Test run $e^-$, $\pi^-$ and $e^+$ cross section

Electron(positron)/pion separation is done by using both Cerenkov counter and shower-preshower detector. For details please refer to previous report posted on http://www.jlab.org/ xiaochao/testrun/memo2.ps.
Cross section can be calculated by:

$$N_{\mathrm{events}} = \frac{\mathrm{d}^2\sigma}{\mathrm{d}\Omega\mathrm{d}E'} \times N_e\times {L\times\Omega_e\times\Delta p}$$

where
$Q$ is the total beam charge during the run,
$\Delta p$ is the momentum accpectance of the spectrometer given by $\Delta p = p_{\mathrm{center}} \times 0.08$,
$\Omega_e$ is the effective solid angle of the spectrometer, for 4cm target, $\Omega_e = 5.0$ msr; for 15cm target, $\Omega_e = 3.9$ msr
$L$ is the target length given by:

$$\mathrm{target}~\mathrm{ length[}\times 10^{21}\mathrm{cm^{-2}]} = \rho\times d$$ (1)

$$= 0.0708 \mathrm{g/cm}^3\times d\mathrm{[cm]} \times 6.02\times 10^{23}/\mathrm{g}$$

$$= 0.0708 \times 602 \times d\mathrm{[cm]}\nonumber$$

and number of events $N_{events}$ is given by:

$$N_{\mathrm{events}} = N\times\frac{\mathrm{scaler}~\mathrm{per}~\mathrm{ charge}} {\mathrm{total}~\mathrm{ accepted}~\mathrm{ triggers}} \times Q$$

where for e$^-$ and e$^+$, $N$ is number of events detected by the spectrometer; for $\pi$, $N$ is number of events corrected by decay ratio.
so

$$\frac{\mathrm{d}^2\sigma}{\mathrm{d}\Omega\mathrm{d}E'}\mathrm{[nb/GeV~sr]} = \frac{\mathrm{counts} \times\frac{\mathrm{scaler}~\mathrm{ per}~\... ...\mathrm{d[cm]} \times 0.005 \times\Delta p\mathrm{[GeV/c]}}\times\frac{1.6}{10}$$ (2)

Results of $e^-$, $\pi^-$ and $e^+$ cross sections are shown in table 1.



Kinematics: Beam energy = 5.650 GeV, $\theta_e=45^O$
Target: 4 cm LH2 for electron runs, 15 cm LH2 for positron runs

$p_e$	run#	Scaler per	total	$e^-$	total	$\pi^-$	$\big(\frac{\mathrm{d}^2\sigma}{\mathrm{d}\Omega\mathrm{d}E'}\big)_{e^-}$	$\big(\frac{\mathrm{d}^2\sigma}{\mathrm{d}\Omega\mathrm{d}E'}\big)_{\pi^-}$
(GeV/c)		Charge(3x)	accepted	($e^+$)	(global	(detected)	(( $\frac{\mathrm{d}^2\sigma}{\mathrm{d}\Omega\mathrm{d}E'}\big)_{e^+}$)	(nb/GeV
		(mC$^{-1}$)	triggers		cuts)		(nb/GeV-sr)	-sr)
1.50	2773	3121.6	393070	29185	318337	289152	0.20141	4.7858
	2774	3151.4	173370	12780	139499	126719	0.20187	4.8006
	2786	62367.3	1803176	(77)	1572702	-	(0.00079)	-
	2788	63072.8	352291	( 9)	305428	-	(0.00048)	-
	2789	63371.2	944823	(46)	818330	-	(0.00092)	-
	2790	62528.3	1804377	(67)	1579627	-	(0.00069)	-
0.90	2775	70717.9	765012	9789	692503	682714	1.3106	249.97
	2776	71144.2	303126	3980	274530	270550	1.3529	251.51
	2791	1171888.0	1805844	(611)	1288158	-	(0.1963)	-
	2793	1173312.6	1805590	(640)	1290782	-	(0.2059)	-
	2794	1173717.5	1808156	(668)	1291353	-	(0.2147)	-
0.55	2777	198758.1	1310365	14570	1159028	1144458	5.2375	1585.2
	2778	198813.6	926232	10372	813698	803326	5.2762	1574.6
	2814	3392409.5	1805373	(1612)	1118462	-	(2.4542)	-
	2815	3394497.9	1809950	(1679)	1122901	-	(2.5513)	-
	2816	3394932.6	1810738	(1655)	1130667	-	(2.5141)	-
	2817	3397113.2	1808348	(1627)	1143697	-	(2.4764)	-