We present a fully relativistic extension of the optimized-potential method ͑ROPM͒, including the transverse electron-electron interaction and vacuum corrections. Using perturbation theory on the basis of the Kohn-Sham Hamiltonian an exact representation of the relativistic exchange-correlation energy E xc in terms of Kohn-Sham orbitals and eigenvalues is derived. The most simple, viable approximation to this E xc is obtained by a second-order expansion in powers of e 2 , which leads to a Mo "ller-Plesset-type correlation functional E c (2) . Due to this origin E c (2) allows a first-principles, seamless description of long-range dispersive forces. The ROPM integral equation that determines the full exchange-correlation four potential v xc is presented, and specified in detail for E c (2) . We also analyze the Krieger-Li-Iafrate ͑KLI͒ approximation to the exact ROPM integral equation, pointing out an inherent ambiguity of the KLI approximation which arises for eigenvalue-dependent E xc . The gauge properties of E xc and the ROPM integral equation are discussed by examining the transversality of the Kohn-Sham current-current response function. It is demonstrated that due to the multiplicative nature of the total effective potential the density functional definition of the no-pair transverse exchange energy guarantees gauge invariance, in contrast to the relativistic Hartree-Fock scheme. On the other hand, the correlation energy is gauge dependent as soon as the no-pair approximation is applied. In addition, we show that the no-pair approximation automatically implies a definite intrinsic gauge for the spatial components of v xc . The significance of the self-consistent treatment of the transverse interaction for heavy atoms is investigated numerically within the exchange-only limit. By comparing self-consistent with first-order perturbative inclusion of the transverse exchange it is shown that second-order transverse corrections cannot be neglected in calculations of ground state or inner-shell transition energies of heavy atoms, if one aims at spectroscopic accuracy. It is furthermore found that the Breit approximation for the full transverse interaction is not as accurate for the exchange potential as it is for the exchange energy. Finally, the KLI approximation is examined numerically, thereby resolving the ambiguity for the case of the transverse exchange.

Perturbation theory on the basis of the Kohn-Sham Hamiltonian leads to an implicit density functional for the correlation energy E(c). In this contribution we investigate the corresponding correlation potential v(c). It is shown that for finite systems the v(c) obtained by direct application of the optimized potential method diverges in the asymptotic region. The presence of unoccupied states, inherent in any perturbative form of E(c), is identified as the origin of this unphysical behavior. An approximate variational procedure is developed in order to avoid this difficulty. The potential resulting from this method qualitatively reproduces the shell structure of the exact atomic v(c).

Plasma measurements were made with a detector aboard the Explorer 10 satellite, launched on a highly elongated elliptical trajectory with the line of apsides about 33° to the antisolar direction. Magnetic field measurements were also carried out on Explorer 10 by the Goddard Space Flight Center of NASA. A plasma moving with a velocity of about 300 km sec−1 was first observed when the satellite reached a distance of about 22 earth radii. During the rest of the observations (which terminated about 40 hours later, at a distance of 42 earth radius, periods in which substantial plasma fluxes were recorded alternated with shorter periods in which the plasma flux was below or just above the detection limit. There was a striking correlation between the plasma flux and the magnetic field: in the absence of plasma the magnetic field direction was nearly radial from the earth, whereas in the presence of plasma, the field was irregular and generally formed large angles with the earth‐satellite direction. The plasma probe did not provide accurate information on the direction of the plasma flow, but placed the direction within a ‘window’ of about 20° by 80°. This window includes the direction pointing radially away from the sun. The flux densities of the positive ions (presumably protons) corresponding to the observed currents were of the order of a few times 108 cm−2 sec−1. They fluctuated over a range of about a factor of 2 during the periods when plasma was observed.

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BackgroundLifestyles profoundly determine the quality of an individual’s health and life since his childhood. Many diseases in adulthood are avoidable if health-risk behaviors are identified and improved at an early stage of life. The aim of the present research was to characterize a cohort of children aged 6–8 years selected in order to perform an epidemiological molecular study (the MAPEC_LIFE study), investigate lifestyles of the children that could have effect on their health status, and assess possible association between lifestyles and socio-cultural factors.MethodsA questionnaire composed of 148 questions was administered in two different seasons to parents of children attending 18 primary schools in five Italian cities (Torino, Brescia, Pisa, Perugia and Lecce) to obtain information regarding the criteria for exclusion from the study, demographic, anthropometric and health information on the children, as well as some aspects on their lifestyles and parental characteristics. The results were analyzed in order to assess the frequency of specific conditions among the different seasons and cities and the association between lifestyles and socio-economic factors.ResultsThe final cohort was composed of 1,164 children (50.9 boys, 95.4% born in Italy). Frequency of some factors appeared different in terms of the survey season (physical activity in the open air, the ways of cooking certain foods) and among the various cities (parents’ level of education and rate of employment, sport, traffic near the home, type of heating, exposure to passive smoking, ways of cooking certain foods). Exposure to passive smoking and cooking fumes, obesity, residence in areas with heavy traffic, frequency of outdoor play and consumption of barbecued and fried foods were higher among children living in families with low educational and/or occupational level while children doing sports and consuming toasted bread were more frequent in families with high socio-economic level.ConclusionsThe socio-economic level seems to affect the lifestyles of children enrolled in the study including those that could cause health effects. Many factors are linked to the geographical area and may depend on environmental, cultural and social aspects of the city of residence.