Expansion of one-, two- and three-body matrix elements on a generic spherical basis for nuclear ab initio calculations

Abstract

Ab initio studies of atomic nuclei are based on Hamiltonians including one-, two- and three-body operators with very complicated structures. Traditionally, matrix elements of such operators are expanded on a Harmonic Oscillator single-particle basis, which allows for a simple separation of the center-of-mass motion from the intrinsic one. A few recent investigations have showed that the use of different single-particle bases can bring significant advantages to numerical nuclear structure computations. In this work, the complete analytical expression of the Hamiltonian matrix elements expanded on a generic spherical basis is presented for the first time. This will allow systematic studies aimed at the determination of optimal nuclear bases.

arXiv comment42 pages, 1 figure

References in corpus (9)

• An accurate nucleon-nucleon potential with charge-independence breaking
• Modern Theory of Nuclear Forces
• Chiral effective field theory and nuclear forces
• Self-consistent Green's function theory for atomic nuclei
• Ab initio calculation of the potential bubble nucleus ${}^{34}$Si
• Local nucleon-nucleon and three-nucleon interactions within chiral effective field theory
• Quasiparticle and quasihole states of nuclei around 56Ni
• Doubly magic nuclei from Lattice QCD forces at $M_{PS}=$469 MeV/c${}^2$
• Gorkov algebraic diagrammatic construction formalism at third order

Cited by in corpus (1)

• Bridging reaction theory and nuclear structure in ${\pi }^{\pm }$-${}^{48}$Ca scattering