Off-diagonal hyperfine interaction and parity nonconservation in cesium

We have performed relativistic many-body calculations of the hyperfine interaction in the $6s$ and $7s$ states of Cs, including the off-diagonal matrix element. The calculations were used to determine the accuracy of the semiempirical formula for the electromagnetic transition amplitude $〈6s|M1\mathrm{}|7s〉$ induced by the hyperfine interaction. We have found that even though the contribution of the many-body effects into the matrix elements is very large, the square-root formula $〈6s|H_{\mathrm{hfs}}|7s〉=\sqrt{〈6s|H_{\mathrm{hfs}}|6s〉〈7s|H_{\mathrm{hfs}}|7s〉}$ remains valid to the accuracy of a fraction of ${10}^{-3}.$ The result for the M1- amplitude is used in the interpretation of the parity-violation measurement in the $6s-7s$ transition in Cs, which claims a possible deviation from the standard model.