Three-nucleon forces

Abstract

The role of three-nucleon forces in ab initio calculations of nuclear systems is investigated. The difference between genuine and induced many-nucleon forces is emphasized. Induced forces arise in the process of solving the nuclear many-body problem as technical intermediaries towards calculationally converged results. Genuine forces make up the hamiltonian; they represent the chosen underlying dynamics. The hierarchy of contributions arising from genuine two-, three-and many-nucleon forces is discussed. Signals for the need of the inclusion of genuine three-nucleon forces are studied in nuclear systems, technically best under control, especially in three-nucleon and four-nucleon systems. Genuine three-nucleon forces are important for details in the description of some observables. Their contributions to observables are small on the scale set by two-nucleon forces.

Impact of three-body forces on elastic nucleon-nucleus scattering observables

“…Recalling the distinction introduced by Sauer in Ref. [40], many-nucleon forces can be generally divided into two categories: genuine contributions arising from the nuclear Hamiltonian and induced terms coming from the process of solving the nuclear manybody problem. Induced many-nucleon forces do not have a fundamental basis.…”

In-medium short-range dynamics of nucleons: Recent theoretical and experimental advances

“…Though such a statement is qualitatively correct, it is nowadays well established that three-nucleon potentials have to be considered in order to explain the groundstate energy of light nuclei [18][19][20] (for a recent review on three-and many-nucleon forces see Refs. [21,22]). Therefore, in a first, realistic approach, the non-relativistic Schrödinger equation assumes the following form 3) and to look for its improvements by considering, e.g., relativistic effects, possible deviations of bound-nucleon properties from the free ones, the effects of non-nucleonic degrees of freedom, etc.…”

“…Section 7), leading to a strong reduction of FSI; (iii) in the range peculiar for the study of SRCs by the process A(e, e ′ p)X , Q 2 ≈ 1-5 (GeV/c) 2 with T kin ≃ Q 2 /(2m N ) ≥ 1 GeV, the most appropriate way to treat FSI appears to be the Glauber approach (GA), based upon the eikonal approximation coupled with the rescattering of the struck nucleon on the spectator nucleons [78]). 22 The application of the GA to the treatment of A(e, e ′ p)B processes is based upon the following assumptions: (i) the NN scattering amplitude is obtained within the eikonal approximation; (ii) the nucleons of the spectator system (A − 1) are stationary during the multiple scattering with the struck nucleon (the frozen approximation), (iii) the interaction between the struck nucleon with the spectator frozen nucleons occurs only by transferring a perpendicular momentum component. GA has two non trivial advantages in that: (i) it does not contain free parameters, being based upon the use of the experimental values characterizing NN scattering processes, and (ii) it can be applied to the treatment of exclusive A(e, e ′ p)B processes off both complex nuclei and few-nucleon systems, where in the last case, the concept of an optical potential is difficult to justify.…”

Impact of Three-Body Forces on Elastic Nucleon-Nucleus Scattering Observables

“…Recalling the distinction introduced by Sauer in Ref. [40], many-nucleon forces can be generally divided into two categories: genuine contributions arising from the nuclear Hamiltonian and induced terms coming from the process of solving the nuclear many-body problem. Induced many-nucleon forces do not have a fundamental basis.…”

“…the 2π exchange diagram between three nucleons must be completed by two more contributions: a one-π-exchange plus a N N contact term and a 3N contact term. For more details and an explicit derivation of the relevant formulae, we refer the reader to Refs [40,63,64]…”