A Solvable Model for Many Quark Systems in QCD Hamiltonians

Motivated by a canonical, QCD Hamiltonian we propose an effective Hamiltonian to represent an arbitrary number of quarks in hadronic bags. The structure of the effective Hamiltonian is discussed and the BCS-type solutions that may represent constituent quarks are presented. The single particle orbitals are chosen as 3-dimensional harmonic oscillators and we discuss a class of exact solutions that can be obtained when a subset of single-particle basis states is restricted to include a certain number of orbital excitations. The general problem, which includes all possible orbital states, can also be solved by combining analytical and numerical methods.Comment: 24 pages, 2 figures, research articl

A useful form of the recurrence relation between relativistic atomic matrix elements of radial powers

Recently obtained recurrence formulae for relativistic hydrogenic radial matrix elements are cast in a simpler and perhaps more useful form. This is achieved with the help of a new relation between the $r^a$ and the $\beta r^b$ terms ($\beta$ is a $4\times 4$ Dirac matrix and $a, b$ are constants) in the atomic matrix elements.Comment: 7 pages, no figure

Limitations on the superposition principle: superselection rules in non-relativistic quantum mechanics

The superposition principle is a very basic ingredient of quantum theory. What may come as a surprise to many students, and even to many practitioners of the quantum craft, is tha superposition has limitations imposed by certain requirements of the theory. The discussion of such limitations arising from the so-called superselection rules is the main purpose of this paper. Some of their principal consequences are also discussed. The univalence, mass and particle number superselection rules of non-relativistic quantum mechanics are also derived using rather simple methods.Comment: 22 pages, no figure

Recurrence relation for relativistic atomic matrix elements

Recurrence formulae for arbitrary hydrogenic radial matrix elements are obtained in the Dirac form of relativistic quantum mechanics. Our approach is inspired on the relativistic extension of the second hypervirial method that has been succesfully employed to deduce an analogous relationship in non relativistic quantum mechanics. We obtain first the relativistic extension of the second hypervirial and then the relativistic recurrence relation. Furthermore, we use such relation to deduce relativistic versions of the Pasternack-Sternheimer rule and of the virial theorem.Comment: 10 pages, no figure

A one way coupled thermo-mechanical model to determine residual stresses and deformations in butt welding of two ASTM A36 steel plates

To simulate the gas metal arc welding (GMAW) process in two ASTM A36 steel plates a finite element numerical model was developed, to obtain the corresponding residual stresses and deformations. The welding process was simulated as a one way coupled thermo-structural problem, considering that the structural field has very little influence in the thermal field, which is widely accepted in the specialized literature. To solve the thermal field, a nonlinear transient problem was created using finite second order elements that have temperature as the only degree of freedom in their nodes. The thermal properties of material were defined as a function of temperature and a combined convection-radiation coefficient was used as boundary condition. The double ellipsoidal model presented by Goldak was used to simulate the heat source and its dimensions were determined from the expressions developed by Christensen. To solve the structural field another nonlinear transient problem was created, considering the same mesh and the same time step of the thermal problem, using finite second order elements that have three displacements as degrees of freedom in their nodes. The mechanical properties of material were defined as a function of temperature, a thermo-elasto-plastic material model was used and the necessary displacement constraints were applied as boundary conditions. The temperature distribution obtained by solving the thermal field at each time step was transferred as a load to the structural problem. In both problems the “birth and death” technique was used to simulate the material deposition, which is implemented in the ANSYS software used in the present study. The activation of “dead” elements of the weld bead in the thermal analysis was performed simultaneously with the passage of the heat source, while in the structural analysis “dead” elements were activated as a function of their temperature. Different activation temperatures of “dead” elements were tested in the structural analysis, obtaining the best results when this temperature takes a value of 80% of material solidification temperature. The model used in this study was validated experimentally, taking as reference the residual displacements in several points of the welded plates. It was verified that there is a good correspondence between numerical and experimental results, with an error of less than 10%

Relativistically extended Blanchard recurrence relation for hydrogenic matrix elements

General recurrence relations for arbitrary non-diagonal, radial hydrogenic matrix elements are derived in Dirac relativistic quantum mechanics. Our approach is based on a generalization of the second hypervirial method previously employed in the non-relativistic Schr\"odinger case. A relativistic version of the Pasternack-Sternheimer relation is thence obtained in the diagonal (i.e. total angular momentum and parity the same) case, from such relation an expression for the relativistic virial theorem is deduced. To contribute to the utility of the relations, explicit expressions for the radial matrix elements of functions of the form $r^\lambda$ and $\beta r^\lambda$ ---where $\beta$ is a Dirac matrix--- are presented.Comment: 21 pages, to be published in J. Phys. B: At. Mol. Opt. Phys. in Apri