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We have performed relativistic many-body calculations of the hyperfineinteraction in the $6s$ and $7s$ states of Cs, including the off-diagonalmatrix element. The calculations were used to determine the accuracy of thesemi-empirical formula for the electromagnetic transition amplitude$<6s|M1|7s>$ induced by the hyperfine interaction. We have found that eventhough the contribution of the many-body effects into the matrix elements isvery large, the square root formula $<6s|H_{hfs}|7s > = \sqrt{< 6s|H_{hfs}|6s >< 7s|H_{hfs}|7s >}$ remains valid to the accuracy of a fraction of $10^{-3}$.The result for the M1-amplitude is used in the interpretation of theparity-violation measurement in the $6s-7s$ transition in Cs which claims apossible deviation from the Standard model.Comment: 13 pages, 4 figures, LaTeX, Submitted to Phys. Rev.

Off-diagonal hyperfine interaction and parity nonconservation in cesium