Related papers: Third derivative of the one-electron density at th…
We prove a priori bounds for all derivatives of non-relativistic Coulombic eigenfunctions, involving negative powers of the distance to the singularities of the many-body potential. We use these to derive bounds for all derivatives of the…
The density of an atom in a state of well-defined angular momentum has a specific finite spherical harmonic content, without and with interactions. Approximate single-particle schemes, such as the Hartree, Hartree-Fock, and Local Density…
We calculate the nuclear energy density functional relevant for N=Z even-even nuclei in the systematic framework of chiral perturbation theory. The calculation includes the one-pion exchange Fock diagram and the iterated one-pion exchange…
Single-particle resonance parameters and wave functions in spherical and deformed nuclei are determined through analytic continuation in the potential strength. In this method, the analyticity of the eigenvalues and eigenfunctions of the…
It is known that the asymptotic decay of the electron density $n(\br)$ outside a molecule is informative about its first ionization potential $I_0$, $n(|\br|\to\infty) \sim \text{exp}(-2\sqrt{2I_0}\,r)$. This dictates the orbital energy of…
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 non-selfadjoint $h$-differential model operator $P_h$ in the semiclassical limit ($h\rightarrow 0$) subject to small random perturbations. Furthermore, we let the coupling constant $\delta$ be $\exp\{-\frac{1}{Ch}\}\leq \delta…
We present a precise measurement of the cross section, proton and $\rm ^3He$ analyzing powers, and spin correlation coefficient $C_{y,y}$ for $p$-$\rm ^3He$ elastic scattering near 65 MeV, and a comparison with rigorous four-nucleon…
The Schr\"odinger equation for a charged particle in the field of a nonrelativistic electric quadrupole in two dimensions is known to be separable in spherical coordinates. We investigate the occurrence of bound states of negative energy…
We reconsider the analysis of the sensitivity of neutron resonance energies $E_i$ to changes in $\alpha$ with a view to resolving uncertainties that plague earlier treatments. We point out that, with more appropriate choices of nuclear…
The separation energy and half-life of some heavy proton emitting nuclei, and the single-particle structure of the unbound 11-N, have been evaluated by implementing a careful numerical treatment to solve Schrodinger equation in a continuum…
We systematically examine the fundamental frequencies of shear torsional oscillations in neutron star crusts in a manner that is dependent on the parameter $L$ characterizing the poorly known density dependence of the symmetry energy. The…
We calculate the spectral function $A_\rho$ of the $\rho$ meson in nuclear matter. The calculation is performed in the {\it low density} approximation, where the in-medium self energy $\Sigma_{med}$ is completely determined by the vacuum…
The "catastrophe" in solving the Dirac equation for an electron in the field of a point electric charge, which emerges for the charge numbers Z > 137, is removed in this work by effective accounting of finite dimensions of nuclei. For this…
The Schwartz kernel of the spectral density for the Schr\"{o}dinger operator with magnetic field in the $n-$dimensional complex ball is given. As applications, we compute the heat, resolvent and the wave kernels. Moreover, the resolvent and…
We develop a uniform semiclassical trace formula for the density of states of a three-dimensional isotropic harmonic oscillator (HO), perturbed by a term $\propto r^4$. This term breaks the U(3) symmetry of the HO, resulting in a spherical…
The scattering matrix of the Schrodinger operator with smooth short-range electric and magnetic potentials is considered. The asymptotic density of the eigenvalues of this scattering matrix in the high energy regime is determined. An…
We model the density dependence of the Gruneisen parameter as gamma(rho) = 1/2 + gamma_1/rho^{1/3} + gamma_2/rho^{q}, where gamma_1, gamma_2, and q>1 are constants. This form is based on the assumption that gamma is an analytic function of…
We consider a relativistic no-pair model of a hydrogenic atom in a classical, exterior magnetic field. First, we prove that the corresponding Hamiltonian is semi-bounded below, for all coupling constants less than or equal to the critical…
Elastic scattering of relativistic electrons from the nucleon yields Lorentz invariant form factors that describe the fundamental distribution of charge and magnetism. The spatial dependence of the nucleon's charge and magnetism is…