Related papers: Compact Formulae for Three-Center Nuclear Attracti…
A Monte Carlo method for evaluating multi-center two-electron-repulsion integrals over any type of orbitals (Slater, Sturmian, finite-range, numerical, etc.) is presented. The approach is based on a simple and universal…
Feynman loop integrals are a key ingredient for the calculation of higher order radiation effects, and are responsible for reliable and accurate theoretical prediction. We improve the efficiency of numerical integration in sector…
We report the three main ingredients to calculate three- and four-electron integrals over Gaussian basis functions involving Gaussian geminal operators: fundamental integrals, upper bounds, and recurrence relations. In particular, we…
Microscopic calculations of neutrino-nucleus scattering cross sections are critical for the success of the neutrino-oscillation program. In addition to retaining nuclear correlations in the initial and final state of the reaction, they are…
Three-body nuclear reactions in two-nucleon plus core systems are described in the framework of exact scattering equations including the core excitation. A nucleon-core optical potential is constructed that can be easily adjusted to the…
Correlation functions measured as a function of $\Delta \eta, \Delta \phi$ have emerged as a powerful tool to study the dynamics of particle production in nuclear collisions at high energy. They are however subject, like any other…
A purely numerical method, Direct ComputationMethod is applied to evaluate Feynman integrals. This method is based on the combination of an efficient numerical integration and an efficient extrapolation. In addition, high-precision…
Objective: The subtraction approach is known for being a theoretically-rigorous and accurate technique for solving the forward problem in electroencephalography by means of the finite element method. One key aspect of this approach consists…
Calculating microscopic optical potentials for elastic nucleon-nucleus scattering has already led to large body of work in the past. For folding first-order calculations the nucleon-nucleon (NN) interaction and the one-body density of the…
The determination of nucleus-nucleus potentials is important not only to describe the properties of the colliding system, but also to extract nuclear-structure information and for modelling nuclear reactions for astrophysics. We present the…
An optimal 3-point quadrature formula of closed type is derived. Various error inequalities are established. Applications in numerical integration are also given.
Circular targets are widely used in LiDAR-camera extrinsic calibration due to their geometric consistency and ease of detection. However, achieving accurate 3D-2D circular center correspondence remains challenging. Existing methods often…
An approximate relativistic two-component Hamiltonian for use in molecular electronic structure calculations is derived in the form of a sum of fixed atom-centered kinetic and spin-orbit operators added to the non-relativistic Hamiltonian.…
The equations of motion of two point masses have recently been derived at the 3PN approximation of general relativity. From that work we determine the location of the innermost circular orbit or ICO, defined by the minimum of the binary's…
A method to compute optimal collision avoidance maneuvers for short-term encounters is presented. The maneuvers are modeled as multiple-impulses to handle impulsive cases and to approximate finite burn arcs associated either with short…
The development and implementation of increasingly accurate methods for electronic structure calculations mean that, for many atomistic simulation problems, treating light nuclei as classical particles is now one of the most serious…
Ozdogan (Int. J. Quantum Chem., 92 (2003) 419) published formulas for evaluating the multielectron multicenter molecular integrals over Slater-type orbitals (STOs). It is demonstrated that the formulas presented in this work are not…
Analytical formulas for some useful three-particles integrals are derived. Many of these integrals include Bessel and/or trigonometric functions of one and two interparticle (relative) coordinates $r_{32}, r_{31}$ and $r_{21}$. The formulas…
The analytic integration and simplification of multi-loop Feynman integrals to special functions and constants plays an important role to perform higher order perturbative calculations in the Standard Model of elementary particles. In this…
Algorithms for numerical computation of symmetric elliptic integrals of all three kinds are improved in several ways and extended to complex values of the variables (with some restrictions in the case of the integral of the third kind).…