Related papers: Some recent results on contact or point supported …
The Dirac delta function potential is considered within the real Hilbert space approach for complex wave functions, as well as quaternionic wave functions. As has been previously determined, the real Hilbert space approach enables the…
We report on some recent work of the authors showing the relations between singular (point) perturbation of the Laplacian and the dynamical system describing a charged point particle interacting with the self-generated radiation field (the…
We studied the van der Waals interactions of two finite, solid, cylindrical rods at arbitrary angle and position with respect to each other. An analytic interpolative formula for the interaction potential energy is constructed, based on…
The pi+ d scattering and the d(p,n) charge exchange reaction are used to study the Delta-Nucleon interaction in the Delta resonance energy region. Various observables, such as inclusive and exclusive cross sections, angular distributions,…
In this paper we study the self-adjointness and spectral properties of two-dimensional Dirac operators with electrostatic, Lorentz scalar, and anomalous magnetic $\delta$-shell interactions with constant weights that are supported on a…
A general method to find an effective potential of interaction between far separated 2D and 3D solitons is elaborated, including the case of 2D vortex solitons. The method is based on explicit calculation of the overlapping term in the full…
It is shown how nucleon-nucleon potentials can be defined in N dimensions, using dimensional regularization to continue amplitudes. This provides an easy way to separate out contact ($\delta$-function) terms arising from renormalization. An…
The path is explored between one-dimensional scattering through Dirac-$\delta$ walls and one-dimensional quantum field theories defined on a finite length interval with Dirichlet boundary conditions. It is found that two $\delta$'s are…
We construct a nuclear interaction in chiral effective field theory with explicit inclusion of the $\Delta$-isobar $\Delta(1232)$ degree of freedom at all orders up to next-to-next-to-leading order (NNLO). We use pion-nucleon ($\pi N$)…
In this paper we prove that the Dirac operator $A_\eta$ with an electrostatic $\delta$-shell interaction of critical strength $\eta = \pm 2$ supported on a $C^2$-smooth compact surface $\Sigma$ is self-adjoint in…
Approximate analytical solutions of the Dirac equation are obtained for some diatomic molecular potentials plus a tensor interaction with spin and pseudospin symmetries with any angular momentum. We find the energy eigenvalue equations in…
We show that the ground state energy is bounded from below when there are infinitely many attractive delta function potentials placed in arbitrary locations, while all being separated at least by a minimum distance, on two dimensional…
Relativistic and non-relativistic modern nucleon-nucleon potentials are mapped on a relativistic operator basis using projection techniques. This allows to compare the various potentials at the level of covariant amplitudes were a…
Let $\Omega\subset\mathbb{R}^3$ be an open set, we study the spectral properties of the free Dirac operator $\mathcal{H}$ coupled with the singular potential $V_\kappa=(\epsilon I_4 +\mu\beta+\eta(\alpha\cdot N))\delta_{\partial\Omega}$.…
We optimize $\Delta$-full nuclear interactions from chiral effective field theory. The low-energy constants of the contact potentials are constrained by two-body scattering phase shifts, and by properties of bound-state of $A=2$ to $4$…
The influence of $\Delta$ isobar components on the ground state properties of nuclear systems is investigated for nuclear matter as well as finite nuclei. Many-body wave functions, including isobar configurations, and binding energies are…
Under certain hypothesis of smallness of the regular potential $\mathbf{V}$, we prove that the Dirac operator in $\mathbb{R}^3$ coupled with a suitable re-scaling of $\mathbf{V}$ converges in the strong resolvent sense to the Hamiltonian…
Understanding electron correlation requires solving inseparable Schrodinger equation. In general, inseparable Schr\"odinger equations cannot be solved analytically. So their solutions are obtained numerically. In this paper we investigate…
We propose a model for energy-dependent $\delta-\delta^{\prime}$ interactions which yields scattering coefficients exhibiting full transmission for high-energy incident particles, also computing the bound solutions in one-dimension…
The interaction of an electron with a local static charge distribution (e.g., an atom or molecule) is dominated at large distances by the radial 1/r Coulomb potential. The second order effect comes from the non-central electric dipole…