Search

A personal account is given of interaction with William T. Carnall during the period 1977–1988, when I made regular visits to the Argonne National Laboratory to discuss the theoretical background to the spectroscopic work he was carrying out on the lanthanides and actinides.

To honour the memory of Brian Garner Wybourne, an analysis is presented of three components of the spin-other-orbit interaction for f electrons using the kind of Lie groups he would have been familiar with. The components have been named z 6, z 8 and z 10. They all belong to the irreducible representation (IR) (30) of Racah’s group G2. Near the middle of the f shell it is often found that fewer independent blocks of numbers are needed to express their matrix elements than the Wigner–Eckart theorem, generalized to the IRs U of G2, would indicate. Each block corresponds to a given U and U ′, and possesses rows and columns labelled by the angular momenta L and L′. The number of independent blocks would be expected to be given by Racah’s multiplicity function c(UU ′ (30)); but near the middle of the shell the number c(UU ′ (20)) (or less) often suffices. For this to occur, z 8 and z 10 have to be replaced by linear combinations corresponding to IRs of the types (20)×(10) and (21)×(10) of the direct product gr...

Quotations from personal letters and other sources are used to give an account of an interaction with Brian Wybourne over the course of a career in theoretcial rare-earth spectroscopy spanning nearly a half-century.

A two-electron effective operator V 2 is constructed to reproduce, to lowest order of perturbation theory, the effect of p-electron admixtures in configurations of f electrons occurring in rare-earth ions located at octahedral sites in elpasolite crystals. These admixtures can arise from excitations of the type f → p as well as p → f, the latter including electron transfer from neighbouring ligands to the central rare-earth ion. The effective operator is decomposed into nine orthogonal components . For octahedral symmetry their strengths are specified by coefficients that depend on just two parameters. The insensitivity of the crystal splitting of of to some , as found by McCaw and Denning, is related to exceptionally small values of the corresponding reduced matrix elements of . The discrepancies that these authors have found in fitting their experimental data for other levels to the standard one-electron crystal-field Hamiltonian V 1 are examined. The effective operator V 2 is found to reproduce the gen...

An account is given of the preliminary steps that led to a parametrization of the absorption bands of rare-earth ions in aqueous solution.

By taking advantage of the automorphisms of the group SO(8), as exhibited by a phase reversal in the quark model of the atomic f shell, it is shown that the part z4 of the magnetic spin-spin interaction possesses matrix elements that go beyond the Wigner-Eckart theorem for Racah's group G2 and can always be expressed as a simple product of two factors rather than a sum over products. By means of the spin-quasispin interchange, this result can be carried over to the operator e3 + Ω, which Racah used in his analysis of the Coulomb interaction between the f electrons. The unexpected proportionalities that are such a striking feature of the matrix elements of e3 + Ω can thus be seen as a consequence of the automorphisms of SO(8).

The part of a one-electron coefficient of fractional parentage (cfp) depending, for the atomic l shell, on the spin S, seniority υ, and electron number n of the daughter state, is factored into two parts, the first with dependence on n and υ, and the second with dependence on υ and S. Various techniques are used to extend these results to the two-electron cfp. These entail deriving analogues of the 6-j symbols for the symplectic group Sp(4l + 2) and the special orthogonal group SO(2l + 1). Explicit algebraic expressions are provided, and the choice of multiplicity indices and their circumvention are discussed.

The correspondence between the five d orbitals and the components of the five-dimensional irreducible representation (IR) of the icosahedral group I is generalized to atomic f orbitals and the seven-dimensional IR of the didodecahedral group D , whose symmetries derive from the non-Euclidean figure possessing 24 regular heptagonal faces meeting in threes at 56 vertices. The group D (limited to rotations of the didodecahedron) is a subgroup of the exceptional Lie group G 2 , which Racah used in his analysis of the f shell, but it is not a subgroup of SO (3), the group of rotations in physical space. The sequence O (7) S 8 D provides an alternative to SO (7) G 2 D , where S 8 is the permutation group that interchanges the eight affinity groups of the didodecahedron among themselves. The analogue for the d shell is O (5) S 6 I , where S 6 permutes the six fivefold axes of the icosahedron and can be used to explain the Coulomb degeneracies of 2 P and 2 H in d3 . To extend these ideas to the f shell, a two-electron Hamiltonian is constructed from operators scalar with respect to both D and the spin S . The corresponding energy levels are given for the configurations f2 and f3 . The absence of SO (3) leads to various coefficients of mixed irrationality. Reflections of the didodecahedron extend D to Dh , and Dh is used to augment the labelling of the operators and states. It is shown that an interchange of spin and quasispin allows a connection to be made between those parts of the didodecahedral Hamiltonian belonging to the IR (30) of G 2 and the (30) components of the spin-other-orbit interaction for the atomic f shell.

