Chiral Three-Nucleon Interactions in Light Nuclei, Neutron-αScattering, and Neutron Matter

Abstract

We present quantum Monte Carlo calculations of light nuclei, neutron-α scattering, and neutron matter using local two-and three-nucleon (3N) interactions derived from chiral effective field theory up to next-to-next-to-leading order (N 2 LO). The two undetermined 3N low-energy couplings are fit to the 4 He binding energy and, for the first time, to the spin-orbit splitting in the neutron-α P -wave phase shifts. Furthermore, we investigate different choices of local 3N-operator structures and find that chiral interactions at N 2 LO are able to simultaneously reproduce the properties of A = 3, 4, 5 systems and of neutron matter, in contrast to commonly used phenomenological 3N interactions.Three-nucleon (3N) interactions are essential for a reliable prediction of the properties of light nuclei and nucleonic matter [1][2][3][4][5]. In quantum Monte Carlo (QMC) calculations phenomenological 3N interactions such as the Urbana [6] and Illinois [7] models have been used with great success [3,8]. However, such models suffer from certain disadvantages: They are not based on a systematic expansion and it was found that the Illinois forces tend to overbind neutron matter [9,10]. It is therefore unlikely that these phenomenological models can be used to correctly predict the properties of heavy neutron-rich nuclei.An approach which addresses these shortcomings is chiral effective field theory (EFT) [2,[11][12][13][14]. Chiral EFT is a low-energy effective theory consistent with the symmetries of quantum chromodynamics and provides a systematic expansion for nuclear forces. It includes contributions from long-range pion-exchange interactions explicitly and expands the short-distance interactions into a systematic set of contact operators accompanied by low-energy couplings fit to experimental data. Chiral EFT enables the determination of theoretical uncertainties and systematic order-by-order improvement; for recent work see Refs. [15][16][17][18].Chiral EFT also predicts consistent many-body interactions. In Weinberg power counting, 3N forces first enter at next-to-next-to-leading order (N 2 LO) [19,20] and contain three contributions: A two-pion-exchange interaction V C , a one-pion-exchange-contact interaction V D , and a 3N contact interaction V E . While the first is accompanied by the couplings c i from the pion-nucleon sector, the latter two are accompanied by the couplings c D and c E , which have to be determined in A > 2 systems.In addition to systematic nuclear forces, reliable manybody methods are required to describe properties of light nuclei and of dense neutron matter. QMC approaches, which solve the many-body Schrödinger equation stochastically, are such a class of methods. Both the Green's function Monte Carlo (GFMC) method and the auxiliary-field diffusion Monte Carlo (AFDMC) method rely on projection in imaginary time τ ,with H the Hamiltonian of the system and |Ψ T a trial wave function not orthogonal to the many-body ground state |Ψ 0 . For a recent review of developments and applications of QMC methods...

In-medium similarity renormalization group for closed and open-shell nuclei

“…While rotational bands emerge naturally in these nuclei even without an initial chiral 3N force, its inclusion markedly improves the agreement of the theoretical excitation energies and level spacings with experimental data [165]. The Shell model's capability to describe intrinsically deformed nuclei allows us to follow up on our discussion of 20 Ne from section 6.3 now. There, we claimed that the MR-IMSRG(2) extracts an excited state with spherical intrinsic structure.…”

“…This is illustrated beautifully in the examples of 20 Ne and 22 Ne, which both have intrinsically deformed ground states [186]. In section 7, we will show that Shell model calculations with IMSRG effective interactions based on the N N +3N (400) Hamiltonian [164,165] yield deformed ground states for 20,22 Ne. In these calculations, we also find intrinsically spherical 0 + 2 excited states whose absolute energies are in excellent agreement with the MR-IMSRG(2) energies.…”

“…From equation (20), it is easy to see that λ (2) encodes the two-nucleon correlation content of the reference state |Φ . If the reference state is a Slater determinant, i.e., an independent-particle state, the full two-body density matrix factorizes, and λ (2) vanishes:…”

“…Here, we use the full density matrices for compactness, but it is easy to express equations (41)- (43) completely in terms of irreducible density matrices by using equations (20) and (21). Note that the normal-ordered zero-, one-, and two-body parts of the Hamiltonian all contain in-medium contributions from the free-space 3N interaction.…”

“…Instead, we start from nuclear interactions that describe low-energy QCD observables in the N N and 3N systems, like scattering data or binding energies. Nowadays, such interactions are derived in Chiral Effective Field Theory (EFT), which provides a constructive framework and organizational hierarchy for N N , 3N , and higher many-nucleon forces, as well as consistent electroweak operators (see, e.g., [14][15][16][17][18][19][20][21][22][23][24][25]). Since Chiral EFT is a lowmomentum expansion, high-momentum (short-range) physics is not explicitly resolved by the theory, but parametrized by the so-called low-energy constants (LECs).…”