Laporte Selection Rule Research Articles

Radiationless Energy Transfer Between Rare-Earth Ions in Solutions and its Application to the Investigation of Complexation Processes

Abstract Radiationless energy transfer between rare-earth ions (Ln3+) in solutions has some features: 1) the electronic transitions in Ln3+ complexes causing the luminescence of energy donor and the absorption of energy acceptors are forbidden by Laporte's rule and are weakly intensive. Therefore the critical radius (Ro) of energy transfer between the rare-earth ions for dipole-dipole mechanism is close to that for exchange-resonant mechanism. This fact presents difficulties for unequivocal interpretation of the energy transfer mechanism. 2) The plus-three lanthanide ions exist in solution as a set of complexes with different number of charged ligands in the inner coordination sphere and hence with different total charge of complexes.

Multipole Lines in the Spectra of Bi ii and Pb ii

Spectra of Bi ii and Pb ii were excited by high-frequency oscillations in a quartz discharge tube conaining the vapor of the metal in an atmosphere of helium. The following five lines, corresponding to transitions among the five lowest levels of Bi ii belonging to the 6s2 6p2 electron configuration and forbidden by the Laporte selection rule, were observed: λ3240.7 (1S0→3P1), a pure magnetic dipole line;λ3683.2 (1S0→3P2), a pure electric quadrupole line; two lines of mixed character, λ4850.2 (1D2 → 3P1) and λ5913.5 (1D2 →3P2); and λ7503.2 (3P1 → 3P0), a pure magnetic dipole line observed for the first time as a nonintercombination transition. In addition, a line was found in the spectrum of Pb ii at λ7099.8 (²P120→²P120). It corresponds to the transition between the two lowest levels of Pb ii belonging to the 6s26p electron configuration. This is a line of mixed character representing the first definite identification of a spin reversal line. By use of Fabry– Perot etalons, the hyperfine structure of each of these lines was photographed, establishing the identity of the lines and, at thesame time, giving the hitherto unknown splittings of the corresponding levelsThe hyperfine structure splitting factors “A” and the quadrupole coupling constants “B” for the levels were calculated from these results and compared with theory. For this purpose, the procedure for the calculation of quadrupole coupling constants as originally given by Casimir was extended to include the case of two equivalent p electrons.

Multipole Lines in Spectra of Elements from the Fifth Group

The excitation of lines forbidden by the Laporte rule and corresponding to transitions between levels, all belonging to the ground configuration, was studied for the elements of the fifth group. The short-wave experimental technique developed permits the recognition of these multipole lines without any knowledge of the spectra investigated, from their behavior at the changeover point of the discharge. Neutral multipole spectra of Bi, Sb, As, and P (s2p3 configuration) were obtained with decreasing intensity in the order listed as well as singly ionized spectra of Bi and Sb (s2p2 configuration). Interesting changes in relative intensities of lines, in particular of the pair 2P3/2,1/2 → 4S3/2 were noted, and an anomalous effect for lines originating from the 2P3/20 level in bismuth observed. A high resolution study of lines in Sb and As gave previously unknown hf separations of levels 3P1 of Sb ii, 2P1/20 of As i and upper limits for those of the levels 2P3/20 and 4S3/20 of As i.

Many-Electron Selection Rules

Selection rules for many-electron transitions are derived by taking into account the first order perturbed eigenfunctions. The perturbations considered are the electrostatic interactions between the pairs of electrons, and the spin-orbit interaction of each electron. It was found that the possibly occurring terms in the first order eigen-function were narrowly limited, and that this limitation provided the selection rules as follows: No more than three electrons can jump at a time. (a) when three electrons jump all change their $n$ by an arbitrary amount, one changes its $l$ by \ifmmode\pm\else\textpm\fi{}1, the others by $\ensuremath{\delta}$ and $\ensuremath{\epsilon}$, $\ensuremath{\delta}+\ensuremath{\epsilon}$ being even. (b) when two electrons jump both can change their $n$ arbitrarily, one changes its $l$ by $\ensuremath{\delta}\ifmmode\pm\else\textpm\fi{}1$, the other one by $\ensuremath{\epsilon}$. Breaking off the series expansion for $\frac{1}{{r}_{FG}}$ in the electrostatic interaction after the second term gives for $\ensuremath{\delta}$ and $\ensuremath{\epsilon}$ only the values 0, \ifmmode\pm\else\textpm\fi{}1. The Heisenberg two-electron selection rule is therefore to be considered as a special case of (b). The Laporte rule is verified making use only of the properties of spherical harmonics. Qualitative rules have been derived to tell when many-electron transitions may be expected to be strong. The first order terms also cause anomalies in the intensities of one-electron transitions.

The Appearance of "Forbidden Lines" in Spectra

A rough calculation shows that the quadrupole term in the radiation of a forbidden line is usually larger than the dipole produced by an external electric field. This is not true, however, when there is an intermediate state, with which both initial and final states combine, and which lies close to one of them.If the $J$ selection rule is violated, and the Laporte rule is obeyed, the radiation cannot be due to the quadrupole term and must be ascribed to the octopole. Hg 2270 is such a line. An octopole transition will have a Zeeman effect distinctively different from that of a dipole or quadrupole.