Relativistic multireference Fock-space coupled-cluster calculation of the forbidden $6s^2{}^{1}S_0\to 6s5d{}^{3}D_1$ magnetic-dipole transition in ytterbium

We report the forbidden $6s^2{}^{1}S_0\to 6s5d{}^{3}D_1$ magnetic-dipole transition amplitude computed using multireference 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 in determining the parity-nonconserving amplitude for the $6s^2{}^{1}S_0\to 6s5d{}^{3}D_1$ transition in atomic Yb. To our knowledge, this calculation is the most accurate to date, and can be very important in the search for physics beyond the standard model. We further report the $6s6p{}^{3}P_0\to 6s6p{}^{1}P_1$ and $6s5d{}^{3}D_1\to 6s6p{}^{3}P_0$ transition matrix elements, which are also in good agreement with the earlier theoretical estimates.

Figure 1

(Color online) Energy levels of the ground and low-lying excited states of Yb. The energies (in ${\mathrm{cm}}^{-1}$) are given with respect to the ground state and are obtained from the NIST database [15]. Electric-dipole (allowed) and magnetic-dipole (forbidden) transitions are represented by “blue (solid)” and “red (dashed)” lines respectively. This diagram helps us to understand the requirement of a multireference theory to describe the atomic states of Yb.

Figure 2

(a) Schematic depiction of the classification of particle and hole orbitals into active and inactive categories. (b) Diagrammatic representation of holes (↓), particles (↑), active particles (double up arrow), inactive holes, and particles (dashed down and up arrows). (c) Diagrammatic representation of $S^{(0,0)}\left(T\right)$, $S^{(0,1)}$, and $S^{(0,2)}$ cluster operators.

Figure 3

Diagrammatic representation of $H_{\mathrm{eff}}^{(0,1)}$ (a) and $H_{\mathrm{eff}}^{(0,2)}$ (b). The one- and two-body dressed operators of $\tilde{H}$ are represented by circles and dashed lines, respectively. Exchange diagrams are not shown here for convenience.

Figure 4

Diagrammatic representation of $⟨{\Psi }_f^{(0,2)}\mid M1\mid {\Psi }_i^{(0,2)}⟩$. The one-body dressed operator $\overline{M1}=\exp \left(T^{†}\right)M1\exp \left(T\right)$ is represented by a line with a circle. Exchange diagrams are not shown here for convenience.