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We have analyzed the magnetic field dependences of intensities of all theoptical transitions between magnetic sublevels of hyperfine levels, excitedwith $\sigma^+$, $\pi$ and $\sigma^-$ polarized light, for the $D_1$ and $D_2$lines of $^{87}$Rb and $^{85}$Rb atoms. Depending on the type of transition andthe quantum numbers of involved levels, the Hamiltonian matrices are of$1\times 1$, $2\times 2$, $3\times 3$ or $4\times 4$ dimension. As an example,analytical expressions are presented for the case of $2\times 2$ dimensionmatrices for $D_1$ line of both isotopes. Eigenvalues and eigenkets are given,and the expression for the transition intensity as a function of $B$ has beendetermined. It is found that some $\pi$ transitions of $^{87}$Rb and $^{85}$Rbget completely canceled for certain, extremely precise, values of $B$. Nocancellation occurs for $\sigma^+$ or $\sigma^-$ transitions of $D_1$ line. Formatrices with size over $2\times 2$, analytical formulas are heavy, and we haveperformed numerical calculations. All the $B$ values cancelling $\sigma^+$,$\pi$ and $\sigma^-$ transitions of $D_1$ and $D_2$ lines of $^{87}$Rb and$^{85}$Rb are calculated, with an accuracy limited by the precision of theinvolved physical quantities. We believe our modeling can serve as a tool fordetermination of standardized values of magnetic field. The experimentalimplementation feasibility and its possible outcome are addressed. We believethe experimental realization will allow to increase precision of the physicalquantities involved, in particular the upper state atomic levels energy.

Transition cancellations of $^{87}$Rb and $^{85}$Rb atoms in a magnetic field setting new standards