If we want to use the World's elastic scattering data on 3He for absolute
normalization we will not be able to obtain precision
better than the following
table shows:
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.
The proposal is to make a good measurement of sig_el(Q2) ( 15000 counts) for the minimum Q2 at the different energies by finding the ratio of cross sections at 1245MeV for the same Q2 as at the other energies. For the 1245 MeV data we will be able to reach values of Q2 where sig_el is well known, as well as having the whole month of March at this beam energy. This means we need to dedicate time during March for the absolute normalization runs, 45-52 hrs at 20uA for example.For the March normalization runs we will use HRSH fixed on quasi-elastic protons to do the relative normalization for each Q2. The elastic cross section at Q2=1.87/fm2 ( 1245MeV,12.5deg) is known to 0.9%. We can check our ability to do absolute cross section measurements by measuring beam heating, and current, and knowing solid angles and efficiencies at this Q2. Then, the relative measurements at the other Q2 can be compared against the deduced absolute cross sections from the earlier runs at the different energies. At the other energies, especially December's runs, we can tie the deduced elastic runs to the data runs by the luminosity scheme as proposed in July, for example.
Rate estimates
Assume that density = 0.090 g/cm3 , d_omega = 6.7 msr, dz = 5.8cm*
horizontal acceptance = -28.7 mr to 28.7 mr, the extra width reflects
the use of an extended target
vertical acceptance = -60 mr to 60 mr , m(3He) = 4.9817e-24g
rate = (dQ/dt)/e*(rho*dz)/m(3He)*(sig-av)*d_omega
Elastic Scattering Rates
Date E
Theta(deg) sig-pt
sig-avg rate@ 1uA
Time(@20uA)** Q2
MeV deg
fm2/sr fm2/sr
sec -1
hours
fm2
12/99 4045. 12.5***
1.62e-8 2.06e-8
0.90
0.23
19.27
12/99 4045. 13.51***
6.86e-9 8.3e-9
0.36
0.58
22.37
12/99 2045. 12.5
3.29e-5 4.08e-5
1788.
0.23#
5.01
2/00 4795.
12.5
3.07e-9 4.01e-9
0.18
1.15
26.91
2/00 2895.
12.5
6.21e-7 9.42e-7 41.3
0.23 #
9.96
2/00 995.
12.5
3.89e-3 4.06e-3
178K
0.23 #
1.2
----------------------------------------------------------------------------------------------------------------------------------
3/00 1245.
12.5
1.26e-3 1.36e-3
59.6K
0. 23 #
1.87 Measure sigma
elastic at these Q2
3/00 1245
43.32*** 1.02e-9
1.05e-9 0.0460
4.5
19.27 These
3/00 1245
47.21*** 4.17e-10
4.24e-10 0.0186
11.1
22.37 runs
3/00 1245
20.72
1.15e-5 1.25e-5
548.
0.23#
5.01 are for
3/00 1245
52.93
1.16e-10 1.18e-10 0.00517
40.0
26.91 absolute
3/00 1245
29.81
9.88e-8 1.07e-7
4.69
0.23#
9.96 normalization
total times@ 20uA
45.2 hrs - 51.8 hrs
----------------------------------------------------------------------------------------------------------------------------------------
commissioning period in December 1999, table prepared by Marat Rvachev,
10/27/99
12/99 845 12.54
7.61e-3 7.85e-3
344K
0.23#
0.870 Use as much
of the commissioning time
845 16.54
1.30e-3 1.35e-3
59.1K
0.23#
1.50
as possible to measure these elastic
845 19.15
4.44e-4 4.60e-4
20.1K
0.23#
2.00
cross sections. This will give us
845 30.94
4.89e-6 5.08e-6
222
0.23#
5.01 information
right at the start of the
845 45.20
3.82e-8 3.95e-8
1.73
0.35
9.96 data taking
as to how well we can
845 67.87
3.26e-10 3.29e-10
0.0144 14.3
19.27 independently determine
cross sections.
845 86.57
2.74e-11 2.75e-11
1.21e-3 170.
26.91
-------------------------------------------------------------------------------------------------------
* This length along the beam assumes that the spectrometer views the
10 cm target at 12.5 deg, and thus the ytg view is 21.6 mm across. Given
a transverse position resolution of 1.5mm ( from WWW) and requiring 3 sigma
separation between the wall and the beginning of the ytg cut means -6.3mm<ytg<6.3mm.
This produces a usable length along the z direction of ztg= ytg/sin(12.5deg)
= 58 mm.
** Assumes we collect 15000 elastic events.
*** We only need to do one of these.
# nominal time, not rate limited
Error Estimates based on pointing uncertainty of HRSE and beam energy uncertainty
| energy | angle | sig_av, fm2/sr | +-dsig_avg fm2/sr * | +-dsig_avg ** | relative *dsig/sig | relative**dsig/sig |
| 4045 | 12.5 | 2.06e-8 | 0.011e-8 | 0.008e-8 | 5.3e-3 | 3.9e-3 |
| 4045 | 13.51 | 8.3e-9 | 0.041e-9 | 0.016e-9 | 4.9e-3 | 1.9e-3 |
| 2045 | 12.5 | 4.08e-5 | 0.022e-5 | 0.008e-5 | 5.4e-3 | 1.1e-3 |
| 4795 | 12.5 | 4.01e-9 | 0.023e-9 | 0.002e-9 | 5.4e-3 | 5e-4 |
| 2895 | 12.5 | 9.42e-7 | 0.065e-7 | 0.058e-7 | 6.9e-3 | 6.1e-3 |
| 995 | 12.5 | 4.12e-3 | 0.014e-3 | 0.055e-3 | 3.4e-3 | 1.2e-3 |
| 1245 | 12.5 | 1.38e-3 | 0.0045e-3 | 0.004e-3 | 3.3e-3 | 2.9e-3 |
| 1245 | 43.32 | 1.05e-9 | 0.001e-9 | 0.004e-9 | 1e-3 | 3.8e-3 |
| 1245 | 47.21 | 4.24e-10 | 0.006e-10 | 0.001e-10 | 1.4e-3 | 2.4e-4 |
| 1245 | 20.72 | 1.25e-5 | 0.004e-5 | 0.000e-5 | 3.2e-3 | 0. |
| 1245 | 52.93 | 1.18e-10 | 0.0015e-10 | 0.002e-10 | 1e-3 | 1.7e-3 |
| 1245 | 29.81 | 1.07e-7 | 0.003e-7 | 0.002e-7 | 2.8e-3 | 1.87e-3 |