Relativistic potential scattering

The integral equations for relativistic potential scattering are conveniently written in terms of a four-dimensional notation for the four-component spinor vp). 

Figure 5.16 Top experimental normal emission (T-L) ARUPS spectrum for Cu (111), hv = 21.2 eV (Geriach etal. 1998). Bottom corresponding calculated ARUPS spectram using the muffin-tin approximation and the full potential version of relativistic multiple scattering theory. Reproduced with permission from Fluchtmann et aL (1998). Elsevier Science.

X. Wang, X.-G. Zhang, W. H. Butler, G. M. Stocks, B. N. Harmon. Relativistic-multiple-scattering theory for space-fiUing potentials. Phys. Rev. B, 46(15) (1992) 9352-9358. 

A reasonable way to estimate the size of the correlation correction to the relativistic tp potential is to make use of the semi-relativistic multiple scattering formalism [Ra 85] discussed in section 4.2. In analogy with the Watson theory, the leading correlation correction is quadratic in the relativistic NN invariant scattering operator and is proportional to two-body correlations in the target nucleus. 

Calculations have recently been made for this case using a coupled diannels Dirac method [Cl 91] in which the full p + C RIA optical potential scattering solution is obtained without using the DWBA. The results indicate that the relativistic DWBA is very accurate for this case. 

The dynamic calculations include all beams with interplanar distances dhki larger than 0.75 A at 120 kV acceleration voltage and thickness between 100 A and 300 A for the different zones. The structure factors have been calculated on the basis of the relativistic Hartree - Fock electron scattering factors [14]. The thermal difiuse scattering is calculated with the Debye temperature of a-PbO 481 K [15] at 293 K with mean-square vibrational amplitude

= 0.0013 A following the techniques of Radi [16]. The inelastic scattering due to single-electron excitation (SEE) is introduced on the base of real space SEE atomic absorption potentials [17]. All calculations are carried out in zero order Laue zone approximation (ZOLZ). 

The simplest form of scattering theory is for a single particle moving in a local external potential. If we ignore relativistic effects and return to the Schrodinger equation... 

An even simpler approach to relativity, for heavy elements, is to use effective core potentials (ECPs) to represent the core electrons, taking the potentials from various compilations in the literature that explicitly include relativistic effects in the generation of the ECPs. References to such ECPs are given by Dyall et al. [103]. These relativistic ECPs (RECPs) allow the inclusion of some relativistic effects into a nonrelativistic calculation. Since ECPs will be treated in detail elsewhere, we will not pursue this approach further here. We may note, however, that recent comparisons with Dirac-Fock calculations suggest that the main weakness in the RECPs is not the treatment of relativity but the quality of the ECPs themselves [103]. Different RECPs gave spectroscopic constants with a noticeable scatter, compared to Dirac-Fock, but the relativistic corrections (difference between an RECP and the corresponding ECP value) were fairly consistent with one another. 



---