Once the separate runs have been processed and the various gated energy spectra extracted in each case the spectra are all summed together. Despite the gamma peak calibration discussed at the end of section the spectra will not be perfectly aligned. This is the result of the actual energy fluctuations in the proton beam from the cyclotron. Small shifts are especially evident between runs occurring several months apart. These shifts are not enough to compromise the data, or affect the azimuthal cuts described above, however, it is necessary to line up the spectra closely in order separate the and data. The small energy corrections are made by lining up the most prominent state from the reaction. This is a state with an excitation energy of MeV [Ajz85]. The state is shown in figure .
Figure: energy spectrum from the reaction at . The (4.15 MeV) state is labelled.
Typically, the cross-section spectra are obtained by subtracting the from the spectra according to the formula
Then the deuterium spin observables would be obtained by a cross section weighted difference of the spin observables for carbon and
where represents a spin observable for target x.
For these experiments true cross-sections were not measured. So, it was necessary to find a method to compare the count spectra from the two targets on an equal basis. This can be done by normalizing the count spectra to total beam on target, live fraction, and target thickness. However, this was not always the best method because for at least part of the experiment the Faraday cups which measured total integrated beam on target were shorted to ground by rain water and entirely useless. The other method for comparing the count spectra is by subtracting a weighted spectra from the spectra until the ground state and 4.15 MeV state have disappeared. A sample of this type of subtraction is shown in figure .
Figure: Overlay of the , and spectra at . The deuterium spectra was obtained by a weighted subtraction of the carbon from the .
In terms of the count, , equation becomes
where is the mass fraction of deuterium in the target and R is the adjustable parameter which determines the weight of the carbon subtraction. Equation can also be expressed in terms of R
This method works best at and where the deuterium final state interaction has a higher excitation energy than the 4.15 MeV state and the part of the neutron spectrum above the final state can be forced to integrate to zero. At and the area of the subtracted spectrum around the 4.15 MeV state is fit to a smooth curve and the optimal R found by minimizing the .