Relativistic multi-reference Fock-space coupled-cluster calculation of the forbidden 6s^2^1 S_0 \longrightarrow 6s5d^3 D_1 magnetic-dipole transition in ytterbium

We report the forbidden 6s^{2} ^{1}S_{0}\longrightarrow6s5d ^{3}D_{1} magnetic-dipole transition amplitude computed using multi-reference Fock-space coupled-cluster theory. Our computed transition matrix element ($1.34\times {10}^{-4}{\mu }_B$) is in excellent agreement with the experimental value ($1.33\times {10}^{-4}$ ${\mu }_B$). This value in combination with other known quantities will be helpful to determine the parity non-conserving amplitude for the 6s^{2} ^{1}S_{0}\longrightarrow6s5d ^{3}D_{1} transition in atomic Yb. To our knowledge our calculation is the most accurate to date and can be very important in the search of physics beyond the standard model. We further report the $6s6p^3{P}_0⟶6s6p^1{P}_1$ and $6s5d ^{3}D_{1}\longrightarrow6s6p ^{3}P_{0}$ transition matrix elements which are also in good agreement with the earlier theoretical estimates.