All magnetic field values cancelling $D_1$ line transitions of alkali metal atoms

TL;DR

This paper analytically derives magnetic field values that cancel specific transitions in alkali atoms' D1 line, revealing a unified formula and analyzing transition intensities under magnetic influence.

Contribution

It introduces a general analytical approach to determine magnetic field values that cancel certain atomic transitions in alkali metals, unifying the understanding across isotopes.

Findings

Derived a single formula for transition cancellation magnetic fields.

Identified transitions with maximum intensity at specific magnetic fields.

Analyzed transition coefficients and their derivatives for intensity maxima.

Abstract

In this work, $\pi$, $\sigma^+$ and $\sigma^-$ transitions between magnetic sublevels of the $D_1$ line of all alkali atoms are considered analytically. General block Hamiltonian matrices in 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, "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 $\pi$ transitions of each isotope. The main result is that we obtain one single formula which expresses the magnetic field values cancelling these transitions. These values also correspond to the case when some of other transitions intensity have their maximum. In addition, we examine the derivative of $\pi$ 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 involved physical quantities.