Fabrizio Ferro

Non extensive resonant reaction rates in astrophysical plasmas

Abstract.We study two different physical scenarios of thermonuclear reactions in stellar plasmas proceeding through a narrow resonance at low energy or through the low-energy wing of a wide resonance at high energy. Correspondingly, we derive two approximate analytical formulae in order to calculate thermonuclear resonant reaction rates inside very coupled and non-ideal astrophysical plasmas in which non-extensive effects are likely to arise. Our results are presented as simple first-order corrective factors that generalize the well-known classical rates obtained in the framework of Maxwell-Boltzmann statistical mechanics. As a possible application of our results, we calculate the dependence of the total corrective factor with respect to the energy at which the resonance is located, in an extremely dense and non-ideal carbon plasma.

Temperature dependence of modified CNO nuclear reaction rates in dense stellar plasmas

We study the dependence of the CNO nuclear reaction rates on temperature, in the range of 107–108K, the typical range of temperature evolution from a Sun-like star towards a white dwarf. We show that the temperature dependence of the CNO nuclear reaction rates is strongly affected by the presence of non-extensive statistical effects in the dense stellar core. A very small deviation from the Maxwell–Boltzmann particle distribution implies a relevant enhancement of the CNO reaction rate and could explain the presence of heavier elements (e.g. Fe, Mg) in the final composition of a white dwarf core. Such a behavior is consistent with the recent experimental upper limit to the fraction of energy that the Sun produces via the CNO fusion cycle.

Metastable and stable equilibrium states of stellar electron-nuclear plasmas

By minimizing free energy density, we show that the stellar core of a hydrogen burning star is not in a global thermodynamical equilibrium unless density, temperature, mass and composition assume given values. The core (as the solar interior) can more appropriately be viewed as a metastable state with very long lifetime. Slightly non-extensive distribution function could be the natural distribution for a weakly non-ideal plasma like a stellar core and represents a more appropriate approximation to this system than a Maxwellian distribution, without affecting bulk properties of stars.

Collisional cross sections and momentum distributions in astrophysical plasmas: dynamics and statistical mechanics link.

We show that in stellar core plasmas, the one-body momentum distribution function is strongly dependent, at least in the high velocity regime, on the microscopic dynamics of ion elastic collisions and therefore on the effective collisional cross sections if a random force field is present. We take into account two cross sections describing ion-dipole and ion-ion screened interactions. Furthermore, we introduce a third unusual cross section to link statistical distributions and a quantum effect originated by the energy-momentum uncertainty owing to many-body collisions. We also propose a possible physical interpretation in terms of a tidal-like force. We show that each collisional cross section gives rise to a slight peculiar correction on the Maxwellian momentum distribution function in a well defined velocity interval. We also find a possible link between microscopic dynamics of ions and statistical mechanics in interpreting our results in the framework of nonextensive statistical mechanics.

Nonextensive interpretation of radiative recombination in electron cooling

Abstract.An interest for the low-energy range of the nonextensive distribution function arises from the study of radiative recombination in electron cooling devices in particle accelerators, whose experimentally measured reaction rates are much above the theoretical prediction. The use of generalized distributions, that differ from the Maxwellian in the low energy part (due to subdiffusion between electron and ion bunches), may account for the observed rate enhancement. In this work, we consider the isotropic distribution function and we propose a possible experiment for verifying the existence of a cut-off in the generalized momentum distribution, by measuring the spectrum of the X-rays emitted from radiative recombination reactions.

Dielectronic recombination rates in astrophysical plasmas

In this work we introduce a new expression of the plasma Dielecronic Recombination (DR) rate as a function of the temperature, derived assuming a small deformation of the Maxwell-Boltzmann distribution and containing corrective factors, in addition to the usual exponential behaviour, caused by non-linear effects in slightly non ideal plasmas. We then compare the calculated DR rates with the experimental DR fits in the low temperature region.

Microdynamical effects on momentum distribution in stellar plasmas

We show that, if a random force is present, the microscopic dynamics of ion elastic collisions and quantum effects may sensibly modify the momentum distribution of ions and electrons in stellar plasmas. We also show that a few microscopic interactions among the particles, that are significant in very specific energy intervals, lead to peculiar slight corrections to the usual MaxwellBoltzmann distribution. All these modifications can be easily taken into account by using the nonextensive statistical mechanics. Consequences on the resonant and non-resonant fusion rates are remarkable and may affect strongly some astrophysical processes. A few examples are reported.