A new way to perform partial-wave decompositions of few-nucleon forces

Abstract

Abstract. We formulate a general and exact method of partial wave decomposition (PWD) of any nucleonnucleon (NN) potential and any three-nucleon (3N) force. The approach allows one to efficiently use symbolic algebra software to generate the interaction dependent part of the program code calculating the interaction. We demonstrate the feasibility of this approach for the one-boson exchange BonnB potential, a recent nucleon-nucleon chiral force and the chiral two-pion-exchange three-nucleon force. In all cases very good agreement between the new and the traditional PWD is found. The automated PWD offered by the new approach is of the utmost importance in view of future applications of numerous chiral N3LO contributions to the 3N force in three nucleon calculations. PACS

Efficient calculation of chiral three-nucleon forces up toN3LOforab initiostudies

“…By using symmetries, it is possible to reduce the dimensionality of the angular integrals from 8 to 5. Traditional methods are based on a direct discretization and numerical evaluation of these angular integrals [38,39]. Due to the large number of external quantum numbers and momentum mesh points such algorithms require very large computational resources for calculating all matrix elements necessary for many-body studies.…”

“…1 have already been worked out [8,9], their decomposition in a suitable form for few-and many-body frameworks represents a highly nontrivial task [37][38][39]. Due to the huge amount of computational resources needed for this decomposition, matrix elements have been so far available only in a limited model space [16].…”

“…In this paper we present a novel framework that allows one to decompose 3N interactions in a plane-wave partial wave basis in a computationally much more efficient way than the framework of Refs. [38,39]. This new method makes explicit use of the fact that all (unregularized) contributions to chiral 3NFs are either local, i.e.…”

3H at Next-to-Next-to-Next-to Leading Order of the Chiral Expansion

“…However, the rich structure of 3NF at N 3 LO makes the traditional PWD very time consuming and impractical. To avoid this obstacle we use a recently developed method [10,11], which utilizes the advantages of software for symbolic algebra. This method allows one to calculate efficiently any 3NF matrix elements in momentum space and was already successfully applied to the Tucson-Melbourne 3NF [11] and some terms of the chiral 3NF [12].…”

Chiral nuclear forces: Recent developments

“…For a related recent work on the electromagnetic currents see [9][10][11][12]. Given that the numerical implementation of the N 3 LO three-nucleon force (3NF) contributions represents a non-trivial task, which could be accomplished only recently [13,14], most of the available ab initio calculations utilized the nuclear Hamiltonian consisting of the N 3 LO nucleon-nucleon (NN) potentials of [4,5] accompanied by the leading, i.e. order-Q 3 (N 2 LO), 3NF.…”