Constant polarizations, only deuterium

Assuming that polarized deuteron is the only nucleus involved in the scattering process makes the normalized counts proportional to the deuterium cross section :

$$N^{hP}\propto \sigma _{D}(h,P,T)$$

Resulting beam-target asymmetry (eq. 2) for constant P and h:

$$A_{BT}=\frac{hPA_{ed}^{V}}{1+TA_{d}^{T}}$$

The appearance of A_d^T in the denominator reflects the fact that T does not change sign with P.

Beam asymmetry (eq. 3 and 4):

$$A_{B\pm }=\frac{hPA_{ed}^{V}\pm hA_{e}\pm hTA_{ed}^{T}}{1+TA_{d}^{T}\pm PA_{d}^{V}}$$

Average of Beam asymmetries:

$$\frac{1}{2}\left( A_{B+}+A_{B-}\right) =\frac{\left( 1+TA_{d}... ...{\left( 1+TA_{d}^{T}\right) ^{2}-\left( PA_{d}^{V}\right) ^{2}}$$

This expression becomes identical to A_BT if one neglects the higher order (square) asymmetry terms .