Lead Converter

A 1.1 mm thick, 35 cm long and 13 cm radius cylindrical lead sheet was wrapped around the $A, A'$ scintillators. This lead sheet converted the real photon-pairs into pairs of $e^+e^-$ tracks.

Table 3.2: RMC Spectrometer dimensions (26). CW denotes the cell half-width at the radial center of the superlayer and S denotes the spacing between IWC anode wires or the cathode strips.

Component	Sectors	Inner Radius (cm)	Dimension
		$r$	$\ell \times 2\pi r \times t$
A Scint.	4 arcs	12.20	508$\times$191.6$\times$3.2 mm
A' Scint.	4 arcs	12.60	508$\times$197.9$\times$3.2 mm
B Scint.	12 sectors	15.20	483$\times$ 81.5$\times$3.2 mm
C Scint.	12 sectors	15.80	457$\times$ 84.7$\times$3.2 mm
D Scint.	16 sectors	59.37	940$\times$236.0$\times$6.4 mm
Pb Converter	1 sheet	13.00	817$\times$ 351$\times$1 mm
IWC
Inner Cathode	384 strips	26.47	-45$^\circ$ S = 3.06 mm
Anode	768 wires	27.02	Axial S = 2.21 mm
Outer Cathode	384 strips	27.57	+45$^\circ$ S = 3.19 mm
Drift Chamber
Inner carbon
fiber cylinder		30.20	90$\times$0.075 cm
Superlayer 1	56 cells	34.70	CW = 1.947 cm
Superlayer 2	64 cells	40.80	CW = 2.003 cm
Superlayer 3
(stereo)	72 cells	46.90	CW = 2.046 cm
Superlayer 4	80 cells	53.00	CW = 2.081 cm
Outer carbon
fiber cylinder		58.00	90$\times$0.1 cm

The optimum thickness of the lead sheet was determined from Monte Carlo simulations (30) of the photon energy resolution ($\Delta E/E$). The energy resolution decreases with increasing thickness while the acceptance of photon detection ( $\epsilon \Omega$) increases with the thickness. The optimum thickness was found to be 1.1 mm from RMC GEANT Monte Carlo simulations. Thus a 1.1 mm lead sheet was used as the photon-converter. The actual thickness of the lead sheet used was also measured. 15 sample measurements with a digital caliper (small scale division=0.0001 in) yielded a mean thickness of 1.120 mm ( $\sigma_{I}$ = 0.025 mm) with standard error of measurement $\sigma$=$\sigma_I$/$\sqrt{14}$ = 0.007 mm, t = 1.120 $\pm$0.007 mm. When this thickness was calculated from the measured weight ($m$ = 1175.4 $\pm$ 14.2 $g$) of a sample (40 $\times$ 23 cm$^2$) of the lead sheet used for the lead converter;

$$\begin{eqnarray*} m = \rho \times Vol. = 11.35 g/{\rm cm}^3 \times 40 {\rm cm} \times 23 {\rm cm} \times t \quad , \end{eqnarray*}$$

the thickness was found to be $t$ = 1.126 $\pm$ 0.015 mm, where the dynamic propagation error is obtained from:

$$\begin{eqnarray*} \frac{\delta t}{t} = \sqrt{ (\frac{\delta W}{W})^2 +(\frac{\de... ...175.8})^2 +(\frac{0.1}{40.0})^2 +(\frac{0.1}{23.0})^2 } = 0.013 \end{eqnarray*}$$

The $e^+e^-$ pairs converted from the photons followed curved tracks due to the axial magnetic field and were tracked by the multi-wire proportional chamber (IWC) and the large volume cylindrical drift chamber (DC).