Multipolar blackbody radiation shifts for single-ion clocks

Appraising the projected 10(-18) fractional uncertainty in the optical frequency standards using singly ionized ions, we estimate the blackbody radiation (BBR) shifts due to the magnetic dipole (M1) and electric quadrupole (E2) multipoles of the applied external electromagnetic field. Multipolar scalar polarizabilities are determined for the singly ionized calcium (Ca+) and strontium (Sr+) ions using the relativistic coupled-cluster method, though the theory can be exercised for any single-ion clocks. The expected energy shifts for the respective clock transitions are estimated to be 4.38(3) x 10(-4) Hz for Ca+ and 9.50(7) x 10(-5) Hz for Sr+. These shifts are large enough and may be a prerequisite for the frequency standards to achieve the foreseen 10(-18) precision goal.