Cancellation of D1 line transitions of alkali-metal atoms by magnetic-field values

In this work, ??, ??+, and ????? transitions between magnetic sublevels of the D1 line of all alkali-metal atoms are considered analytically. General block Hamiltonian matrices in the presence of a magnetic-field for the ground and excited states are built in order to describe all the transitions. Eigenvalues and eigenkets describing ground and excited levels are calculated and modified and unperturbed transfer coefficients as a function of the nuclear spin I, the magnetic quantum number m, and the magnetic-field magnitude B are defined. Transition cancellations are observed only for some ?? transitions of each isotope. The main result is that we obtain a single formula which expresses the magnetic-field values canceling these transitions. These values also correspond to the case when the intensities of some of the other transitions reach their maximum. In addition, we examine the derivative of ?? transition modified transfer coefficients in order to find the magnetic-field values which correspond to the intensities??? maximum. The accuracy of the magnetic-field B values is only limited by the uncertainty of the physical quantities involved.