Variable polarizations

Polarizations (h, P) not constant but changing over time. No other nuclei than deuterium involved. Using eq. 5 for summation and normalization leads makes the normalized counts proportional to the deuteron cross section only:

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

Beam-target asymmetry (eq. 2):

$$A_{BT}=\frac{\left\langle hP\right\rangle A_{ed}^{V}+\left\la... ...\right\rangle A_{d}^{V}+\left\langle T\right\rangle A_{ed}^{T}}$$

1..k (k+1..m) runs with positive (negative) target polarization and assuming that positive and negative beam helicity are the same. For the averaged polarizations we get:

     

$$\left\langle hP\right\rangle \frac{1}{2}\left( \frac{1}{k}\sum ^{k}_{i=1}h_{i}P_{i}-\frac{1}{m-k}\sum _{i=k+1}^{m}h_{i}P_{i}\right)$$ = (6)

$$\left\langle hT\right\rangle \frac{1}{2}\left( \frac{1}{k}\sum ^{k}_{i=1}h_{i}T_{i}-\frac{1}{m-k}\sum _{i=k+1}^{m}h_{i}T_{i}\right)$$ = (7)

$$\left\langle P\right\rangle \frac{1}{2}\left( \frac{1}{k}\sum ^{k}_{i=1}P_{i}+\frac{1}{m-k}\sum _{i=k+1}^{m}P_{i}\right)$$ = (8)

$$\left\langle T\right\rangle \frac{1}{2}\left( \frac{1}{k}\sum ^{k}_{i=1}T_{i}+\frac{1}{m-k}\sum _{i=k+1}^{m}T_{i}\right)$$ = (9)

$$\left\langle h\right\rangle \frac{1}{2}\left( \frac{1}{k}\sum ^{k}_{i=1}h_{i}-\frac{1}{m-k}\sum _{i=k+1}^{m}h_{i}\right)$$ = (10)