Related papers: Computation of Two-Body Matrix Elements From the A…
We discuss two approaches to the calculation of matrix elements of the Argonne v18 potential. The first approach is applicable in the case of a single-particle basis of harmonic-oscillator wave functions. In this case we use the Talmi…
In this document we present our approach to the computation of three-body matrix elements, based on the Urbana family of three-nucleon potentials. The calculations refer only to the necessary matrix elements needed to include the…
Electronic structure methods that exploit nonorthogonal Slater determinants face the challenge of efficiently computing nonorthogonal matrix elements. In a recent publication, H. G. A. Burton, J. Chem. Phys. 154, 144109 (2021), I introduced…
Two-body matrix elements of arbitrary local interactions are written as the sum of separable terms in a way that is well suited for the exchange and pairing channels present in mean-field calculations. The expansion relies on the…
Starting from the matrix elements of the nucleon-nucleon interaction in momentum space we present a method to derive an operator representation with a minimal set of operators that is required to provide an optimal description of the…
We calculate the deuteron anapole moment with the wave functions obtained from the Argonne $v18$ nucleon-nucleon interaction model. The anapole moment operators are considered at the leading order. To minimize the uncertainty due to a lack…
We present new formulae for the matrix elements of one-body and two-body physical operators in compact forms, which are applicable to arbitrary Hartree-Fock-Bogoliubov wave functions, including those for multi-quasiparticle excitations. The…
We derive a formalism, the separation method, for the efficient and accurate calculation of two-body matrix elements for a Gaussian potential in the cylindrical harmonic-oscillator basis. This formalism is of critical importance for…
This paper gives a momentum-space representation of the Argonne V18 potential as an expansion in products of spin-isospin operators with scalar coefficient functions of the momentum transfer. Two representations of the scalar coefficient…
The two-body t-matrix is calculated directly as function of two vector momenta for different Malfliet-Tjon type potentials. At a few hundred MeV projectile energy the total amplitude is quite a smooth function showing only a strong peak in…
Matrix elements between shifted correlated Gaussians of various potentials with several form-factors are calculated analytically. Analytic matrix elements are of importance for the correlated Gaussian method in quantum few-body physics.
We introduce a method for calculating individual elements of matrix functions. Our technique makes use of a novel series expansion for the action of matrix functions on basis vectors that is memory efficient even for very large matrices. We…
This work presents an elegant formalism to model the evolution of the full two rigid body problem. The equations of motion, given in a Cartesian coordinate system, are expressed in terms of spherical harmonics and Wigner D-matrices. The…
We compute the matrix elements for elastic scattering of dark matter (DM) particles off light nuclei ($^2$H, $^3$H, $^3$He, $^4$He and $^6$Li) using quantum Monte Carlo methods. We focus on scalar-mediated DM-nucleus interactions and use…
Methods of angular momenta are modified and used to solve some actual problems in quantum mechanics. In particular, we re-derive some known formulas for analytical and numerical calculations of matrix elements of the vector physical…
We present two methods for computing dimensionally-regulated NRQCD heavy-quarkonium matrix elements that are related to the second derivative of the heavy-quarkonium wave function at the origin. The first method makes use of a hard-cutoff…
We employ the Unitary Correlation Operator Method (UCOM) to construct correlated, low-momentum matrix elements of realistic nucleon-nucleon interactions. The dominant short-range central and tensor correlations induced by the interaction…
Recoupling matrix elements are evaluated, in the harmonic oscillator approximation, for all possible angular and radial excitations in processes where quarks recombine. A diagrammatic representation is given. Their use is demonstrated in…
We present a Pfaffian formula to calculate matrix elements of three-body operators in symmetry-restoration beyond-mean-field methods, including the case of multiple quasi-particle configurations. Detailed derivation based on [Mizusaki et…
Exact analytical expressions for the matrix elements of the Uehling potential in a basis of explicitly correlated exponential wave functions are presented. The obtained formulas are then used to compute with an improved accuracy the vacuum…