Effective-range function for doublet nd scattering from an analysis of modern data

Orlov, Yu. V.; Nikitina, L. I.

doi:10.1134/s1063778806040077

Cited by 6 publications

(13 citation statements)

References 28 publications

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“…The results for 3 He agree with the conclusion in [18,19,35] concerning the convergence domain of expansion (2) limited by the energies |E cm | ≤ 0.74 MeV. This domain is determined by the position of the nearby singularity of the partial wave amplitude for the pd scattering at the energy E cm = −ǫ d /3 (ǫ d is the deuteron binding energy) corresponding to the Feynman diagram for the one-nucleon exchange.…”

Section: Vertex Constants For Particular Nucleisupporting

confidence: 92%

“…It can be described by the exponentially increasing function at ξ → 1 or as a function with a pole at ξ > 1. It should be stressed here that the relation (35) is by no means universal. Obviously, this is not valid for the system in which the effective-range function has a pole close to the scattering channel threshold.…”

Section: Subthreshold Resonance Of the Pd Systemmentioning

confidence: 94%

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Effect of Coulomb forces on the position of the pole in the scattering amplitude and on its residue

2010

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Explicit expressions of the vertex constant for the decay of a nucleus into two charged particles for an arbitrary orbital momentum l are derived for the standard expansion of the effective-range function K l (k 2 ), as well as when the function K0(k 2 ) has a pole. As physical examples, we consider the bound state of the nucleus 3 He and the resonant states of the nuclei 2 He and 3 He in the s-wave, and those of 5 He and 5 Li in the p-wave. For the systems N p and N d the pole trajectories are constructed in the complex planes of the momentum and of the renormalized vertex constant. They correspond to a transition from the resonance state to the virtual state while the Coulomb forces gradually decrease to zero.

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Section: Vertex Constants For Particular Nucleisupporting

confidence: 92%

Section: Subthreshold Resonance Of the Pd Systemmentioning

confidence: 94%

Effect of Coulomb forces on the position of the pole in the scattering amplitude and on its residue

2010

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“…This function crosses the physical point at r 0 /a B = 0.457, from which the triton virtual state E p = 0.48 MeV can be extracted. The Gaussian characterization explains this value in agreement with experimental determinations and theoretical investigations (50,61,(89)(90)(91)(92).…”

Section: The Three-nucleon Systemsupporting

confidence: 88%

Efimov Physics and Connections to Nuclear Physics

Kievsky

Gattobigio

Girlanda

et al. 2021

Annu. Rev. Nucl. Part. Sci.

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Physical systems characterized by a shallow two-body bound or virtual state are governed at large distances by continuous scale invariance, which is broken into discrete scale invariance when three or more particles come into play. This symmetry induces a universal behavior for different systems that is independent of the details of the underlying interaction and rooted in the smallness of the ratio ℓ[Formula: see text] a B ≪ 1, where the length a B is associated with the binding energy of the two-body system [Formula: see text], and ℓ is the natural length given by the interaction range. Efimov physics refers to this universal behavior, which is often hidden by the onset of system-specific nonuniversal effects. In this review, we identify universal properties by providing an explicit link of physical systems to their unitary limit, in which a B → ∞, and we show that nuclear systems belong to this class of universality. Expected final online publication date for the Annual Review of Nuclear and Particle Science, Volume 71 is September 2021. Please see http://www.annualreviews.org/page/journal/pubdates for revised estimates.

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“…For the pole of the effective-range function K(k 2 ) and the residue at this pole, we find in accordance with (18) and (19) that…”

Section: Results Of Numerical Calculationssupporting

confidence: 89%

“…It can easily be shown that, apart from the form of the presentation, the pole expression (13) coincides with the empirical van Oers-Seagrave formula (5). It is worth noting that various forms of the pole structure of the effective-range function K(k 2 ) have long since been repeatedly discussed and used to describe the neutron-deuteron system [2][3][4][5][8][9][10][11][12][13][14][15][16][17][18] and two-nucleon systems [19][20][21][22][23][24][25].…”

Section: Pole Approximation Of the Effective-range Function K Cot δmentioning

confidence: 99%

10.1007/s11450-008-1005-z

2010

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On the basis of the Bargmann representation of the S matrix, the pole approximation is obtained for the effective-range function k cot δ. This approximation is optimal for describing the neutrondeuteron system in the doublet spin state. The values of r 0 = 412.469 fm and v 2 = −35 495.62 fm 3 for the doublet low-energy parameters of neutron-deuteron scattering and the value of D = 172.678 fm 2 for the respective pole parameter are deduced by using experimental results for the triton binding energy E T , the doublet neutron-deuteron scattering length a 2 , and van Oers-Seagrave phase shifts at energies below the deuteron-breakup threshold. With these parameters, the pole approximation of the effective-range function provides a highly precise description (the relative error does not exceed 1%) of the doublet phase shift for neutron-deuteron scattering at energies below the deuteron-breakup threshold. Physical properties of the triton in the ground (T ) and virtual (v) states are calculated. The results are B v = 0.608 MeV for the virtuallevel position and C 2 T = 2.866 and C 2 v = 0.0586 for the dimensionless asymptotic normalization constants. It is shown that, in the Whiting-Fuda approximation, the values of physical quantities characterizing the triton virtual state are determined to a high precision by one parameter, the doublet neutron-deuteron scattering length a 2 . The effective triton radii in the ground (ρ T = 1.711 fm) and virtual (ρ v = 74.184 fm) states are calculated for the first time.

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Effective-range function for doublet nd scattering from an analysis of modern data

Cited by 6 publications

References 28 publications

Effect of Coulomb forces on the position of the pole in the scattering amplitude and on its residue

Effect of Coulomb forces on the position of the pole in the scattering amplitude and on its residue

Efimov Physics and Connections to Nuclear Physics

10.1007/s11450-008-1005-z

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