Analyticity of the One-Particle Density Matrix

It is proved that the one-particle density matrix $$\gamma (x, y)$$ γ ( x , y ) for multi-particle Coulombic systems is real analytic away from the nuclei and from the diagonal $$x = y$$ x = y .

Hyperspherical three-body model calculation for the bound 3,1S-states of Coulombic systems

In this paper, hyperspherical three-body model formalism has been applied for the calculation of energies of the low-lying bound [Formula: see text]-states of neutral helium and helium like Coulombic three-body systems having nuclear charge (z) in the range [Formula: see text]. Energies of [Formula: see text]-states are also calculated for those having nuclear charge in the range [Formula: see text]. The calculation of the coupling potential matrix elements of the two-body potentials has been simplified by the use of Raynal–Revai Coefficients (RRC). The three-body wave function in the Schrödinger equation when expanded in terms of hyperspherical harmonics (HH), leads to an infinite set of coupled differential equation (CDE) which for practical purposes is truncated to a finite set and the truncated set of CDE’s are solved by renormalized Numerov method (RNM) to get the energy (E). The calculated energy is compared with the ones of the literature.