Matrix elements of all two-electron and three-electron operators that are scalar with respect to the icosahedral group I have been tabulated for the icosahedral configurations hN. These operators represent the Coulomb interaction between electrons occupying h orbitals, and also the effects (to the lowest orders of perturbation theory) of configuration interaction on the levels of hN. States and operators are labelled by the irreducible representations (irreps) of the continuous groups SO(3) and SO(5) in addition to the irreps of I. An alternative scheme is introduced in which the irreps W of SO(5) are retained, but the orbital angular-momentum quantum numbers L associated with SO(3) are replaced by the irreps of the permutation groups S5 and S6, the latter corresponding to the interchanges (possibly nonfeasible) of the six fivefold axes of an icosahedron among themselves. The kaleidoscope operator K, which rotates the weight space of SO(5) by π/2, is an element of S5 and S6, and can be used to characteriz...

The four components of an icosahedral g orbital are represented by the irreducible spinor representation of (or, equivalently, SO(4)), where the two SO(3) groups are associated with the irreducible representations (IRs) and of the icosahedral group I. This enables the properties of the icosahedral configurations to be calculated by the familiar techniques of angular-momentum theory. The Coulomb interaction is broken into three parts , two of which ( and ) are SO(4) scalars, the third belonging to a combination of the various components and of the IR (22) that form the scalar IR A of I. The similar matrix elements of for different N are explained by introducing the concepts of quasispin and complementarity that are analogous to those used in atomic shell theory. Our angular-momentum basis is related to the icosahedral basis of Pooler with the aid of automorphisms of I that interchange and . This is formalized through the introduction of the kaleidoscope operator , and the degeneracy of the and terms for all is expressed as a result of the invariance of the Coulomb interaction to the operations of the cyclic automorphism group .

DROSOPHILA polytene chromosomes have been used for more than 60 years to explore eukaryotic chromosome organization and the nature of genes. T. S. Painter ([1934][1]), noting the distinctive and constant chromomeric patterns of the synapsed multistranded chromosomal arms, wrote “ … it was clear

AIM—To determine the consequences of renal calcification in preterm infants. METHODS—A cohort of 11 preterm babies was studied at the age of 4 to 5 years. They had had renal calcification as neonates. Seventeen matched controls were also studied. Each child had a renal ultrasound scan, a calcium load test, and a desmopressin test for renal concentrating ability (RCA). The study group also had glomerular filtration rate (GFR) estimated, using the height:creatinine ratio, and tubular phosphate reabsorption, without phosphate load, per glomerular filtration rate (Tp/GFR) calculated. RESULTS—In the study group the median GFR was 61 ml/min/1.73m2 (range 46-79 ml/min/1.73m2) and the median calculated Tp/GFR SD score was −0.94 (range −2.8- 0.68). Five children out of the study group had ultrasonic evidence of renal calcification. There was no significant difference between the two groups in renal size, calciuria, before or after calcium load, or RCA. Eight children (three patients, five controls) had an abnormal calcium load test. The RCA of the children in the study and control groups combined was below that of published values, with a median calculated SD score −0.71 (95% CI −1.21 to −0.23). CONCLUSIONS—There was evidence of renal dysfunction in children who had been born preterm. Renal calcification detected in the neonatal period does not seem to be a major predisposing factor for the abnormalities of renal function subsequently observed in these infants. Keywords: renal calcification; glomerular filtration rate; tubular phosphate reabsorption

AntiHermitian operators that are scalar with respect to the total angular momentum J and that act simultaneously on n electrons of the shell are shown to possess quasispin ranks K of opposite parity to n provided two conditions are satisfied. Examples of such operators for the f shell are four three-electron operators scalar with respect to S and L, and eight two-electron operators whose simultaneous spin and orbital ranks are 1 or 2. Connections are made to familiar Hermitian operators by commutation with respect to Casimir's operator for Racah's group . Applications of the Wigner - Eckart theorem for to both the and to the components of the spin - other-orbit interaction frequently go beyond what would be expected on the basis of Racah's multiplicity index for matrix elements of the type , where the labels refer to irreducible representations (IRs) of . This property is examined by parallel methods for the antiHermitian and Hermitian forms, and several unexpected proportionalities are thereby explained.

