4,351 research outputs found
Continuum and Symmetry-Conserving Effects in Drip-line Nuclei Using Finite-range Forces
We report the first calculations of nuclear properties near the drip-lines
using the spherical Hartree-Fock-Bogoliubov mean-field theory with a
finite-range force supplemented by continuum and particle number projection
effects. Calculations were carried out in a basis made of the eigenstates of a
Woods-Saxon potential computed in a box, thereby garanteeing that continuum
effects were properly taken into account. Projection of the self-consistent
solutions on good particle number was carried out after variation, and an
approximation of the variation after projection result was used. We give the
position of the drip-lines and examine neutron densities in neutron-rich
nuclei. We discuss the sensitivity of nuclear observables upon continuum and
particle-number restoration effects.Comment: 5 pages, 3 figures, Phys. Rev. C77, 011301(R) (2008
Scattering states of a particle, with position-dependent mass, in a double heterojunction
In this work we obtain the exact analytical scattering solutions of a
particle (electron or hole) in a semiconductor double heterojunction -
potential well / barrier - where the effective mass of the particle varies with
position inside the heterojunctions. It is observed that the spatial dependence
of mass within the well / barrier introduces a nonlinear component in the plane
wave solutions of the continuum states. Additionally, the transmission
coefficient is found to increase with increasing energy, finally approaching
unity, whereas the reflection coefficient follows the reverse trend and goes to
zero.Comment: 7 pages, 6 figure
Extensions of the auxiliary field method to solve Schr\"{o}dinger equations
It has recently been shown that the auxiliary field method is an interesting
tool to compute approximate analytical solutions of the Schr\"{o}dinger
equation. This technique can generate the spectrum associated with an arbitrary
potential starting from the analytically known spectrum of a particular
potential . In the present work, general important properties of the
auxiliary field method are proved, such as scaling laws and independence of the
results on the choice of . The method is extended in order to find
accurate analytical energy formulae for radial potentials of the form , and several explicit examples are studied. Connections existing
between the perturbation theory and the auxiliary field method are also
discussed
Fringe spacing and phase of interfering matter waves
We experimentally investigate the outcoupling of atoms from Bose-Einstein
condensates using two radio-frequency (rf) fields in the presence of gravity.
We show that the fringe separation in the resulting interference pattern
derives entirely from the energy difference between the two rf fields and not
the gravitational potential difference. We subsequently demonstrate how the
phase and polarisation of the rf radiation directly control the phase of the
matter wave interference and provide a semi-classical interpretation of the
results.Comment: 4 pages, 3 figure
Anomaly Cancellation in 2+1 dimensions in the presence of a domainwall mass
A Fermion in 2+1 dimensions, with a mass function which depends on one
spatial coordinate and passes through a zero ( a domain wall mass), is
considered. In this model, originally proposed by Callan and Harvey, the gauge
variation of the effective gauge action mainly consists of two terms. One comes
from the induced Chern-Simons term and the other from the chiral fermions,
bound to the 1+1 dimensional wall, and they are expected to cancel each other.
Though there exist arguments in favour of this, based on the possible forms of
the effective action valid far from the wall and some facts about theories of
chiral fermions in 1+1 dimensions, a complete calculation is lacking. In this
paper we present an explicit calculation of this cancellation at one loop valid
even close to the wall. We show that, integrating out the ``massive'' modes of
the theory does produce the Chern-Simons term, as appreciated previously. In
addition we show that it generates a term that softens the high energy
behaviour of the 1+1 dimensional effective chiral theory thereby resolving an
ambiguity present in a general 1+1 dimensional theory.Comment: 17 pages, LaTex file, CU-TP-61
Bound states of bosons and fermions in a mixed vector-scalar coupling with unequal shapes for the potentials
The Klein-Gordon and the Dirac equations with vector and scalar potentials
are investigated under a more general condition, . These intrinsically relativistic and isospectral problems
are solved in a case of squared hyperbolic potential functions and bound states
for either particles or antiparticles are found. The eigenvalues and
eigenfuntions are discussed in some detail and the effective Compton wavelength
is revealed to be an important physical quantity. It is revealed that a boson
is better localized than a fermion when they have the same mass and are
subjected to the same potentials.Comment: 3 figure
Scattering states of a particle, with position-dependent mass, in a symmetric heterojunction
The study of a particle with position-dependent effective mass (pdem), within
a double heterojunction is extended into the complex domain --- when the region
within the heterojunctions is described by a non Hermitian
symmetric potential. After obtaining the exact analytical solutions, the
reflection and transmission coefficients are calculated, and plotted as a
function of the energy. It is observed that at least two of the characteristic
features of non Hermitian symmetric systems --- viz., left / right
asymmetry and anomalous behaviour at spectral singularity, are preserved even
in the presence of pdem. The possibility of charge conservation is also
discussed.Comment: 12 pages, including 6 figures; Journal of Physics A : Math. Theor.
(2012
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
Correlated two-particle scattering on finite cavities
The correlated two-particle problem is solved analytically in the presence of
a finite cavity. The method is demonstrated here in terms of exactly solvable
models for both the cavity as well as the two-particle correlation where the
two-particle potential is chosen in separable form. The two-particle phase
shift is calculated and compared to the single-particle one. The two-particle
bound state behavior is discussed and the influence of the cavity on the
binding properties is calculated.Comment: Derivation shortened and corrected, 14 pages 10 figure
The Woods-Saxon Potential in the Dirac Equation
The two-component approach to the one-dimensional Dirac equation is applied
to the Woods-Saxon potential. The scattering and bound state solutions are
derived and the conditions for a transmission resonance (when the transmission
coefficient is unity) and supercriticality (when the particle bound state is at
E=-m) are then derived. The square potential limit is discussed. The recent
result that a finite-range symmetric potential barrier will have a transmission
resonance of zero-momentum when the corresponding well supports a half-bound
state at E=-m is demonstrated.Comment: 8 pages, 4 figures. Submitted to JPhys
- …