Radioactive Behaviour of the Rare Isotope K-58: A Theoretical Prediction of Its Decay chains

The neutron-rich isotope 58K lies at the extreme boundary of the potassium isotopic chain, where experimental measurements remain limited and theoretical predictions are essential for understanding nuclear structure far from stability. In this work, we investigated the complete radioactive decay behaviour of 58K using Q-values extracted and a semi-empirical β− decay model incorporating shell corrections. All possible decay channels including α, β−,β+ and electron capture were examined using nuclear mass differences and energy conditions. The analysis shows that β− decay is the only energetically allowed and dominant decay mode for 58K, consistent with its large neutron excess and the general behaviour of nuclei approaching the neutron dripline. Successive Q-value calculations and half-life estimates were performed for each daughter nucleus along the decay sequence. The results demonstrate a systematic decrease in Q-values as the nuclei approach stability, accompanied by pronounced odd-even staggering arising from nuclear pairing effects. The full decay chain constructed from these predictions reveals a sequence of seven successive β− transitions, terminating at the stable nucleus 58Fe, in agreement with its high binding energy per nucleon and the absence of any energetically allowed decay modes. This theoretical study provides the first comprehensive mapping of the decay pathway of 58K, offering valuable guidance for future experimental investigations of extremely neutron-rich potassium isotopes.