Related papers: Existence of ground states for negative ions at th…
It is well known that $N$-electron atoms undergoes unbinding for a critical charge of the nucleus $Z_c$, i.e. the atom has eigenstates for the case $Z> Z_c$ and it has no bound states for $Z<Z_c$. In the present paper we derive upper bound…
We show that the $N$-electron Hamiltonian $H(N, Z)$ with the total nuclear charge $Z$ has no normalizable ground state if the ground state energy $E(N, Z)$ satisfies $E(N, Z)= E(N-1, Z)$ for $Z=N-1$. For anions $\mathrm{He}^-,…
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…
The eigenvalue absorption for a many-particle Hamiltonian depending on a parameter is analyzed in the framework of non-relativistic quantum mechanics. The long-range part of pair potentials is assumed to be pure Coulomb and no restriction…
We examine the binding conditions for atoms in non-relativistic QED, and prove that removing one electron from an atom requires a positive energy. As an application, we establish the existence of a ground state for the Helium atom.
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…
The excited states of a charged particle interacting with the quantized electromagnetic field and an external potential all decay, but such a particle should have a true ground state--one that minimizes the energy and satisfies the…
We study atoms with N electrons, and nuclear charge Z. It is well known that the cationic regime, Z > N is qualitatively described by Thomas-Fermi theory. The anionic regime, Z < N, on the other hand, is characterized by an instability…
Within the framework of nonrelativisitic quantum electrodynamics we consider a single nucleus and $N$ electrons coupled to the radiation field. Since the total momentum $P$ is conserved, the Hamiltonian $H$ admits a fiber decomposition with…
We show that the Hamiltonian describing N nonrelativistic electrons with spin, interacting with the quantized radiation field and several fixed nuclei with total charge Z has a ground state when N <Z+1. The result holds for any value of the…
In this note we establish the existence of ground states for atoms within several restricted Hartree-Fock theories. It is shown, for example, that there exists a ground state for closed shell atoms with $N$ electrons and nuclear charge $Z…
The ground states of N-electron parabolic quantum dots in the presence of a perpendicular magnetic field are investigated. Rigorous lower bounds to the ground-state energies are obtained. It is shown that our lower bounds agree well with…
We give a rigorous argument that long--range repulsion stabilizes quantum systems; ground states of such quantum systems exist even when the ground state energy is precisely at the ionization threshold. For atomic systems at the critical…
Bounds are studied for the maximum number, $N_c$, of electrons that can be bound to $K$ atoms of the total nuclear charge $Z$. It is proved that $N_c < \min\{2Z+1, 1.22Z + 3Z^{1/3}\}$ in Schr\"odinger theory. This improves Lieb's bound $N_c…
The critical nuclear charge Zc required for a heliumlike atom to have at least one bound state was recently determined with high accuracy from variational calculations. Analysis of the wave functions further suggested that the bound state…
We prove that the maximum number $N_c$ of non-relativistic electrons that a nucleus of charge $Z$ can bind is less than $1.22Z+3Z^{1/3}$. This improves Lieb's upper bound $N_c<2Z+1$ [{\it Phys. Rev. A} {\bf 29}, 3018-3028 (1984)] when $Z\ge…
We prove that the ground state energy of an atom confined to two dimensions with an infinitely heavy nucleus of charge $Z>0$ and $N$ quantum electrons of charge -1 is $E(N,Z)=-{1/2}Z^2\ln Z+(E^{\TF}(\lambda)+{1/2}c^{\rm H})Z^2+o(Z^2)$ when…
We consider bosonic Coulomb systems with $N$-particles and $K$ static nuclei. Let $E_N^Z$ denote the ground state energy of a bosonic molecule of the total nuclear charge $Z$. We prove that the system has no normalizable ground state when…
We study the stability and universal behaviour of the ionization energy of N-electron atoms with nuclear charge Z in the anionic domain (Z<N), considering the nuclear charge Z as an arbitrary (non-integral) parameter. HF and CISD ground…
The electronic structure of the ground and some excited states of neutral atoms with the nuclear charge numbers $1\leq Z \leq 10$ and their single positive ions are investigated by means of our 2D mesh Hartree-Fock method for strong…