Matrix elements of U(2n) generators in a multishell spin-orbit basis. II. The two-shell nonzero shift ACCs and U(2n) generator MEs

This is the second in a series of articles whose ultimate goal is the evaluation of the matrix elements (MEs) of the U(2n) generators in a multishell spin-orbit basis. This extends the existing unitary group approach to spin-dependent configuration interaction (CI) and many-body perturbation theory calculations on molecules to systems where there is a natural partitioning of the electronic orbital space. As a necessary preliminary to obtaining the U(2n) generator MEs in a multishell spin-orbit basis, we must obtain a complete set of adjoint coupling coefficients for the two-shell composite Gelfand-Paldus basis. The zero-shift coefficients were obtained in the first article of the series. in this article, we evaluate the nonzero shift adjoint coupling coefficients for the two-shell composite Gelfand-Paldus basis. We then demonstrate that the one-shell versions of these coefficients may be obtained by taking the Gelfand-Tsetlin limit of the two-shell formulas. These coefficients,together with the zero-shift types, then enable us to write down formulas for the U(2n) generator matrix elements in a two-shell spin-orbit basis. Ultimately, the results of the series may be used to determine the many-electron density matrices for a partitioned system. (C) 1998 John Wiley & Sons, Inc.

Weathering geochronology by (U-Th)/He dating of goethite

Nine samples of supergene goethite (FeOOH) from Brazil and Australia were selected to rest the suitability of this mineral for (U-Th)/He dating. Measured He ages ranged from 61 to 8 Ma and were reproducible to better than a few percent despite very large Variations in [U] and [Th]. In all Samples with internal stratigraphy or independent age constraints, the He ages corroborated the expected relationship's. These data demonstrate that internally consistent He ages can be obtained on goethite. but do not prove quantitative 4 He retention. To assess possible diffusive He loss, stepped-heating experiments were performed on two goethite samples that were subjected to proton irradiation to produce a homogeneous distribution of spallogenic He-3. The He-3 release pattern indicates the presence of at least two diffusion domains, one with high helium retentivity and the other with very low retentivity at Earth surface conditions. The low retentivity domain, which accounts for similar to 5% of He-3, contains no natural He-4 and may represent poorly crystalline or intergranular material which has lost all radiogenic He-4 by diffusion in nature. Diffusive loss of He-3 from the high retentivity domain is independent of the macroscopic dimensions of the analyzed polycrystalline aggregate, so probably represents diffusion from individual micrometer-size goethite crystals. The He-2/He-3 evolution during the incremental heating experiments shows that the high retentivity domain has retained 90%-95% of its radiogenic helium. This degree of retentivity is in excellent agreement with that independently predicted from the helium diffusion coefficients extrapolated to Earth surface temperature and held for the appropriate duration. Considering both the high and low retentivity domains, these data indicate that one of the samples retained 90% of its radiogenic He-4 over 47.5 Ma and the other retained 86% over 12.3 Ma. Thus while diffusive-loss corrections to supergene goethite He ages are required. these initial results indicate that the corrections are not extremely large and can be rigorously quantified using the proton-irradiation He-4/He-3 method. Copyright (C) 2005 Elsevier Ltd.

Weathering Geochronology by (U-Th)/He Dating of Geothite

Ten samples of supergene goethite (FeOOH) from Brazil and Australia were selected to test the suitability of this mineral for (U-Th)/He dating. Measured He ages ranged from 8 to 61 Ma, and were reproducible to better than a few percent despite very large variations in [U] and [Th]. In all samples with internal stratigraphy or independent age constraints, the He ages honored the expected relationships. These data demonstrate that internally consistent He ages can be obtained on goethite, but do not prove quantitative 4He retention. To assess possible diffusive He loss, stepped-heating experiments were performed on two goethite samples that were subjected to proton irradiation to produce a homogeneous distribution of spallogenic 3He. The 3He release pattern indicates the presence of at least two diffusion domains, one with high helium retentivity and the other with very low retentivity at Earth surface conditions. The low retentivity domain, which accounts for ~ 5% of 3He, contains no natural 4He, and may represent poorly crystalline or intergranular material which has lost all radiogenic 4He by diffusion in nature. Diffusive loss of 3He from the high retentivity domain is independent of the macroscopic dimensions of the analyzed polycrystalline aggregate, so probably represents diffusion from individual micrometer-size goethite crystals. The 4He/3He evolution during the step heating experiments shows that the high retentivity domain has retained 90-95% of its radiogenic helium. This degree of retentivity is in excellent agreement with that independently predicted from the helium diffusion coefficients extrapolated to Earth surface temperature and held for the appropriate duration. These data indicate that one of the samples retained 90% of its radiogenic 4He over 46.8 Ma and the other retained 86% over 11.9 Ma. Thus while diffusive-loss corrections to supergene goethite He ages are required, these initial results indicate that the corrections are not extremely large and can be rigorously quantified using the proton-irradiation 4He/3He method.

