Related papers: Pre-Born-Oppenheimer Dirac-Coulomb-Breit computati…
A simple method to compute QED bound state properties is presented, in which binding energy effects are treated non-perturbatively. It is shown that to take the effects of all ladder Coulomb photon exchanges into account, one can simply…
Relativistic Faddeev equations for three-body scattering are solved at arbitrary energies in terms of momentum vectors without employing a partial wave decomposition. Relativistic invariance is incorporated withing the framework of…
We formulate a Herglotz-type variational principle on a Lie algebroid and derive the corresponding Euler--Lagrange--Herglotz equations for a Lagrangian depending on an additional scalar variable $z$. This provides a geometric framework for…
We consider a reformulation of QED in which covariant Green functions are used to solve for the electromagnetic field in terms of the fermion fields. It is shown that exact few-fermion eigenstates of the resulting Hamiltonian can be…
In this paper, we consider the Dirac-Hartree-Fock equations for system has many-particles. The difficulties associated with Gaussians model are likely to be more complex in relativistic Dirac-Hartree-Fock calculations. To processing these…
Two numerical methods are used to evaluate the relativistic spectrum of the two-centre Coulomb problem (for the $H_{2}^{+}$ and $Th_{2}^{179+}$ diatomic molecules) in the fixed nuclei approximation by solving the single particle…
It usually writes the boundary condition of the wave equation in the Coulomb field as a rough form without considering the size of the atomic nucleus. The rough expression brings on that the solutions of the Klein-Gordon equation and the…
An old conjecture claims that commuting Hamiltonians of the double-elliptic integrable system are constructed from the theta-functions associated with Riemann surfaces from the Seiberg-Witten family, with moduli treated as dynamical…
We study the three-body Coulomb problem in two dimensions and show how to calculate very accurately its quantum properties. The use of a convenient set of coordinates makes it possible to write the Schr\"{o}dinger equation only using…
We suggest a new adiabatic approach for description of three charged particles in the continuum. This approach is based on the Coulomb-Fourier transformation (CFT) of three body Hamiltonian, which allows to develop a scheme, alternative to…
The multiconfiguration Dirac-Fock (MCDF) model uses a linear combination of Slater determinants to approximate the electronic $N$-body wave function of a relativistic molecular system, resulting in a coupled system of nonlinear eigenvalue…
Physicists such as Green, Vanhove, et al show that differential equations involving automorphic forms govern the behavior of gravitons. One particular point of interest is solutions to $(\Delta-\lambda)u=E_{\alpha} E_{\beta}$ on an…
The electronic spectra of light one-electron quasi-molecular compounds H-H$^+$, He$^+$-He$^2+$ and He$^+$-H$^+$ are analyzed. To this end, the two-center Dirac equation is solved by the dual-kinetically balanced finite-basis-set method for…
In this paper, calculated energies of the lowest bound state of Coulomb three-body systems containing an electron ($e^-$), a negatively charged muon ($\mu^-$) and a nucleus ($N^{Z+}$) of charge number Z are reported. The 3-body relative…
We study the possible existence of nonstrange dibaryons and tribaryons by solving the bound-state problem of the two- and three-body systems composed of nucleons and deltas. The two-body systems are $NN$, $N\Delta$, and $\Delta\Delta$,…
Coulomb and nuclear dissociation of $^{17}$Ne on light and heavy targets are studied theoretically. The dipole E1 strength function is determined in a broad energy range including energies of astrophysical interest. Dependence of the…
We describe a method for computing near-exact energies for correlated systems with large Hilbert spaces. The method efficiently identifies the most important basis states (Slater determinants) and performs a variational calculation in the…
The equations for the electromagnetic two-body problem are neutral-delay equations that for generic initial data have solutions with discontinuous derivatives. If one wants to use these neutral-delay equations with arbitrary initial data,…
By application of a straightforward variational procedure we derive a simple, analytic upper bound on the ground-state energy eigenvalue of a semirelativistic Hamiltonian for (one or two) spinless particles which experience some…
In the covariant quark-diquark model the effective Bethe-Salpeter (BS) equations for the nucleon and the $\Delta$ are solved including scalar {\em and axialvector} diquark correlations. Their quark substructure is effectively taken into…