Abstract
According to classical physics theories, a moving particle cannot move to an environment with greater potential energy than its total energy during movement. But according to quantum theories, this event is known to be. This event is called tunneling. Tunneling is a probability, and it is measured by a transition coefficient. Correct calculation of this coefficient is very important because very sensitive and important instruments have been developed based on this event, and many events in nature can be explained by tunneling. This coefficient is generally calculated by semi-classical approaches (WKB) and the known formula is an approximate formula. In this paper, the general transmission coefficient of a potential barrier with arbitrary form is calculated by a simple method without any approximation. The results are applied to calculate the half-life values of the nuclei that emit alpha particles. The half-life values obtained from our calculations and the classical method (WKB) have been compared, and it has been found that the new half-life values are exactly consistent with the experimental values.
Highlights
When a flowing particle or particle current is encountered with a potential energy barrier greater than its total energy, it cannot pass the potential barrier and return to its environment or disappear within the potential according to classical physics
The general transmission coefficient formula for a potential barrier with an arbitrary form has been calculated without making any approximation
The new method that we developed for the solution of the radial Schrödinger Equation (SE) has been used
Summary
When a flowing particle or particle current is encountered with a potential energy barrier greater than its total energy, it cannot pass the potential barrier and return to its environment or disappear within the potential according to classical physics. The observations indicate that such a particle or particle current may pass the potential barrier In quantum physics, this phenomenon is called tunneling. It is a fact that some very sensitive instruments are based on the phenomenon of this formula This well-known formula is obtained by a semi-classical calculation method called Wentzel-Kramers-Brillouin (WKB) Method in Quantum Mechanics and is an approximate formula as its name suggests. A new formula is obtained without any approximation and this formula can be applied to any form of potential barrier This formula is shown to be more accurate and realistic, applying to the alpha decay of some well-known atomic nuclei in nuclear physics. The time-independent radial Schrödinger Equation (SE) in spherical polar coordinates for a particle in a spherical symmetric potential is given as follows:
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