The 4He total photo-absorption cross section with two- plus three-nucleon interactions from chiral effective field theory

Abstract

The total photo-absorption cross section of 4 He is evaluated microscopically using two-(NN) and three-nucleon (NNN) interactions based upon chiral effective field theory (χEFT). The calculation is performed using the Lorentz integral transform method along with the ab initio no-core shell model approach. An important feature of the present study is the consistency of the NN and NNN interactions and also, through the Siegert theorem, of the two-and three-body current operators. This is due to the application of the χEFT framework. The inclusion of the NNN interaction produces a suppression of the low-energy peak and enhancement of the high-energy tail of the cross section. We compare to calculations obtained using other interactions and to representative experiments. The rather confused experimental situation in the giant resonance region prevents discrimination among different interaction models.Key words: PACS: 25.20.Dc, 21.60.Cs, 27.10.+h Interactions among nucleons are governed by quantum chromodynamics (QCD). In the low-energy regime relevant to nuclear structure and reactions, this theory is nonperturbative, and, therefore, hard to solve. Thus, theory has been forced to resort to models for the interaction, which have limited physical basis. New theoretical developments, however, allow us to connect QCD with low-energy nuclear physics. Chiral effective field theory (χEFT) [1,2] provides a promising bridge to the underlying theory, QCD. Beginning with the pionic or the nucleon-pion system [3] one works consistently with systems of increasing number of nucleons [4]. One makes use of spontaneous breaking of chiral symmetry to systematically expand the strong interaction in terms of a generic small momentum and takes the explicit breaking of chiral symmetry into account by expanding in the pion mass. Nuclear interactions are nonperturbative, because diagrams with purely nucleonic intermediate states are enhanced [1,2]. Therefore, the chiral perturbation expansion is performed for the potential. The χEFT predicts, along with the nucleon-nucleon (NN) interaction at the leading order, a three-nucleon (NNN) interaction at the next-to-next-to-leading order or N 2 LO [2,5,6], and even a four-nucleon (NNNN) interaction at the fourth Email addresses: quaglioni1@llnl.gov (Sofia Quaglioni), navratil1@llnl.gov (Petr Navrátil). order (N 3 LO) [7]. The details of QCD dynamics are contained in parameters, low-energy constants (LECs), not fixed by the symmetry, but can be constrained by experiment. At present, high-quality NN potentials have been determined at N 3 LO [8]. A crucial feature of χEFT is the consistency between the NN, NNN and NNNN parts. As a consequence, at N 2 LO and N 3 LO, except for two parameters assigned to two NNN diagrams, the potential is fully constrained by the parameters defining the NN interaction. The full interaction up to N 2 LO was first applied to the analysis of nd scattering [6] and later the N 3 LO NN potential was combined with the available NNN at N 2 LO to study the 7 Li stru...

Local three-nucleon interaction from chiral effective field theory

“…We note that 4 He results obtained with the identical Hamiltonian but with c D = −1 and c E = −0.331 are presented in Ref. [17]. We use the Jacobi coordinate HO basis antisymmentrized according to the method described in Ref.…”

“…In that study, a preferred choice of the two NNN LECs, c D and c E , was found and the fundamental importance of the χEFT NNN interaction was demonstrated for reproducing the structure of mid-p-shell nuclei. In a subsequent study, the same Hamiltonian was used to calculate microscopically the photo-absorption cross section of 4 He [17].…”

“…[14,17] and present its matrix elements in the three-nucleon basis. Technical details of dealing with NNN interactions were investigated in many papers [28,29,30,31,32,33,34].…”

Theoretical Study of the 4He(γ, p)3H and 4He(γ, n)3He Reactions

“…Unlike the exclusive case, the total, i.e., inclusive cross section of 4 He photoabsorption has already been calculated with state-of-the-art nuclear forces, including three-nucleon forces (3NF), of either a phenomenological type [8] or from a chiral perturbation effective field theory (χEFT) [9]. These two calculations, which also utilize the UDA, are in excellent agreement with one another, and in reasonable agreement with the majority of experimental data.…”

Operator evolution forab initiotheory of light nuclei

“…We choose the total dipole strength because it is used to compute important quantities such as photo-absorption cross sections [31] and electric polarizabilities [27]. Our second investigation focuses on operator renormalization as a function of range, following a prescription similar to that of Ref.…”