Matrix elements of U(2n) generators in a multishell spin-orbit basis. I. The del-operator MEs in a two-shell composite Gelfand-Paldus basis

This is the first in a series of three articles which aimed to derive the matrix elements of the U(2n) generators in a multishell spin-orbit basis. This is a basis appropriate to many-electron systems which have a natural partitioning of the orbital space and where also spin-dependent terms are included in the Hamiltonian. The method is based on a new spin-dependent unitary group approach to the many-electron correlation problem due to Gould and Paldus [M. D. Gould and J. Paldus, J. Chem. Phys. 92, 7394, (1990)]. In this approach, the matrix elements of the U(2n) generators in the U(n) x U(2)-adapted electronic Gelfand basis are determined by the matrix elements of a single Ll(n) adjoint tensor operator called the del-operator, denoted by Delta(j)(i) (1 less than or equal to i, j less than or equal to n). Delta or del is a polynomial of degree two in the U(n) matrix E = [E-j(i)]. The approach of Gould and Paldus is based on the transformation properties of the U(2n) generators as an adjoint tensor operator of U(n) x U(2) and application of the Wigner-Eckart theorem. Hence, to generalize this approach, we need to obtain formulas for the complete set of adjoint coupling coefficients for the two-shell composite Gelfand-Paldus basis. The nonzero shift coefficients are uniquely determined and may he evaluated by the methods of Gould et al. [see the above reference]. In this article, we define zero-shift adjoint coupling coefficients for the two-shell composite Gelfand-Paldus basis which are appropriate to the many-electron problem. By definition, these are proportional to the corresponding two-shell del-operator matrix elements, and it is shown that the Racah factorization lemma applies. Formulas for these coefficients are then obtained by application of the Racah factorization lemma. The zero-shift adjoint reduced Wigner coefficients required for this procedure are evaluated first. All these coefficients are needed later for the multishell case, which leads directly to the two-shell del-operator matrix elements. Finally, we discuss an application to charge and spin densities in a two-shell molecular system. (C) 1998 John Wiley & Sons.

Liveweight gains of steers at different stocking rates on monospecific Gatton panic and Estrella grass pastures in the Chaco Central region of Paraguay

A grazing trial to study the effect of stocking rate on animal production and botanical composition of Gallon panic (Panicum maximum) and Estrella grass (Cynodon nlemfuensis) was conducted in the central region of the Paraguayan Chaco between 1992 and 1998. The experiment included 6 stocking rates (0.5, 0.8. 1.1, 1.4. 1.7 and 2.0 AU/ha) on individual 4-ha paddocks. The pasture treatments were continuously grazed by yearling steers. replaced annually, over a 4-year grazing period. No fertiliser was used. Botanical composition was recorded annually in autumn from 1992 to 1998 while animal production data were recorded monthly from 1992 to 1996. Relationships between animal productivity and stocking rates were determined by regression analysis. Gallon panic produced greater liveweight gains per head than Estrella grass at low and intermediate stocking rates. However, the slope of the linear relationship between liveweight gain per head and stocking rate increased each year in Gallon panic indicating that the productivity of this grass progressively declined at higher stocking rates over the period of observation. Estrella grass showed less sensitivity to stocking rate but was affected severely by periods of low rainfall.

Petrology and geochemistry of the Bandas del Sur Formation, Las Canadas Edifice, Tenerife (Canary Islands)

