Second-order perturbation theory for ${}^{3}\mathrm{He}$ and<i>pd</i>scattering in pionless EFT

König, S.

doi:10.1088/1361-6471/aa60d6

Cited by 22 publications

(24 citation statements)

References 90 publications

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“…We remove the arbitrary Λ dependence from observables by demanding that the two inverse scattering lengths vanish at LO and enter linearly at NLO. Renormalization is achieved if [54].…”

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confidence: 99%

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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“…We remove the arbitrary Λ dependence from observables by demanding that the two inverse scattering lengths vanish at LO and enter linearly at NLO. Renormalization is achieved if [54].…”

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confidence: 99%

Nuclear Physics Around the Unitarity Limit

et al. 2017

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“…(12). The corrections t (n) i for n > 0 can conveniently be obtained by solving similar integral equations [26,24]. For the unitarity expansion, corrections from the finite scattering length enter at NLO via C (1) 0,i , yielding a separable potential V (1) 2,i with the same form as Eq.…”

Section: Effective Field Theory For Systems Near Unitaritymentioning

confidence: 99%

“…which, just like the LO equation, can be solved algebraically (see Ref. [24] for explicit details). From this procedure one obtains…”

Section: Effective Field Theory For Systems Near Unitaritymentioning

confidence: 99%

“…For example, second-order corrections to binding energies can be obtained in a way that is numerically much simpler than the procedure used in Ref. [24] to extract such second-order shifts from off-shell T -matrix corrections. An abstract operator notation is used throughout this section, and conventions for sub-and superscripts differ from the usage in the main text in order to simplify the notation.…”

Section: B Perturbative Expansion Of Few-body Bound Statesmentioning

confidence: 99%

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Energies and radii of light nuclei around unitarity

König

2020

Eur. Phys. J. A

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Light nuclei fall within a regime of universal physics governed by the fact that the two-nucleon scattering lengths are large compared to the typical nuclear interaction range set by one-pion exchange. This places nuclear physics near the so-called unitarity limit in which the scattering lengths are exactly infinite. Effective field theory provides a powerful theoretical framework to capture this separation of scales in a systematic way. It is shown here that the nuclear force can be constructed as a perturbative expansion around the unitarity limit and that this expansion has good convergence properties for both the binding energies of A = 3, 4 nuclei as well as for the radii of these states.

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“…The Breit-Wigner resonances were incorporated accurately to the optical amplitude to obtain a fair agreement for the 10.5 MeV proton-oxygen scattering data [1]. More reliable theoretical and experimental data [7][8][9][10][11][12][13][14][15][16] at various energies are available with regard to the protondeuteron (p-2 H 1 ) elastic scattering to explain different off-shell behaviours in realistic potential models of two-nucleon systems. In general, the nucleon-nucleon interactions are described in a phenomenological way to fit the observed scattering data.…”

Section: Introductionmentioning

confidence: 99%

On the $$\text{p}{-}^{{2}}\text{H}_{{1}} $$ and $$\text{p}{-}^{{16}}\text{O}\,$$ elastic scattering

2021

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We solve the wave equation with the Manning-Rosen plus rank one separable non-local potential to obtain exact analytical solutions through ordinary differential equation method. The regular, Jost and physical state solutions are found to involve special functions of mathematics. As an application of the Jost function and Fredholm determinant, the bound-state energies and the scattering phase parameters for the p− 2 H 1 and p− 16 O systems are computed. The results achieved are in good agreement with the other methods published earlier.

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

Cited by 22 publications

References 90 publications

Nuclear Physics Around the Unitarity Limit

Nuclear Physics Around the Unitarity Limit

Energies and radii of light nuclei around unitarity

On the $$\text{p}{-}^{{2}}\text{H}_{{1}} $$ and $$\text{p}{-}^{{16}}\text{O}\,$$ elastic scattering

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