Physicists of the RUDN University have calculated how much energy it takes to "take away" an electron from an atom, thereby turning the latter into a charged particle -- an ion. They determined the value of this parameter for different levels in the helium atom with best known precision - up to 35 decimal digits. It turned out that the solutions used earlier for the hydrogen ion H?, with 40 decimal points, deviates from the "true" value already at the 35th decimal place.

Scientists carried out calculations for a system of helium atoms interacting according to Coulomb's law. In the normal state, the atoms are neutral and do not interact with each other. For this to happen, it is necessary to ionize the helium atom -- that is, to take an electron away from the ion. Then the atom will acquire a positive charge. This requires to get some energy (the so-called ionization energy). Its value determines the strength of the interaction of an ion with other charged particles and the trajectory of its motion in space.

"We developed an approach based on the variational method, the so-called "exponential" expantion, which allows one to numerically solve the quantum three-body problem bound by the Coulomb interaction, with almost arbitrary precision. This method is used to calculate the ionization energies of a helium atom for different energy levels of arbitrary orbital angular momentum. Our approach demonstrated effectiveness and flexibility in the study of Coulombic systems. Furthermore, obtaining such values does not require the use of supercomputers," says Vladimir Korobov, one of the authors of the work, a head of research group at the Laboratory of Theoretical Physics of the Joint Institute for Nuclear Research, an employee of the RUDN University.

In classical mechanics, there is a three-body problem, which consists in determining the trajectories of the motion of three objects in space relative to each other. This problem has no general solution in the form of finite functions for trajectories, only particular solutions are found for certain initial velocities and coordinates. In quantum mechanics, the three-body problem also has no analytical solution.

High-precision calculation methods will help in solving many fundamental physical problems -- in the studies of exotic helium atoms consisting of antiprotons electrons and helium nucleus, for instance. They are of particular interest because they allow high-precision measurements of the energy spectrum of this exotic system and compare the theoretical results with those obtained in experiments. Their results will allow us to better understand the nature of antimatter and amplify our knowledge of the quantum world.

###

The work was carried out jointly with colleagues from the Joint Institute for Nuclear Research (JINR).

#### Journal

Physical Review A