Absolute Normalization Scheme for e89044, September 16, 1999
Updated October 27, 1999

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
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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
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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
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* 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
* d_th = 0.1mr (WWW)
**d_E = 1e-4