Tables are provided for the matrix elements of an orthogonal set of Hermitian three-electron operators t{sub i} for the states of the f shell. The t{sub i} are scalar with respect to the total spin S and total orbital angular momentum L, and they are among the effective operators needed to be included in an f-electron Hamiltonian in order to represent the coupling of the ground configuration f{sup N} to excited configurations via the interelectronic Coulomb interaction. 15 refs., 2 tabs.

The formula due to Trees for calculating the matrix elements of two-electron operators within the configuration has been generalized from to other groups. This is done to account for regularities appearing in the partial sums over parents when the Trees formula is applied to spin - spin and spin - other-orbit interactions within the f shell. Several examples are described.

Single-electron excitations of the atomic f shell are usually taken into account in analyses of lanthanide and actinide spectra by including six three-electron scalar operators t i in the Hamiltonian. Their matrix elements have been factorized for all f N by using the Wigner–Eckart theorem applied to Racah's groups SO (7) and G 2 . The two component parts, namely a reduced matrix element in G 2 and an isoscalar factor, are tabulated. This provides a compact representation of the values of the matrix elements and also enables unusual selection rules and proportionalities to be exposed.

The quark model of the atomic f shell, in which the angular properties of the states of the electrons are represented by the quark configuration (s+f)4, is generalized by assigning spins I=2 and 1 to the s and f quarks. This provides 5s+3f as a basis for the 26-dimensional irreducible representation (IR) of F4 and corresponds to the inclusions F4 contains/implies SOI(3)*G2 contains/implies SOI(3)*SOL(3). The shift operators I+or- make it possible to connect different IR's of SO(8) such as the three IR's of dimension 8, any one of which can be taken to span the 8 states of s+f in virtue of the automorphisms of that group. The additional symmetries associated with null triality are thereby subsumed. Application of the Wigner-Eckart theorem to SOI(3) provides a new perspective on relations between matrix elements of atomic operators within the f shell.

The bound-state and continuum solutions of the Schr\"odinger equation in a Coulomb potential are presented once again, but in a form that makes similarities in their structure much more apparent than before. The similarity is particularly striking if Laplace transforms are used. Not only are both bound state and continuum solutions of the same form, but they also have a simple structure for arbitrary energy eigenvalues. The usefulness of the formalism is illustrated by considering a number of examples involving infinite sums over bound states and integrals over continuum states of matrix elements that were relevant in past work.

The use of the quark configuration (s+f)4 to represent the states of the atomic f shell calls for a simultaneous transformation of operators. Operator equivalences are developed for z0, a two-electron operator associated with spin-spin interactions, and t11, a scalar three-electron operator appearing in third order in perturbation theory. Both belong to the irreducible representation (IR) (111) of Racah's group SO(7), and can be represented by combinations of the single-quark operators of the types (ftheta Dagger ftheta )(2) and (ftheta Dagger ftheta )(0)-712/stheta Dagger stheta , where theta distinguishes the four quarks. The group SO(7)' (which plays the same role for the f quarks as SO(7) does for the f electrons) is used to establish relations between matrix elements of z0 and those of other electronic operators such as U(2) and W(12), thereby accounting for various unexpected connections and proportionalities that go beyond what would be expected from straightforward applications of the Wigner-Eckart theorem.

The atomic d shell is explored from the perspective of the quark model of the atom. In this scheme, all the states are generated by four statistically independent fictitious particles (the quarks), each with angular momentum 3/2, augmented by two parity labels. The detailed quark expansions are given for the two 2D terms of d3, and the results are compared to the classic analysis of Condon and Shortley (1935). Matrix elements of single-electron tensor operators and of the Coulomb interaction are calculated in the quark scheme, and the connection to the conventional approach is made. The diagonal sum method of Slater is applied to the quark states and extensions to many-electron operators are discussed. The correspondence between the quark model and the traditional method implies relations between various n-j symbols, and this is illustrated by two special cases.

