A minimum hypothesis explanation for an IMF with a lognormal body and power law tail

We present a minimum hypothesis model for an IMF that resembles a lognormal distribution at low masses but has a distinct power-law tail. Even if the central limit theorem ensures a lognormal distribution of condensation masses at birth, a power-law tail in the distribution arises due to accretion from the ambient cloud, coupled with a non-uniform (exponential) distribution of accretion times.Comment: 2 pages, 1 figure, to appear in IMF@50, eds. E. Corbelli, F. Palla, and H. Zinnecker, Kluwer, Astrophysics and Space Science Librar

Nuclear fusion in a dense plasma

The standard theory of nuclear fusion rates in a strongly interacting plasma can be (correctly) derived only when the energy release, Q, is large compared to other energies in the problem. We exhibit a result for rates that provides a basis for calculating the finite Q corrections. Crude estimates indicate a significant defect in the conventional results for some regions of high density and strong plasma coupling. We also lay some groundwork for a path integral calculation of the new effects.Comment: Final version to appear in Phys. Rev. Lett

A Variational Approach to the Spinless Relativistic Coulomb Problem

By application of a straightforward variational procedure we derive a simple, analytic upper bound on the ground-state energy eigenvalue of a semirelativistic Hamiltonian for (one or two) spinless particles which experience some Coulomb-type interaction.Comment: 7 pages, HEPHY-PUB 606/9

The stability of the spectator, Dirac, and Salpeter equations for mesons

Mesons are made of quark-antiquark pairs held together by the strong force. The one channel spectator, Dirac, and Salpeter equations can each be used to model this pairing. We look at cases where the relativistic kernel of these equations corresponds to a time-like vector exchange, a scalar exchange, or a linear combination of the two. Since the model used in this paper describes mesons which cannot decay physically, the equations must describe stable states. We find that this requirement is not always satisfied, and give a complete discussion of the conditions under which the various equations give unphysical, unstable solutions

Nuclear Reaction Rates in a Plasma

The problem of determining the effects of the surrounding plasma on nuclear reaction rates in stars is formulated ab initio, using the techniques of quantum statistical mechanics. We derive a result that expresses the complete effects of Coulomb barrier penetration and of the influence of the surrounding plasma in terms of matrix elements of well defined operators. We find that possible "dynamical screening" effects that have been discussed in the literature are absent. The form of our results suggests that an approach that relies on numerical calculations of the correlation functions in a classical Coulomb gas, followed by construction of an effective two body potential and a quantum barrier penetration calculation, will miss physics that is as important as the physics that it includes.Comment: 66 pages, revtex, Errors Fixed, Explanation Adde

Deuterium-burning in substellar objects

We consider the depletion of primordial deuterium in the interior of substellar objects as a function of mass, age and absolute magnitude in several photometric passbands. We characterize potential spectroscopic signatures of deuterium in the lines of deuterated water HDO. These results will serve as a useful, independent diagnostic to characterize the mass and/or the age of young substellar objects, and to provide an independent age determination of very young clusters. These results can serve to identify objects at the deuterium-burning limit and to confront the theoretical prediction that D-burning is a necessary condition to form star-like objects.Comment: 13 pages, Latex file, uses aasms4.sty, accepted for publication in ApJ Letter

Modified Debye-Huckel Electron Shielding and Penetration Factor

Screened potential, modified by non standard electron cloud distributions responsible for the shielding effect on fusion of reacting nuclei in astrophysical plasmas, is derived. The case of clouds with depleted tails in space coordinates is discussed. The modified screened potential is obtained both from statistical mechanics arguments based on fluctuations of the inverse of the Debye-Huckel radius and from the solution of a Bernoulli equation used in generalized statistical mechanics. Plots and tables useful in evaluating penetration probability at any energy are provided.Comment: 9 pages, 3 figures, 3 table

Are Neutron-Rich Elements Produced in the Collapse of Strange Dwarfs ?

The structure of strange dwarfs and that of hybrid stars with same baryonic number is compared. There is a critical mass (M~0.24M_sun) in the strange dwarf branch, below which configurations with the same baryonic number in the hybrid star branch are more stable. If a transition occurs between both branches, the collapse releases an energy of about of 3x10^{50} erg, mostly under the form of neutrinos resulting from the conversion of hadronic matter onto strange quark matter. Only a fraction (~4%) is required to expel the outer neutron-rich layers. These events may contribute significantly to the chemical yield of nuclides with A>80 in the Galaxy, if their frequency is of about one per 1500 years.Comment: Accepted for publication in IJMP