Major processes (e.g. presupernova evolution in massive stars, supernova explosions, rp, r, s processes) taking place in astrophysical environment consists of unstable nuclei and decay spontaneously. There is a need to determine the accurate value of half-life of these unstable nuclei. The reliability of the half-life value is one of the key factors to calculate weak inter action rates in the stellar environment. Many experimentalists and theorists paid attention in this direction to perform reliable measurements as well as calculations. Present work is believed to contribute in this direction, to calculate half-life in more delicate and reliable manner, by implementing both approaches (experimental and theoretical model). The ex perimental part was performed at FEN Faculty, Physics Department Akdeniz University, Antalya Turkey. The β decay half-life of 44Sc was measured by photon activation analysis (PAA) and later calculated by proton neutron quasiparticle random phase approximation (pn-QRPA). As a result of this experiment, the obtained spectra were analyzed by MAESTRO and ROOT package. The photonuclear reaction is produced using a clinical linear accelerator (cLINAC) which generate bremsstrahlung photon beam to activate the desired sample. One aspect of this analysis is the comparison of measured results by PAA and those calculated by pn QRPA. A decent comparison between measured and calculated results with literature value is established. Accurate value of phase space factor (PSF) is a prerequisite for the calculation of half life. In my second analysis I report a new recipe for the calculaton of PSF. This work is being done in collaboration with the Romanian Collaborators (Horia Hulubei Foundation, Magurele, Romania). To obtain the electron/positron wave function, a code is developed by solving the Dirac equation with a nuclear potential derived from a realistic proton density distribution in the nucleus. For the electron capture (EC) process, it is found that the screening effect has a notable influence on the computed PSF values especially for light nuclei. Further the calculated PSFs are utilized for calculation of β-decay half-lives for fp-shell and heavier nuclei of astrophysical interest. This investigation also explores the improvement in calculated β-decay half-lives, using a given set of nuclear matrix elements, employing the recently introduced prescription for calculation of phase space factors PSFs. The role of proton neutron residual interaction for the calculation of beta decay half-life is also explored. The proton neutron residual interaction is another important feature influ encing the calculated β-decay half-lives and is studied in my third part of the work. Pairing gaps may have effect on calculated half-lives and is being studied in current investigation. Gamow-Teller (GT) strength distribution may have implications on stellar weak rates and associated nucleosynthesis in stellar environment. GT strength for β-decay of medium mass nuclei for supernovae core collapse are calculated. The calculated GT strength distribution, stellar weak rates employing deformed pn-QRPA formalism in comparison with shell model and experimentally extracted GT strengths is presented. It is expected that the current study of β-decay half-life measurement and developed theoretical techniques may contribute to a reliable estimation of half-life values both under terrestrial and stellar conditions. Consequently this work may contribute towards a better understanding of astrophysical processes.