The various spin-dependent operators that contribute to electric-dipole radiation are examined. It is shown that the operator Vs of Wang and Stedman (1993) is cancelled by an operator Vx that comes from a spatial variation of the electromagnetic field vectors. The order of ( alpha Z)2 at which this cancellation takes place also includes effects produced by the spin-orbit mixing of levels that possess identical azimuthal quantum numbers l. A detailed analysis of these mechanisms is carried out for the Ly- alpha transition of a hydrogen-like atom with nuclear charge Ze.

In his studies of f electrons in atoms, Racah introduced the group SO(7) and its subgroup G2, with irreducible representations (irreps) W and U. By using a quarklike basis, these groups can be conveniently embedded in SO(8). This larger group, with irreps V, possesses two other SO(7) groups as subgroups that themselves contain G2 as a common subgroup. One of them, SO(7)' (with irreps W'), has been used to derive new selection rules on operators of physical interest. We describe methods for calculating the overlaps (VWU mod VW' U), the ultimate aim being to facilitate the transformations between SO(7) and SO(7)'. A table of relevant 6-U symbols (the G2 generalizations of 6-j symbols) is given. When V possesses null triality (that is, when the symbols labelling the open ends of the Dynkin diagram for SO(8) are equal), an undetermined phase in the overlaps can be used to generate matrix representations of S3, the permutation group on three objects. A brief table of zero overlaps is given. A remarkable factorization of the overlaps ((4310)W(40) I(4310)W'(40)) is noted, where (4310) is the irrep of SO(8) with dimension 25725.

Slater determinants and the group-theoretical basis of Racah are expressed in terms of quark-like states by means of explicit examples drawn from the atomic f shell. Four distinct quark-like objects (which, for convenience, the authors refer to simply as quarks) together with two parity labels are required. Racah's group SO(7), which acts on the seven states of an f electron, is augmented by SO(7)', the group acting on the seven states of an f quark. The assignment of group labels is illustrated by means of the commuting generators of these groups. The components of Sz and Qz of the spin and the quasispin are constructed as operators acting on two quarks at a time, and their eigenvalues, Ms and 1/2(N-7), are used to identify states generated by the shift operator L-. The complementary group to SO(7)' is exemplified by two 1N terms of f6 and f10 spanning a two-dimensional irreducible representation of the permutation group for the four quarks. Connection is made with the quark model for the p and d shells.

The quark model of the atom is studied with particular regard to its complementary groups. For an atomic l shell one finds that the group complementary to the basic quark group U(2l) is isomorphic to the double group of the tesseract, W*4. Character tables for W*4 and its subgroup SW*4 are provided. When l=3, the extra symmetry afforded by the automorphisms of SO(8) shows up by providing two further complementary groups. The group SOQ(3)*SOs(3) is complementary to SO(7) and the group W'4, also isomorphic to the group of the tesseract, is complementary to SU(7)'. The quark states of the f shell are calculated by diagonalizing a suitably chosen W*4 scalar operator, and the generalization to the g shell is discussed.

A procedure is described for drawing a correspondence between the states and operators occurring in standard atomic shell theory and those based on a quark-like model. Quasiparticle creation and annihilation operators for electrons are expressed as coupled products of pairs of quark operators in which Dirac gamma matrices make their appearance. The method is illustrated by calculating some matrix elements of the single-electron tensors V(k) for F3.

Criticism is presented for the arguments that lead Wang and Stedman to recommend that attempts to distinguish the roles of Hermitian and anti-Hermitian operators be abandoned.

exemple d£taill£ est dorm£ pour la configuration £lectronique f. Abstract. It is shown that the SO(7) group used by Racah to define states and operators in the f shell can be usefully augmented by the two similar groups, SO(?I' and SO(7)~', discovered over ten years ago by Labarthe. Their properties are studied by two approaches : ii) using multi- electron operators, and (2) regarding the 16 384 states of the atomic f shell to be generated by the quark-like configuration (s + f)~, augmented by two parity labels. By sandwiching the irreducible representations of SO(?) and SO(71' between representations of SO (8) and G~, an explanation can be found for some of the unexpected relations between matrix elements. The method is illustrated by a detailed example in the electron configuration f~.

