相关论文: Helium- and Lithium-like ionic sequences: Critical…

Let us consider some Coulomb systems of several infinitely massive centers of charge Z and one-two electrons: $(Z,e)$, $(2Z,e)$, $(3Z,e)$, $(4Z,e)$, $(2Z,e,e)$, $(3Z,e,e)$. It is shown that the physical, integer charges $Z=1,2,...$ do not…

We consider a Coulomb system of one electron and five or six infinitely massive centers of charge $Z$: $(5Z,e)$ and $(6Z,e)$. Critical charges and the possible optimal geometrical configurations are found. It is shown that the domain of…

The second (unphysical) critical charge in the 3-body quantum Coulomb system of a nucleus of positive charge $Z$ and mass $m_p$, and two electrons, predicted by F~Stillinger has been calculated to be equal to $Z_{B}^{\infty}\ =\ 0.904854$…

We investigate the behavior of the critical charge for spontaneous pair production, $Z_C$, defined as the charge at which the total energy of a $K$-shell electron is $E=-m_e$, as a function of the radius $R$ of the charge distribution. Our…

As a continuation of Part I, dedicated to the ground state of He-like and Li-like isoelectronic sequences for nuclear charges $Z \leq 20$, and Part II, dedicated to two excited states of He-like sequence, two ultra-compact wave functions in…

The $1/Z$-expansion for the ground state energy of the Coulomb system of an infinitely massive center of charge Z and two electrons (two electron ionic sequence) is studied. A critical analysis of the $1/Z$ coefficients presented in Baker…

The $1/Z$-expansion for the Coulomb system of infinitely massive center of charge Z and two electrons is discussed. Numerical deficiency in Baker et al, {\em Phys. Rev. \bf A41}, 1247 (1990) is indicated which continue to raise doubts in…

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…

As a continuation of Parts I \cite{Part-1:2020}, II \cite{Part-2:2021}, III \cite{Part-3:2022}, where ultra-compact wave functions were constructed for a few low-lying states of He-like and Li-like sequences, the family of spin-singlet…

A general scenario that leads to Coulomb quantum criticality with the dynamical critical exponent z=1 is proposed. I point out that the long-range Coulomb interaction and quenched disorder have competing effects on z, and that the balance…

As a generalization and extension of JMP 54 (2013) 022901, the classical dynamics of three non-relativistic Coulomb charges $(e_1, m_1)$, $(e_2, m_2)$ and $(e_3, m_3)$ on the plane placed in a constant magnetic field perpendicular to the…

We consider the quantum-mechanical problem of a relativistic Dirac particle moving in the Coulomb field of a point charge $Ze$. In the literature, it is often declared that a quantum-mechanical description of such a system does not exist…

Just after the Dirac equation was established, a number of physicists tried to comment on and solve the spectral problem for the Dirac Hamiltonian with the Coulomb field of arbitrarily large charge $Z$, especially with $Z$ that is more than…

As a continuation of Part I \cite{Part-1:2020} (Int. Journal of Quantum Chem. 2021; 121: qua.26586), dedicated to the ground state of He-like and Li-like isoelectronic sequences for nuclear charges $Z \leq 20$, a few ultra-compact wave…

The grand potential of a classical Coulomb system has universal finite-size corrections similar to the ones which occur in the free energy of a simple critical system : the massless Gaussian field. Here, the Coulomb system is assumed to be…

We study the ground state properties of classical Coulomb charges interacting with a 1/r potential moving on a plane but confined either by a circular hard wall boundary or by a harmonic potential. The charge density in the continuum limit…

Topological quantum phase transitions intrinsically intertwine self-similarity and topology of many-electron wave-functions, and divining them is one of the most significant ways to advance understanding in condensed matter physics. Our…

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…

The one-component Coulomb gas on the sphere, consisting on $N$ unit charges interacting via a logarithmic potential, and in the presence of two external charges each of strength proportional to $N$, is considered. There are two spherical…

We propose a relativistic one-parameter Hermitian theory for the Coulomb problem with an electric charge greater than 137. In the non-relativistic limit, the theory becomes identical to the Schr\"odinger-Coulomb problem for all Z. Moreover,…