Physicists from Canada, China and Russia have carried out a detailed calculation of the energies and widths of several levels of pion helium. In their calculations, they achieved a relative error of four billionths of a fraction, which is almost a thousand times more accurate than previous calculations. Such accuracy will be enough for the upcoming experiment with pion helium to significantly improve the value of the mass of the pion.
Different areas of experimental physics have their own level of accuracy. For example, in elementary particle physics, relative errors of one ten-thousandth of a fraction are considered record-breaking, while precision atomic spectroscopy boasts a value of 10-15. For this reason, physicists are actively looking for opportunities to apply the achievements of spectroscopy to other fields.
A lot of work in this direction is connected with the spectroscopic study of exotic atoms, that is, the bound states of not only the usual electrons, neutrons and protons, but also less long-lived particles. We have already told how physicists were able to capture the spectra of muon atoms, antihydrogen, muonium, antiproton and pionic helium. These studies make it possible not only to check the fulfillment of various symmetries, but also to measure the masses of particles and their relations with accuracy unattainable on particle accelerators.
For example, the relative error in measuring the mass of a peony today reaches a millionth of a fraction. It is determined by the widths of the spectral lines that the experimenters measured. Now they are busy looking for new lines and new conditions for the experiment, and it is expected that future accuracy will increase by three orders of magnitude. This means that theorists also need to improve their formulas.
A group of physicists from Canada, China and Russia decided to do this with the participation of Vladimir Korobov (Vladimir Korobov) from the Joint Institute for Nuclear Research in Dubna. Focusing on the expected accuracy of the experiment with pion helium, which will soon be conducted at the Paul Scherrer Institute, the theorists brought the relative error in calculating the spectral lines of this exotic atom to several fractions of a billion.
Experimenters obtain pion helium by irradiating a target with liquid helium with pions. With some probability, the pion displaces the electron in the helium atom, forming the bound state nHe+. In the case when the pion is delayed in a high-lying (the main quantum number N of the order 16) circular (the orbital quantum number l is close to H) orbit, the exotic atom exists long enough to be able to study its spectra. Then the pion relaxes, which leads to the emission of an Auger electron and absorption by the core of the pion, followed by decay. This process determines the widths of the levels.
To calculate the frequency of a spectral line, it is first necessary to know the energy of each of the two states that have their own pair of quantum numbers (n, l). Physicists use the apparatus of quantum electrodynamics for this, in which the answer can be represented as a decomposition of the expression for energy by degrees of the fine structure constant α. The claimed accuracy required the authors to include the terms of the fourth and fifth order in the sum, which no one has done for pionic helium yet.
The fourth—order terms contained relativistic and radiation corrections, and to calculate the fifth-order corrections, physicists used formulas derived for the hydrogen atom - this approximation was enough to achieve the desired accuracy. The terms of lower orders, in addition to the eigenvalues of the nonrelativistic three-particle Hamiltonian, contained corrections for recoil, finiteness of the sizes of the helium and pion nuclei, as well as leading radiation corrections.
The constructed theory made it possible to calculate the energies and widths of several levels of pion helium, as well as the frequencies and widths of the corresponding spectral lines with a relative error of four billionths, which is almost a thousand times more accurate than previous calculations. The authors paid special attention to the transition (17,16)→(16,15), which is expected to be studied in detail by experimenters from the Paul Scherrer Institute. Its frequency was 1,125,306,339 4(45) gigahertz. Scientists have not forgotten about the frequency shift caused by collisions of an exotic atom with neighboring atoms (mainly helium atoms). For a target density of 2×1018 atoms per cubic centimeter, the corresponding shift was equal to 1.14×10-8 gigahertz.
The article is published in Letters with a Physical Review
PHOTO: © D.Ilyin / Wikimedia Commons
Source: Marat Khamadeev,

Certificate of registration of mass media ЭЛ № ФС 77 - 78868 issued by Roskomnadzor on 07.08.2020