The states of the atomic f shell are constructed by coupling together four quark-like objects belonging to the eight-dimensional spinor irreducible representation (irrep) (1/2 1/2 1/2) of SO(7). Two parity labels are also required. Transformations among the eight components of each quark lead to the groups U(8) and SO(8), which can be used to augment the labels provided by the groups SO(7) and G2 that Racah (1943,1949) used in his classic analysis. Coefficients of fractional parentage (CFP) have been calculated for the quark configurations q2, q3 and q4. To allow for the automorphisms of SO(8), the groups SO(7)' and SO(7)" of Labarthe (1980) are used as alternative intermediaries to SO(7) between SO(8) and G2. Parallel tables of CFP are provided. As an example of the usefulness of the quark model, a correspondence is established between a three-electron operator t4 used in configuration-interaction studies and a two-quark operator. Some matrix elements of the latter in q4 are calculated by means of the quark CFP, thereby giving the corresponding matrix elements of t4 in the electronic configurations f6 and f7. By using the irreps of SO(7)', an unexpected proportionality between the sets of matrix elements can be accounted for.

The F+ center in CaO consists of an electron trapped in an oxygen vacancy. The interaction between the electron and the even normal modes of the surrounding octahedron of calcium ions can be represented by an approximate Hamiltonian possessing an oscillator term of U(5) symmetry and an interaction term of O(3) symmetry. To separate repeated angular-momentum quantum numbers L in the symmetric irreducible representations of O(5), four independent methods have been studied.A remarkable coalescence of these approaches in the case of L=6 suggests a natural way to make the separation.

The method devised by Cerkaski (1987) has been used for the group Sp(2n) to find some 6-j symbols for which a single multiplicity index is required. This approach possesses some advantages over that based on Racah's techniques for SO(3): the formulae for the 6-j symbols are comparatively simple, and they automatically exhibit the symmetries of Jucys (1973). Elementary means are used to show that the eigenvalues of Casimir's operator C2 for Sp(2n) are identical to those of C2 for O(2d) if the authors take d=-n and replace the irreps of Sp(2n) by their transposed counterparts for O(2d), where d is integral or half-integral. This enables the formulae for Sp(2n) to be used to generate expressions for some 6-j symbols for the orthogonal groups O(2d) and SO(2d). Illustrations are provided by SO(2l+1) and O(4).

The establishing of operator orthogonality for atomic configurations C by means of group theory is extended to operators Hi requiring arbitrary multiplicity labels to distinguish them. By including the zero-electron operator in the set of orthogonal operators, each N-electron operator can be constructed to belong to the irreducible representation (irrep) (1N041+2-2N-1N) of SU(41+2), with the result that: (a) operator orthogonality for C=1n is equivalent to a relation between 3-j symbols for the group SU(41+2), and (b) the effect of electron-hole conjugation is simplified and no quasispin ranks of mixed parity appear. A second kind of orthogonality relation, in which the running index is the operator label i, yields new relations satisfied by the matrix elements of the orthogonal operators. The dependence of operator normalisation on N and n is derived from a group-theoretical formula of Hecht (1975) and confirmed by an approach using fractional parentage. Generalisations to other atomic configurations are briefly considered.

The tables of f-electron matrix elements calculated by Nielson and Koster (1963) for single-electron tensors of the types V(k) and W(11) are examined for proportionalities that go beyond what would be expected on the basis of a straightforward application of the Wigner-Eckart theorem. The tensors V(k) (for k even) transform according to the irreducible representation (irrep) (20) of th exceptional Lie group G2, and the -triple Kronecker product U*(20)*U' that occurs when a matrix element is being evaluated frequently contains the G2 scalar (00) twice in its reduction. In spite of this, blocks of matrix elements are often proportional to each other, especially when U or U' is the irrep (20) or (21). Various methods are considered to explain such proportionalities (as well as a few unexpected orthogonalities), the aim being to avoid a detailed calculation of the type undertaken by Nielson and Koster. Commutation relations provide the most striking approach, though separating the spin-up and spin-down electrons and using UU coupling to bring the two parts together can also be effective. In the case of W(11), the analysis is extended to embrace operators that possess the same G2 label (namely the irrep (11)) and that come from two-electron interactions of the spin-other-orbit type. Proportionalities are much less common here. Although the authors have been unable to account in a direct way for a few relations, their special nature suggests that they arise from some particular set of circumstances and not as a result of some underlying group-theoretical structure that has eluded their detection.

