Spectrum of a superconducting tunnel detector in a simple spherical model of electron loss

The loss in the initial stage of energy relaxation in the absorber of a superconducting tunnel detector is considered using a simple spherical model that describes the escape of a cloud of secondary electrons (formed upon relaxation of the primary excitations caused by X-ray absorption) from the absorber. The foundations of this model are justified. Three situations dependent on the ratio of the detector thickness L and electron range R leading to different types of spectra are examined. The position, amplitude, and width of the line recorded by the detector are determined as well.