We have proposed and validated an ansatz as effective potential for confining electron/hole within spherical quantum dot in order to understand quantum confinement and its consequences associated with energy states and band gap of Spherical Quantum Dot. Within effective mass approximation formalism, considering an ansatz incorporating a conjoined harmonic oscillator and coulomb interaction as the effective potential for confining an electron or a hole within a spherical quantum dot and by employing appropriate boundary conditions we have calculated the shifts in energy of minimum of conduction band(CBM) and maximum of valence band(VBM) with respect to size of spherical quantum dot. We have also determined the quantum confinement induced shift in band gap energy of spherical quantum dot. In order to verify our theoretical predictions as well as to validate our ansatz, we have performed phenomenological analysis in comparison with available experimental results for quantum dots made of CdSe and observe a very good agreement in this regard. Our experimentally consistent theoretical results also help in mapping the probability density of electron and hole inside spherical quantum dot. The consistency of our results with available experimental data signifies the capability as well as applicability of the ansatz for the effective confining potential to have reasonable information in the study of real nano-structured spherical systems.
A calculation of the non-singlet part of spin dependent structure function, xg N S 1 (x, Q 2 ) and associated sum rule, the Bjorken Sum rule up to next-next-to-leading order(NNLO) is presented. We use a unified approach incorporating Regge theory and the theoretical framework of perturbative Quantum Chromodynamics. Using a Regge behaved model with Q 2 dependent intercept as the initial input, we have solved the Dokshitzer-GribovLipatov-Altarelli-Parisi (DGLAP) evolution equation up to NNLO at small-2 ) and the solutions are utilised to calculate the polarised Bjorken sum rule(BSR). We have also extracted the higher twist contribution to BSR based on a simple parametrisation. These results for both of xg2 ) and BSR, along with higher twist corrections are observed to be consistent with the available data taken from SMC, E143, HERMES, COM-PASS and JLab experiments. In addition, our results are also compared with that of other theoretical and phenomenological analysis based on different models and a very good agreement is also observed in this regard. Further a very good consistency between our calculated results and theoretical QCD predictions of BSR is also achieved.
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