Relaxation final state

This suggests a very simple way to include a substantial part of the correlations. One may simply perform a Hartree-Fock calculation for the ground and for the excited states, calculate the length and velocity forms of the cross section and take the geometric mean of the two. This is referred to as the HFU approximation if the continuum states are unrelaxed, and as the HFR if the Hartree-Fock geometric mean is calculated using relaxed final states. 

Figure 11 VBCI model developed to define electronic relaxation, i.e., the difference between the unrelaxed final state (Koopmans state) and the true relaxed final state/" The left side of the diagram represents the initial state configuration interaction between the d") ground configuration and the charge transfer...

For an ideal gas and a diathemiic piston, the condition of constant energy means constant temperature. The reverse change can then be carried out simply by relaxing the adiabatic constraint on the external walls and innnersing the system in a themiostatic bath. More generally tlie initial state and the final state may be at different temperatures so that one may have to have a series of temperature baths to ensure that the entire series of steps is reversible. 

K, L, M,. ..), 5 is the energy shift caused by relaxation efiects and cp is the work fimction of tlie spectrometer. The 5 tenn accounts for the relaxation effect involved in the decay process, which leads to a final state consisting of a heavily excited, doubly ionized atom. 

The first type of interaction, associated with the overlap of wavefunctions localized at different centers in the initial and final states, determines the electron-transfer rate constant. The other two are crucial for vibronic relaxation of excited electronic states. The rate constant in the first order of the perturbation theory in the unaccounted interaction is described by the statistically averaged Fermi golden-rule formula... 

The physical mechanism of entirely nonadiabatic and partially adiabatic transitions is as follows. Due to the fluctuation of the medium polarization, the matching of the zeroth-order energies of the quantum subsystem (electrons and proton) of the initial and final states occurs. In this transitional configuration, q, the subbarrier transition of the proton from the initial potential well to the final one takes place followed by the relaxation of the polarization to the final equilibrium configuration. 

The SE term accounts for the relaxation effects involved in the decay process, which leads to a final state consisting of a heavily excited, doubly ionized atom. 

The term S0 k) in (6-9) is a correction for relaxation or final state effects in the emitting atom, such as the shake-up, shake-off and plasmon excitations discussed in Chapter 3. The result of these processes is that some absorbed X-ray quanta of energy hv are converted not into photoelectrons of kinetic energy hv-Eb, but into electrons with lower kinetic energy as well. 

At Rc = y, the system can be described as being in a distorted state of the products. At last, product region, y > B, reaction force diminishes as the system relaxes structurally to its final state. An energy AE(y > B) is released ... 

A mathematical function used in fast-reaction kinetics to describe how a perturbation of definable strength and duration leads to a change in the kinetic parameters from an initial condition or state to a final state preceding or overlapping with the ensuing chemical relaxation process under investigation. 

It was argued that by the use of this method it is possible to increase the precision in the T value by a factor of two, as compared to what can be obtained by the FIR method with the same measurement time. With the constant-relaxation-period method, the number of systematic errors should decrease, since both the initial and final states are recorded for every phase. 

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