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The negative-parity states of 24Mg nucleus are investigated within the shell model. We are based on the calculations of energy levels, total squared form factors, and transition probability using the p-sd-pf (PSDPF) Hamiltonian in a large model space (0 + 1) hW. The comparison between the experimental and theoretical states showed a good agreement within a truncated model space. The PSDPF-based calculations successfully reproduced the data on the total squared form factors and transition probabilities of the negative-parity states in 24Mg nucleus. These quantities depend on the one-body density matrix elements that are obtained from the PSDPF Hamiltonian. The wave functions of radial one-particle matrix elements calculated with the harmonic-oscillator potential are suitable to predict experimental data by changing the center-of-mass corrections.

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The adiabatic effects of electron-positron pair-production on the dynamical instability of very-massive stars is investigated from stellar progenitors of carbon-oxygen cores within the range of 64 M < MCO < 133 M  both with and without rotation. At a very high temperature and relatively low density; the production of electron-positron pairs in the centres of massive stars leads the adiabatic index to below 4/3. The adiabatic quantities are evaluated by constructing a model into a thermodynamically consistent electron-positron equation of state (EoS) table. It is observed that the adiabatic indices in the instability regions of the rotating models are fundamentally positive with central temperature and density. Similarly, the mass of the oxygen core within the instability region has accelerated the adiabatic indices in order to compress the star, while the mass loss and adiabatic index in the non-rotating model exponentially decay. In the rotating models, a small amount of heat is required to increase the central temperature for the end fate of the massive stars. The dynamic of most of the adiabatic quantities show a similar pattern for all the rotating models. The non-rotating model may not be suitable for inducing the instability. Many adiabatic quantities have shown great effects on the dynamical instability of the massive stars due to electron-positron pair-production in their centres. The results of this work would be useful for better understanding of the end fate of very-massive stars.