Present: M.D., A.D., J.S.,
S.Š: (By email):
I have coded the unpolarized Bethe-Heitler cross-section for a nuclear (carbon) target, and the result is shown in the attached figure in orange: the elastic part (dotted), the elastic+quasielastic (dashed) and the elastic+quasielastic+inelastic = total (full curve). I used the parameterizations (B49), (B52,53) and (B56,57) from Tsai (1974).
Now how does that compare to the free proton case? For now the only meaningful comparison I was able to make was in the elastic part. Assuming (B49) for the nuclear elastic form-factor I learn that this scales as mass*Z^2 (!!!). So I have multiplied the elastic part of free-proton Bethe-Heitler by 12*36 (!!!) and got the green dotted line.
Am I telling you that we should have multiplied the proton BH cross-sections by 12*36 = 432 instead of 6 or 12 ?? I was hoping that the target mass ("mi" in the paper) cancels somewhere, but it does not seem so. In Eq. (2.1), for instance, there is a mi in the numerator, but (k*pi) in the denominator is just Egamma*mi, so both mi cancel. So there is this unfortunate 12 in the form-factor and there is a 36 factor due to the charge in (B49), I am afraid, unless I am missing something.
It is harder to compare the inelastic parts on the same plot, as these scale linearly with Z, as in (B52,53) and (B56,57).
J. S.: TAC reports are expected around July 20th.
- Remembered why so far the GDH data on neutron have not been published in spite of the available deuteron data from MAMI/ELSA. This is because of the very large contribution from deuteron 2-body breakup at very low nu. With the 1/nu weighting, the 2-body breakup cancels almost exactly the resonance+large nu part. Accurately correcting for it to get the neutron information is very delicate without a very good model of the deuteron structure, see the study by H. Arenhövel concluding that "It is very doubtful, if not impossible, that one can extract in a simple manner the neutron spin asymmetry from the spin asymmetry of the deuteron." A later paper confirms this, stating "This means that a direct experimental access to the neutron spin asymme- try from a measurement of the spin asymmetry of the deuteron by subtracting the one of the free proton is not possible. On the other hand, polarization data of me- son production on the deuteron certainly will provide a more detailed test of meson production on the neutron and thus, in an indirect manner, on its spin asymmetry." This is a problem for the MAMI/ELSA data, but less for us because at large nu, the problematic contribution from the 2-body breakup is gone. Therefore, our extraction of the neutron information will be reliable, and consequently:
- The short-term goal of the proposal (studying the sum convergence) is unaffected by the issue;
- The longer term goal for the neutron (test of the GDH sum rule) is somewhat affected by the issue, but there are solutions:
- instead of complementing the possibly problematic MAMI/ELSA data, we can complement the JLab electroproduction data on neutron from 3He, extrapolated to Q=0 (the 3He data does not suffer from this problem). Since the electroproduction data are also limited to nu < 1.7 GeV (to compare to photoproduction: nu < 1.8 GeV) the point of the longer term goal remains.
- The development of models and expected data on the deuteron 2-body breakup from HIγS may solve the issue for the deuteron photoproduction data.
- Got a message from Eugene C. (for TAC purpose?) regarding target polarization with spins anti-parallel to the solenoid B-field. Answered that it was possible to do, but with 1/2 the relation time of the parallel configuration. This is still 1400h, so it is no issue for the short GDH run time.