The dynamics and helium distribution in hydrogen-helium fluid planets

The simple case of a homogeneous planet without first-order phase transitions is considered and an investigation is conducted concerning a pure hydrogen planet in which a first-order phase transition takes place from fluid molecular hydrogen to fluid metallic hydrogen. Attention is also given to convection in the presence of a compositional gradient, the effects of helium insolubility in a cooling hydrogen-helium planet, a hydrogen-helium planet in its early evolution, and the case in which influence of phase transition occurs much later in the evolution of the planet

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

Electromagnetic form factor via Minkowski and Euclidean Bethe-Salpeter amplitudes

The electromagnetic form factors calculated through Euclidean Bethe-Salpeter amplitude and through the light-front wave function are compared with the one found using the Bethe-Salpeter amplitude in Minkowski space. The form factor expressed through the Euclidean Bethe-Salpeter amplitude (both within and without static approximation) considerably differs from the Minkowski one, whereas form factor found in the light-front approach is almost indistinguishable from it.Comment: 3 pages, 2 figures. Contribution to the proceedings of the 20th International Conference on Few-Body Problems in Physics (FB20), Pisa, Italy, September 10-14, 2007. To be published in "Few-Body Systems

Cross-ladder effects in Bethe-Salpeter and Light-Front equations

Bethe-Salpeter (BS) equation in Minkowski space for scalar particles is solved for a kernel given by a sum of ladder and cross-ladder exchanges. The solution of corresponding Light-Front (LF) equation, where we add the time-ordered stretched boxes, is also obtained. Cross-ladder contributions are found to be very large and attractive, whereas the influence of stretched boxes is negligible. Both approaches -- BS and LF -- give very close results.Comment: 11 pages, 7 figure

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

Bethe-Salpeter equation in Minkowski space with cross-ladder kernel

A new method for solving the Bethe-Salpeter equation is developed. It allows to find the Bethe-Salpeter amplitudes both in Minkowski and in Euclidean spaces and, as a by product, the light-front wave function. The method is valid for any kernel given by irreducible Feynman graphs. Bethe-Salpeter and Light-Front equations for scalar particles with ladder + cross-ladder kernel are solved.Comment: 7 pages, 5 figures, to appear in the proceedings of the Workshop on Light-Cone QCD and Nonperturbative Hadron Physics, Cairns, Australia, July 7-15, 200

Analysis of the instantaneous Bethe-Salpeter equation for qqˉq\bar{q}-bound-states

We investigate the structure of the instantaneous Bethe-Salpeter equation for $q\bar{q}$-bound states in the general case of unequal quark masses and develop a numerical scheme for the calculation of mass spectra and Bethe-Salpeter amplitudes. In order to appreciate the merits of the various competing models beyond the reproduction of the mass spectra we present explicit formulas to calculate electroweak decays. The results for an explicit quark model will be compared to experimental data in a subsequent paperComment: 11 pages, RevTeX, TK-93-1

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.

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