Fine and hyperfine structure of the (37,35) state of the 4He+(p)over-bar atom

Recently new calculations of the hyperfine structure (HFS) for the metastable state (37, 35) of the He-4(+) (p) over bar atom have been performed using the variational coupled rearrangement channel method. They reveal a discrepancy of similar to 200 ppm with our previous result on HFS based on molecular type variational expansion. In order to solve this disagreement we undertake new calculations of the HFS for this particular state using a more accurate variational method based on exponential basis functions, which yields the non-relativistic energy with 15 significant digits for the state.