Calculating the size of positronium

Abstract

Background. A fairly common error has been established in the particular case of the problem of two bodies of the same mass performing circular motion around a fixed center of their mass, which consists in the fact that the radius of rotation is found using a formula obtained under conditions that are not satisfied for material points of the same mass. This error leads to a twofold decrease in the calculated radius of rotation, which is a very large error. This error is transferred to the positronium atom, as a result of which its Bohr radius is determined significantly incorrectly. The purpose of the research is to correct the value of the Bohr radius of positronium. Materials and methods. When determining the Bohr radius of positronium, a method for solving the two-body problem was used, borrowed from theoretical mechanics, the key element of which is the reduced mass. In the particular case under consideration, the method of the two-body problem is redundant and can be successfully replaced by solving the problem of the motion of one of the bodies moving relative to the center of mass. Results. It has been established that the calculated minimum radius of positronium (the distance from its center of mass at which the probability of finding an electron/positron is maximum) is equal to four, and not two Bohr radii of hydrogen, as indicated in the literature. Conclusions. An error in the special case of the two-body problem led to an error in determining the size of positronium.

Keywords

• positronium
• hydrogen
• electron
• positron
• bohr radius