We investigate the stability and e ^ { + } e ^ { - } pair creation of supercritical charged superheavy nuclei , ud QM nuggets , strangelets , and strangeon nuggets based on Thomas-Fermi approximation .
The model parameters are fixed by reproducing their masses and charge properties reported in earlier publications .
It is found that ud QM nuggets , strangelets , and strangeon nuggets may be more stable than ^ { 56 } Fe at A \gtrsim 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 \geq 177 , ud QM nuggets with Z \geq 163 , strangelets with Z \geq 192 , and strangeon nuggets with Z \geq 212 .
A universal relation Q / R _ { e } = \left ( m _ { e } - \bar { \mu } _ { e } \right ) / \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 .
This predicts the maximum charge number by taking \bar { \mu } _ { e } = - m _ { e } .
For supercritical charged objects with \bar { \mu } _ { e } < - m _ { e } , the decay rate for e ^ { + } e ^ { - } pair production is estimated based on the JWKB approximation .
It is found that most positrons are emitted at t \lesssim 10 ^ { -15 } s , while a long lasting positron emission is observed for large objects with R \gtrsim 1000 fm .
The emission and annihilation of positrons from supercritical 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 .