CORRELATED WAVE-FUNCTIONS AND HYPERFINE SPLITTINGS OF THE 2S STATE OF MUONIC HE-3,HE-4 ATOMS

The correlated wave functions of the 2s state, (1s)e(2s)-mu of muonic He-4 and He-3 atoms are calculated by the variational approach, employing an improved set of the Hylleraas-type basis functions to study the 2s state of muonic He atoms. The energy and radial expectation values are calculated. Our proposed wave functions for the muonic He-4 and He-3 atoms are good enough to describe the electron and muon at small, intermediate, and large values of radial coordinates. The hyperfine splittings of the (1s)e(2s)-mu muonic He-4 and He-3 atoms are also presented. Including relativistic, QED, and other corrections up to O(alpha(2)), we arrive at the values DELTA-nu = (4287.01 +/- 0.10 and 4052.64 +/- 0.10 MHz for the total hyperfine splittings of the 2s state of muonic He-4 and He-3 atoms, respectively.