Landau-Zener parameter

Thus, the Landau-Zener parameter determining adiabatic or nonadiabatic character of transitions is [see Eqs. (34.15), (34.16), and (34.18)]... 

It gives 1 and dir/Lz in the limit of large and small values of the Landau-Zener parameter, respectively. 

The height of the potential barrier is lower than that for nonadiabatic reactions and depends on the interaction between the acceptor and the metal. However, at not too large values of the effective eiectrochemical Landau-Zener parameter the difference in the activation barriers is insignihcant. Taking into account the fact that the effective eiectron transmission coefficient is 1 here, one concludes that the rate of the adiabatic outer-sphere electron transfer reaction is practically independent of the electronic properties of the metal electrode. 

FIGURE 34.7 Dependence of the effective electron transmission coefficient on the electrochemical Landau-Zener parameter. 

An exact calculation gives the following expression for the adiabaticity parameter (Landau-Zener parameter) y, differing by a coefficient 2tt from the approximate estimate obtained by the... 

The Landau-Zener transition probability is derived from an approximation to the frill two-state impact-parameter treatment of the collision. The single passage probability for a transition between the diabatic surfaces H, (/ ) and R AR) which cross at is the Landau-Zener transition probability... 

In the above numerical examples the held parameter F is taken to be the laser frequency and the nonadiabatic transition used is the Landau-Zener type of curve-crossing. The periodic chirping method, however, can actually be more... 

Figure A.l. Schematic adiabatic potentials and various parameters used in the ZN formulas, (a) Landau-Zener type, (b) Nonadiabatic tunneling type. Taken from Ref. [9].

It has been realized recently that the parameter O is of importance in calculating differential scattering. This, in turn, stimulated calculation of for the earliest model of nonadiabatic coupling, the Landau-Zener-Stueckel-berg model [28-30]. The model is formulated for a Hamiltonian with AH linear in R ... 

In connection with the two-state approximation we mention paper [107] giving detailed analysis of the Landau-Zener-Stueckelberg model in which transition probabilities have been calculated for a wide set of parameters of the model, and also papers devoted to extensions of the model [108-110]. The exponential model with the Hamiltonian given by equation (26) was discussed in [111] and extended in [112],... 

The recently available spectroscopic data and the RKR potentials of the alkali hydrides allow us to determine the "experimental" values of the parameters relevant to the transition probability of the charge transfer processes. In the Landau-Zener model these parameters are the energy gap between the and X S adiabatic potentials at the avoided crossing distance and the coupling matrix elements. In this paper the coupling matrix elements are evaluated in a two-state ionic-covalent interaction model. The systema-tic trends found in the alkali hydride series for their X e potentials are presented. This leads to a simple model for the ionic potentials. 

In this study we first examine the systematics that exist in the RKR potentials of the state to establish that the potential curves are strongly ionic for R R. (R. is the distance of the pseudocrossing point). Next we evaluate an essentially experimental value of the parameters relevant to the cross section for the charge transfer process in the Landau-Zener approximation, We also construct a model ionic potential which can be used to describe the charge transfer process in the ionic region. 

On the basis of the Landau-Zener formula (Eq. 59), the parameter for discriminating between the adiabatic and the non-adiabatic limits of ET should be given by... 

The Landau Zener (LZ) problem The two-level Hamiltonian as well as the basis used to describe it are taken to depend on a parameter R in the form... 

Paulsen et al. (1972) developed an optical model for vibrational relaxation in reactive systems. Only collinear atom-diatom collisions were considered, i.e. impact parameter dependencies were omitted. The model was applied to vibrational relaxation of electronically excited I2 in inert gases, in which case dissociation of I2 is responsible for flux loss. Olson (1972) used an absorbing-sphere model for calculating integral cross sections of ion-ion recombination processes A++B ->A + B + AE, with A or B atoms or molecules. He employed the Landau-Zener formula to obtain a critical crossing distance Rc, and assumed the opacity to be unity for distances... 

Figure 6 clearly demonstrates the insufficiency of the simple Landau-Zener formula (10). This figure depicts the results for the linear potential model (in R), in which, as will be shown in the next section, the quantum mechanically exact analytical solutions have been obtained. The following two parameters can describe this model completely ... 

---