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

The charmonium and bottomonium mass spectroscopy with a simple approximaton of the kinetic term

In this paper we propose a particular description of meson spectroscopy, with emphasis in heavy bound states like charmonia and bottomonia, after working on the main aspects of the construction of an effective potential model. We use the prerogatives from ``soft QCD'' to determine the effective potential terms, establishing the asymptotic Coulomb term from one gluon exchange approximation. At the same time, a linear confinement term is introduced in agreement with QCD and phenomenological prescription. The main aspect of this work is the simplification in the calculation, consequence of a precise and simplified description of the kinetic term of the Hamiltonian. With this proposition we perform the calculations of mass spectroscopy for charmonium and bottomonium mesons and we discuss the real physical possibilities of developing a generalized potential model, its possible advantages relative to experimental parameterization and complexity in numerical calculations

Effective boost and "point-form" approach

Triangle Feynman diagrams can be considered as describing form factors of states bound by a zero-range interaction. These form factors are calculated for scalar particles and compared to point-form and non-relativistic results. By examining the expressions of the complete calculation in different frames, we obtain an effective boost transformation which can be compared to the relativistic kinematical one underlying the present point-form calculations, as well as to the Galilean boost. The analytic expressions obtained in this simple model allow a qualitative check of certain results obtained in similar studies. In particular, a mismatch is pointed out between recent practical applications of the point-form approach and the one originally proposed by Dirac.Comment: revised version as accepted for publicatio

Screening of Nuclear Reactions in the Sun and Solar Neutrinos

We quantitatively determine the effect and the uncertainty on solar neutrino production arising from the screening process. We present predictions for the solar neutrino fluxes and signals obtained with different screening models available in the literature and by using our stellar evolution code. We explain these numerical results in terms of simple laws relating the screening factors with the neutrino fluxes. Futhermore we explore a wider range of models for screening, obtained from the Mitler model by introducing and varying two phenomenological parameters, taking into account effects not included in the Mitler prescription. Screening implies, with respect to a no-screening case, a central temperat reduction of 0.5%, a 2% (8%) increase of Beryllium (Boron)-neutrino flux and a 2% (12%) increase of the Gallium (Chlorine) signal. We also find that uncertainties due to the screening effect ar at the level of 1% for the predicted Beryllium-neutrino flux and Gallium signal, not exceeding 3% for the Boron-neutrino flux and the Chlorine signal.Comment: postscript file 11 pages + 4 figures compressed and uuencoded we have replaced the previous paper with a uuencoded file (the text is the same) for any problem please write to [email protected]

Rigorous theory of nuclear fusion rates in a plasma

Real-time thermal field theory is used to reveal the structure of plasma corrections to nuclear reactions. Previous results are recovered in a fashion that clarifies their nature, and new extensions are made. Brown and Yaffe have introduced the methods of effective quantum field theory into plasma physics. They are used here to treat the interesting limiting case of dilute but very highly charged particles reacting in a dilute, one-component plasma. The highly charged particles are very strongly coupled to this background plasma. The effective field theory proves that this mean field solution plus the one-loop term dominate; higher loop corrections are negligible even though the problem involves strong coupling. Such analytic results for very strong coupling are rarely available, and they can serve as benchmarks for testing computer models.Comment: 4 pages and 2 figures, presented at SCCS 2005, June 20-25, Moscow, Russi

Mg II Absorber Number Density at z~0.05: Implications for Omega_DLA Evolution

An unbiased sample of 147 quasar/AGN spectra, obtained with the FOS/HST, has been searched for intervening MgII absorbers over the redshift range 0<z<0.15. The total redshift path searched is 18.8, with the survey being 80% complete to a 5-sigma rest-frame equivalent width, W_r(2796), of 0.6 Ang. Main results of this work are: [1] Four systems were found, with a mean redshift of =0.06, yielding a redshift number density dN/dz=0.22(+0.12)(-0.09) for absorbers with W_r(2796)>0.6 Ang. This is consistent with the value expected if these systems do not evolve from higher redshifts (z=2.2). [2] No systems with W_r(2796)<0.6 Ang were found. It is a 2-sigma result to have a null detection of smaller W_r(2796) systems. If this implies a turnover in the low W_r(2796) region of the equivalent width distribution at z~0, then there is at least a 25% reduction in the average galaxy gas cross section from z<0.2 galaxies. [3] These systems have strong FeII absorption and are good candidates for damped Ly-alpha absorbers DLAs (see Rao & Turnshek 2000, ApJS, 130, 1). This translates to a redshift number density of dN/dz=0.08(+0.09)(-0.05) for DLAs at z~0. In tandem with the data analyzed by Rao & Turnshek, these results indicate that the redshift number density of DLAs does not evolve from z~4 to z~0. If the HI mass function does not evolve from z~0.5 to z~0, then the cosmological HI mass density is also deduced to not evolve from z~4 to z~0. These z~0 results for MgII absorption-selected DLAs are at odds with those based upon 21-cm emission from HI galaxies by a factor of five to six.Comment: 23 pages, 7 Figures, accepted to ApJ. Replaced version includes additional figures and tables and substantial modifications to the tex

