Magnetic dipole and electric quadrupole transitions in the trivalent lanthanide series: Calculated emission rates and oscillator strengths

Abstract

Given growing interest in optical-frequency magnetic dipole transitions, we use intermediate coupling calculations to identify strong magnetic dipole emission lines that are well suited for experimental study. The energy levels for all trivalent lanthanide ions in the 4f n configuration are calculated using a detailed free ion Hamiltonian, including electrostatic and spin-orbit terms as well as two-body, three-body, spin-spin, spin-other-orbit, and electrostatically correlated spin-orbit interactions. These free ion energy levels and eigenstates are then used to calculate the oscillator strengths for all ground-state magnetic dipole absorption lines and the spontaneous emission rates for all magnetic dipole emission lines including transitions between excited states. A large number of strong magnetic dipole transitions are predicted throughout the visible and near-infrared spectrum, including many at longer wavelengths that would be ideal for experimental investigation of magnetic light-matter interactions with optical metamaterials and plasmonic antennas.

Radiative Decay Rates for Electric Dipole, Magnetic Dipole and Electric Quadrupole Transitions in Triply Ionized Thulium (Tm IV)

“…However, we note that, for these particular transitions, the cancellation factor as defined by Cowan [22] is very small (<0.05), indicating that the corresponding decay rates might be affected by larger uncertainties in our calculations. For all of the other forbidden lines reported in Table 3, an accuracy of about 10% can reasonably be estimated for our computed gA-values in view of their excellent agreement with the results obtained using a completely independent theoretical method [23]. …”

“…Transition probabilities obtained using our physical model A for the most intense magnetic dipole (M1) and electric quadrupole (E2) lines are reported in Table 3. They are compared with the results recently published by Dodson and Zia [23] who calculated radiative transition probabilities for some M1 and E2 Tm IV lines using a detailed free ion Hamiltonian including electrostatic and spin-orbit terms as well as two-body, three-body, spin-spin, spin-other-orbit and electrostatically correlated spin-orbit interactions. When looking at Table 3, we can note that their results are generally in good agreement (within a few percent) with our transition probabilities, if we except some E2 transitions located at 3038.774, 3847.249, 4264.491, 4437.432, 4721.408, 5759.349, 6401.911 and 7967.695 Å for which larger discrepancies are observed.…”

“…Using a detailed free ion Hamiltonian, including electrostatic and spin-orbit terms, as well as two-body, three-body, spin-spin, spin-other-orbit, and electrostatically correlated spin-orbit interactions, Dodson and Zia [23] calculated magnetic dipole and electric quadrupole lines and corresponding oscillator strengths within the ground configurations 4f k throughout the full trivalent lanthanide series, including Tm IV.…”

Relativistic Hartree–Fock calculations of transition rates for allowed and forbidden lines in Nd IV

“…For this reason, radiative properties of such forbidden lines within the 4f 3 configurations were also computed in the present work. Transition probabilities for the most intense magnetic dipole (M1) and electric quadrupole (E2) lines are reported in table 5 where they are compared to the data recently published by Dodson and Zia (2012). These latter authors reported radiative transition probabilities for some M1 and E2 Nd IV lines using a detailed free ion Hamiltonian including electrostatic and spin-orbit terms as well as two-body, three-body, spin-spin, spin-other-orbit and electrostatically correlated spin-orbit interactions.…”

Spectroscopic properties of the Pr3+ ion in TeO2-WO3-PbO-La2O3 and TeO2-WO3-PbO-Lu2O3 glasses

“…1) and the values of the reduced matrix elements for particular electric-dipole transitions from [21] have been used. For the sake of completeness, generally weak magnetic-dipole transitions have been taken into account, with the values of the oscillator strengths and radiative probabilities from [26]. Due to similarity of the absorption spectra of TWPLa:Pr and TWPLu:Pr glasses (see Fig.…”