We studied 13 children subjected to elective tonsillectomy, 6 of whom (study patients) received supplemental intravenous isotonic saline during and after operation, and 7 of whom (controls) did not. Clinical and biochemical evidence of hypovolaemia was present in the control but not in the study patients. Plasma antidiuretic hormone (ADH) and urine osmolality were higher in controls (p less than 0.005 and p less than 0.05 respectively). Plasma sodium concentration and osmolality were similar in the two groups. We conclude that hypovolaemia is the principal stimulus to ADH release following surgery and that, in addition to replacement of observed losses of blood and other fluids by fluids of appropriate composition, hypovolaemia should be prevented by the administration of maintenance quantities of isotonic fluid, rather than exacerbated by fluid restriction, in patients in whom oral fluid intake is interrupted for more than a brief period. Hypotonic and sodium free fluids should be avoided because of the risk of hyponatraemia.

Starting from a primitive 6-j symbol for SO (2l+1) in which four elementary spinor irreducible representations (irreps) (. . .) appear, and using the properties of the Kronecker products of partially stretched irreps, the authors develop a bootstrap procedure, based on a generalisation of the Biedenharn-Elliott sum rule, for calculating other 6-j and 9-j symbols for SO(2l+1). Several of their formulae can be expressed in terms of SO(3) 3-j symbols and rotation matrices d jmn( pi ). An explanation for this is found by using the complementary groups whose generators involve the spin S and quasispin Q of electrons in an atomic l shell. The relation between the two kinds of coupling, that of the irreps of SO(2l+1) and that of the SO(3) angular momenta, is particularly fruitful if the quasiparticle description is employed for the electrons. A further bootstrap leads to a formula for an SO(2l+1) 6-j symbol whose six irreps are all of the type (11 . . . 10 . . . 0), and this is shown to be consistent with a formula for an Sp(2n) 6-j symbol if one replaces 2n by the negative dimensions -2l-1.

A convectively cooled, recirculating thermoelectric generator based on β‘ alumina has been designed and operated over the temperature range of 400–600 °C. The design employs a stainless‐steel wick and flame sprayed molybdenum electrodes and the unit can be assembled and operated with ease. A full treatment of all thermal and electrical flows is given and theoretical efficiencies of 10%–15% are predicted. Critical parameters are the internal resistance and radiation coefficients for thermal losses, while it is also shown that the flow of sodium within the electrode and the geometry of the evaporating and condensing surfaces is of importance in limiting the measured efficiency to 1%–3%. Units have been operated for up to 3000 h.

Mise au point sur le calcul des trajectoires des «coordinats» oscillants dans une molecule polyatomique du fait de l'effet Jahn-Teller, en utilisant des representations irreductibles des groupes de symetrie

The 6-j and 9-j symbols that occur in angular-momentum theory can be generalized from the group S0(3) to other compact Lie groups. The initial motivation for doing so stems from the Jahn-Teller effect, where the Hamiltonian for a particular octahedral system possesses an approximate SO(5) symmetry. Several methods are described for finding formulas for multiplicity-free 6-j and 9-j symbols, including generalizations of Schwinger's generating functions. The recent method of Cerkaski for finding a class of 6-j symbols with one multiplicity index is illustrated with an example for Sp(6).

Objectives: To examine the value of an intravenous urogram (IVU) in patients with abnormal differential 99mTc dimercaptosuccinic acid (DMSA) uptake without scarring or ultrasound abnormality. Study design: Forty patients (age 0–19 years) were identified over a two year period in whom the differential renal uptake was >10%, who had smooth renal outlines, and had no evidence of scarring. All patients had an ultrasound examination. Two had marked urological abnormalities on ultrasound and eight had a duplex system in the kidney with greater DMSA uptake. In 18 patients where no explanation was apparent for the discrepant DMSA uptake, an IVU was performed. Results: Eight patients had a normal IVU. In the remaining 10 patients, six had duplex systems without scarring and four had appearances of scarring in the kidney with reduced DMSA uptake. Conclusions: In this small selected group an IVU will identify a significant number of patients with normal kidneys, unrecognised simple duplex systems, or scarring where the DMSA scan has been inconclusive. This will help in planning long term follow up.