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

Spectrum for Heavy Quankonia and Mixture of the Relevant Wave Functions within the Framework of Bethe-Salpeter Equation

Considering the fact that some excited states of the heavy quarkonia (charmonium and bottomonium) still missing in experimental observations and potential applications of the relevant wave functions of the bound states, we re-analyze the spectrum and the relevant wave functions of the heavy quarkonia within the framework of Bethe-Salpeter (B.S.) equation with a proper QCD-inspired kernel. Such a kernel for the heavy quarkonia, relating to potential of non-relativistic quark model, is instantaneous, so we call the corresponding B.S. equation as BS-In equation throughout the paper. Particularly, a new way to solve the B.S. equation, which is different from the traditional ones, is proposed here, and with it not only the known spectrum for the heavy quarkonia is re-generated, but also an important issue is brought in, i.e., the obtained solutions of the equation `automatically' include the 'fine', 'hyperfine' splittings and the wave function mixture, such as $S-D$ wave mixing in $J^{PC}=1^{--}$ states, $P-F$ wave mixing in $J^{PC}=2^{++}$ states for charmonium and bottomonium etc. It is pointed out that the best place to test the wave mixture probably is at $Z$-factory ($e^+e^-$ collider running at $Z$-boson pole with extremely high luminosity).Comment: 26 pages, 8 figure

Theoretical Uncertainties in Red Giant Branch Evolution: The Red Giant Branch Bump

A Monte Carlo simulation exploring uncertainties in standard stellar evolution theory on the red giant branch of metal-poor globular clusters has been conducted. Confidence limits are derived on the absolute V-band magnitude of the bump in the red giant branch luminosity function (M_v,b) and the excess number of stars in thebump, R_b. The analysis takes into account uncertainties in the primordial helium abundance, abundance of alpha-capture elements, radiative and conductive opacities, nuclear reaction rates, neutrino energy losses, the treatments of diffusion and convection, the surface boundary conditions, and color transformations. The uncertainty in theoretical values for the red giant bump magnitude varies with metallicity between +0.13/-0.12 mag at [Fe/H] = -2.4 and +0.23/-0.21 mag at [Fe/H] = -1.0$. The dominant sources of uncertainty are the abundance of the alpha-capture elements, the mixing length, and the low-temperature opacities. The theoretical values of M_v,b are in good agreement with observations. The uncertainty in the theoretical value of R_b is +/-0.01 at all metallicities studied. The dominant sources of uncertainty are the abundance of the alpha-capture elements, the mixing length, and the high-temperature opacities. The median value of R_b varies from 0.44 at [Fe/H] = -2.4$ to 0.50 at [Fe/H] = -1.0. These theoretical values for R_b are in agreement with observations.Comment: 30 pages, 6 figures. To appear in Ap

Instantaneous Bethe-Salpeter equation: utmost analytic approach

The Bethe-Salpeter formalism in the instantaneous approximation for the interaction kernel entering into the Bethe-Salpeter equation represents a reasonable framework for the description of bound states within relativistic quantum field theory. In contrast to its further simplifications (like, for instance, the so-called reduced Salpeter equation), it allows also the consideration of bound states composed of "light" constituents. Every eigenvalue equation with solutions in some linear space may be (approximately) solved by conversion into an equivalent matrix eigenvalue problem. We demonstrate that the matrices arising in these representations of the instantaneous Bethe-Salpeter equation may be found, at least for a wide class of interactions, in an entirely algebraic manner. The advantages of having the involved matrices explicitly, i.e., not "contaminated" by errors induced by numerical computations, at one's disposal are obvious: problems like, for instance, questions of the stability of eigenvalues may be analyzed more rigorously; furthermore, for small matrix sizes the eigenvalues may even be calculated analytically.Comment: LaTeX, 23 pages, 2 figures, version to appear in Phys. Rev.