P(l,Q)$ where $Q$ is the particle-decay energy, $\gamma ^2$ is the Wigner single-particle width, $P(l,Q)$ is the penetrability, and $l$ is the angular momentum of the transition. The penetrabilities are calculated in a Woods-Saxon well using the correct number of nodes of the wave functions.

The calculated decay schemes are similar to those presented in [@blank]. The calculated $^{22}Al$ half-life is 80 ms in the $3^+$ case and 85 ms in the $4^+$ case. It is similar to a previous study [@brown], where half-lives of $T_{1/2} = 78~ms$ for a $3^+$ state and of $T_{1/2} = 85~ms$ for a $4^+$ state were found. The difference between $3^+$ and $4^+$ calculations is not enough significant to prefer one or the other hypothesis.

However, the differences in the calculated branching ratios are more significant. For a $4^+$ ground state of $^{22}Al$, the branching ratio of $\beta$-$\gamma$ decay is 39.4%, whereas the same branching ratio is 48.9% for a $3^+$ ground state. Similarly, a $\beta$-p branching ratio of 53% is obtained in the $4^+$ case, while this number drops to 39.5% in the $3^+$ case.

$\beta$-2p emission has also been investigated as a sequential emission, a first proton is emitted from $^{22}Mg$, followed 