B. R. Judd

Bio: B. R. Judd is an academic researcher from Johns Hopkins University. The author has contributed to research in topics: Irreducible representation & Matrix (mathematics). The author has an hindex of 17, co-authored 44 publications receiving 8364 citations. Previous affiliations of B. R. Judd include University of California, Berkeley.

Optical absorption intensities of rare-earth ions

Abstract: Electric dipole transitions within the $4f$ shell of a rare-earth ion are permitted if the surroundings of the ion are such that its nucleus is not situated at a center of inversion. An expression is found for the oscillator strength of a transition between two states of the ground configuration $4{f}^{N}$, on the assumption that the levels of each excited configuration of the type $4{f}^{N}{n}^{\ensuremath{'}}d$ or $4{f}^{N}{n}^{\ensuremath{'}}g$ extend over an energy range small as compared to the energy of the configuration above the ground configuration. On summing over all transitions between the components of the ground level ${\ensuremath{\psi}}_{J}$ and those of an excited level ${{\ensuremath{\psi}}^{\ensuremath{'}}}_{{J}^{\ensuremath{'}}}$, both of $4{f}^{N}$, the oscillator strength $P$ corresponding to the transition ${\ensuremath{\psi}}_{J}\ensuremath{\rightarrow}{{\ensuremath{\psi}}^{\ensuremath{'}}}_{{J}^{\ensuremath{'}}}$ of frequency $\ensuremath{ u}$ is found to be given by $P=\ensuremath{\Sigma}{T}_{\ensuremath{\lambda}}\ensuremath{ u}{({\ensuremath{\psi}}_{J}\ensuremath{\parallel}{U}^{(\ensuremath{\lambda})}\ensuremath{\parallel}{{\ensuremath{\psi}}^{\ensuremath{'}}}_{{J}^{\ensuremath{'}}})}^{2},$ where ${\mathrm{U}}^{(\ensuremath{\lambda})}$ is a tensor operator of rank $\ensuremath{\lambda}$, and the sum runs over the three values 2, 4, and 6 of $\ensuremath{\lambda}$. Transitions that also involve changes in the vibrational modes of the complex comprising a rare-earth ion and its surroundings, provide a contribution to $P$ of precisely similar form. It is shown that sets of parameters ${T}_{\ensuremath{\lambda}}$ can be chosen to give a good fit with the experimental data on aqueous solutions of Nd${\mathrm{Cl}}_{3}$ and Er${\mathrm{Cl}}_{3}$. A calculation on the basis of a model, in which the first hydration layer of the rare-earth ion does not possess a center of symmetry, leads to parameters ${T}_{\ensuremath{\lambda}}$ that are smaller than those observed for ${\mathrm{Nd}}^{3+}$ and ${\mathrm{Er}}^{3+}$ by factors of 2 and 8, respectively. Reasons for the discrepancies are discussed.

Operator Techniques in Atomic Spectroscopy

Abstract: In the 1920s, when quantum mechanics was in its infancy, chemists and solid state physicists had little choice but to manipulate unwieldy equations to determine the properties of even the simplest molecules. When mathematicians turned their attention to the equations of quantum mechanics, they discovered that these could be expressed in terms of group theory, and from group theory it was a short step to operator methods. In this book, first published in 1963, Brian Judd made the operator techniques of mathematicians comprehensible to physicists and chemists. He extended the existing methods so that they could handle heavier, more complex molecules and calculate their energy levels, and from there, it was another short step to the mathematical analysis of spectra. The book provides an introduction to continuous groups for physicists and chemists.

INTRA-ATOMIC MAGNETIC INTERACTIONS FOR f ELECTRONS.

Abstract: An examination is made of the effects of spin-spin and spin-other-orbit interactions on the energy levels of $f$-electron configurations. The theory is applied to several rare-earth atoms and ions under a number of simplifying assumptions. Considerable improvements in the fits between experiment and theory are obtained, particularly for the sextets of Gd iv. Electrostatically correlated spin-orbit interaction is studied and found not to be susceptible to parametric absorption into the ordinary spin-orbit and spin-other-orbit interactions. The various contributions to the effective Hamiltonian for two electrons are decomposed into parts having well-defined group-theoretical properties, in preparation for their calculation for any configuration ${f}^{N}$.

First-principles calculations of the electronic structure and spectra of strongly correlated systems: the LDA+ U method

Abstract: The generalization of the Local Density Approximation (LDA) method for the systems with strong Coulomb correlations is presented which gives a correct description of the Mott insulators. The LDA+U method is based on the model hamiltonian approach and allows to take into account the non-sphericity of the Coulomb and exchange interactions. parameters. Orbital-dependent LDA+U potential gives correct orbital polarization and corresponding Jahn-Teller distortion. To calculate the spectra of the strongly correlated systems the impurity Anderson model should be solved with a many-electron trial wave function. All parameters of the many-electron hamiltonian are taken from LDA+U calculations. The method was applied to NiO and has shown good agreement with experimental photoemission spectra and with the oxygen Kα X-ray emission spectrum.

Taking advantage of luminescent lanthanide ions

Abstract: Lanthanide ions possess fascinating optical properties and their discovery, first industrial uses and present high technological applications are largely governed by their interaction with light. Lighting devices (economical luminescent lamps, light emitting diodes), television and computer displays, optical fibres, optical amplifiers, lasers, as well as responsive luminescent stains for biomedical analysis, medical diagnosis, and cell imaging rely heavily on lanthanide ions. This critical review has been tailored for a broad audience of chemists, biochemists and materials scientists; the basics of lanthanide photophysics are highlighted together with the synthetic strategies used to insert these ions into mono- and polymetallic molecular edifices. Recent advances in NIR-emitting materials, including liquid crystals, and in the control of luminescent properties in polymetallic assemblies are also presented. (210 references.)

Electronic Energy Levels in the Trivalent Lanthanide Aquo Ions. I. Pr3+, Nd3+, Pm3+, Sm3+, Dy3+, Ho3+, Er3+, and Tm3+

Abstract: The free‐ion energy‐level schemes of the Pr3+, Nd3+, Pm3+, Sm3+, Dy3+, Ho3+, Er3+, and Tm3+ aquo ions have been determined from their absorption spectra in dilute acid solution at 25°. Energy‐level assignments were made by comparison with crystal spectra, and on the basis of correlations between calculated and observed band intensities. For most of the ions, it was possible to identify several transitions giving rise to bands at energies as high as 45 000–50 000 cm−1. Sufficient numbers of assignments were made to justify inclusion of the effects of configuration interaction in the calculation of the energy‐level parameters. Variation of the electrostatic, spin–orbit coupling, and configuration‐interaction parameters across the lanthanide series is examined.

Upconversion Nanoparticles: Design, Nanochemistry, and Applications in Theranostics

Abstract: Applications in Theranostics Guanying Chen,*,†,‡ Hailong Qiu,†,‡ Paras N. Prasad,*,‡,§ and Xiaoyuan Chen* †School of Chemical Engineering and Technology, Harbin Institute of Technology, Harbin, Heilongjiang 150001, China ‡Department of Chemistry and the Institute for Lasers, Photonics, and Biophotonics, University at Buffalo, State University of New York, Buffalo, New York 14260, United States Department of Chemistry, Korea University, Seoul 136-701, Korea Laboratory of Molecular Imaging and Nanomedicine, National Institute of Biomedical Imaging and Bioengineering, National Institutes of Health, Bethesda, Maryland 20892-2281, United States