3,590 research outputs found
Auxiliary field method and analytical solutions of the Schr\"{o}dinger equation with exponential potentials
The auxiliary field method is a new and efficient way to compute approximate
analytical eigenenergies and eigenvectors of the Schr\"{o}dinger equation. This
method has already been successfully applied to the case of central potentials
of power-law and logarithmic forms. In the present work, we show that the
Schr\"{o}dinger equation with exponential potentials of the form can also be analytically solved by using the
auxiliary field method. Formulae giving the critical heights and the energy
levels of these potentials are presented. Special attention is drawn on the
Yukawa potential and the pure exponential one
Influence of anisotropic ion shape, asymmetric valency, and electrolyte concentration on structural and thermodynamic properties of an electric double layer
Grand canonical Monte Carlo simulation results are reported for an electric
double layer modelled by a planar charged hard wall, anisotropic shape cations,
and spherical anions at different electrolyte concentrations and asymmetric
valencies. The cations consist of two tangentially tethered hard spheres of the
same diameter, . One sphere is charged while the other is neutral. Spherical
anions are charged hard spheres of diameter . The ion valency asymmetry 1:2
and 2:1 is considered, with the ions being immersed in a solvent mimicked by a
continuum dielectric medium at standard temperature. The simulations are
carried out for the following electrolyte concentrations: 0.1, 1.0 and 2.0 M.
Profiles of the electrode-ion, electrode-neutral sphere singlet distributions,
the average orientation of dimers, and the mean electrostatic potential are
calculated for a given electrode surface charge, , while the contact
electrode potential and the differential capacitance are presented for varying
electrode charge. With an increasing electrolyte concentration, the shape of
differential capacitance curve changes from that with a minimum surrounded by
maxima into that of a distorted single maximum. For a 2:1 electrolyte, the
maximum is located at a small negative value while for 1:2, at a small
positive value.Comment: 10 pages, 6 figure
A (p/E) Calculation of Strong Pionic Decays of Baryons
Strong pionic decays of baryons are studied in a non-relativistic quark model
framework via a convergent (p/E) expansion of the transition operator. Results
are compared to the ones obtained within a more conventional (p/m) expansion.Comment: 16 pages, LaTeX, using amssymb.st
The few-body problem in terms of correlated gaussians
In their textbook, Suzuki and Varga [Y. Suzuki and K. Varga, {\em Stochastic
Variational Approach to Quantum-Mechanical Few-Body Problems} (Springer,
Berlin, 1998)] present the stochastic variational method in a very exhaustive
way. In this framework, the so-called correlated gaussian bases are often
employed. General formulae for the matrix elements of various operators can be
found in the textbook. However the Fourier transform of correlated gaussians
and their application to the management of a relativistic kinetic energy
operator are missing and cannot be found in the literature. In this paper we
present these interesting formulae. We give also a derivation for new
formulations concerning central potentials; the corresponding formulae are more
efficient numerically than those presented in the textbook.Comment: 10 page
Semirelativistic Hamiltonians and the auxiliary field method
Approximate analytical closed energy formulas for semirelativistic
Hamiltonians of the form are obtained within
the framework of the auxiliary field method. This method, which is equivalent
to the envelope theory, has been recently proposed as a powerful tool to get
approximate analytical solutions of the Schr\"odinger equation. Various shapes
for the potential are investigated: power-law, funnel, square root, and
Yukawa. A comparison with the exact results is discussed in detail
Synthesis of sub-5 nm Co-doped SnO nanoparticles and their structural, microstructural, optical and photocatalytic properties
A swift chemical route to synthesize Co-doped SnO nanopowders is
described. Pure and highly stable SnCoO (0 x
0.15) crystalline nanoparticles were synthesized, with mean grain sizes <
5 nm and the dopant element homogeneously distributed in substitutional sites
of the SnO matrix. The UV-visible diffuse reflectance spectra of the
SnCoO samples reveal red shifts, the optical bandgap
energies decreasing with increasing Co concentration. The Urbach energies of
the samples were calculated and correlated with their bandgap energies. The
photocatalytic activity of the SnCoO samples was
investigated for the 4-hydroxylbenzoic acid (4-HBA) degradation process. A
complete photodegradation of a 10 ppm 4-HBA solution was achieved using 0.02%
(w/w) of SnCoO nanoparticles in 60 min of
irradiation.Comment: 29 pages, 2 tables, 10 figure
A mass formula for light mesons from a potential model
The quark dynamics inside light mesons, except pseudoscalar ones, can be
quite well described by a spinless Salpeter equation supplemented by a Cornell
interaction (possibly partly vector, partly scalar). A mass formula for these
mesons can then be obtained by computing analytical approximations of the
eigenvalues of the equation. We show that such a formula can be derived by
combining the results of two methods: the dominantly orbital state description
and the Bohr-Sommerfeld quantization approach. The predictions of the mass
formula are compared with accurate solutions of the spinless Salpeter equation
computed with a Lagrange-mesh calculation method.Comment: 5 figure
Faddeev approach to confined three-quark problems
We propose a method that allows for the efficient solution of the three-body
Faddeev equations in the presence of infinitely rising confinement
interactions. Such a method is useful in calculations of nonrelativistic and
especially semirelativistic constituent quark models. The convergence of the
partial wave series is accelerated and possible spurious contributions in the
Faddeev components are avoided. We demonstrate how the method works with the
example of the Goldstone-boson-exchange chiral quark model for baryons.Comment: 6 page
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