EXPERIMENTAL REQUIREMENTS

**Table 2:** Kinematics for the proposed measurements. All data will be taken at 6 GeV beam energy. The run time includes time for all four targets, plus dummy running and overhead for target and momentum changes.
$\theta$	E'	x	Q²	W²	time
(deg)	(GeV)		(GeV/c)²	(GeV)²	(hours)
15	3.0-5.0	0.21-1.0	1.2-2.0	0.9-5.4	22
	(4 settings)
23	2.1-4.0	0.27-1.0	2.0-3.8	0.9-6.2	28
	(5 settings)
30	1.5-3.2	0.29-1.0	2.4-5.2	0.9-6.9	33
	(6 settings)
45	0.75-2.1	0.27-1.0	2.6-7.3	0.9-8.0	44
	(8 settings)
60	0.51-1.4	0.30-1.0	3.1-8.6	0.9-8.0	79
	(8 settings)

Table 2 lists the kinematics we propose to measure. Target and momentum changes are included in the total time at each scattering angle. In all cases, data will be obtained utilizing 4 cm hydrogen, deuterium, ³He, and ⁴He cryogenic targets and a 3% (radiation length) aluminum target. We will run at currents between 20 and 50 $\mu$ A with 6 GeV beam energy. Table 3 is a summary of the beam time required for the measurement. In addition to the data acquisition time, we have allocated time for checkout and background measurements, spectrometer angle changes, and one changeover from hydrogen and deuterium targets to helium targets.

One of the possible significant backgrounds for the measurement is electrons coming from charge symmetric processes such as the decay of neutral pions or pair production. We will make measurements of positrons in order to subtract the charge symmetric background. JLab experiment E89-008 was run at 4 GeV over a similar range of angles. For a scattering angle of 55 $^\circ$ , they saw a maximum e⁺/e^- ratio of 15%. However, this was for x>1 and a thick target. At lower x values, the e⁺/e^- ratio was typically at or below 10% for the thick target. For a thin target (similar in thickness to the targets we propose to use) the e⁺/e^- ratio at larger angles (74 $^\circ$ ) was $\sim 20$ %. SLAC experiment E139 ran at higher energies (8-25 GeV) and found that the charge symmetric background was negligible for most of their kinematics, and largest ( $\sim$ 10% on deuterium) at their lowest x and Q² values (x<0.1). We do not expect large backgrounds except possibly at the lowest electron momentum settings and largest angle. Pions are the other main source of background for the measurement. For the E89-008 experiment, the combination of lead glass shower counter and gas Cerenkov detector in the HMS (and SOS) provided pion rejection at $\sim$ 15,000:1 for a pion momentum of 1.0 GeV/c, and almost 100,000:1 for momenta above 1.5 GeV/c. For the high momentum settings, this is more than adequate to remove any pion contamination from the measurement. For lower momenta, the pion contamination may become non-negligible. Since E89-008, the calorimeter has been modified so that the front two layers are read out from both ends, so we expect the pion rejection for the low momentum pions to be better than the estimates above. The only place where we anticipate the possibility of insufficient pion rejection is the lowest x values at 60 $^\circ$ . As we will have direct measurements of the pion and charge symmetric backgrounds, we will be able to tell if the effect of these backgrounds is large. Even if they are large, these backgrounds should not have a significant impact on the proposed measurement. In both cases, the region where we anticipate possible problems is at very low x at the largest angle setting. However, the data at lower angles covers the same range in x and is only slightly lower in Q².

We estimate a systematic uncertainty of $\sim 3$ % in the measured cross sections for most of the kinematics. To correct for density changes due to localized heating in the cryotargets, we will measure rate as a function of current for each target. As this effect depends on the intrinsic beam spot size in addition to the raster size, we will make regular checks of the beam size, to insure that it does not vary significantly. Many sources of uncertainty will cancel in the cross section ratios for different targets, and we estimate a final systematic uncertainty in the ratios of $\sim 1.5$ %. Table 4 shows the contributions to the systematic uncertainties in the target ratios.

**Table 3:** Beam time request for the proposed experiment. The time shown is for HMS running. The SOS will be used for more extensive measurements of the charge symmetric background, and for parasitic data acquisition at the highest x values at 60 $^\circ$ .
Activity	Time
	(hours)
Production Running	206
Target Boiling Studies	20
Angle Changes (10)	10
Target Changeover	12
e⁺ measurements	8
Beam spot monitoring	4
checkout/calibration	24
Total	284
	(12 days)

**Table 4:** Systematic uncertainties in the ratio $\sigma_A/\sigma_D$ . The last column includes only the portion of the systematic uncertainty that does not cancel when taking the target ratios. Note that the uncertainty in the thickness of the deuterium target is a common uncertainty for the $\sigma_A/\sigma_D$ ratios for ³He, ⁴He, and aluminum.
Source	Uncertainty	Uncertainty in
		$\sigma_A/\sigma_D$ (%)
Beam Energy	$1\cdot 10^{-3}$	0.1
HMS Angle	0.5 mr	0.1
HMS Momentum	$1\cdot 10^{-3}$	0.1
Target Thickness	0.5-1.0%	1.2
Beam Charge	0.5%	0.7
Target Boiling	<2.0%	0.5
Endcap Subtraction	<2.0%	0.5
Acceptance	<2.0%	0.2
Radiative Corrections	<2.0%	0.2
Detector Efficiency	<1.0%	0.1
Deadtime Corrections	<1.0%	0.1
Total systematic uncertainty		1.6%