Effects of chiral three-nucleon forces on 4He-nucleus scattering in a wide range of incident energies

Abstract

Background: It is a current important subject to clarify properties of chiral three-nucleon forces (3NFs) not only in nuclear matter but also in scattering between finite-size nuclei. Particularly for the elastic scattering, this study has just started and the properties are not understood in a wide range of incident energies (Ein). Aims and approach: We investigate basic properties of chiral 3NFs in nuclear matter with positive energies by using the Brueckner-Hartree-Fock method with chiral two-nucleon forces at N 3 LO and 3NFs at NNLO, and analyze effects of chiral 3NFs on 4 He elastic scattering from targets 208 Pb, 58 Ni and 40 Ca over a wide range of 30 < ∼ Ein/AP < ∼ 200 MeV by using the g-matrix folding model, where AP is the mass number of the projectile. Results: In symmetric nuclear matter with positive energies, chiral 3NFs make the single-particle potential less attractive and more absorptive. The effects mainly come from the Fujita-Miyazawa 2π-exchange 3NF and slightly become larger as Ein increases. These effects persist in the optical potentials of 4 He scattering. As for the differential cross sections of 4 He scattering, chiral-3NF effects are large in Ein/AP > ∼ 60 MeV and improve the agreement of the theoretical results with the measured ones. Particularly in Ein/AP > ∼ 100 MeV, the folding model reproduces measured differential cross sections pretty well. Cutoff (Λ) dependence is investigated for both nuclear matter and 4 He scattering by considering two cases of Λ = 450 and 550 MeV. The uncertainty coming from the dependence is smaller than chiral-3NF effects even at Ein/AP = 175 MeV. PACS numbers: 21.30.Fe, 24.10.Ht, 25.55.Ci FIG. 1: 3NFs in NNLO. Diagram (a) corresponds to the Fujita-Miyazawa 2π-exchange 3NF [1], and diagrams (b) and (c) correspond to 1π-exchange and contact 3NFs. The solid and dashed lines denote nucleon and pion propagations, respectively, and filled circles and squares stand for vertices. The strength of the filled-square vertex is often called cD in diagram (b) and cE in diagram (c).tact 3NFs, respectively. The filled-square vertex has a strength c D in the diagram (b) and c E in the diagram (c). Quantitative roles of chiral 3NFs were extensively investigated, particularly for light nuclei and nuclear matter [6]; more precisely, see Ref.[7] for light nuclei, Refs. [8,9] for ab initio nuclear-structure calculations in lighter nuclei and Refs. [10][11][12][13][14][15][16] for nuclear matter. In addition, effects of chiral four-nucleon forces were found to be small in nuclear matter [17,18]. The chiral g matrix, calculated from chiral 2NF+3NF with the Brueckner-Hartree-Fock (BHF) method, yields a reasonable nuclear matter sat-

nEoS: neutron star equation of state from hadron physics alone

“…The higher order sets typically treat the two-body nucleon-nucleon interaction properly but use an approximation to the three-body force (or include it only at the lowest order). We acknowledge that this causes a systematic bias, lowering the repulsion of the nuclear interaction and thus the stiffness of the EoS (since it is known that three-body forces lower the attraction [19]). This is an aspect where systematic improvement is possible in the next few years.…”

Study of ($p,n$)IAS and ($^3$He,$t$)IAS charge-exchange reactions with the $G$-matrix folding method

“…G-matrix full-folding calculations for the study of (p, n)IAS reactions at proton energies between 80 MeV and 800 MeV were performed by Arellano and Love [38] using six different NN potential models (Paris, Nijmegen I and II, Reid 93, CDBONN and Argonne Av18) in the construction of the G-matrix. Recently, microscopic calculations of nucleon-nucleus and nucleus-nucleus scattering have been also performed using modern chiral twoand three-nucleon forces [39][40][41][42][43].…”

Pauli rearrangement potential for a scattering state with the nucleon-nucleon interaction in chiral effective field theory

“…Recent microscopic calculations by several groups [6][7][8] with various realistic N N forces are remarkably successful in accounting for nucleon-nucleus scattering data. The OMP by Amos et al [6], the Melbourne group, with the Paris [9] or Bonn-B [10] potentials worked well, in spite of the fact that those interactions fail to reproduce proper nuclear saturation properties.…”

“…Furumoto et al [7] were concerned with the saturation properties by adding the effects of phenomenological three-nucleon forces (3NFs) to the Nijmegen extended soft-core N N potential [11,12]. The Kyushu group [8] employed the next-to-next-to-next-to-leading order (N 3 LO) interaction in chiral effective field theory (ChEFT) [13] with including the effect of the next-to-next-to-leading order (N 2 LO) 3NFs [14] in the normal-ordering prescription [15]. These calculations remain in the lowest-order in the Brueckner expansion for the OMP.…”

“…The next-order contribution was discussed in the early stage of microscopic studies [2]. It was recognized that the contribution of the second-order rearrangement process becomes smaller with increasing the incident energy, and therefore the actual incorporation of this contribution has been left out in the recent microscopic OMPs [6][7][8]. For a deeper understanding of the microscopic OMP, however, it is worthwhile to revisit the issue of the Pauli rearrangement for the OMP.…”