Abstract
The energy spectrum of bound states and hyperfine structure of muonic helium is calculated on the basis of stochastic variational method. The basis wave functions of muonic helium are taken in the Gaussian form. The matrix elements of the Hamiltonian are calculated analytically. For numerical calculation a computer code is written in the MATLAB system. As a result, numerical values of bound state energies and hyperfine structure are obtained. We calculate also correction to the structure of the nucleus, vacuum polarization and relativistic correction.
Highlights
The muonic helium atoms, are the simple three-body atomic systems composed of negative muon, electron and nucleus
Contrary to two-particle bound states three-particle systems were studied on the basis of perturbation theory (PT) and variational approach with smaller accuracy
In this work we study hyperfine structure and the electron Lamb shift in muonic helium atom using the stochastic variational approach [16-18]
Summary
The muonic helium atoms (μμee HHHH), (μμee HHHH) are the simple three-body atomic systems composed of negative muon, electron and nucleus. As a result the muon and αα-particle (or helion) compose the pseudonucleus (μμ , HHHH) and muonic helium atom looks as a two particle system in first approximation The existence of such mass hierarchy enables to formulate a perturbation theory for the calculation of the energy levels. It should be noted that new precise measurement of hyperfine structure of muonic helium is planned at J-PARC MUSE [13] because high intensity pulsed negative muon beam gives an opportunity to improve the result (1) by two orders of magnitude. Another important energy interval that could be investigated experimentally could be the electron Lamb shift (2P-2S) [14-15]. In this work we study hyperfine structure and the electron Lamb shift in muonic helium atom using the stochastic variational approach [16-18]
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