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Journal of Science of Teachers' College and University

Research on α-particle scattering with quantum mechanics

Lixia Li

Published Jan 1, 2006• 0 citations
OpenAlex

Abstract

The Rutherford formula cannot explain α-particle's small angle scattering question.This paper deals with this problem using the quantum scattering theory-born approximation,takes account of the influence of the shielding effect of the electron and limited quality of the atomic nucleus to scattering cross-section,carries on the revision to the Rutherford scattering formula according to experimental result.

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The Rutherford formula cannot explain α-particle's small angle scattering question.This paper deals with this problem using the quantum scattering theory-born approximation,takes account of the influence of the shielding effect of the electron and limited quality of the atomic nucleus to scattering cross-section,carries on the revision to the Rutherford scattering formula according to experimental result.
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.
Figure 1.1 represents schematically a typical scattering experiment, in fact this is the sketch of E. Rutherford experiment in 1910 [ 1 ]. Projectiles (here, α -particles) from a source go through a collimator and collide with a target (gold foil in Rutherford’s experiment). Some projectiles are scattered by the target and reach the detector (here, a fluorescent screen). Rutherford expected them to go straight through with perhaps a minor deflection. Most did go straight through, but to his surprise some particles bounced directly off the gold sheet! What did this mean? Rutherford hypothesized that the positive alpha particles had hit a concentrated mass of positive particles, which he termed the nucleus. We shall describe the Rutherford scattering theoretically later in this chapter.
The theory of scattering is a very important part of the quantum mechanics.The Born approximation and Eikonal approximation of the Scattering cross-section are calculated with the Gauss potential and Lenz-jensen potential under a particular incident energy.The results show that the bigger the Electronic energy is,the smaller the total scattering crossection is and the weaker the electron scattering of potential field is.There is little influence of potential to the energetic particle about the Lenz-jensen potential.And the majority of scattered particles are concentrated on a narrow range.
There are several ways of gathering experimental evidence about microscopic systems. Spectral analysis gives information about the bound states of the system, while scattering experiments probe their inner structure. Rutherford's pioneering alpha scattering experiments yielded the first glimpse into the structure of atoms. Such experiments opened the door to modern collider experiments, allowing us to peer deeper into the structure of matter. In this chapter, we will study only elastic collisions, in which the nature of the scattered particles does not change. This is expected for low energies in the non-relativistic regime. We first introduce the concept of cross-section and then study two complementary approaches to scattering: the Born approximation, which is suitable when the energy of the incoming particles is high in comparison with the potential energy of the target, and the partial waves method, which applies best when the two energies are comparable.
Chapter 18 is entirely devoted to the quantum theory of scattering, which is normally covered in more detail in a course on quantum field theory. We introduce the main concepts, including scattering amplitude, differential and total cross sections, and form factors, and derive the main formulas for elastic scattering, in a nonrelativistic framework; this allows us to appreciate how the information obtained from scattering experiments is used to explore the intricacies of quantum particles that are otherwise inaccessible. The Born approximation is studied and applied to scattering by a periodic potential, a weak potential, and Rutherford scattering. The partial wave expansion is derived and applied to obtain the optical theorem. The chapter concludes with a complementary section on resonant scattering.