Calculating the size of positronium
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 tha...
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| Format: | Article |
| Language: | English |
| Published: |
Penza State University Publishing House
2024-12-01
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| Series: | Известия высших учебных заведений. Поволжский регион: Физико-математические науки |
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| Summary: | 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. |
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| ISSN: | 2072-3040 |