AbstractWe use superconducting Al‐tunnel junctions as tunable phonon generators in the meV‐range to determine ground state splitting at zero stress of positively charged states associated with single acceptors in Si and double acceptors in Ge. From the stress and energy dependence of the conductivity induced by high frequency phonon irradiation of the corresponding two‐ and three‐hole states we find that the splitting is below 0.1 meV for the ground states of Si:B+ and Ge:Be+, and 1 meV and 1.2 meV for Si:Ga+ and Si:Al+, respectively. These level separations are comparable to those found previously for the ground states of the corresponding acceptor bound excitons A0X. For the deeper acceptors Si:In+, Si:Tl+, and Ge:Zn+ the results are qualitatively different.