A number of minor errors have been detected in the computer output frequently used to fit the strengths of the three-electron operators ti to the experimental spectroscopic data for lanthanide and actinide ions in crystals. A table of corrections is given. The five new zeros appearing in this table can be accounted for on the basis of the quark model for the atomic f shell.

Following recognition of foreign antigens, the T cell antigen receptor (TCR) transduces signals leading to clonal expansion and differentiation into effector cells. Engagement of the TCR results first in the activation of cytosolic protein tyrosine kinases, followed by initiation of multiple signaling cascades. Recently, it has been shown that regulation and integration of these signaling pathways requires formation of multimolecular complexes and the recruitment of these complexes to specific regions within the cell. This review focuses on the events leading to T cell activation including the signaling cascades and the role of adapter molecules in coordination of these pathways. In addition, the mechanism by which TCR ligation can lead to T cell removal following elimination of an antigenic challenge is discussed.

OBJECTIVES—To investigate the seroconversion rate and duration of persistence of protective antibody titres after varicella immunisation in children with renal failure. DESIGN—32 children (25 end stage and 7 pre-end stage renal failure) were immunised using 2 × 2000 plaque forming unit doses of varicella vaccine 3 months apart. Varicella antibody titres were measured by enzyme linked immunosorbent assay. RESULTS—All children initially seroconverted after immunisation. At a mean follow up of 20.3 months, 23 of 28 had protective antibody titres, 4 children having died of unrelated causes. Two children required a third booster dose. 11 children underwent renal transplantation; 10 had protective titres at the time of transplantation and, at a mean of 23.4 months after immunisation, 6 currently have protective titres. Minor side effects occurred after 11 vaccine doses in 9 children. No child developed varicella, despite 10 clear episodes of exposure to the wild-type virus. CONCLUSIONS—Varicella immunisation in children with end stage and pre-end stage renal failure results in a high rate of seroconversion and persistence of protective antibody titres. More widespread use of the vaccine before renal transplantation is recommended.

Four quarklike eight-dimensional spinors are used to generate the states of the atomic f shell. The automorphisms of SO(8) are put to work through the three SO(7) subgroups of Labarthe. As an example, selection rules are derived for two three-electron operators used in rare-earth and actinide spectroscopy

The symmetric group $S_6$ that permutes the six five-fold axes of an icosahedron is introduced to go beyond the simple rotations that constitute the icosahedral group $I$. Owing to the correspondence $h\leftrightarrow d$, the calculation of the Coulomb energies for the icosahedral configurations $h^N$ based on the sequence $O(5) \supset S_6 \supset S_5 \supset I$ can be brought to bear on Racah's classic theory for the atomic d shell based on $SO(5) \supset SO_L(3) \supset I$. Among the elements of $S_6$ is the kaleidoscope operator ${\cal K}$ that rotates the weight space of SO(5) by $\pi/2$. Its use explains some puzzling degeneracies in d^3 involving the spectroscopic terms ^2P, ^2F, ^2G and ^2H., Comment: Tentatively scheduled to appear in Physical Preview Letters Apr 5, 99. Revtex, 1 ps figure

Age differences in syllogistic reasoning in relation to crystallized and fluid ability were studied in 278 adults from 19 to 96 years of age. Two reasoning tasks, the evaluation and the construction of conclusions for syllogisms of varying complexity and believability, a vocabulary test, and 3 tasks of working memory were administered. The magnitude of age-related variance on selected reasoning tasks was only partially reduced by statistically controlling measures of both working memory and vocabulary. Additional age-related effects on reasoning were found to be significantly associated with number of mental models and bias produced by conflict between belief and logic. A significant bias was also found toward acceptance of invalid syllogisms as valid, even when contents were abstract. These sources of error in logic are discussed in relation to Johnson-Laird's (1983) theory of mental models and Evan's (1989) account of bias in human reasoning.