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Register a new userLocal chiral EFT potentials in nuclei and neutron matter: results and issues
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In recent years, the combination of advanced quantum Monte Carlo (QMC) methods and local interactions derived from chiral effective field theory (EFT) has been shown to provide a versatile and systematic approach to nuclear systems. Calculations at next-to-next-to-leading order in chiral EFT have lead to fascinating results for nuclei and nucleonic matter. On the one hand, ground-state properties of nuclei are well reproduced up to $Aleq16$, even though these potentials have been fit to nucleon-nucleon scattering and few-body observables only. On the other hand, a reasonable description of neutron-matter properties emerges. While regulator functions applied to two- and three-nucleon forces are a necessary ingredient in these many-body calculations, the use of local regulators leads to a substantial residual regulator and cutoff dependence that increases current theoretical uncertainties. In this contribution, we review local chiral interactions, their applications, and QMC results for nuclei and neutron matter. In addition, we address regulator issues for such potentials and present a possible path forward.
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We closely investigate NN potentials based upon the Delta-full version of chiral effective field theory. We find that recently constructed NN potentials of this kind, which (when applied together with three-nucleon forces) were presented as predicting accurate binding energies and radii for a range of nuclei from A=16 to A=132 and providing accurate equations of state for nuclear matter, yield a chi^2/datum of 60 for the reproduction of the pp data below 100 MeV laboratory energy. We compare this result with the first semi-quantitative $NN$ potential ever constructed in the history of mankind: the Hamada-Johnston potential of the year of 1962. It turns out that the chi^2 for the new Delta-full potentials is more than three times what was already achieved some 60 years ago. In fact, there has not been any known NN potential during the entire history of nuclear forces with a chi^2 as large as the ones of these recent Delta-full potentials of the Gothenburg-Oak Ridge group of the year of 2020. We perceive this historical fact as highly disturbing in view of the current trend for which the term precision has become the most frequently used label to characterize contemporary advances in microscopic nuclear structure physics. We are able to trace the very large chi^2 as well as the apparent success of the potentials in nuclear structure to unrealistic predictions for P-wave states, in which the Delta-full NNLO potentials are off by up to 40 times the NNLO truncation errors. In fact, we show that, the worse the description of the P-wave states, the better the predictions in nuclear structure. Misleading results of the above kind are unhelpful to the communitys efforts in microscopic nuclear structure, because they obscure a correct understanding of the nature of the remaining problems and, thus, hamper sincere attempts towards genuine solutions.
We compute from chiral two- and three-nucleon interactions the energy per particle of symmetric nuclear matter and pure neutron matter at third-order in perturbation theory including self-consistent second-order single-particle energies. Particular attention is paid to the third-order particle-hole ring-diagram, which is often neglected in microscopic calculations of the equation of state. We provide semi-analytic expressions for the direct terms from central and tensor model-type interactions that are useful as theoretical benchmarks. We investigate uncertainties arising from the order-by-order convergence in both many-body perturbation theory and the chiral expansion. Including also variations in the resolution scale at which nuclear forces are resolved, we provide new error bands on the equation of state, the isospin-asymmetry energy, and its slope parameter. We find in particular that the inclusion of third-order diagrams reduces the theoretical uncertainty at low densities, while in general the largest error arises from omitted higher-order terms in the chiral expansion of the nuclear forces.
Determination of the proper power-counting scheme is an important issue for the systematic application of Chiral Effective Field Theory in nuclear physics. We analyze the cutoff dependence of three-nucleon observables (the neutron-deuteron scattering lengths and the triton binding energy) at the leading and next-to-leading orders of a power counting that ensures order-by-order renormalization in the two-nucleon system. Our results imply that three-body forces are not needed for renormalization of the three-nucleon system up to next-to-leading order, as usually assumed in the literature. (Erratum to the original article is included)
Quantum Monte Carlo methods are powerful numerical tools to accurately solve the Schrodinger equation for nuclear systems, a necessary step to describe the structure and reactions of nuclei and nucleonic matter starting from realistic interactions and currents. These ab-initio methods have been used to accurately compute properties of light nuclei -- including their spectra, moments, and transitions -- and the equation of state of neutron and nuclear matter. In this work we review selected results obtained by combining quantum Monte Carlo methods and recent Hamiltonians constructed within chiral effective field theory.
We study the equation of state of neutron matter using a family of unitarity potentials all of which are constructed to have infinite $^1S_0$ scattering lengths $a_s$. For such system, a quantity of much interest is the ratio $xi=E_0/E_0^{free}$ where $E_0$ is the true ground-state energy of the system, and $E_0^{free}$ is that for the non-interacting system. In the limit of $a_sto pm infty$, often referred to as the unitary limit, this ratio is expected to approach a universal constant, namely $xisim 0.44(1)$. In the present work we calculate this ratio $xi$ using a family of hard-core square-well potentials whose $a_s$ can be exactly obtained, thus enabling us to have many potentials of different ranges and strengths, all with infinite $a_s$. We have also calculated $xi$ using a unitarity CDBonn potential obtained by slightly scaling its meson parameters. The ratios $xi$ given by these different unitarity potentials are all close to each other and also remarkably close to 0.44, suggesting that the above ratio $xi$ is indifferent to the details of the underlying interactions as long as they have infinite scattering length. A sum-rule and scaling constraint for the renormalized low-momentum interaction in neutron matter at the unitary limit is discussed.
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