相关论文: Non-isotropic cusp conditions and regularity of th…
We study electron densities of eigenfunctions of atomic Schroedinger operators. We prove the existence of rho~'''(0), the third derivative of the spherically averaged atomic density rho~ at the nucleus. For eigenfunctions with corresponding…
We prove that the electronic density of atomic and molecular eigenfunctions is smooth away from the nuclei. The result is proved without decay assumptions on the eigenfunctions.
We show that electronic wave functions Psi of atoms and molecules have a representation Psi=F*phi, where F is an explicit universal factor, locally Lipschitz, and independent of the eigenvalue and the solution Psi itself, and phi has…
We study the regularity at the positions of the (fixed) nuclei of solutions to (non-relativistic) multiconfiguration equations (including Hartree--Fock) of Coulomb systems. We prove the following: Let {phi_1,...,phi_M} be any solution to…
The rho meson spectral function in hot and dense asymmetric nuclear matter (number densities of proton and neutron different) is evaluated in an effective chiral SU(3) model within the mean field approximation (MFA). The dependence of the…
The explicit density (rho) dependence in the coupling coefficients of the non-relativistic nuclear energy-density functional (EDF) encodes effects of three-nucleon forces and dynamical correlations. The necessity for a coupling coefficient…
Local(multiplicative) effective potential energy theories of electronic structure comprise the transformation of the Schr{\"o}dinger equation for interacting fermi systems to model noninteracting fermi or bose systems whereby the equivalent…
Lower bound for ${\bar \rho}''(0)$, the second derivative of the spherically averaged atomic electronic density at the nucleus, and upper bound for ${\bar \rho}'''(0)$, the third derivative, are obtained respectively. It is shown that, for…
We prove that the electron densities of electronic eigenfunctions of atoms and molecules are smooth away from the nuclei.
With a special `Ansatz' we analyse the regularity properties of atomic electron wavefunctions and electron densities. In particular we prove an a priori estimate, $\sup_{y\in B(x,R)}|\nabla\psi(y)| \leq C(R) \sup_{y\in B(x,2R)}|\psi(y)|$…
A new formula that relates the electron density at the nucleus of atoms,rho(0,Z), and the atomic number,Z, is proposed. This formula,rho(0,Z)=a(Z-bZ^(0.5))^3, contains two unknown parameters (a,b) that are derived using a least square…
We consider a pseudorelativistic model of atoms and molecules, where the kinetic energy of the electrons is given by $\sqrt{p^2+m^2}-m$. In this model the eigenfunctions are generally not even bounded, however, we prove that the…
Unitary and analytic ten-resonance model of the nucleon electromagnetic (e.m.) structure with canonical normalizations and asymptotics is constructed on a four-sheeted Riemann surface. It describes well all existing experimental space-like…
We give a new, short proof of the regularity away from the nuclei of the electronic density of a molecule obtained in [1,2]. The new argument is based on the regularity properties of the Coulomb interactions underlined in [3,4] and on…
We investigate properties of the spherically averaged atomic one-electron density rho~(r). For a rho~ which stems from a physical ground state we prove that rho~ > 0. We also give exponentially decreasing lower bounds to rho~ in the case…
We prove that the electronic densities of atomic and molecular eigenfunctions are real analytic in ${\mathbb R}^3$ away from the nuclei.
The interpretation of future precise experiments on atomic parity violation in terms of parameters of the Standard Model could be hampered by uncertainties in the atomic and nuclear structure. While the former can be overcome by measurement…
We consider an electronic bound state of the usual, non-relativistic, molecular Hamiltonian with Coulomb interactions, fixed nuclei, and N electrons (N>1). Near appropriate electronic collisions, we determine the regularity 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…
E2 properties of A=6--10 nuclei, including those of nuclei far from stability, are studied by a $(0+2)\hbar\omega$ shell-model calculation which includes E2 core-polarization effects explicitly. The quadrupole moments and the E2 transition…