Calculation of the nonrelativistic Bethe logarithm in the velocity gauge

Abstract: We consider a general procedure to evaluate the Bethe logarithm for a general few-body atomic or molecular system. As benchmarks we use calculation for the ground states of a helium atom and H_2^+ molecular ion. The obtained values are: \beta_He=4.37016022306(2) for the helium atom and \beta_{H_2^+} = 3.012230335(1) for the H_2^+. Both results substantially improve the best known values for these quantities.