22,667 research outputs found
Relativistic Coulomb scattering of spinless bosons
The relativistic scattering of spin-0 bosons by spherically symmetric Coulomb
fields is analyzed in detail with an arbitrary mixing of vector and scalar
couplings. It is shown that the partial wave series reduces the scattering
amplitude to the closed Rutherford formula exactly when the vector and scalar
potentials have the same magnitude, and as an approximation for weak fields.
The behavior of the scattering amplitude near the conditions that furnish its
closed form is also discussed. Strong suppressions of the scattering amplitude
when the vector and scalar potentials have the same magnitude are observed
either for particles or antiparticles with low incident momentum. We point out
that such strong suppressions might be relevant in the analysis of the
scattering of fermions near the conditions for the spin and pseudospin
symmetries. From the complex poles of the partial scattering amplitude the
exact closed form of bound-state solutions for both particles and antiparticles
with different scenarios for the coupling constants are obtained. Perturbative
breaking of the accidental degeneracy appearing in a pair of special cases is
related to the nonconservation of the Runge-Lenz vector
New solutions of the D-dimensional Klein-Gordon equation via mapping onto the nonrelativistic one-dimensional Morse potential
New exact analytical bound-state solutions of the D-dimensional Klein-Gordon
equation for a large set of couplings and potential functions are obtained via
mapping onto the nonrelativistic bound-state solutions of the one-dimensional
generalized Morse potential. The eigenfunctions are expressed in terms of
generalized Laguerre polynomials, and the eigenenergies are expressed in terms
of solutions of irrational equations at the worst. Several analytical results
found in the literature, including the so-called Klein-Gordon oscillator, are
obtained as particular cases of this unified approac
Spin and Pseudospin symmetries in the Dirac equation with central Coulomb potentials
We analyze in detail the analytical solutions of the Dirac equation with
scalar S and vector V Coulomb radial potentials near the limit of spin and
pseudospin symmetries, i.e., when those potentials have the same magnitude and
either the same sign or opposite signs, respectively. By performing an
expansion of the relevant coefficients we also assess the perturbative nature
of both symmetries and their relations the (pseudo)spin-orbit coupling. The
former analysis is made for both positive and negative energy solutions and we
reproduce the relations between spin and pseudospin symmetries found before for
nuclear mean-field potentials. We discuss the node structure of the radial
functions and the quantum numbers of the solutions when there is spin or
pseudospin symmetry, which we find to be similar to the well-known solutions of
hydrogenic atoms.Comment: 9 pages, 2 figures, uses revte
Topologically Protected Zero Modes in Twisted Bilayer Graphene
We show that the twisted graphene bilayer can reveal unusual topological
properties at low energies, as a consequence of a Dirac-point splitting. These
features rely on a symmetry analysis of the electron hopping between the two
layers of graphene and we derive a simplified effective low-energy Hamiltonian
which captures the essential topological properties of twisted bilayer
graphene. The corresponding Landau levels peculiarly reveal a degenerate
zero-energy mode which cannot be lifted by strong magnetic fields.Comment: 5 pages, 3 figures; published versio
Restoring observed classical behavior of the carbon nanotube field emission enhancement factor from the electronic structure
Experimental Fowler-Nordheim plots taken from orthodoxly behaving carbon
nanotube (CNT) field electron emitters are known to be linear. This shows that,
for such emitters, there exists a characteristic field enhancement factor (FEF)
that is constant for a range of applied voltages and applied macroscopic fields
. A constant FEF of this kind can be evaluated for classical CNT
emitter models by finite-element and other methods, but (apparently contrary to
experiment) several past quantum-mechanical (QM) CNT calculations find
FEF-values that vary with . A common feature of most such
calculations is that they focus only on deriving the CNT real-charge
distributions. Here we report on calculations that use density functional
theory (DFT) to derive real-charge distributions, and then use these to
generate the related induced-charge distributions and related fields and FEFs.
We have analysed three carbon nanostructures involving CNT-like nanoprotrusions
of various lengths, and have also simulated geometrically equivalent classical
emitter models, using finite-element methods. We find that when the
DFT-generated local induced FEFs (LIFEFs) are used, the resulting values are
effectively independent of macroscopic field, and behave in the same
qualitative manner as the classical FEF-values. Further, there is fair to good
quantitative agreement between a characteristic FEF determined classically and
the equivalent characteristic LIFEF generated via DFT approaches. Although many
issues of detail remain to be explored, this appears to be a significant step
forwards in linking classical and QM theories of CNT electrostatics. It also
shows clearly that, for ideal CNTs, the known experimental constancy of the FEF
value for a range of macroscopic fields can also be found in appropriately
developed QM theory.Comment: A slightly revised version has been published - citation below -
under a title different from that originally used. The new title is:
"Restoring observed classical behavior of the carbon nanotube field emission
enhancement factor from the electronic structure
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