Relativistic factor

In this work we treat classical and quantum relativistic kicked rotor problem. Using the relativistic standard map, we calculate the average energy of the classical rotor for various values of the relativistic factor. The relativistic quantum rotor is treated using the same approach as in the pioneering work (Casati et.al., 1979). 

It is clear that the relativistic standard map depends on two parameters K and (3. Here (3 is defined as a relativistic factor for the group velocity, oj/k. 

In Fig. 1(b) we compare the time-dependence of the energy for various valus of the relativistic factor, (3 = c-1. For smaller values of / it behaves as its nonrelativistic counterpart, while in strongly relativistic regime the saturation occurs quite quickly. 

The minimum impact parameter will correspond to those collisions in which the maximum amount of kinetic energy is transferred to the electron. Due to conservation of momentum, the maximum electron energy is Wmax = (j)me(2yv)2 where we have included the relativistic factor y due to the low mass of the electron. Recall that... 

The incorporation of relativistic correction factors, similar to Gryzinski s relativistic factor [22], on the QIBED model. The resulting model, referred to as MUIBED in Ref. [58], has been successfully tested with various experimental EIICS data for K-, L-, and M-shell ionization of atoms. 

In extending the CVTS model to relativistic energies, Haque et al. [48] incorporated in their XCVTS model a Gryzniski-type [22] relativistic factor R(U) given by... 

Here, q is the effective charge of the target as seen by the incident electron, n is the ionic parameter for the relevant orbit, and Xni is the kinetic energy of an electron in the relevant ionized orbit. While s i influences both the peak position and magnitude, qni controls only the magnitude. The KLV model of Kolbenstvedt [23] fixes ijls = 0.499 for the E-shell ionization, such that Nu r)ni = 0.998 with Nu = 2. The appropriate forms of the relativistic factor RF and the scaling factor FM, which are detailed in Ref. [50], are, respectively, given by... 

With Rb and RM in Eq. (20), the relativistic factors for the K-shell ionization [58] in line with Gryzinski s relativistic factor [22] are as follows ... 

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