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$\delta$-electrons and the Si detector

One of the first problems encountered is that of the $\delta$-electron contamination of the detector. The $\delta$-electrons are copiously produced by the $Pb$ beam nuclei passing through the $Pb$ target. The thickness of the target is 1.15 $g/cm^2$, or 18% of the radiation length. Due to the $z^2$ dependence of the ionization energy loss on the charge of the projectile, a passage of a beam nucleus without nuclear interaction (statistically, the predominant event) produces, typically, more $\delta$-electrons than originate from (even a central) interaction. Kinematically, the problem is that of an elastic scattering of a relativistic heavy incident nucleus on an (effectively resting) atomic electron - a particular case of a relativistic elastic two-body scattering (analyzed in [75] and other textbooks). For an electron initially at rest in the lab, the dependence of its final state energy on the emittance angle $\theta$ is unique, and there is no kinemitical restriction on the angle. The differential cross-section

$$\frac{\,d\sigma}{\,d\theta} \propto \frac{\sin \theta}{\sqrt{1-\sin^2\theta}}$$ (54)

grows with the polar angle for the angles of interest ( $\theta<\pi/2$). This results in a peculiar pattern of detector occupancy, with maximum occupancy at the outer rings of the detector - opposite to the trend seen in the nuclear interactions. In valid beam triggered runs (I looked at both field polarities, to disentangle effects of $\delta$-electrons from those of the geometrical misalignment) it was noticed that in the outer rings, the extra multiplicity on the outer rings, ascribed to the $\delta$-electrons, is comparable with the contribution of the nuclear interaction vertex. In the T0-amplitude triggered runs without magnetic field, $\delta$-electrons dominate the picture. In this situation, we decided to

• use runs with field on
• ignore the contaminated half of the detector in the physics analysis

In the 4 $GeV/c$ setting, the magnetic field strength in the first dipole (which includes the target area) is $\approx 0.8 Tl$. The kinetic energy spectrum of $\delta$- electrons falls off like

$$\frac{\,dN}{\,d(T/m_e)} \propto \Big(T/m_e\Big)^{-2}$$ (55)

Simple estimates, based on the kinetic energy spectrum (as well as GEANT simulations) lead to the conclusion that for all practical purposes the residual contribution of $\delta$-electrons to the multiplicity on the $\delta$-clean side is negligible for the field and geometry in question.