Related papers: Extended Hylleraas three-electron integral
We construct a tridiagonal matrix representation for the three dimensions Dirac-Coulomb Hamiltonian that provides for a simple and straightforward relativistic extension of the complex scaling method. Besides the Coulomb interaction,…
Methods for calculating lower bounds to the exact energy using the variance of the upper bound energy are discussed and explored. All the matrix elements of the Hamiltonian squared are collected and considered, and those for which no known…
The series expansion formulae are established for the one- and two-center charge densities over complete orthonormal sets of exponential type orbitals introduced by the author. Three-center overlap integrals of appearing in these relations…
We present a systematic technique to expand the Einstein-Hilbert Lagrangian in inverse powers of the speed of light squared. The corresponding result for the non-relativistic gravity Lagrangian is given up to next-to-next-to-leading order.…
The effective potential of electron--electron interaction and the two-particle \textquotedblleft density--density\textquotedblright\ correlation function have been calculated for a simple semiinfinite metal making allowance for the…
In these proceedings we discuss a representation for modular forms that is more suitable for their application to the calculation of Feynman integrals in the context of iterated integrals and the differential equation method. In particular,…
The electron repulsion integrals over the Slater-type orbitals with non-integer principal quantum numbers are considered. These integrals are useful in both non-relativistic and relativistic calculations of many-electron systems. They…
We survey the results of a long-term study of the process of radiative recombination. A rigorous theory of nonrelativistic electron radiative recombination with a hydrogen-like ion is used to calculate the total cross section of the…
We develop the superfield approach to the effective potential in three dimensions and calculate the one-loop and two-loop k\"{a}hlerian effective potential in commutative and noncommutative cases.
In the spirit of the Head-Gordon-Pople algorithm, we report vertical, transfer and horizontal recurrence relations for the efficient and accurate computation of four-electron integrals over Gaussian basis functions. Our recursive approach…
Chiral effective field theories have been used with success in the study of nuclear structure. It is of interest to systematically improve these energy functionals (particularly that of quantum hadrodynamics) through the inclusion of…
We describe a formulation of multi-reference perturbation theory that obtains a rigorous upper bound to the second order energy by minimizing the Hylleraas functional in the space of matrix product states (MPS). The first order…
We use the multipole technique to derive four equivalent expressions for the bipolar expansion of the inverse distance, valid in all the regions of configuration space. Using the first-order perturbation theory, we calculate the overlap…
We give a complete analytical computation of three-point one-loop integrals with one heavy propagator, up to the third tensor rank, for arbitrary values of external momenta and masses.
In this paper, we obtain some formulas for double nonlinear Euler sums involving harmonic numbers and alternating harmonic numbers. By using these formulas, we give new closed form sums of several quadratic Euler series through Riemann zeta…
Short-range corrections to long-range selected configuration interaction calculations are derived from perturbation theory considerations and applied to harmonium (with two to six electrons for some low-lying states). No fitting to…
We applied the method of finite-part integration [Galapon E.A Proc.R.Soc A 473, 20160567(2017)] to evaluate in closed-form the exact one-loop integral representations of the Heisenberg-Euler Lagrangian from QED for a constant magnetic field…
We present an efficient approach to evaluate two-center two-electron integrals with exponential functions and with an arbitrary polynomial in electron-nucleus and electron-electron distances. We show that the master integral with the single…
We compute the contribution from the longitudinally polarized proton to the twist-3 double-spin asymmetry $A_{LT}$ in inclusive (light) hadron production from proton-proton collisions,i.e., $p^\uparrow \vec{p}\to h\,X$. We show that using…
Accurate results for nonrelativistic energy, relativistic, QED, and finite nuclear mass corrections are obtained for $2^1S_{1/2}$, $3^1S_{1/2}$ and $2^1P_{1/2}$ states of the Li atom and Be$^+$ ion. Our computational approach uses the…