=\frac{N_{p (E5 \textgreater 0) Gaus}}{N_{p (E5 \textgreater 0)}}$\
        $R_2$ is the ratio between the Gaussian area of the proton peak and the total proton peak area in the conditioned spectrum. This takes into account that the Gaussian does not perfectly describe the peak in the conditioned spectrum.

    In practice, the low-energy part of the proton peak in the conditioned spectrum (E5 &gt;0) is fitted by a Gaussian. The area obtained is divided by $R_2$. This yields the total area of the proton peak in the conditioned spectrum. This value is divided by $R_1$ to obtain the area of the total proton peak (without condition). Finally, the branching ratio is determined by dividing this area by the total number of $^{22}Al$ implanted.\
    The simulations showed that the ratios $R_1$ and $R_2$ depend weakly on the $\beta$-particle energy (a maximum of 10% relative error). However, since they depend on the geometry, we need to determine these ratios from experimental data at least for one proton peak (for one $\beta$-particle energy) and use these ratios for the determination of the other proton peak areas.\

-   The $\beta$-trigger efficiency:\
    In the present experiment, the acquisition system was triggered by charged particles detected in E3, 