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Equation of motion under DRIFT EXTERNAL command

The present version of CAIN accepts a constant external field only. The covariant form of the equation of motion
where tex2html_wrap_inline9624 is the proper time and tex2html_wrap_inline9626 the electromagnetic field tensor, can be solved exactly when the field is constant. The eigenvalues of the matrix tex2html_wrap_inline9628 is given by tex2html_wrap_inline9630 and tex2html_wrap_inline9632, where
Then, the solution is
where the upper (lower) sign applies to tex2html_wrap_inline9634 (tex2html_wrap_inline9636) and tex2html_wrap_inline9638 with tex2html_wrap_inline9640 being the antisymmetric tensor of rank 4.

The classical spin motion of electrons is given by the Thomas-BMT equation  
where a is the coefficient of anomalous magnetic moment  and

Figure 1: Field dependence of the anomalous magnetic moment of electron

When the field is very strong, a is different from the well-known value tex2html_wrap_inline9646 but is a function of the field strength characterized the parameter tex2html_wrap_inline9648.
The functional form of tex2html_wrap_inline9650 is shown in Fig.1. Simple polynomial approximations are used in CAIN.

Toshiaki Tauchi
Thu Dec 3 17:27:26 JST 1998