Our calculations are done for the single nucleon current operator and the calculations using 2N operators
are in progress. We present results obtained within two approaches: without and with relativistic
corrections. The capture rates results for the μ− + d → νμ + n + n reaction are calculated for both
doublet (F = 1/2) and quadruplet (F = 3/2) capture rates (see Table 1). Also the results for the
capture rates in the μ− + 3He → νμ + 3H case are shown in Table 2. In our calculations new methods
have been developed based on an intensive use of Mathematica . We would like to inform the reader
that the theoretical error caused by neglecting all contributions beyond the single nucleon term.