness. 

The rotational levels are extrapolated to high J values according to the method of Khachkuruzov (7) who proposed a simpler form of Wooley s method (8). The rotational levels are weighted in accordance with the nuclear spin-rotation interaction (9) as follows even J weight = 0.625, odd J weight = 0.375. The so-called quasibound rotational levels were not Included in the calculation. No suitable spectroscopic information exists for any of the excited states of BSg. It should be noted that the... 

The so-called quasibound rotational levels above the dissociation limit (2,3) are also included. For a given vibrational quantum number, v, the summation over rotational states is carried out up to a rotational quantum number, J, given by lim ... 

We shall first address query (a), noting the important differences between the system in Ref. [Fischer 2001], characterized by a slightly tilted, shallow sinusoidal potential supporting a single quasibound band, and a biased JJ, de-scribable by a strongly tilted potential, characterized by a near-critical acceleration (a < ac = 2ki Uo/m) and supporting many bound levels [Barone 1982 Leggett 1987 Clarke 1988 Fisher 1988], The sinusoidal potential in Eq. (4) can be effectively replaced in a biased JJ by the cubic form (Fig. 1-upper inset)... 

To investigate different treatments of the spin-free relativistic effects, Wahlgren [38] performed some comparative calculations for Hg2 ", and the results are shown in Table XI. The calculations were for simplicity done at the SCF level, but the conclusions drawn should also be valid when correlation effects are added. To read Table XI correctly, it is important to note that Hg2 is only quasibound in a local potential minimum, with a large negative binding energy at the SCF level. The first comment that should be made on the results in Table XI is that the inclusion of relativistic effects is very important for both the geometry... 

A variational method within a diabatic scheme as well as a Diffusion Monte Carlo (DMC) method are applied to study the quasibound states of CI2 — He and CI2 — He2 van der Waals (vdW) clusters. The ground energy levels and the corresponding probability density distributions for aU relevant vdW modes are calculated for both clusters with the two methods. From the comparison of the results numerically obtained we conclude that the DMC method is a good way to determine the ground energy and the corresponding distributions of these complexes, in order to use them as initial states for a dynamical calculation. 

In Table 2 the vdWenergies of ChHe and ChHe2 determined by the variational and the DMC method, in the scheme of the diabatic separation, are presented. It can be noticed that energies within both approaches differ at most by 0.1 cm" . This result confirms the validity of the diffusion Monte Carlo method to provide accurate energy levels of quasibound states within a vibrational diabatic approximation. 

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