Related papers: Resonances in two-electron atoms below the critica…
The hydrogen negative ion H$^-$ is the simplest two-electron system that exists in nature. This system is not only important in astrophysics but it also serves as an ideal ground to study electron-electron correlations. The peculiar balance…
Bound and resonance states of the dipole-bound anion of hydrogen cyanide HCN$^-$ are studied using a non-adiabatic pseudopotential method and the Berggren expansion technique involving bound states, decaying resonant states, and…
In this paper it is proposed that the charged charmonium-like state $Z_c(3900)$ is a resonance above the threshold from the $D\bar{D}^*$ interaction. The $D\bar{D}^*$ interaction is described by the one-boson exchange model with light meson…
We describe bound states, resonances and elastic scattering of light ions using a $\delta$-shell potential. Focusing on low-energy data such as energies of bound states and resonances, charge radii, asymptotic normalization coefficients,…
In bound states in the continuum (BIC) the mass of a composite particle is greater than the total mass of its constituents. Using the ladder Bethe-Salpeter equation, the BIC state in a system of two charged particles $a$ and $b$ with…
A two-level atom coupled to the quantized radiation field is studied. In the physical relevant situation, the coupling function modeling the interaction between the two component behaves like $|k|^{-1/2}$, as the photon momentum tends to…
We present an investigation on the resonances of a doubly excited helium atom in a strong magnetic field covering the regime B = 0-100 a.u. A full-interaction approach which is based on an anisotropic Gaussian basis set of one-particle…
In the Nelson model particles interact through a scalar massless field. For hydrogen-like atoms there is a nucleus of infinite mass and charge $Ze$, $Z > 0$, fixed at the origin and an electron of mass $m$ and charge $e$. This system forms…
In non-relativistic quantum mechanics we study the Coulomb systems of infinitely massive center of charge Z and two-three electrons: $(Z,e,e)$ and $(Z,e,e,e)$. It is shown that in both cases the total energy curve in $Z$ is smooth, without…
As the nuclear charge Z is continuously decreased an N-electron atom undergoes a binding-unbinding transition at some critical Z_c. We investigate whether the electrons remain bound when Z=Z_c and whether the radius of the system stays…
The resonance states of one- and two-particle Hamiltonians are studied using variational expansions with real basis-set functions. The resonance energies, $E_r$, and widths, $\Gamma$, are calculated using the density of states and an…
The ground state properties of the two-electron atom with atomic number $Z\geq 2$ in the spherical vacuum cavity with general boundary conditions of "not going out" are studied. It is shown that for certain parameters of the cavity such…
This paper establishes new bounds on the maximum number of electrons $ N_c(Z) $ that an atom with nuclear charge $Z$ can bind. Specifically, we show that \begin{equation*} N_c(Z) < 1.1185Z + O(Z^{1/3}) \end{equation*} with an explicit bound…
We consider a model of three electrons and one hole confined in a two-dimensional (2D) plane, interacting with one another through Coulomb forces. Using a Ritz variational method we find an upper bound of \approx -0.0112me^4/8\pi^2 \epsilon…
Potential resonances are usually investigated either directly in the complex energy plane or indirectly in the complex angular momentum plane. Another formulation complementing these two is presented in this work. It is an indirect method…
The Dirac equation offers a precise analytical description of relativistic two-particle bound states, when one of the constituent is very heavy and radiative corrections are neglected. Looking at the high-Z hydrogen-like atom in the…
The energy spectrum of the extended attractive potential of a crystallographic row for negatively charged particles has quasi-bound states. It follows that a negatively charged particle with small transversal momentum component ($p_{\bot} R…
Resonance states of a two-electron quantum dot are studied using a variational expansion with both real basis-set functions and complex scaling methods. We present numerical evidence about the critical behavior of the density of states in…
We study the effect of geometric constraints on the formation of indirect excitonic complexes with excess charge by considering the problem of two identical electrons moving in half-space subject to mutual Coulomb repulsion and the Coulomb…
A simple model of an atom interacting with the quantized electromagnetic field is studied. The atom has a finite mass $m$, finitely many excited states and an electric dipole moment, $\vec{d}_0 = -\lambda_{0} \vec{d}$, where $\| d^{i}\| =…