Quantum Mechanical Approach for Rutherford Scattering and Nuclear Scattering with Born Approximation  

作　　者：Saleem Iqbal Farhana Sarwar Syed Mohsin Raza Saleem Iqbal;Farhana Sarwar;Syed Mohsin Raza(Department of Mathematics, University of Balochistan, Quetta, Pakistan;Department of Mathematics, F. G. Girls Degree College, Quetta, Pakistan;Department of Physics, University of Balochistan, Quetta, Pakistan)

机构地区：[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

出　　处：《World Journal of Nuclear Science and Technology》2016年第1期71-78,共8页核科学与技术国际期刊（英文）

摘　　要：Rutherford classical scattering theory, as its quantum mechanical analogue, is modified for scattering cross-section and the impact parameter by using quantum mechanical momentum, (de Broglie hypothesis), energy relationship for matter oscillator (Einstein’s oscillator) and quantum mechanical wave vectors, and , respectively. It is observed that the quantum mechanical scattering cross-section and the impact parameter depended on inverse 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 inside 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 scattering, 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 eigenfunctions. 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, δ_l for each of the energy profile (partial) will be different and indeed their corresponding wave vectors for exchange energy eigenvalues.Rutherford classical scattering theory, as its quantum mechanical analogue, is modified for scattering cross-section and the impact parameter by using quantum mechanical momentum, (de Broglie hypothesis), energy relationship for matter oscillator (Einstein’s oscillator) and quantum mechanical wave vectors, and , respectively. It is observed that the quantum mechanical scattering cross-section and the impact parameter depended on inverse 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 inside 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 scattering, 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 eigenfunctions. 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, δ_l for each of the energy profile (partial) will be different and indeed their corresponding wave vectors for exchange energy eigenvalues.

关 键 词：Rutherford Classical Scattering Theory Scattering Cross Section Impact Parameter Born Approximation Ruptured and Unruptured Nucleus 

分 类 号：O41[理学—理论物理]