2,206 research outputs found
Evaluation of Spectrograms of High Speed Steels for Minor Elements Plate Calibration Method
Minor elements occurring in high speed steels do not exceed a total of two percent Such steels of our Works manufacture designated as T.H.S. a are of the conventional type 18-4-1. The time-scale method of plate calibration due to Smith
has been adopted and applied to the ferrous analysis of the above samples; the spectra evaluated and compared with the usual method of log ratio of galvanometer deflections against composition. The elements receiving attention were manganese, silicon and vanadium. Conventional spark technique for exciting spectra was used. The standard deviations of results which have been computed, do not exceed 2 to 3 per cent of contents
Relativistic U(3) Symmetry and Pseudo-U(3) Symmetry of the Dirac Hamiltonian
The Dirac Hamiltonian with relativistic scalar and vector harmonic oscillator
potentials has been solved analytically in two limits. One is the spin limit
for which spin is an invariant symmetry of the the Dirac Hamiltonian and the
other is the pseudo-spin limit for which pseudo-spin is an invariant symmetry
of the the Dirac Hamiltonian. The spin limit occurs when the scalar potential
is equal to the vector potential plus a constant, and the pseudospin limit
occurs when the scalar potential is equal in magnitude but opposite in sign to
the vector potential plus a constant. Like the non-relativistic harmonic
oscillator, each of these limits has a higher symmetry. For example, for the
spherically symmetric oscillator, these limits have a U(3) and pseudo-U(3)
symmetry respectively. We shall discuss the eigenfunctions and eigenvalues of
these two limits and derive the relativistic generators for the U(3) and
pseudo-U(3) symmetry. We also argue, that, if an anti-nucleon can be bound in a
nucleus, the spectrum will have approximate spin and U(3) symmetry.Comment: Submitted to the Proceedings of "Tenth International Spring
Seminar-New Quests in Nuclear Structure", 6 page
Cost and benefits of intermediate water storage structures: case study of diggies in Rajasthan
Water storageWater deliveryIrrigation schedulingWater controlIrrigation canalsWatercoursesFarmsCrop productionCost benefit analysis
The thermodynamic limit for fractional exclusion statistics
I discuss Haldane's concept of generalised exclusion statistics (Phys. Rev.
Lett. {\bf 67}, 937, 1991) and I show that it leads to inconsistencies in the
calculation of the particle distribution that maximizes the partition function.
These inconsistencies appear when mutual exclusion statistics is manifested
between different subspecies of particles in the system. In order to eliminate
these inconsistencies, I introduce new mutual exclusion statistics parameters,
which are proportional to the dimension of the Hilbert sub-space on which they
act. These new definitions lead to properly defined particle distributions and
thermodynamic properties. In another paper (arXiv:0710.0728) I show that
fractional exclusion statistics manifested in general systems with interaction
have these, physically consistent, statistics parameters.Comment: 8 page
Simple Analytical Particle and Kinetic Energy Densities for a Dilute Fermionic Gas in a d-Dimensional Harmonic Trap
We derive simple analytical expressions for the particle density
and the kinetic energy density for a system of noninteracting
fermions in a dimensional isotropic harmonic oscillator potential. We test
the Thomas-Fermi (TF, or local-density) approximation for the functional
relation using the exact and show that it locally
reproduces the exact kinetic energy density , {\it including the shell
oscillations,} surprisingly well everywhere except near the classical turning
point. For the special case of two dimensions (2D), we obtain the unexpected
analytical result that the integral of yields the {\it
exact} total kinetic energy.Comment: 4 pages, 4 figures; corrected versio
Electromagnetic nucleon form factors in instant and point form
We present a study of the electromagnetic structure of the nucleons with
constituent quark models in the framework of relativistic quantum mechanics. In
particular, we address the construction of spectator-model currents in the
instant and point forms. Corresponding results for the elastic nucleon
electromagnetic form factors as well as charge radii and magnetic moments are
presented. We also compare results obtained by different realistic nucleon wave
functions stemming from alternative constituent quark models. Finally, we
discuss the theoretical uncertainties that reside in the construction of
spectator-model transition operators.Comment: 13 pages, 9 figures, updated and extended version for publicatio
Four-quark spectroscopy within the hyperspherical formalism
We present a generalization of the hyperspherical harmonic formalism to study
systems made of quarks and antiquarks of the same flavor. This generalization
is based on the symmetrization of the body wave function with respect to
the symmetric group using the Barnea and Novoselsky algorithm. The formalism is
applied to study four-quark systems by means of a constituent quark model
successful in the description of the two- and three-quark systems. The results
are compared to those obtained by means of variational approaches. Our analysis
shows that four-quark systems with exotic and non-exotic
quantum numbers may be bound independently of the mass of the quark.
and states become attractive only for larger mass of the quarks.Comment: 20 pages, 3 figure
Number Fluctuation in an interacting trapped gas in one and two dimensions
It is well-known that the number fluctuation in the grand canonical ensemble,
which is directly proportional to the compressibility, diverges for an ideal
bose gas as T -> 0. We show that this divergence is removed when the atoms
interact in one dimension through an inverse square two-body interaction. In
two dimensions, similar results are obtained using a self-consistent
Thomas-Fermi (TF) model for a repulsive zero-range interaction. Both models may
be mapped on to a system of non-interacting particles obeying the Haldane-Wu
exclusion statistics. We also calculate the number fluctuation from the ground
state of the gas in these interacting models, and compare the grand canonical
results with those obtained from the canonical ensemble.Comment: 11 pages, 1 appendix, 3 figures. Submitted to J. Phys. B: Atomic,
Molecular & Optica
The Vector Analyzing Power in Elastic Electron-Proton Scattering
We compute the vector analyzing power (VAP) for the elastic scattering of
transversely polarized electrons from protons at low energies using an
effective theory of electrons, protons, and photons. We study all contributions
through second order in , where and are the electron energy and
nucleon mass, respectively. The leading order VAP arises from the imaginary
part of the interference of one- and two-photon exchange amplitudes.
Sub-leading contributions are generated by the nucleon magnetic moment and
charge radius as well as recoil corrections to the leading-order amplitude.
Working to , we obtain a prediction for that is free of
unknown parameters and that agrees with the recent measurement of the VAP in
backward angle scattering.Comment: 24 pages, 11 figures. Typos fixe
Universal behaviour of ideal and interacting quantum gases in two dimensions
I discuss ideal and interacting quantum gases obeying general fractional
exclusion statistics. For systems with constant density of single-particle
states, described in the mean field approximation, the entropy depends neither
on the microscopic exclusion statistics, nor on the interaction. Such systems
are called {\em thermodynamically equivalent} and I show that the microscopic
reason for this equivalence is a one-to-one correspondence between the excited
states of these systems. This provides a method, different from the
bosonisation technique, to transform between systems of different exclusion
statistics. In the last section the macroscopic aspects of this method are
discussed.
In Appendix A I calculate the fluctuation of the ground state population of a
condensed Bose gas in grandcanonical ensemble and mean field approximation,
while in Appendix B I show a situation where although the system exhibits
fractional exclusion properties on microscopic energy intervals, a rigorous
calculation of the population of single particle states reveals a condensation
phenomenon. This also implies a malfunction of the usual and simplified
calculation technique of the most probable statistical distributions.Comment: About 14 journal pages, with 1 figure. Changes: Body of paper: same
content, with slight rephrasing. Apendices are new. In the original
submission I just mentioned the condensation, which is now detailed in
Appendix B. They were intended for a separate paper. Reason for changes:
rejection from Phys. Rev. Lett., resubmission to J. Phys. A: Math. Ge
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