The Theory of the Magnetic Quenching of Iodine Fluorescence and of Λ -Doubling in Π 0 3 States

A theoretical basis is given for Turner's proposal that the magnetic quenching of iodine fluorescence is a predissociation phenomenon. To this end it is shown that a magnetic field introduces matrix elements in the Hamiltonian function between the ${^{3}\ensuremath{\Pi}_{0}}^{+}$ and ${^{3}\ensuremath{\Pi}_{0}}^{\ensuremath{-}}$ (or possibly the ${^{3}\ensuremath{\Pi}_{0}}^{+}$ and ${^{3}\ensuremath{\Sigma}_{0}}^{+}$) states, respectively stable and unstable in ${\mathrm{I}}_{2}$. This confirms Mulliken's assignment of ${^{3}\ensuremath{\Pi}_{0}}^{+}$ to the upper state of the halogen visible bands. The magnetic field has a unique role for so-called ${0}^{+}$, ${0}^{\ensuremath{-}}$ levels because perturbations between these particular states cannot arise from rotational distortion, the cause of the usual Kronig predissociation, or from electric fields unless they are very large or else markedly inhomogeneous. The magnetic quenching should be independent of the rotational quantum number (section 5) and should depend on field strength in the form $\frac{b{\mathfrak{H}}^{2}}{(a+b{\mathfrak{H}}^{2})}$. The observed mode of frequency dependence demands that in ${\mathrm{I}}_{2}$ the potential curves of ${^{3}\ensuremath{\Pi}_{0}}^{+}$, ${^{3}\ensuremath{\Pi}_{0}}^{\ensuremath{-}}$ states, which are the two components of a $\ensuremath{\Lambda}$-doublet, be extremely close for certain values of $r$ or else actually cross each other. This crossing is shown to be theoretically possible under certain conditions. The possibility of magnetic predissociation in other molecules is also discussed. The predissociation due to collision observed by Turner, Kaplan, and others probably arises because electric fields can blend $u$ and $g$ states, and also ${0}^{+}$ and ${0}^{\ensuremath{-}}$ states if inhomogeneous.Incidental points in halogen band spectra are discussed. Schlapp's intensity theory confirms Brown's assignment of $^{3}\ensuremath{\Pi}_{1}$ to his new level in ${\mathrm{I}}_{2}$, ${\mathrm{Br}}_{2}$. A calculation is given showing why the ${^{3}\ensuremath{\Pi}_{0}}^{+}$ level in ICl appears derived from $^{2}P_{\frac{3}{2}}(\mathrm{I})+^{2}P_{\frac{1}{2}}(\mathrm{Cl})$ when configuration theory (the non-crossing rule) suggests $^{2}P_{\frac{3}{2}}+^{2}P_{\frac{3}{2}}$. An explicit mechanism is thus furnished for Brown and Gibson's interpretation of the predissociation of ICl published elsewhere in this issue.The writer's previous formulas for the width of $\ensuremath{\Lambda}$-doublets in $^{3}\ensuremath{\Pi}_{0}$ states are extended to include investigation of the sign of the doublet and the perturbations from $^{1}\ensuremath{\Sigma}$, $^{5}\ensuremath{\Sigma}$ states previously omitted although coordinate in importance with those from $^{3}\ensuremath{\Sigma}$. The need of considering these inter-system interactions is caused by the fact that the doubling is a second rather than first order spin-orbit effect. The structural form of the secular determinants inclusive of spin-orbit terms is exhibited for molecules arising from $^{2}P+^{2}P$, $^{2}P+^{2}P^{\ensuremath{'}}$, and $^{2}P+^{2}S$.