Outgoing channel

However at long times a sample of prepared complex molecules will deplete according to the law, N(t) = N(0)e /T, where the lifetime r is related to the resonance width according to r = h/F. Furthermore, the decay flux into each outgoing channel is locked in fixed proportion at all... 

In a transmutation reaction, the incident neutron is absorbed, forming a compound nucleus that decays so that the residual nucleus is different from the target nucleus and the outgoing channel typically includes two particles. A transmutation reaction can be written as... 

In this reaction, a neutron is incident on a target atom with the elemental symbol T (atomic number Z and atomic weight A). The outgoing channel has a light and a heavy particle. The light particle, indicated by an elemental symbol r , is typically a proton, a deuteron, or an alpha particle, 2He". The heavy residual atom, denoted by the elemental symbol R, represents the target atom changed by whatever neutrons and/or protons that were transferred/picked up from the incident neutron. 

Figure 8.7 External field suppression of the role of centrifugal barriers in outgoing reaction channels. The incoming collision channels are shown by the full curves the outgoing channels - by the dashed curves. An applied (magnetic or electric) field separates the energies of the initial and final channels and increases the kinetic energy of the particles in the outgoing collision channels, thus accelerating their separation. Adapted from Ref. [91] Copyright 2005.

Finally, we bring attention to an experiment by Schepper et al.132 on vibrational excitation of N2 and CO in collisions with ground-state potassium without electronic excitation, who observe a special type of oscillations in the differential cross section. This may be of importance in a detailed discussion of quenching processes in the outgoing channel. 

In the second case, reading eq.(26), it is necessary that at least one of the Q-space states has the same parity as the operator p. Then, in (26) there may be a non-zero off-diagonal element connecting the ingoing to the outgoing channels. This state is called here a transition state (TS) and the coordinates of the stationary arrangement of external Coulomb sources a°TS (or otTS) is defined as a transition state structure (TSS). The TSS is a fundamental electronic property, while the quantum states of the TS include translational and rovibrational states with their characteristic density of states. 

Equation (2.35)]. Equation (15.6b) is formally equivalent to (2.66) with the exception that in the present case the outgoing channel also includes, in addition to the vibrational state, the particular electronic state. It is important to realize that because of the nonadiabatic coupling both excited electronic states and both electronic product channels are populated, even if one transition dipole moment is exactly zero for all nuclear geometries. Furthermore, the superposition of two complex-valued amplitudes in the case that both transition moments are non-zero can lead to interesting interference patterns. 

Magnitude of the wave function for a model collinear problem. The left panel in shows results on the ground potential surface, and the light panel shows results on potential surface. Times shown are at various intervals from t = 50 a.u. to t — 1900 te only a slight increase in probability density in outgoing channel A on the ground al surface at last time shown. (From Fig, 2, Ref, [104].)... 

For the sake of simplicity, assume that one construction using the channel concept. For Cav-1 the quantum state can be constructed with a simplified model for which only d5/2 states are given the possibility to show nonzero amplitudes. The outgoing channel looks like ... 

Table 2 Explosive nucleosynthesis in supemovae. Similar to Table 1, but for the explosion of the star. The (A, B) notation means A is on the ingoing channel and B is on the outgoing channel. An a is same as " He, y denotes a photon, i.e., a photodisintegration reaction when on the ingoing channel, n is a neutron, /3 shows 3-decay, and...

Wigner s scattering theory revolves around three matrices which couple the incoming and outgoing channels, viz. 

Finally, an example in which all three types of coupling (radial, rotational and spin-orbit) are operative is the charge-transfer reaction Ar ( P)-l- H- Ar( S)-l-H. All three have been calculated as a function of intemuclear separation. The entrance channel correlates with B 2, a Il, A II and b Z states, while the outgoing channel possesses only Z symmetry. (The angular coupling involves the term with a maximum around 0.4 a.u. the radial coupling is only about half of this and finally the spin-orbit operator couples the output channel X Z with the upper state of the ingoing partners. 

For the purpose of the Wigner laws, a transition is classed as inelastic if the kinetic energy released is large compared to the centrifugal barrier in the outgoing channels. 

The states of the system described in this way without taking into account the exchange interaction energy are called the ingoing and the outgoing channels of the reaction. 

When the system moves from left to right on the diagram in Figure 3.8, it is first in the initial state (the channel term U.)> meaning thereby that the electron is localized on A. After this it passes to the adiabatic term (the electron is common to both A and B). Finally, the system goes over to the term of the outgoing channel, i.e. the electron is localized on B. 

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