Resonance bound state

Table 5.18. Calculated energies (meV) of the first even-parity resonant bound states of isocoric and non-isocoric acceptors in silicon and germanium with respect to the 1 7+ VB [14]...

Theoretically, the process can be treated by adiabatically eliminating the continuum and all off-resonance bound states, as done in our discussion of partitioning theory. The result is an effective (2 x 2) Hamiltonian involving only the initial and target states. It has been shown [237] that in the counterintuitive" pulse ordering, the "dark" state of the system evolves, as in three-state STIRAP, from the initial state to the target state, provided the evolution is adiabatic. 

REMPI Resonance-enhanced multiphoton ionization— the ionization process whereby an atomic or molecular species absorbs two or more photons through a transition from an intermediate resonant bound state to a bound state. 

The energies of the selective adsorption resonances are very sensitive to the details of the physisorption potential. Accurate measurement allied to computation of bound state energies can be used to obtain a very accurate quantitative fonn for the physisorption potential, as has been demonstrated for helium atom scattering. For molecules, we have... 

In a time-dependent picture, resonances can be viewed as localized wavepackets composed of a superposition of continuum wavefimctions, which qualitatively resemble bound states for a period of time. The unimolecular reactant in a resonance state moves within the potential energy well for a considerable period of time, leaving it only when a fairly long time interval r has elapsed r may be called the lifetime of the almost stationary resonance state. 

Marcus R A 1973 Semiclassical theory for collisions involving complexes (compound state resonances) and for bound state systems Faraday Discuss. Chem. Soc. 55 34—44... 

Wang D and Bowman J M 1995 Complex L calculations of bound states and resonances of HCO and DCO Cham. Phys. Latt. 235 277-85... 

The wavepacket is propagated until a time where it is all scattered and is away from the interaction region. This time is short (typically 10-100 fs) for a direct reaction. Flowever, for some types of systems, e.g. for reactions with wells, the system can be trapped in resonances which are quasi-bound states (see section B3.4.7). There are eflScient ways to handle time-dependent scattering even with resonances, by propagating for a short time and then extracting the resonances and adding their contribution [69]. 

Figure B3.4.10. Schematic figure of a ID double-well potential surface. The reaction probabilities exliibit peaks whenever the collision energy matches the energy of the resonances, which are here the quasi-bound states in the well (with their energy indicated). Note that the peaks become wider for the higher energy resonances—the high-energy resonance here is less bound and Teaks more toward the asymptote than do the low-energy ones.

B3.4.7.2 NUMERICALLY EXTRACTING BOUND STATES AND RESONANCE FUNCTIONS... 

An alternative is to use iterative methods. The simplest iterative teclniique for calculating bound state or resonances is to pick a random initial wavefimction vi/q(a ) and propagate it forward in time, producing a wavepacket ... 

Of course, the distinction between reactive- and bound-state wave functions becomes blurred when one considers very long-lived reactive resonances, of the sort considered in Section IV.B, which contain Feynman paths that loop many times around the CL Such a resonance, which will have a very narrow energy width, will behave almost like a bound-state wave function when mapped onto the double space, since e will be almost equal to Fo - The effect of the GP boundary condition would be therefore simply to shift the energies and permitted nodal structures of the resonances, as in a bound-state function. For short-lived resonances, however, Te and To will differ, since they will describe the different decay dynamics produced by the even and odd n Feynman paths separating them will therefore reveal how this dynamics is changed by the GP. The same is true for resonances which are long lived, but which are trapped in a region of space that does not encircle the Cl, so that the decay dynamics involves just a few Feynman loops around the CL... 

The first term of Eq. (34) describes a direct transition from the bound state to the scattering projection of the structured continuum. The second term describes a resonance-mediated transition. 

Next, we discuss the J = 0 calculations of bound and pseudobound vibrational states reported elsewhere [12] for Li3 in its first-excited electronic doublet state. A total of 1944 (1675), 1787 (1732), and 2349 (2387) vibrational states of A, Ai, and E symmetries have been computed without (with) consideration of the GP effect up to the Li2(63 X)u) +Li dissociation threshold of 0.0422 eV. Figure 9 shows the energy levels that have been calculated without consideration of the GP effect up to the dissociation threshold of the lower surface, 1.0560eV, in a total of 41, 16, and 51 levels of A], A2, and E symmetries. Note that they are genuine bound states. On the other hand, the cone states above the dissociation energy of the lower surface are embedded in a continuum, and hence appear as resonances in scattering experiments or long-lived complexes in unimolecular decay experiments. They are therefore pseudobound states or resonance states if the full two-state nonadiabatic problem is considered. The lowest levels of A, A2, and E symmetries lie at —1.4282,... 

The relative merit of the two recursive methods in computing both the bound-state and the resonance spectra have been examined and discussed by several of authors,41,42,80,247,314-318 and the consensus is that their efficiency... 

Bound States and Resonances of the Hydroperoxyl Radical H02. An Accurate Quantum Mechanical Calculation Using Filter Diagonalization. 

The drawback of methods which are based on observation of ligand resonances is that they rely on a significant exchange of ligand between bound state and free state during... 

Alternatively, the much more common situation in trNOE studies involves fast exchange on the chemical shift time scale where the observed resonance shifts are weighted averages of the corresponding shift in the free and bound state [13]. A full account of the complete relaxation matrix and conformational exchange effects for n spins has been performed by London et al. [13], and a similar treatment was later incorporated into the programme CORCEMA [14]. 

---