Resonance state shape-type resonances

As the name suggests, shape-type resonances result from the shape of the potential at hand. But, what attributes must a potential have in order to trap the particle for a finite time and thus form a metastable state The wave nature of particles in quantum mechanics provides two typical ways for a... 

In the previous sections, we introduced resonance states and discussed situations in which resonances can be observed. In this section, we address the question of the origin for the appearance of resonances, or in other words, the basic question is what can bring about the formation of metastable states. In a very general manner, it is common to classify resonances into two main groups shape-type resonances and Feshbach-type resonances. Although the classification is not unique and may depend on the chosen representation of the Hamiltonian [46, 47], it can be extremely helpful in understanding the physical mechanism that leads to the formation of the metastable state. 

The situation depicted above is an example for the most common and vivid manner for the appearance of a resonance due to the shape of the potential. However, such metastable states can form even when the energy of the resonance state does not reside within some effective local well in the potential under study. A second way by which shape-type metastable states can form has much in common with optical resonators. In order to form a... 

Feshbach-type resonances [51], also known as Fano resonances [52] and Floquet resonances [22] depending on the system studied, are formed in a different manner. We encounter this type of metastable states whenever a bound system is coupled to an external continuum. In the same spirit as before, one can define a reference Hamiltonian in which the closed channel containing the bound states is uncoupled from the open channel through which the asymptote can be reached. When the coupling is introduced, the previously bound state decays into the continuum of the open channel. The distinction from shape-type resonances, described above, is that the resonance state decays into a different channel of the reference Hamiltonian. 

This paper will show that an Pt-H anti-bonding state shape resonance is present for both strongly and weakly adsorbed hydrogen. Both types of hydrogen are thus atomically... 

Fig. 7.Calculated Raman heterodyne signals of the detection beam showing Ramsey-type resonance line shapes. The sublevel detuning is normalized to the ground state relaxation rate Yg and the laser detuning is given in units of the Doppler width cte.Yvcc < notes the rate of velocity changing collisions.

Disregarding incorrect matching of the ENDOR resonance condition, the line shape of the EI-EPR spectrum is only identical to that of the EPR spectrum if35 (a) the induced ENDOR transition belongs to an I = 1/2 nucleus, (b) only cross relaxation processes of the type (ms, m() <- (ms - 1, mi 1) occur, (c) no relaxation takes place between different mr-states within a given ms-manifold. 

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