Thermal ionization mass spectrometry U-series dating of a hominid site near Nanjing, China

Mass spectrometric U-series dating of speleothems from Tangshan Cave, combined with ecological and paleoclimatic evidence, indicates that Nanjing Man, a typical Homo erectus morphologically correlated with Peking Man at Zhoukoudian, should be at least 580 k.y. old, or more likely lived during the glacial oxygen isotope stage 16 (similar to 620 ka). Such an age estimate, which is similar to 270 ka older than previous electron spin resonance and alpha counting U-series dates, has significant implications for the evolution of Asian H. erectus. Dentine and enamel samples from the coexisting fossil layer yield significantly younger apparent ages, that of the enamel sample being only less than one-fourth of the minimum age of Nanjing Man. This suggests that U uptake history is far more complex than existing models can handle. As a result, great care must be taken in the interpretation of electron spin resonance and U-series dates of fossil teeth.

U-Series dating of Liujiang hominid site in Guangxi, Southern China

It has been established that modern humans were living in the Levant and Africa ca. 100 ka ago. Hitherto, this has contrasted with the situation in China where no unequivocal specimens of this species have been securely dated to more than 30 ka. Here we present the results of stratigraphic studies and U-series dating of the Tongtianyan Cave, the discovery site of the Liujiang hominid, which represents one of the few well-preserved fossils of modern Homo sapiens in China. The human fossils are inferred to come from either a refilling breccia or a primarily deposited gravel-bearing sandy clay layer. In the former case, which is better supported, the fossils would date to at least similar to 68 ka, but more likely to similar to 111-139 ka. Alternatively, they would be older than, similar to 153 ka. Both scenarios would make the Liujiang hominid one of the earliest modem humans in East Asia, possibly contemporaneous with the earliest known representatives from the Levant and Africa. Parallel studies on other Chinese localities have provided supporting evidence for the redating of Liujiang, which may have important implications for, the origin of modem humans. (C) 2002 Elsevier Science Ltd. All rights reserved.

Adaptation of rainbow fish to lake and stream habitats

Fish occupy a range of hydrological habitats that exert different demands on locomotor performance. We examined replicate natural populations of the rainbow fishes Melanotaenia eachamensis and M. duboulayi to determine if colonization of low-velocity (lake) habitats by fish from high-velocity (stream) habitats resulted in adaptation of locomotor morphology and performance. Relative to stream conspecifics, lake fish had more posteriorly positioned first dorsal and pelvic fins, and shorter second dorsal fin bases. Habitat dimorphism observed between wild-caught fish was determined to be heritable as it was retained in M. eachamensis offspring raised in a common garden. Repeated evolution of the same heritable phenotype in independently derived populations indicated body shape divergence was a consequence of natural selection. Morphological divergence between hydrological habitats did not support a priori expectations of deeper bodies and caudal peduncles in lake fish. However, observed divergence in fin positioning was consistent with a family-wide association between habitat and morphology, and with empirical studies on other fish species. As predicted, decreased demand for sustained swimming in takes resulted in a reduction in caudal red muscle area of lake fish relative to their stream counterparts. Melanotaenia duboulayi lake fish also had slower sustained swimming speeds (U-crit) than stream conspecifics. In M. eachamensis, habitat affected U-crit of males and females differently. Specifically, females exhibited the pattern observed in M. duboulayi (lake fish had faster U-crit than stream fish), but the opposite association was observed in males (stream males had slower Ucrit than lake males). Stream M. eachamensis also exhibited a reversed pattern of sexual dimorphism in U-crit (males slower than females) relative to all other groups (males faster than females). We suggest that M. eachamensis males from streams responded to factors other than water velocity. Although replication of muscle and U,,it phenotypes across same habitat populations within and/or among species was suggestive of adaptation, the common garden experiment did not confirm a genetic basis to these associations. Kinematic studies should consider the effect of the position and base length of dorsal fins.