A detailed $\beta$-decay spectroscopic study of ${}^{22}\mathrm{Al}$ was performed at the Radioactive Ion Beam Line in Lanzhou. With the $\beta \text{−}\gamma$-particle coincidence measurement by a high-resolution DSSD particle detection array and a high efficiency $\gamma$-ray detection array, total eight excited states in ${}^{22}\mathrm{Mg}$ fed by Gamow-Teller transitions was newly identified. The one-proton, two-proton, and $\alpha$ decays of the IAS at 14046(5) keV in ${}^{22}\mathrm{Mg}$, which were partly observed in different experiments before, were identified simultaneously in the present work, providing accurate spectroscopic information about its decay. A more complete $\beta$-decay scheme of ${}^{22}\mathrm{Al}$ was constructed and compared to the shell-model calculations with the USD-type Hamiltonians, USDC and USDB.

The study of the origin of asymmetries in mirror $\beta$ decay is extremely important to understand the fundamental nuclear force and the nuclear structure. The experiment was performed at the National Laboratory of Heavy Ion Research Facility in Lanzhou (HIRFL) to measure the $\beta$-delayed $\gamma$ rays of ${}^{26}$P by silicon array and Clover-type high-purity Germanium (HPGe) detectors. Combining with results from the $\beta$ decay of ${}^{26}$P and its mirror nucleus ${}^{26}$Na, the mirror asymmetry parameter $\delta$ ( ≡$f{t}^{+}$/$f{t}^{-}$− 1) was determined to be 46(13)% for the transition feeding the first excited state in the daughter nucleus. Our independent results support the conclusion that the large mirror asymmetry is close to the proton halo structure in ${}^{26}$P.