  We presented experimental and theoretical studies of the effect of an
external magnetic field on the forbidden transition in the bosonic Sr atom. In
our ultra-cold atomic system, the excitation fraction of
$5s5p$~$^3P_0$~-~$5s^2$~$^1S_0$ forbidden transition was measured under the
circumstance of the different magnetic field strengths by using the normalized
detection method. Based on perturbation theory, we calculated the
magnetic-field-induced $5s5p$~$^3P_0$~-~$5s^2$~$^1S_0$ transition rate. The
excitation fraction as a function of the magnetic field strength was deduced
according to the calculated results. A good agreement was found between the
experimental measurements and the calculations. This study should be helpful in
evaluating the magnetic field effects on the forbidden transition rate with
higher accuracy. Moreover, it can help to understand the ultra-cold atomic
interaction in the external magnetic field.
