Abstract
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, δl for each of the energy profile (partial) will be different and indeed their corresponding wave vectors for exchange energy eigenvalues.
Highlights
It has not been successful, to our knowledge, to find such reported results anywhere in any literature the world over
The phase shifts for each diverse case under consideration for quantum mechanical scattering are different with substitution of such phase shifts with appropriate selection of equations
For quantum mechanical scattering from the nucleus of the atom, highly energetic incident particles are needed
Summary
It has not been successful, to our knowledge, to find such reported results anywhere in any literature the world over. Quantum mechanical scattering theory [5] and fundamental results with born approximation functions (energy profile) were reanalyzed by considering the nucleus analogous to onion. The shape of scattering eigenfunctions can be reproduced provided the wave vectors of incident and scattered beams are known. Formulas need testing for their validity on high energy accelerators These formulas are good enough for Coulombic field (target material) provided the incident particles are charged particles. For quantum mechanical scattering from the nucleus of the atom, highly energetic incident particles (charged or uncharged) are needed. Energy profile (eigenfunctions) is deciphered both even and odd, for reflection and quantum mechanical tunneling from nuclear surface barrier, and the quantum mechanical scattering profiles from each inside layer of the nucleus of the atom. With scattering profiles (scattering eigenfunctions), the shape and size of scattering through modeling and simulation can be reproduced
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