Polarized Target in CLAS

Dilution Factor - Discussion

We are discussing the relative PHYSICS merits for different choices of Background target materials. Ideally, the background target should contain EXACTLY the same materials, in EXACTLY the same amount, as the Physics target (NH3 or ND3, plus LHe4, foils, coils, etc.), MINUS the hydrogen content. Therefore, the target material of choice would be N15; however, we would ALSO have to guarantee that we have the same amount of N15 in that target as in the ammonia targets. This is of course close to impossible. Also, N15 boils around 77K and is liquid even below that, which makes it a very difficult material to handle.

In this note, I argue that TO FIRST ORDER, we do not need ANY background target at all. This is based on a specific analysis method: instead of the classical method of determining the target and beam polarization and the dilution factor independently and then correct the raw data, I propose that we use the ratio between the measured raw asymmetry at a given kinematic point (Q², W) of interest and the measured asymmetry in the elastic peak region (W=0.939). That way, not only do the polarizations of beam and target cancel, but we also need only to know the RATIO of dilution factors, which we can determine from our NH3/ND3 total count rate and the measured spectrum from hydrogen (E1 running period) alone.

The handwritten formulas are supposed to convince you of this. The symbols used have the following meaning:

P_el is the electron beam polarization.
n_Amm is the number density of Ammonia (NH3/ND3) molecules in our "production target".
Sigma_p and A||_p are the cross section and asymmetry on Hydrogen. The term with asterisk (Sigma_p A||_p)* comes from the single polarizable 1p1/2 proton in N15; the asterisk is supposed to indicate that the cross section and asymmetry are slightly changed from a free proton due to Fermi motion and binding effects.
P_H is the polarization of the free Hydrogen in NH3, while P_15N is the polarization of the N15 nucleus. The factor (-1/3) comes from the Clebsch-Gordan for the 1p1/2 proton; P_15N itself is also negative relative to P_H so that the overall contribution is positive (but small). Please excuse a small mistake I made: In all but the first formula, P_15N should appear as P_15N/P_H (normalized to the hydrogen polarization).

Hopefully the rest is self-explanatory.

Of course, one would still want to compare this method to the more "traditional" one, so we should not do away completely with a background target. However, it seems to me that we don't have to put such a very high premium on getting the best possible background target, especially if it requires extensive redesign.

Just as a starting point, I would propose to consider C12 for the background target. Clearly it's very easy to handle. In addition, its properties are not too different from N15. At least the binding energy per nucleon is the same to better than 10 keV (!) and the first excited states are relatively close (4.4 MeV vs. 5.3 MeV). The separation energy for a proton is 6 MeV higher in C12, but that shouldn't matter too much at our energy transfers. Although there are not data on Fermi momenta of N15, it is generally true that above A=12, the fermi momentum varies only slowly from nucleus to nucleus, so these should be comparable, too. The biggest correction we will have to make is likely due to the fact that the Z/N ratio is slightly (7%) larger in the case of C12, so we have to correct for the difference in the proton and neutron cross sections.

B.T.W., I am no longer so hot about CO2, since O16, as a doubly magic nucleus, is quite a bit more tightly bound (and probably more dense) than N15. In any case, please send you comments to the EG1 email distribution list or directly to me. - Sebastian