Technical Note
radphi-2001-201

Energy nonlinearity and depth correction of showers in the LGD



Richard Jones
University of Connecticut, Storrs CT

Jan 11, 2001

Abstract:

Prior work on energy calibration of the Radphi lead-glass calorimeter showed that the total light yield in an electromagnetic shower rises somewhat faster than linearly with shower energy. This has been explained as a consequence of the dependence of the average shower depth on energy, coupled with light attenuation in the glass block. Energy loss through leakage out the back of the block is also present, but would cause the light yield to rise slower than linearly with shower energy. At angles below 20$^0$ where showers see over 45cm of glass, it is plausible that the attenuation effect would win out over leakage. But above 20$^0$ (almost 50% of the solid angle subtended by the LGD is above 20$^0$) the effective thickness of the glass decreases, and somewhere one would expect the sign of the nonlinear effect to reverse. Thus the nonlinear energy correction must be a strong function of the polar angle of the shower. The same is true of the $z$-centroid of the shower in the glass. This report gives the results of a detailed Monte Carlo simulation that reproduces the known nonlinear behavior of the LGD for normal-incidence showers and provides the information required to carry out this correction at larger angles where the shower leakage is substantial.