Microscopic nuclear structure based upon a chiral<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>NN</mml:mi></mml:math>potential

Coraggio, L.; Covello, A.; Gargano, A.; Itaco, N.; Kuo, T.T.S.; Entem, D. R.; Machleidt, R.

doi:10.1103/physrevc.66.021303

Cited by 44 publications

(114 citation statements)

References 32 publications

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“…Furthermore, it is a smooth potential and can be used directly in nuclear many body calculations, avoiding the calculation of the Brueckner G-matrix [12,13,14,18,19,20]. Shell model nuclear structure calculations using V low−k have indeed yielded very encouraging results [13,19,20]. These calculations apply the same V low−k to a wide range of nuclei, including those in the sd-shell, tin region, and heavy nuclei in the lead region.…”

Section: Introductionmentioning

confidence: 99%

“…This corresponds to the pion production threshold, a scale often not considered in traditional EFT methods, even though it represents the limit of available 2-nucleon data; experiments give a unique effective interaction only up to this scale. This cutoff has been employed recently by several authors [12,13,14,15,16,17,18,19,20] in a new development for the nucleon-nucleon (NN) interaction: the derivation of a low momentum NN potential, V low−k . Despite some general similarities, we would like to stress that V low−k is not a traditional EFT construct, and would like to now attempt to clarify this issue.…”

Section: Introductionmentioning

confidence: 99%

“…As summarized recently [27,28], a thesis now develped for some time posits that by combining the SNPA, based on potentials fit to experiments, with modern effective field theory, one can achieve more predictive power than the purist's EFT alone. This combination of SNPA and effective field theory, called EFT* by Kubodera [29], but more properly called more effective effective field theory (MEEFT) as noted by Kubodera, was rediscovered in [12,13,14,15,16,17,18,19,20], and consists of an RGtype approach which limits Λ to 2.1fm −1 , because this is equal to the center of mass momentum up to which experiments measuring the nucleon-nucleon scattering phase shifts have been carried out.…”

Section: Introductionmentioning

confidence: 99%

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Counter terms for low momentum nucleon–nucleon interactions

et al. 2004

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There is much current interest in treating low energy nuclear physics using the renormalization group (RG) and effective field theory (EFT). Inspired by this RG-EFT approach, we study a lowmomentum nucleon-nucleon (NN) interaction, V low−k , obtained by integrating out the fast modes down to the scale Λ ∼ 2fm −1 . Since NN experiments can only determine the effective interaction in this low momentum region, our chief purpose is to find such an interaction for complex nuclei whose typical momenta lie below this scale. In this paper we find that V low−k can be highly satisfactorily accounted for by the counter terms corresponding to a short range effective interaction. The coefficients Cn of the power series expansion Cnq n for the counter terms have been accurately determined, and results derived from several meson-exchange NN interaction models are compared. The counter terms are found to be important only for the S, P and D partial waves. Scaling behavior of the counter terms is studied. Finally we discuss the use of these methods for computing shell model matrix elements.

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Counter terms for low momentum nucleon–nucleon interactions

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“…Concerning the latter, the matrix elements of bare nucleon-nucleon interactions that contain a repulsive core display a qualitatively different momentum dependence than that displayed by the Gogny interaction. We instead consider here the v low-k interaction, which has been devised to reproduce the low-momentum properties of the nucleon-nucleon force, including the experimental phase shifts, without the introduction of a repulsive core [12]. In particular, we employ a parametrization of v low-k devised to reproduce the properties of v 14 Argonne potential.…”

Section: Matrix Elementsmentioning

confidence: 99%

Pairing matrix elements and pairing gaps with bare, effective, and induced interactions

et al. 2005

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The dependence on the single-particle states of the pairing matrix elements of the Gogny force and of the bare low-momentum nucleon-nucleon potential v low-k -designed so as to reproduce the low-energy observables avoiding the use of a repulsive core-is studied for a typical finite, superfluid nucleus ( 120 Sn). It is found that the matrix elements of v low-k follow closely those of v Gogny on a wide range of energy values around the Fermi energy e F , those associated with v low-k being less attractive. This result explains the fact that around e F the pairing gap Gogny associated with the Gogny interaction (and with a density of single-particle levels corresponding to an effective k mass m k ≈ 0.7 m) is a factor of about 2 larger than low-k , being in agreement with exp = 1.4 MeV. The exchange of low-lying collective surface vibrations among pairs of nucleons moving in time-reversal states gives rise to an induced pairing interaction v ind peaked at e F . The interaction (v low-k + v ind ) Z ω arising from the renormalization of the bare nucleon-nucleon potential and of the single-particle motion (ω-mass and quasiparticle strength Z ω ) associated with the particle-vibration coupling mechanism, leads to a value of the pairing gap at the Fermi energy ren that accounts for the experimental value. An important question that remains to be studied quantitatively is to what extent Gogny , which depends on average parameters, and ren , which explicitly depends on the parameters describing the (low-energy) nuclear structure, display or not a similar isotopic dependence and whether this dependence is borne out by the data.

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“…First calculations applying the N 3 LO NN potential [ 18] in the (no-core) shell model [ 28,29,30,31,32], the coupled cluster formalism [ 33,34,35,36,37], and the unitary-model-operator approach [ 38] have produced promising results.…”

Section: Discussionmentioning

confidence: 99%

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

Machleidt

2007

Nuclear Physics A

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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.

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Microscopic nuclear structure based upon a chiralNNpotential

Cited by 44 publications

References 32 publications

Counter terms for low momentum nucleon–nucleon interactions

Counter terms for low momentum nucleon–nucleon interactions

Pairing matrix elements and pairing gaps with bare, effective, and induced interactions

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

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