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

Absence of Klein's paradox for massive bosons coupled by nonminimal vector interactions

A few properties of the nonminimal vector interactions in the Duffin-Kemmer-Petiau theory are revised. In particular, it is shown that the space component of the nonminimal vector interaction plays a peremptory role for confining bosons whereas its time component contributes to the leakage. Scattering in a square step potential with proper boundary conditions is used to show that Klein's paradox does not manifest in the case of a nonminimal vector coupling

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

On the regular-geometric-figure solution to the N-body problem

The regular-geometric-figure solution to the $N$-body problem is presented in a very simple way. The Newtonian formalism is used without resorting to a more involved rotating coordinate system. Those configurations occur for other kinds of interactions beyond the gravitational ones for some special values of the parameters of the forces. For the harmonic oscillator, in particular, it is shown that the $N$-body problem is reduced to $N$ one-body problems.Comment: To appear in Eur. J. Phys. (5 pages

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

Comparison of solar radio and EUV synoptic limb charts during the present solar maximum

The present solar cycle is particular in many aspects: it had a delayed rising phase, it is the weakest of the last 100 years, and it presents two peaks separated by more than one year. To understand the impact of these characteristics on the solar chromosphere and coronal dynamics, images from a wide wavelength range are needed. In this work we use the 17~GHz radio continuum, formed in the upper chromosphere and the EUV lines 304 and 171~{\AA}, that come from the transition region (He II) and the corona (Fe IX, X), respectively. We analyze daily images at 304 and 171~{\AA} obtained by the Atmospheric Imaging Assembly (AIA). The 17~GHz maps were obtained by the Nobeyama Radioheliograph (NoRH). To construct synoptic limb charts, we calculated the mean emission of delimited limb areas with 100" wide and angular separation of $5^\circ$. At the equatorial region, the results show an hemispheric asymmetry of the solar activity. The northern hemisphere dominance is coincident with the first sunspot number peak, whereas the second peak occurs concurrently with the increase in the activity at the south. The polar emission reflects the presence of coronal holes at both EUV wavelengths, moreover, the 17~GHz polar brightenings can be associated with the coronal holes. Until 2013, both EUV coronal holes and radio polar brightenings were more predominant at the south pole. Since then they have not been apparent in the north, but thus appear in the beginning of 2015 in the south as observed in the synoptic charts. This work strengthens the association between coronal holes and the 17~GHz polar brightenings as it is evident in the synoptic limb charts, in agreement with previous case study papers. The enhancement of the radio brightness in coronal holes is explained by the presence of bright patches closely associated with the presence of intense unipolar magnetic fields.Comment: 6 pages, 5 figures. Acccepted for publication in Astronomy & Astrophysic

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 $F_\text{M}$. 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 $F_\text{M}$. 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