What is ab initio? Machleidt, R.
Few-body systems,
10/2023, Letnik:
64, Številka:
4
Journal Article
Recenzirano
Microscopic nuclear theory is based on the tenet that atomic nuclei can be accurately described as collections of point-like nucleons interacting via two- and many-body forces obeying nonrelativistic ...quantum mechanics—and the concept of the
ab initio
approach is to calculate nuclei accordingly. The forces are fixed in free-space scattering and must be accurate. We will critically review the history of this approach from the early beginnings until today. An analysis of current
ab initio
calculations reveals that some mistakes of history are being repeated today. The ultimate goal of nuclear theory are high-precision
ab initio
calculations which, as it turns out, may be possible only at the fifths order of the chiral expansion. Thus, for its fulfillment, nuclear theory is still facing an enormous task.
My personal encounter with Weinberg’s proposal of 1990 was a really entertaining one: My collaborator David Entem and I had embarked to show that Weinberg’s idea, though smart and beautiful, was ...essentially useless in practice (like so many of those genius ideas of the 1980s where people claimed to have “derived the nuclear force from QCD”). However, in trying to do so, we showed the opposite; namely, we showed that Weinberg’s idea worked better than allowed by any reasonable means.
We review how nuclear forces emerge from low-energy QCD via chiral effective field theory. The presentation is accessible to the non-specialist. At the same time, we also provide considerable ...detailed information (mostly in appendices) for the benefit of researchers who wish to start working in this field.
During the past two decades, chiral effective field theory has become a popular tool to derive nuclear forces from first principles. Two-nucleon interactions have been worked out up to sixth order of ...chiral perturbation theory and three-nucleon forces up to fifth order. Applications of some of these forces have been conducted in nuclear few- and many-body systems-with a certain degree of success. But in spite of these achievements, we are still faced with great challenges. Among them is the issue of a proper uncertainty quantification of predictions obtained when applying these forces in ab initio calculations of nuclear structure and reactions. A related problem is the order by order convergence of the chiral expansion. We start this review with a pedagogical introduction and then present the current status of the field of chiral nuclear forces. This is followed by a discussion of representative examples for the application of chiral two- and three-body forces in the nuclear many-body system including convergence issues.
We employ interactions from chiral effective field theory and compute the binding energies and low-lying excitations of calcium isotopes with the coupled-cluster method. Effects of three-nucleon ...forces are included phenomenologically as in-medium two-nucleon interactions, and the coupling to the particle continuum is taken into account using a Berggren basis. The computed ground-state energies and the low-lying J(π) = 2+ states for the isotopes (42,48,50,52)Ca are in good agreement with data, and we predict the excitation energy of the first J(π) = 2+ state in (54)Ca at 1.9 MeV, displaying only a weak subshell closure. In the odd-mass nuclei (53,55,61)Ca we find that the positive parity states deviate strongly from the naive shell model.
We employ interactions from chiral effective field theory and compute binding energies, excited states, and radii for isotopes of oxygen with the coupled-cluster method. Our calculation includes the ...effects of three-nucleon forces and of the particle continuum, both of which are important for the description of neutron-rich isotopes in the vicinity of the nucleus 24O. Our main results are the placement of the neutron drip line at 24O, the assignment of spins, parities and resonance widths for several low-lying states of the drip line nucleus, and an efficient approximation that incorporates the effects of three-body interactions.
We optimize the nucleon-nucleon interaction from chiral effective field theory at next-to-next-to-leading order (NNLO). The resulting new chiral force NNLO(opt) yields χ(2)≈1 per degree of freedom ...for laboratory energies below approximately 125 MeV. In the A=3, 4 nucleon systems, the contributions of three-nucleon forces are smaller than for previous parametrizations of chiral interactions. We use NNLO(opt) to study properties of key nuclei and neutron matter, and we demonstrate that many aspects of nuclear structure can be understood in terms of this nucleon-nucleon interaction, without explicitly invoking three-nucleon forces.
Can chiral EFT give us satisfaction? Machleidt, R.; Sammarruca, F.
The European physical journal. A, Hadrons and nuclei,
03/2020, Letnik:
56, Številka:
3
Journal Article
Recenzirano
We compare nuclear forces derived from chiral effective field theory (EFT) with those obtained from traditional (phenomenological and meson) models. By means of a careful analysis of paralleles and ...differences, we show that chiral EFT is superior to all earlier approaches in terms of both formal aspects and successful applications in ab initio calculations. However, in spite of the considerable progress made possible by chiral EFT, complete satisfaction cannot be claimed until outstanding problems – the renormalization issue being the most important one – are finally settled.
We present N N potentials through five orders of chiral effective field theory ranging from leading order (LO) to next-to-next-to-next-to-next-to-leading order (N4LO). The construction may be ...perceived as consistent in the sense that the same power counting scheme as well as the same cutoff procedures are applied in all orders. Moreover, the long-range parts of these potentials are fixed by the very accurate πN low-energy constants (LECs) as determined in the Roy-Steiner equations analysis by Hoferichter, Ruiz de Elvira and coworkers. In fact, the uncertainties of these LECs are so small that a variation within the errors leads to effects that are essentially negligible, reducing the error budget of predictions considerably. The N N potentials are fit to the world N N data below pion-production threshold of the year of 2016. The potential of the highest order (N4LO) reproduces the world N N data with the outstanding χ2/datum of 1.15, which is the highest precision ever accomplished for any chiral N N potential to date. The N N potentials presented may serve as a solid basis for systematic ab initio calculations of nuclear structure and reactions that allow for a comprehensive error analysis. In particular, the consistent order by order development of the potentials will make possible a reliable determination of the truncation error at each order. Our family of potentials is non-local and, generally, of soft character. This feature is reflected in the fact that the predictions for the triton binding energy (from two-body forces only) converges to about 8.1 MeV at the highest orders. This leaves room for three-nucleon-force contributions of moderate size.
PDF
