Simultaneous measurement of G

The electric form factor of the proton G can also be measured during this experiment with a minimum of overhead and additional instrumentation. There are two ways of determining G with polarized ammonia targets: measuring the inclusive cross section asymmetry for elastic e-p scattering on the polarized hydrogen nuclei in NH , and measuring the asymmetry for electrodisintegration of the deuteron, with detection of the polarized protons in ND . Both methods can be used in the present experiment. The former approach is of interest for an accurate determination of G, the latter method provides an ideal test of our understanding of the reaction mechanism of the reaction used for the determination of G as the same reaction with the same potential complications (FSI, MEC) is used to measure a known quantity , G.

For a precise determination of G the easiest way is the measurement of the asymmetry

by detecting the electrons scattered elastically from the protons in ammonia. The experimental asymmetry

is related to through the beam and target polarizations and , and the dilution factor f, which is just the ratio of the number of polarizable hydrogen nuclei times the e-p unpolarized cross section to the sum of the number of nuclei of each atomic species in the target material times their respective e-A cross sections , integrated over the experimental width of the elastic peak:

 

In the region of energy loss of the elastically scattered electrons, is dominated by the quasielastic scattering contribution. For an estimate of the rates, the full magnitude of can be calculated with the aid of the QFS code of Lightbody and O'Connell. The experimental width of the elastic peak has been estimated from the beam and final electron energy resolutions, spectrometer angular resolution and contributions from energy losses and multiple scattering in the target and electron path. The estimates range from MeV at low Q to 17 MeV at high Q .

For the input values of , , and using the HMS solid angle acceptance of 10.4 msr we have computed the expected counting rates and required time to measure with a 2% statistical precision. The luminosity assumed is the same as that of the part of this proposal: 40 Hz cm . The results are shown in the table 3.

 

0.5 -13.7% 438 309 0.80 226 0.5

1.0 -14.2% 60 29 0.84 29.2 3.1

1.5 -16.5% 9.7 4.6 0.84 4.8 14.1

2.0 -18.3% 2.2 0.95 0.86 1.1 46

In this type of measurement, a correction has to be made for the asymmetry (entirely quasielastic) induced by the polarization of the nitrogen. This small systematic effect can be estimated with reasonable accuracy from the shape of the scattered electron spectrum on both sides of the elastic peak. Its magnitude is small because the contribution to this asymmetry comes from the unpaired proton in N only, the paired nucleons in this nucleus cannot be polarized. In addition, this asymmetry can actually be computed from the easily measured polarization of N and its shell structure, which places the unpaired seventh proton in a state, with a net 1/3 probability of being aligned opposite to the N spin. Measurements of the N polarization in NH indicate that % for %, so the expected nitrogen contribution is % of the proton asymmetry. The uncertainty in this contribution is less than 10%.

The above estimates show that is a highly competitive method for a precision determination of G. The corresponding data taking times are actually considerably smaller than the ones discussed in the proposal of Perdrisat et al (PR89-014).

Of more direct interest to the determination of G is the option to measure G via the reaction. This reaction involves the same complications as the reaction used for the determination of G and a measurement of the known G allows to check our understanding of the reaction mechanism in an ideal way. FSI and MEC influence and in a nearly identical way.

Such a measurement of G via is obviously much easier than the measurement of G: G is much larger than G, and the detection efficiency for protons is close to one. The rate for G is 10 - 100 times higher.

The main difficulty involved with the detection of protons is that the strong target magnetic field produces a substantial deflection of the protons. For the integrated field times path length magnitude of 1.34 Tesla-meters table 4 shows the total vertical deflection of the protons at the plastic detector location.

The column labelled contains the deflections of the scattered electrons that start in the horizontal plane; are the deflections of the corresponding protons that also leave the scattering point horizontally; on the other hand is the deflection angle of the protons associated with electrons that enter the spectrometer at the horizontal plane after being deflected downward, from an upward initial direction. The latter protons would correspond to an electron phase space that is symmetric about the horizontal plane and therefore are the preferred ones for detection. Their deflections are tabulated in the last column. It should be pointed out that these values correspond to protons along the central momentum transfer. For momentum transfers corresponding to the upper or lower limits of the electron spectrometer's horizontal acceptance, the deflections (in parentheses) are smaller or larger, respectively. The worst case is for Q =0.5 (GeV/c) .

 

0.50 2.0 0.760 17.3 10.4 3.4 0.62 (0.51 to 0.78)

1.00 2.3 1.136 11.6 4.6 3.4 0.27 (0.19 to 0.34)

1.50 2.8 1.465 9.0 2.9 5.5 0.28 (0.22 to 0.35)

2.00 3.2 1.773 7.4 2.1 8. 0.29 (0.26 to 0.36)

It is apparent from the above table that, with the exception of the Q =0.5 (GeV/c) point, the deflection of the proton represents no problem. The neutron detector has large enough an acceptance to detect the recoil protons, and the proton data will be obtained simultaneously with the neutron data. If the test of the reaction mechanism needs to be extended to Q =0.5 (GeV/c) , a (very short) run with the neutron detector raised by 60cm could be performed.

The contributions of the polarized protons in nitrogen are somewhat larger than in the case of inclusive measurements, even if ND is used, because the nitrogen polarization is of the deuteron, so the correction is -1/18 = -5.5%, a correction that easily can be calculated to the accuracy desired for the check envisaged here. On the other hand this choice of N as target material has the very important additional advantage of entirely eliminating the nitrogen polarization contributions to the neutron measurement since will be measured with electron-neutron coincidence spectra, which obviously contain no proton contamination, except from second order processes, as discussed elsewhere in the proposal.