Supercritically Charged Objects and Electron-positron Pair Creation

Xia, Chengjun

We investigate the stability and $e^+e^-$ pair creation of supercritically charged superheavy nuclei, $ud$QM nuggets, strangelets, and strangeon nuggets based on the Thomas-Fermi approximation. The model parameters are fixed by reproducing masses and charge properties of these supercritically charged objects reported in earlier publications. It is found that $ud$QM nuggets, strangelets, and strangeon nuggets may be more stable than $^{56}$Fe at the baryon number $A \ge 315$, $5 \times 10^4$, and $1.2 \times 10^8$, respectively. For those stable against neutron emission, the most massive superheavy element has a baryon number $\sim 965$, while $ud$QM nuggets, strangelets, and strangeon nuggets need to have baryon numbers larger than 39, 433, and $2.7 \times 10^5$. The $e^+e^-$ pair creation will inevitably start for superheavy nuclei with charge numbers $Z \ge 177$, for $ud$QM nuggets with $Z \ge 163$, for strangelets with $Z \ge 192$, and for strangeon nuggets with $Z \ge 212$. A universal relation $Q/R_e = (m_e - \bar{\mu}_e)/\alpha$ is obtained at a given electron chemical potential $\bar{\mu}_e$, where $Q$ is the total charge and $R_e$ the radius of electron cloud. The maximum number of $Q$ without causing $e^+e^-$ pair creation is then fixed by taking $\bar{\mu}_e < -m_e$. For supercritically charged objects with $\bar{\mu}_e < -m_e$, the decay rate for $e^+e^-$ pair production is estimated based on the Jeffreys-Wentzel-Kramers-Brillouin (JWKB) approximation. It is found that most positrons are emitted at $t \le 10^{-15}$ s, while a long lasting positron emission can be observed for large objects with $R \ge 1000$ fm. The emission of positrons and electron-positron annihilation from supercritically charged objects may be partially responsible for the short $\gamma$-ray burst during the merger of binary compact stars, the 511 keV continuum emission, as well as the narrow faint emission lines in x-ray spectra from galaxies and galaxy clusters.