World Journal of Nuclear Science and Technology, 2016, 6, 71-78 Published Online January 2016 in SciRes. http://www.scirp.org/journal/wjnst http://dx.doi.org/10.4236/wjnst.2016.61007 How to cite this paper: Iqbal, S., Sarwar, F. and Raza, S.M. (2016) Quantum Mechanical Approach for Rutherford Scattering and Nuclear Scattering with Born Approximation. World Journal of Nuclear Science and Technology, 6, 71-78. http://dx.doi.org/10.4236/wjnst.2016.61007 Quantum Mechanical Approach for Rutherford Scattering and Nuclear Scattering with Born Approximation Saleem Iqbal 1 , Farhana Sarwar 1,2 , Syed Mohsin Raza 3 1 Department of Mathematics, University of Balochistan, Quetta, Pakistan 2 Department of Mathematics, F. G. Girls Degree College, Quetta, Pakistan 3 Department of Physics, University of Balochistan, Quetta, Pakistan Received 19 December 2015; accepted 19 January 2016; published 22 January 2016 Copyright © 2016 by authors and Scientific Research Publishing Inc. This work is licensed under the Creative Commons Attribution International License (CC BY). http://creativecommons.org/licenses/by/4.0/ Abstract Rutherford classical scattering theory, as its quantum mechanical analogue, is modified for scat- tering cross-section and the impact parameter by using quantum mechanical momentum, k  (de Broglie hypothesis), energy relationship for matter oscillator (Einstein’s oscillator) and quantum mechanical wave vectors, = free 2mE k  and ( ) = quantum 2mE V k  − , respectively. It is observed that the quantum mechanical scattering cross-section and the impact parameter depended on in- verse square law of quantum action (Planck’s constant). Born approximation is revisited for quantum mechanical scattering. Using Bessel and Neumann asymptotic functions and response of nuclear surface potential barrier, born approximations were modified. The coulombic fields in- side the nucleus of the atom are studied for reflection and transmission with corresponding wave vectors, phase shifts and eigenfunctions Bulk quantum mechanical tunneling and reflection scat- tering, both for ruptured and unruptured nucleus of the atom, are deciphered with corresponding wave vectors, phase shifts and eigenfunction. Similar calculation ware accomplished for quantum surface tunneling and reflection scattering with corresponding wave vectors, phase shifts and ei- genfunctions. Such diverse quantum mechanical scattering cross-section with corresponding wave vectors for tunneling and reflection, phase shifts and eigenfunctions will pave a new dimension to understanding the behavior of exchange fields in the nucleus of the atom with insides layers both ruptured and unruptured. Phase shifts, l δ for each of the energy profile (partial) will be different and indeed their corresponding wave vectors for exchange energy eigenvalues.