Algorithm for calculations of asymptotic nuclear coefficients using phase-shift data for charged-particle scattering

Orlov, Yu. V.; Irgaziev, B. F.; Nabi, Jameel-Un

doi:10.1103/physrevc.96.025809

Cited by 28 publications

(26 citation statements)

References 28 publications

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“…Finally, the analytic decomposition of the irregular Coulomb function G η (x) can be derived from Eq. (40) and the definition (24). Indeed, the decomposition of H − η (x) is obtained by changing the signs of g + (η) and I + η (x) in Eq.…”

Section: B Analytic Structure Of Coulomb Wave Functionsmentioning

confidence: 99%

Effective-range function methods for charged particle collisions

Gaspard

Sparenberg

2018

Phys. Rev. C

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Different versions of the effective-range function method for charged particle collisions are studied and compared. In addition, a novel derivation of the standard effective-range function is presented from the analysis of Coulomb wave functions in the complex plane of the energy. The recently proposed effective-range function denoted as ∆ [Phys. Rev. C 96, 034601 (2017)] and an earlier variant [Hamilton et al., Nucl. Phys. B 60, 443 (1973)] are related to the standard function. The potential interest of ∆ for the study of low-energy cross sections and weakly bound states is discussed in the framework of the proton-proton 1 S0 collision. The resonant state of the protonproton collision is successfully computed from the extrapolation of ∆ instead of the standard function. It is shown that interpolating ∆ can lead to useful extrapolation to negative energies, provided scattering data are known below one nuclear Rydberg energy (12.5 keV for the protonproton system). This property is due to the connection between ∆ and the effective-range function by Hamilton et al. that is discussed in detail. Nevertheless, such extrapolations to negative energies should be used with caution because ∆ is not analytic at zero energy. The expected analytic properties of the main functions are verified in the complex energy plane by graphical color-based representations.

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Section: B Analytic Structure Of Coulomb Wave Functionsmentioning

confidence: 99%

Effective-range function methods for charged particle collisions

Gaspard

Sparenberg

2018

Phys. Rev. C

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“…Furthermore, the real value of C 2 presented in Ref. [11] is also erroneous. This is due to the improper manipulation with the absolute value sign for the residue off 0 .…”

Section: Version 1 Approximation Of the Functionmentioning

confidence: 99%

“…In Ref. [11] the excited state was taken into account, however, the approximated analytic form of ∆ 0 (E) used by the authors ignored the existence of the pole of ∆ 0 (E) at E < 0. This fact is the reason for the wrong sign of the residue of the partial-wave scattering amplitudef 0 at the pole corresponding to the ground state.…”

Section: Version 1 Approximation Of the Functionmentioning

confidence: 99%

“…Note that the attempts to determine C 2 by extrapolating the function K 0 (E) or ∆ 0 (E) from the positive to the negative energy region were made in Refs. [11,19]. In these papers, the parameters of the analytic approximation of K 0 (E) and ∆ 0 (E) were fitted to the results of the phase-shift analysis of the elastic α− 12 C scattering at low energies.…”

Section: Version 1 Approximation Of the Functionmentioning

confidence: 99%

“…[9] can be smoothly continued from the positive to the negative energy region along the real E axis (see also Ref. [11]). In what follows, using the ∆ l (E) function for extrapolation to the negative-energy region to find the ANC is referred to as a ∆-method.…”

Section: Introductionmentioning

confidence: 99%

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Extrapolation of scattering data to the negative-energy region. II. Applicability of effective range functions within an exactly solvable model

et al. 2018

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A problem of analytical continuation of scattering data to the negative-energy region to obtain information about bound states is discussed within an exactly solvable potential model. This work is continuation of the previous one by the same authors [L. D. Blokhintsev et al., Phys. Rev. C 95, 044618 (2017)]. The goal of this paper is to determine the most effective way of analytic continuation for different systems. The d+α and α+ 12 C systems are considered and, for comparison, an effective-range function approach and a recently suggested ∆-method [O. L. Ramírez Suárez and J.-M. Sparenberg, Phys. Rev. C 96, 034601 (2017)] are applied. We conclude that the ∆-method is more effective for heavier systems with large values of the Coulomb parameter, whereas for light systems with small values of the Coulomb parameter the effective-range function method might be preferable.

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Elastic $$\alpha $$-$$^{12}$$C Scattering at Low Energies with the Bound States of $$^{16}$$O in EFT

Ando

2020

Recent Progress in Few-Body Physics

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The elastic α-12 C scattering for l = 0, 1, 2, 3 channels at low energies is studied, including the energies of excited bound states of 16 O, in effective field theory. We introduce a new renormalization method due to the large suppression factor produced by the Coulomb interaction when fitting the effective range parameters to the phase sift data. After fitting the parameters, we calculate asymptotic normalization constants of the 0 + 2 , 1 − 1 , 2 + 1 , 3 − 1 states of 16 O. We also discuss the uncertainties of the present study when the amplitudes are interpolated to the stellar energy region of the 12 C(α,γ) 16 O reaction.

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Algorithm for calculations of asymptotic nuclear coefficients using phase-shift data for charged-particle scattering

Cited by 28 publications

References 28 publications

Effective-range function methods for charged particle collisions

Effective-range function methods for charged particle collisions

Extrapolation of scattering data to the negative-energy region. II. Applicability of effective range functions within an exactly solvable model

Elastic $$\alpha $$-$$^{12}$$C Scattering at Low Energies with the Bound States of $$^{16}$$O in EFT

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