Volkoff

A. I. Akhiezer and V.B. Berestetskii, Quantum Electrodynamics, Translated from 2nd Russian ed. by G.M. Volkoff, 1965, Interscience, New York. 

In the early thirties of the last century Baade and Zwicky conjectured in their studies of supernova explosions that supemovae represent a transition from ordinary stars to compact objects, whose size is an order of magnitude smaller than the size of a white dwarf. At that time it was already known that the atomic nucleus consists of neutrons and it was clear that the density of the remnant objects must be of the same order as the nuclear density. Baade and Zwicky predicted that a supernova explosions will result in objects composed of closely packed neutrons (neutron stars). Prior to the beginning of the second World War (1939) a number of theoretical works by Landau, Oppenheimer, Volkoff and Snider showed, that indeed objects could exist with sizes about 10 km and masses about a solar mass. The density in these objects is about the nuclear saturation density and they basically consist of neutrons with a small amount of protons and electrons. The studies of neutron stars were subsequently stopped most likely due to the engagement of the nuclear scientists in the development of the nuclear bomb both in the West and the East. 

The first neutron star model in GR was constructed by Oppenheimer and Volkoff (1939). They derived the equations governing a spherically symmetric stellar equilibrium in GR using a metric of the form... 

Figure 1. The relation between central density and the mass of various degenerate star models. Chandrasekhar s curve is for white dwarfs with a mean molecular weight 2 of atomic mass units. Rudkjobing s curve is the same except for inclusion of the relativistic spin-orbit effects Rudkjobing (1952). The curve labeled Oppenheimer and Volkoff is for a set of neutron star models. The solid line marked Wheeler is a set of models computed with a generalized equation of state, from Cameron (1959).

The spherically symmetric, static star configurations are defined by the well known Tolman-Oppenheimer-Volkoff equations [30] for the mechanical equilibrium of self-gravitating matter (see also [14, 31])... 

The possibility to have metastable hadronic stars, together with the feasible existence of two distinct families of compact stars, demands an extension of the concept of maximum mass of a neutron star with respect to the classical one introduced by Oppenheimer Volkoff (1939). Since metastable HS with a short mean-life time are very unlikely to be observed, the extended concept of maximum mass must be introduced in view of the comparison with the values of the mass of compact stars deduced from direct astrophysical observation. Having in mind this operational definition, we call limiting mass of a compact star, and denote it as Mum, the physical quantity defined in the following way ... 

Energy release due to (anti)neutrino untrapping. The configurations for the quark stars are obtained by solving the Tolman-Oppenheimer-Volkoff equations for a set of central quark number densities nq for which the stars are stable. In Fig. 13 the configurations for different antineutrino chemical potentials are shown. The equations of state with trapped antineutrinos are softer and therefore this allows more compact configurations. The presence of antineutrinos tends to increase the mass for a given central density. 

Volkoff, B., and Cerri C. (1987). Carbon isotopic fractionation in subtropical Brazilian grassland soils, Comparison with tropical forest soils. Plant Soil. 102,27-31. 

Cerri, C. C., B. Volkoff, and F. Andreux. 1991. "Nature and behavior of organic matter in soils under natural forest, and after deforestation, burning and cultivation, near Manaus." Forest Ecology and Management 38 247-257. 

Chond, T., F. Andreux, J. C. Correa, B. Volkoff, and C. C. Cerri. 1991. "Changes in organic matter in an oxisol from the central Amazonian forest during eight years as pasture, determined by C composition." In Diversity of environmental biogeochemistry, ed. J. Berthelin (Elsevier, New York), pp. 307-405. 

Moraes, J. F., B. Volkoff, C. C. Cerri, and M. Bemoux. 1996. "Soil properties under Amazon forest and changes due to pasture installation in Rondonia, Brazil." Geoderma... 

Bernoux, M., D. Arrouays, M. Volkoff, C.C. Cerri, and C. Jolivet. 1998c. Bulk densities of Brazilian Amazon soils related to other soil properties. Soil Science and Society of America Journal 62(3) 743-749. 

The soils of the Amazon Basin belong mainly to the red ferralitic soil family. Their mineralogy is dominated by quartz, Al and Fe oxydes, and kaolinite, with a few accessory minerals such as anatase and zircon (Soembroek, 1984 Volkoff, 1985). Compared to cmstal abundances, these soils are more siliceous and aluminous with considerably lower levels of major cations. Numerous podzol zones exist on the central plain (Konhauser et al. 1994). 

Volkoff, B. 1985. "Organisations tegionales de la couverture p6dologique du Bresil. Chronologie des differencia-tions." Cah. ORSTOM, ser pedol., vol XXI, n 4, 225-236. 

De.sjardin, T., Andreux, E, Volkoff, B., and Cerri, C. C. (1993). Organic carbon and C contents in soils and soil size fractions, and their changes due to deforestation and pasture installation in eastern Amazonia. Geoderma 61, 103-118. 

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