Abstract
The ground-state hyperfine structure and other properties are calculated for muonic helium atoms (3 He +2μ-e- and 4 He +2μ-e-), with the use of some local properties of the wave functions in the domains where two particles are close to each other or far away. Simple wave functions incorporating these properties with one variational parameter is developed. Also, the electron-muon correlation function is considered in proposed wave functions. It has a correct behavior for r12 tending to zero and infinity. The calculated values for hyperfine structure, energy and expectation values of r2n in ground-state, are compared with the multibox variational approach and the correlation function hyperspherical harmonic method. Our obtained results are very close to the values calculated by mentioned methods and giving strong indications that the proposed wave functions in addition to being very simple, provide relatively accurate values for hyperfine structure, energy and expectation values of r2n, emphasizing on the importance of the local properties of the wave functions.
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