E (MeV)data/pwb | th_e(degree) | Q2(/fm2) | Amroun - sigma
fm2, e-5 |
dsigma,% | PWBA*
sigma fm2,e-5 |
data/PWBA* | PWBA **
sigma fm2,e-5 |
data/PWBA** |
640 | 35 | 1.92 | 1.29 | 3.7 | 1.29 | 1.00 | 1.56 | 0.83 |
413.3 | 30 | 1.16 | 65.47 | 3.2 | 64.4 | 1.017 | 69.8 | 0.94 |
35 | 1.55 | 23.14 | 3.3 | 22.7 | 1.019 | 24.9 | 0.93 | |
40 | 1.99 | 8.69 | 3.2 | 8.43 | 1.031 | 9.40 | 0.92 | |
45 | 2.47 | 3.33 | 3.5 | 3.27 | 1.018 | 3.70 | 0.9 | |
50 | 2.98 | 1.32 | 3.2 | 1.31 | 1.008 | 1.52 | 0.87 | |
394.5 | 50 | 2.73 | 1.83 | 3.4 | 1.82 | 1.005 | 2.09 | 0.88 |
53 | 3.02 | 1.06 | 3.1 | 1.09 | 0.972 | 1.26 | 0.84 | |
55 | 3.22 | 0.787 | 3.1 | 0.775 | 1.015 | 0.909 | 0.87 |
Determining accurate cross sections from form factors derived from
global fits
In Amroun's paper the form factors they determine come from a large
body of data. We should be able to use those form factors to calculate
cross sections to a better accuracy than the cross sections Amroun et al.
measured. From their global fit we can deduce the following uncertainties
in the charge form factor and thus the uncertainty in sigma elastic. These
values are read from the graphs. The first column shows the beam energies
and the minimum Q2 we can reach. Actually for the 995 and 1245 MeV runs
we can get to 1.2 and 1.87 /fm2.
E(MeV) Q2 /fm2 | Fchg | dFchg | dsigma/sigma (%) |
995,1245 2. | 3.5 e-1 | 1.5e-3 | 0.9 |
2045 5. | 9.e-2 | 1.e-3 | 2.2 |
2895. 10 | 5.0e-3 | 1.8e-4 | 3.6 |
4045. 20 | 3.5e-3 | 1.3e-4 | 7.4 |
4795 27 | 2.0e-3 | 1.e-4 | 10. |
Issues and questions
1) It would be useful to see how accurately the U. Mass. people judge
their form factor to be. Otterman's form factors give much closer
agreement with the data of Amroun.
Perhaps Akio could find out for us?
2) From the comparison of the data and PWBA in the first table it is clear we need to take Coulomb distortions into account to calculate cross sections from the form factors. Does any one have access to such a program?
3) Is it plausible that we could use the 2045 MeV elastic scattering
run to normalize the 4045 MeV quasi-elastic data? We would need to take
current scans for the beam heating effect at both energies.
If the current monitoring is accurate we could deduce the product of
(target density)*(solid angle) to within 2.2% from the elastic scattering.
As long as the target is leak tight we will not have lost any 3He switching
between 4045 and 2045 MeV.
a) at 4045 MeV, Nqe(4045,13.51)/Q(4045) = (rho*length @ 4045)*sig_qe(4045,13.51)*domega
b) at 2045 MeV, Nelastic(2045,12.5))/Q(2045)/sig_el(2045,12.5) = (rho*length@2045)*domega
c) so sig_qe(4045,13.51) = Nqe(4045,13.51)/Q4045)/Nelastic(2045,12.5)*Q(2045)*sig_el(2045,12.5)
Q is the total number of incident electrons in each run.
We could then use the quasi elastic electron scattering to normalize the 4045 MeV data.