ОПРЕДЕЛЕНИЕ УТОЧНЕННОГО РАЗМЕРА ПОЗИТРОНИЯ

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. It is shown that there is a fairly common error in one particular case of solving the two-body problem. This error is transferred to the positronium atom, as a result of which its Bohr radius is determined significantly incorrectly. The goal of the work is to correct the value of the Bohr radius of positronium. The prerequisite for the error in one particular case of solving the two-body problem is the circular motion of two material points with equal masses around a fixed cen ter of their masses. The premise itself is not wrong. The mistake is that the radius of rotation (relative to the center of mass) is found using a formula obtained under conditions that are not satisfied for material points of the same mass. In accordance with the erroneous solution scheme, it is believed that the radius of positronium is twice the Bohr radius of hydrogen. The doubly refined value of the positronium radius was established by methods of theo retical (classical) mechanics. However, positronium is a quantum object. Therefore, the work performs a quantum mechanical solution. If, hypothetically, the positron is excluded from positronium, and a hypothetical particle with a charge equal to a quarter of the positron’s charge is fixedly installed at the center of mass, then the electron will not “notice” the substitution, and the nature of its movement will not change. The only difference between the hypothetical system under consideration and the hydrogen atom is that its potential energy is four times less. Therefore, it is possible to use the textbook quantum mechanical solution for the hydrogen atom, corrected for the potential energy reduced by four. 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.