Bethe approximation

Figure 5 Stopping power for protons on He calculated with the standard basis (basis A), with two consistent bases (B and C), and in the Bethe approximation using the kinetic theory [17, 18],...

The Born-Bethe approximation for low-energy electrons requires correction for two reasons. First, the integrals defining the total oscillator strength and the... 

The most essential step in a mean-field theory is the reduction of the many-body problem to a scheme that treats just a small number of molecules in an external field. The external field is chosen such that it mimics the effect of the other molecules in the system as accurately as possible. In this review we will discuss the Bragg Williams approach. Here the problem is reduced to behaviour of a single chain (molecule) in an external field. Higher order models (e.g. Quasi-chemical or Bethe approximations) are possible but we do not know applications of this for bilayer membranes. 

Sharma and Kern [95] have also performed a theoretical analysis, based on the Born-Bethe approximation, of V-R transfer between CO and para-H2. A difference betweenp-H2 and o-H2 in the quenching rate of vibra-tionally excited CO was first observed in 1964 by Millikan and Osburg [96], and more recently over a larger temperature range by Millikan and Switkes [97], The reaction... 

Figure 2.45. Bethe approximation surface LDOS of the (111) surface of the face-centered cubic lattice.

These results are an improvement of the simple molecular-field approximation, and are referred to as the quasi-chemical approximation. It is known to be equivalent to the Bethe approximation in the theory of ferromagnets. 

Figure 10 Experimental (solid symbols) and theoretical (dashed line, distorted-wave Born approximation full line, Deutsch-Maerk formula and BEB (Binary-Encounter-Bethe) approximation) electron ionization cross section for helium.

Figure 14 Experimental (solid circles and full line) and theoretical K-shell electron ionization cross section for argon dashed line, Born-Bethe approximation dash-dotted line, Deutsch-Maerk formula open circles, Born-Bethe including relativistic corrections.

A review of quantum theories (Born approximation, Bethe approximation, impulse approximation, etc.) as well as information on the classical calculations can be found in [4] (up to 1968) see also [5]. 

---