Exact aymptotic expansions for the thermodynamics of hydrogen gas in the Saha regime

We consider the hydrogen quantum plasma in the Saha regime, where it almost reduces to a partially ionized atomic gas. We briefly review the construction of systematic expansions of thermodynamical functions beyond Saha theory, which describes an ideal mixture of ionized protons, ionized electrons and hydrogen atoms in their ground-state. Thanks to the existence of rigorous results, we first identify the simultaneous low-temperature and low-density limit in which Saha theory becomes asymptotically exact. Then, we argue that the screened cluster representation is well suited for calculating corrections, since that formalism accounts for all screening and recombination phenomena at work in a more tractable way than other many-body methods. We sketch the corresponding diagrammatical analysis, which leads to an exact asymptotic expansion for the equation of state. That scaled low-temperature expansion improves the analytical knowledge of the phase diagram. It also provides reliable numerical values over a rather wide range of temperatures and densities, as confirmed by comparisons to quantum Monte Carlo data.Comment: 10 page

On the Static Dielectric Permittivity for Coulomb System in the Long Wavelength Limit

On the basis of the exact relations the general formula for the static dielectric permittivity for Coulomb system is found in the region of small wave vectors. The obtained formula describes the dielectric function of the Coulomb system in both limits: in the "metallic" state and in the "dielectric" one. On this basis the determinations of the "apparent" dielectric and the "apparent" radius of screening are introduced. In the random phase approximation (RPA) the exact relations for the function dielectric function of the electron gas in the long-wavelength region of the wave vectors are found for an arbitrary degeneration of the particles.Comment: 5 pages, no figure

Continuing the Discussion on Administrative Discretion

The article continues the discussion on the topical issue of administrative discretion for Russian administrative-legal theory and legal practice, organized by the editors of the journal “Siberian Law Review” on the pages of two previous issues of the journal with the participation of P. P. Serkov and Yu. P. Solovey. The Author focuses on the state of the modern domestic doctrine of administrative discretion, the contribution of Russian legal scholars to its development, the need and possibility (including criteria and limits) of delimiting administrative discretion from other types of discretion. It is proved that the Russian jurisprudence demonstrates, contrary to the assertions of some experts, not confusion in the face of the problematic category of discretion, but ontological and methodological certainty, although sometimes reaching extremes. At the same time, there is no single Russian doctrine of discretion, there are many such doctrines, and some scholars have the right to claim that specific doctrines are associated with their names. The Author draws attention to the fact that discretion in general and administrative discretion in particular are interdisciplinary (interscientific) categories, so they must first of all be rid of the semantic and meaningful “layers” of other sciences. The sooner a pure theory of discretion appears, the more mistakes and risks will be insured against by legal science and law enforcement practice. In order to avoid terminological confusion and preserve the subject matter of the study, it is absolutely important to distinguishfour concepts: 1) administrative discretion; 2) judicial control over administrative discretion; 3) judicial discretion; 4) judicial discretion in the exercise of judicial control over administrative discretion. These concepts have a certain connection with each other, however, they designate different (partly even by their branch affiliation) categories, phenomena, processes and institutions. As a conclusion, it is indicated that the motives of each discretionary decision of the public administration must sooner or later (better sooner than later) be made public. To make this a reality, legal science needs to develop and offer effective legal guarantees for ensuring the rights of citizens and their associations when public authorities exercise their discretionary powers

Nonextensive statistics in stellar plasma and solar neutrinos

Nonextensive and quantum uncertainty effects (related to the quasiparticles composing the stellar core) have strong influence on the nuclear rates and, of course, affect solar neutrino fluxes. Both effects do coexist and are due to the frequent collisions among the ions. The weakly nonextensive nature of the solar core is confirmed. The range of predictions for the neutrino fluxes is enlarged and the solar neutrino problem becomes less dramatic.Comment: 4 pages. Proc. of TAUP99, Sept. 6-10 1999, Paris. To appear in Nucl. Phys. B, Proc. Supp

Equation of state SAHA-S meets stellar evolution code CESAM2k

We present an example of an interpolation code of the SAHA-S equation of state that has been adapted for use in the stellar evolution code CESAM2k. The aim is to provide the necessary data and numerical procedures for its implementation in a stellar code. A technical problem is the discrepancy between the sets of thermodynamic quantities provided by the SAHA-S equation of state and those necessary in the CESAM2k computations. Moreover, the independent variables in a practical equation of state (like SAHA-S) are temperature and density, whereas for modelling calculations the variables temperature and pressure are preferable. Specifically for the CESAM2k code, some additional quantities and their derivatives must be provided. To provide the bridge between the equation of state and stellar modelling, we prepare auxiliary tables of the quantities that are demanded in CESAM2k. Then we use cubic spline interpolation to provide both smoothness and a good approximation of the necessary derivatives. Using the B-form of spline representation provides us with an efficient algorithm for three-dimensional interpolation. The table of B-spline coefficients provided can be directly used during stellar model calculations together with the module of cubic spline interpolation. This implementation of the SAHA-S equation of state in the CESAM2k stellar structure and evolution code has been tested on a solar model evolved to the present. A comparison with other equations of state is briefly discussed. The choice of a regular net of mesh points for specific primary quantities in the SAHA-S equation of state, together with accurate and consistently smooth tabulated values, provides an effective algorithm of interpolation in modelling calculations. The proposed module of interpolation procedures can be easily adopted in other evolution codes.Comment: 8 pages, 5 figure