The theory of nuclear forces: Is the never-ending story coming to an end?

Abstract

I review the recent progress in our understanding of nuclear forces in terms of an effective field theory (EFT) for low-energy QCD and put this progress into historical perspective. This is followed by an assessment of the current status of EFT based nuclear potentials. In concluding, I will summarize some unresolved issues. Historical PerspectiveThe theory of nuclear forces has a long history. Based upon the Yukawa idea [ 1] and the discovery of the pion, the 1950's became the first period of "pion theories". These, however, resulted in failure-for reasons we understand today: pion dynamics is ruled by chiral symmetry, a constraint that was not realized in the theories of the 1950's.The 1960's and 70's represent the main period for theories that also include heavy mesons ("meson theories") [ 2], but the work on meson models continued all the way into the 1990's when the family of the so-called high-precision NN potentials was developed. This family includes the Nijm-I, Nijm-II, and Reid93 potentials [ 3], the Argonne V 18 [ 4], and the CD-Bonn potential [ 5,6]. Later, also the highly non-local potential by Doleschall et al. [ 7] and the "CD-Bonn + ∆" model by Deltuva et al. [ 8] joined the club. All these potentials have in common that they are charge-dependent, use about 40-50 parameters, and reproduce the 1992 Nijmegen NN data base with a χ 2 /datum ≈ 1.Over the past ten years, the high-precision potentials have been applied intensively in exact few-body calculations and miscroscopic nuclear structure theory. Already the first few applications of the high-precision potentials in three-nucleon reactions [ 9] clearly revealed sizable differences between the predictions from NN potentials with a χ 2 /datum ≈ 1 (i.e., the new generation of potentials) and NN potentials with a χ 2 /datum ≈ 2 (the old generation of the 1970's and 80's which includes the old Nijmegen, the Paris, and the old Bonn potentials). Thus, once for all, the standard of precision was established that must be met by any future work in microscopic nuclear structure and exact few-body calculations: The input NN potential must reproduce the NN data with a χ 2 /datum ≈ 1 or the uncertainty in the predictions will make it impossible to draw reliable conclusions.In spite of these great practical achievements, the high-precision potentials cannot be the end of the story, because they are all phenomenological in nature. Ultimately, we need potentials that are based on proper theory and yield quantitative results.

Ab initiosymplectic no-core shell model

“…The fundamental theory of strong interactions, QCD, is non-perturbative in the low-energy regime characteristic of nuclear physics and hence derivation of the nuclear forces from the fundamental theory of strongly coupled quarks and gluons is an incredibly complicated task. A promising advance in the theory of nuclear forces emerged when the concept of an effective field theory [26] was applied to low-energy QCD giving rise to chiral perturbation theory [27,28]. This approach represents a best up-to-date bridge between QCD and the nuclear structure.…”

“…As noted in section 2, these higher-order many-body forces are a direct consequence of the quark substructure of the nucleons. They appear naturally in nuclear potentials that are derived from the low-energy limit of the QCD using the chiral perturbation theory [26][27][28] or the quark-meson coupling model [40]. For simplicity, however, here we limit the discussion to just two-body interactions.…”

Applications of the Similarity Renormalization Group to the Nuclear Interaction

“…. 121 5.6 Ground-state energy of 3 H as a function of the basis size N max for an N 3 LO NN interaction [49] with and without an initial NNN interaction [70,74]. Unevolved ("bare") and Lee-Suzuki (L-S) results with Ω = 28 MeV are compared with SRG at ω = 20 MeV evolved to λ = 2.0 fm −1 .…”

Realistic shell-model calculations: current status and open problems

“…An interesting feature of this approach is that three-nucleon forces arise naturally at third order (N 2 LO). We will not go further into this subject and refer the reader to [16] for a survey of the current status of the chiral potentials. However, a general comment may be in order here.…”