Description of light nuclei in pionless effective field theory using the stochastic variational method

Lensky, Vadim; Birse, Michael C.; Walet, Niels R.

doi:10.1103/physrevc.94.034003

Cited by 18 publications

(17 citation statements)

References 59 publications

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“…Indeed, the rate of convergence in observables provides ample evidence that Q 3 R is much smaller than its a priori estimate, see, e.g., Refs. [12,21,23,[58][59][60][61], and is suggestive that Q 4 R is smaller, too [29,32,46]. There is also circumstantial evidence that this may hold for A > 4 [10].…”

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confidence: 88%

“…At present, no calculation of these effects in Pionless EFT exists, except for Ref. [46], where higher orders were, however, not treated perturbatively. With the uncertainty expected to be dominated by range corrections Oðr s;t =a s;t Þ ≃ 30%, we obtain ðB α Þ NLOðr¼0Þ ¼ 29.5 AE 8.7 MeV with zero effective ranges.…”

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confidence: 99%

“…The absence of an essential four-body parameter has also been verified in the context of potential models with a short range [38][39][40][41] and of renormalization-group analyses [42][43][44]. As a consequence, the 3N LO strength parameter Λ ⋆ , together with the LO two-body interactions, determines the spectrum and scattering for systems with more particles [10,[25][26][27][28][29][30][31][32][33][34]45,46]. This single relevant 3N parameter generates correlations among few-body observables such as the Phillips [47] and Tjon [48] lines.…”

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confidence: 99%

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Nuclear Physics Around the Unitarity Limit

et al. 2017

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We argue that many features of the structure of nuclei emerge from a strictly perturbative expansion around the unitarity limit, where the two-nucleon S waves have bound states at zero energy. In this limit, the gross features of states in the nuclear chart are correlated to only one dimensionful parameter, which is related to the breaking of scale invariance to a discrete scaling symmetry and set by the triton binding energy. Observables are moved to their physical values by small perturbative corrections, much like in descriptions of the fine structure of atomic spectra. We provide evidence in favor of the conjecture that light, and possibly heavier, nuclei are bound weakly enough to be insensitive to the details of the interactions but strongly enough to be insensitive to the exact size of the two-nucleon system. DOI: 10.1103/PhysRevLett.118.202501 For the purposes of nuclear physics, QCD, the theory of strong interactions, has essentially two independent parameters, namely the up and down quark masses. Their average controls the pion mass and consequently, the range of the nuclear force R ∼ M −1 π ≃ 1.4 fm. Their difference, plus electromagnetism, generates small differences in masses and interactions between neutrons and protons. At the physical point, the two-nucleon (NN) scattering length in the 3 S 1 channel is a t ≃ 5.4 fm, with the deuteron as a shallow bound state (B D ≃ 2.224 MeV); in the 1 S 0 channel, a s ≃ −23.7 fm, and a shallow virtual bound state exists at B NN Ã ≃ 0.068 MeV. With relatively small changes in quark masses, these states become, respectively, unbound and bound [1][2][3][4]. In the physics of cold atoms near Feshbach resonances, external magnetic fields play a role similar to the quark masses and allow the scattering length to be tuned arbitrarily [5].Approximate correlations B D;NN Ã ≈ 1=ðM N a 2 t;s Þ, with M N ≃ 940 MeV the nucleon mass, hold because the size of all these scales is unnatural compared to the typical interaction range R. The NN system therefore appears close to the unitarity (or unitary) limit, where both states cross zero energy, the scattering lengths become infinite (1=a t;s ¼ 0), and cross sections saturate the unitarity bound. It has indeed been suggested that this happens not far from the physical point [6]. While this presumed proximity has been discussed qualitatively for a long time, it has traditionally not played any special role in constructing nuclear forces, and it is neither assessed nor exploited in order to simplify the description of nuclei. As an exception, Refs. [7,8] use potential models to map out correlations between observables in three-and fournucleon systems as the limit is approached at fixed a t =a s .Here, we argue that the typical particle binding momentum Q A of the A-nucleon system satisfies 1=a s;t < Q A < 1=R so that a combined expansion in Q A R and 1=ðQ A a s;t Þ converges quickly and quantitatively reproduces the physical systems. With this, the gross features of states in the nuclear chart are determined by a very simple le...

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Nuclear Physics Around the Unitarity Limit

et al. 2017

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“…For A = 4 this result applies also to fermions with four internal states, such as the nucleon. Previous calculations for the 4 He nucleus [49][50][51] could not observe this effect because range corrections were treated nonperturbatively, thereby breaking RG invariance already at the two-body level. It will be interesting to investigate in future work to what extent the enhancement of many-body forces discussed here is modified in nuclear systems with A > 4 due to the Pauli principle.…”

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confidence: 92%

Four-Body Scale in Universal Few-Boson Systems

et al. 2019

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The role of an intrinsic four-body scale in universal few-boson systems is the subject of active debate. We study these systems within the framework of effective field theory. For systems of up to six bosons we establish that no four-body scale appears at leading order (LO). However, we find that at next-to-leading (NLO) order a four-body force is needed to obtain renormalized results for binding energies. With the associated parameter fixed to the binding energy of the four-boson system, this force is shown to renormalize the five-and six-body systems as well. We present an original ansatz for the short-distance limit of the bosonic A-body wave function from which we conjecture that new A-body scales appear at N A−3 LO. As a specific example, calculations are presented for clusters of helium atoms. Our results apply more generally to other few-body systems governed by a large scattering length, such as light nuclei and halo states, the low-energy properties of which are independent of the detailed internal structure of the constituents.

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“…It has become clear that if perturbative renormalization is to be maintained, including electromagnetic effects is not as simple as adding a Coulomb potential to the short-range terms, as it is typically done in calculations based on effective pionless potentials [41][42][43][44]. Based on studying the regulator (cutoff) dependence of the amplitude, it was realized that in the presence of nonperturbative Coulomb effects an isospin breaking three-nucleon force is required to ensure renormalization at next-to-leading order (NLO) [24,45].…”

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Second-order perturbation theory for ${}^{3}\mathrm{He}$ andpdscattering in pionless EFT

König¹

2017

J. Phys. G: Nucl. Part. Phys.

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This work implements pionless effective field theory with the two-nucleon system expanded around the unitarity limit at second-order perturbation theory. The expansion is found to converge well. All Coulomb effects are treated in perturbation theory, including two-photon contributions at next-to-next-to-leading order. After fixing a three-nucleon force to the 3 He binding energy at this order, proton-deuteron scattering in the doublet S-wave channel is calculated for moderate center-of-mass momenta. * koenig.389@osu.edu 1 arXiv:1609.03163v2 [nucl-th]

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Description of light nuclei in pionless effective field theory using the stochastic variational method

Cited by 18 publications

References 59 publications

Nuclear Physics Around the Unitarity Limit

Nuclear Physics Around the Unitarity Limit

Four-Body Scale in Universal Few-Boson Systems

Second-order perturbation theory for ${}^{3}\mathrm{He}$ andpdscattering in pionless EFT

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