We explore the \(\beta \) -decay features of the doubly magic nucleus \(^{100}\) Sn and proton-rich Sn isotopes within the mass range 100 \(\le \) A \(\le \) 110. Our calculations yield a Gamow–Teller (GT) strength of 4.157 for the transition from the ground state to the lowest excited state of \(^{100}\) Sn, which closely aligns with the recently measured value of 4.381 at RIKEN. The GT strength distributions computed for \(^{102-104, 106, 108}\) Sn exhibit good agreement with experimental observations. Additionally, we compare our GT data with previous theoretical calculations. The predicted half-lives are reproduced within a factor of 2 relative to the experimental values for \(^{100-110}\) Sn. For the first time, we present microscopic calculations of electron capture, \(\beta ^{+}\) decay, and proton emission rates for proton-rich Sn isotopes under stellar conditions. As the core density of a star reaches \(10^{11}\) g/cm \(^3\) , electron capture rates calculated by up to seven orders of magnitude. In contrast, \(\beta ^{+}\) decay rates remain largely unchanged with variations in core density but exhibit changes of up to three orders of magnitude with increasing core temperatures. A decreasing trend in stellar rates is observed with increasing neutron number N, specifically for even-even and odd-A Sn isotopes. The reported stellar rates provide valuable insights for the rp-process and simulation of post-silicon evolution of massive stars.