The Bandas del Sur Formation preserves a Quaternary extra-caldera record of central phonolitic explosive volcanism of the Las Canadas volcano at Tenerife. Volcanic rocks are bimodal in composition, being predominantly phonolitic pyroclastic deposits, several eruptions of which resulted in summit caldera collapse, alkali basaltic lavas erupted from many fissures around the flanks. For the pyroclastic deposits, there is a broad range of pumice glass compositions from phonotephrite to phonolite. The phonolite pyroclastic deposits are also characterized by a diverse, 7-8-phase phenocryst assemblage (alkali feldspar + biotite + sodian diopside + titanomagnetite + ilmenite + nosean-hauyne + titanite + apatite) with alkali feldspar dominant, in contrast to interbedded phonolite lavas that typically have lower phenocryst contents and lack hydrous phases. Petrological and geochemical data are consistent with fractional crystallization (involving the observed phenocryst assemblages) as the dominant process in the development of phonolite magmas. New stratigraphically constrained data indicate that petrological and geochemical differences exist between pyroclastic deposits of the last two explosive cycles of phonolitic volcanism. Cycle 2 (0.85-0.57 Ma) pyroclastic fall deposits commonly show a cryptic compositional zonation indicating that several eruptions tapped chemically, and probably thermally stratified magma systems. Evidence for magma mixing is most widespread in the pyroclastic deposits of Cycle 3 (0.37-0.17 Ma), which includes the presence of reversely and normally zoned phenocrysts, quenched mafic glass blebs in pumice, banded pumice, and bimodal to polymodal phenocryst compositional populations. Syn-eruptive mixing events involved mostly phonolite and tephriphonolite magmas, whereas a pre-eruptive mixing event involving basaltic magma is recorded in several banded pumice-bearing ignimbrites of Cycle 3. The periodic addition and mixing of basaltic magma ultimately may have triggered several eruptions. Recharge and underplating by basaltic magma is interpreted to have elevated sulphur contents (occurring as an exsolved gas phase) in the capping phonolitic magma reservoir. This promoted nosean-hauyne crystallization over nepheline, elevated SO3 contents in apatite, and possibly resulted in large, climatologically important SO2 emissions.

Permian Palynofloral Assemblages of the Chaco-Paraná Basin (Argentina): Systematics and Stratigraphic Significance

Core samples from an upper Palaeozoic, partly glaciogene borehole section (Ordóñez: YPF Cd O es-1) in the southern Chaco-Paraná Basin (Córdoba Province, northeastern Argentina) have produced variable palynological results. Samples from the lower part of the section (i.e., from the diamictite-bearing upper Ordóñez Formation) proved non-palyniferous. Those from the overlying, essentially post-glacial Victoriano Rodríguez Formation yielded spore-pollen assemblages in varying concentrations and in good to excellent states of preservation, thus providing the material basis for the present account. The palynomorph taxa represented in the assemblages comprise 20 species of spores (distributed among 14 genera) and 25 species of pollen grains (14 genera). The majority of the species are described in systematic detail. One trilete spore species -Convolutispora archangelskyi- is newly proposed. Several other, possibly new species (three of trilete spores, one of monosaccate pollen) are represented insufficiently for other than informal naming. The following new combinations, also of trilete spore species, are instituted: Converrucosisporites confluens (Archangelsky & Gamerro, 1979), C. micronodosus (Balme & Hennelly, 1956), and Anapiculatisporites tereteangulatus (Balme & Hennelly, 1956). Sculptural intergradation (granulate through verrucate) among three species -Granulatisporites austroamericanus Archangelsky & Gamerro, 1979, C. confluens, and C. micronodosus- prompts their informal grouping, proposed herein, as the Converrucosisporites confluens Morphon, which is also recognizable elsewhere in the Gondwanan Permian. The possibility, if not the likelihood, that G. austroamericanus is conspecific with Microbaculispora tentula Tiwari, 1965 is canvassed. The palynologically productive borehole section of the Victoriano Rodríguez Formation studied here is assignable to the middle to upper Cristatisporites Zone and to the succeeding Striatites Zone, thus signifying an Early Permian age for this section and facilitating correlation with strata of the Paraná and Paganzo Basins. From this and prior work, the Ordóñez well sequence embracing the Ordóñez and Victoriano Rodríguez Formations includes, in addition to the latter two zones, the preceding (late Pennsylvanian) Potonieisporites-Lundbladispora Zone which is known from the lower to mid-upper part of the Ordóñez Formation. Thus, the Carboniferous-Permian boundary can be inferred to lie within the upper part of the latter formation