Background: The advent of radioactive ion beams has helped considerably to explore exotic decay modes like proton radioactivity in extremely proton-rich nuclei lying on or beyond the proton drip line. Recently, an experimental study was reported on the structural properties of proton-rich nucleus ${}^{11}\mathrm{O}$. Interestingly, ${}^{11}\mathrm{O}$ is the mirror nucleus of the widely studied $2n$ halo system ${}^{11}\mathrm{Li}$. In addition, ${}^{11}\mathrm{O}$ formed in the experiment was identified through its decay by $2p$ emission. A similar kind of interdependence between neutron halo and its mirror counterpart for $2p$ emission was reported [Charity, Elson, Komarov, Sobotka, Manfredi, and Shane, J. Phys.: Conf. Series 420, 012073 (2013)].

Purpose: To study and analyze whether the mirror nuclei of known $1n$/$2n$ halo systems are $1p$/$2p$ emitters.

Method: The preference for the mirror nuclei of $1n$/$2n$ halo systems for $1p$/$2p$ emission over the other ($2p$/$1p$ emission) is studied by $Q$-value systematics and potential energy minimization using a cluster-core model. The half-lives of the mirror nuclei of neutron halo systems were determined using a recently proposed empirical formula [Sreeja and Balasubramaniam, Eur. Phys. J. A 54, 106 (2018); Sreeja and Balasubramaniam, Eur. Phys. J. A 55, 33 (2019)].

Results: Among the mirror nuclei of $1n$ halo systems, ${}^{11}\mathrm{N}$ (the mirror of ${}^{11}\mathrm{Be}$) and ${}^{15}\mathrm{F}$ (the mirror of ${}^{15}\mathrm{C}$) were found to have a preference for $1p$ emission over $2p$ emission by $Q$-value systematics. The potential energy surface analysis supported the result where both ${}^{11}\mathrm{N}$ and ${}^{15}\mathrm{F}$ were found to be ground-state $1p$ emitters. The trend got changed with an increase in angular momentum where the minimum in potential shifted from $1p$ to $2p$ cluster. Moreover, the half-life calculation matches with the result obtained from $Q$-value systematics.

Conclusion: For the $2n$ halo systems, all the studies made indicate that the respective mirror nuclei have a preference for $2p$ emission. A similar conclusion cannot be drawn for the mirror nuclei of $1n$ halo systems except for ${}^{11}\mathrm{N}$ and ${}^{15}\mathrm{F}$, which were found to be ground-state $1p$ emitters. All the remaining mirror nuclei of $1n$ halo systems prefers $2p$ emission as favorable decay mode than the expected $1p$ emission. The empirical formula can be used as a good tool to evaluate half-life values of proton emitters provided the $Q$ values are known with desirable accuracy.

• Received 21 June 2019
• Revised 29 August 2019

DOI:https://doi.org/10.1103/PhysRevC.100.054611