1.2 Calibration method for the -counters in the Mass-8 experiment

J.P.S. van Schagen, K.B. Swartz and D. Wright

To obtain the coefficients a₁ and a₂ in the angular correlation (see Section 1.1) as measured with the Mass-8 apparatus, an accurate knowledge of the calibration of the -counters is necessary.

This calibration must be obtained in situ, since no natural mono-chromatic -sources of sufficient energy are available. However, the -decay feeds a broad final state in ⁸Be which subsequently decays into two -particles.² A Si-counter placed at 90° with respect to all seven -counters measured the -particle kinetic energy T with high resolution. This energy, corrected for the energy loss in the catcher foil, can be related to the (total relativistic) -endpoint energy E₀ by:

(1)

In measuring -particles in coincidence with an -particle in the Si-counter, spectra for different endpoint energies were obtained. These spectra were then fitted simultaneously to the theoretical spectral distribution for the electron/positron decay in a -minimization procedure. Only the values for the offset a_cal, the linear coefficient b_cal and the normalization constant N_nrom for each value E₀ were varied. The spectral distribution is given by:

(2)

which is valid for allowed transitions and includes folding with the -counter response. F(Z,E',^+/-) is the Fermi-function, pc the electron/positron momentum. For the lineshape R(E,E') a Gaussian peak with an exponential tail is used.³

As a typical example, Fig. 1.2-1 shows the results of the fit for an endpoint energy E₀ = 14.262 MeV where both the data and the fit have been converted to a Kurie-plot for easy comparison. The data in between the two markers were included in the region. Excellent agreement can be observed.

Fig. 1.2-1. Data and theoretical spectral distribution plotted as a Kurie-plot for E₀ = 14.3 MeV. The calibration coefficients are given by a_cal = 1.43 MeV, b_cal = 0.0135 MeV/CH.