<i>Ab initio</i>
 translationally invariant nonlocal one-body densities from no-core shell-model theory

Burrows, M.; Elster, Ch.; Popa, Gabriela; Launey, Kristina D.; Nogga, A.; Maris, Pieter

doi:10.1103/physrevc.97.024325

Cited by 25 publications

(35 citation statements)

References 43 publications

(103 reference statements)

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“…The task is then to find suitable approximations and solutions of Eqs. (77) and (78). The effective interaction can be obtained from the free T -matrix by correcting the propagator for the binding associated with the nucleon that the projectile interacts with as well as allowing for its possible mean-field corrections.…”

Section: Alternative Derivation Linking the Nucleon Self-energy To Thmentioning

confidence: 99%

“…[77] for unstable He isotopes). Recent developments focus on generating translation-invariant one-body density matrices obtained from no-core shell-model calculations [78]. This procedure has the advantage that the one-body density matrix can be generated from the same underlying NN interaction that is employed to calculate the T -matrix.…”

Section: Some Applications Of the Multiple-scattering Approachmentioning

confidence: 99%

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Recent developments for the optical model of nuclei

Dickhoff¹,

Charity²

2019

Progress in Particle and Nuclear Physics

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A brief overview of various approaches to the optical-model description of nuclei is presented. A survey of some of the formal aspects is given which links the Feshbach formulation for either the hole or particle Green's function to the time-ordered quantity of many-body theory. The link between the reducible self-energy and the elastic nucleon-nucleus scattering amplitude is also presented using the development of Villars. A brief summary of the essential elements of the multiple-scattering approach is also included. Several ingredients contained in the time-ordered Green's function are summarized for the formal framework of the dispersive optical model (DOM). Empirical approaches to the optical potential are reviewed with emphasis on the latest global parametrizations for nucleons and composites. Various calculations that start from an underlying realistic nucleon-nucleon interaction are discussed with emphasis on more recent work. The efficacy of the DOM is illustrated in relating nuclear structure and nuclear reaction information. Its use as an intermediate between experimental data and theoretical calculations is advocated. Applications of the use of optical models are pointed out in the context of the description of nuclear reactions other than elastic nucleon-nucleus scattering. arXiv:1811.03111v1 [nucl-th] 7 Nov 2018The number of works that are encompassed by the title of "optical model" is immense and any review must be selective. The topics and studies present in this review are biased by the interests of the authors. We start with several theoretical derivations of the optical potential and its connection to the self-energy in many-body formulations in Sec. 2. In Sec. 2.1 the analysis of Capuzzi and Mahaux [6] will be employed to link the Feshbach approach to the many-body perspective provided by the time-ordered Green's function. We complement this in Sec. 2.2 with a derivation by Villars [7] that formalizes the work of Ref.[8] that demonstrates the equivalence of the nucleon-nucleus T -matrix to the on-shell reducible nucleon self-energy Σ red associated with the time-ordered Green's function. This approach is important as it can be extended to the description of more complicated reactions involving composite projectiles or ejectiles. In Sec. 2.3 we briefly summarize some elements of the multiple-scattering approach but refrain from a detailed presentation which is available in Ref. [9]. We will take particular interest in the empirical dispersive optical model (DOM) where the real and imaginary potentials are connected by dispersion relations thereby enforcing causality. This approach allows one to exploit the formal properties of the time-ordered Green's function including its link to the nucleon self-energy through the Dyson equation [10,11]. As the dispersion relations require the optical potentials to be defined at both positive and negative energy, the formalism makes connections between nuclear reactions and nuclear structure needed for a better understanding of rare isotopes. Some ingredients...

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Section: Alternative Derivation Linking the Nucleon Self-energy To Thmentioning

confidence: 99%

Section: Some Applications Of the Multiple-scattering Approachmentioning

confidence: 99%

Recent developments for the optical model of nuclei

Dickhoff¹,

Charity²

2019

Progress in Particle and Nuclear Physics

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“…The nonlocal densities are created translationally invariant as laid out in Ref. [47]. Recoil and frame transformation factors are implemented in the calculation of the scattering observables in their complete form.…”

Section: Discussionmentioning

confidence: 99%

“…The procedure for computing this quantity from ab initio NCSM calculations has been described in detail in Ref. [47], and the derivation will not be repeated here. The convolution of the nonlocal OBD with the fully off-shell NN tmatrix and the Møller frame transformation factor is carried out in momentum space in three dimensions without partial wave decomposition, and the integration is performed using Monte Carlo integration techniques.…”

Section: The First-order Folding Potentialmentioning

confidence: 99%

“…After computing the first-order folding potential using as input a nonlocal translationally invariant OBD based on the NNLO opt chiral potential [44] obtained as outlined in Ref. [47] and the Wolfenstein amplitudes A and C based on the same interaction, we compute total, reaction, and differential cross sections for elastic scattering as well as the analyzing power A y and the spin-rotation parameter Q. Our choice of energies for which we show observables is dictated by the availability of experimental data, and we concentrate on the energy regime between 100 and 200 MeV projectile laboratory kinetic energy since we expect that the first-order term governs the scattering process at those energies.…”

Section: A Elastic Scattering Observables For 4 He and 16 Omentioning

confidence: 99%

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Ab initio folding potentials for nucleon-nucleus scattering based on no-core shell-model one-body densities

et al. 2019

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Background: Calculating microscopic optical potentials for elastic nucleon-nucleus scattering has already led to large body of work in the past. For folding first-order calculations the nucleon-nucleon (NN) interaction and the one-body density of the nucleus were taken as input to rigorous calculations in a spectator expansion of the multiple scattering series.Purpose: Based on the Watson expansion of the multiple scattering series we employ a nonlocal translationally invariant nuclear density derived from a chiral next-to-next-to-leading order (NNLO) and the very same interaction for consistent full-folding calculation of the effective (optical) potential for nucleon-nucleus scattering for light nuclei.Methods: The first order effective (optical) folding potential is computed by integrating over the nonlocal, translationally invariant NCSM one-body density and the off-shell Wolfenstein amplitudes A and C. The resulting nonlocal potential serves as input for a momentum-space Lippmann-Schwinger equation, whose solutions are summed to obtain the nucleon-nucleus scattering observables. Results:We calculate scattering observables, such as total, reaction, and differential cross sections as well as the analyzing power and the spin-rotation parameter, for elastic scattering of protons and neutrons from 4 He, 6 He, 12 C, and 16 O, in the energy regime between 100 and 200 MeV projectile kinetic energy, and compare to available data.Conclusions: Our calculations show that the effective nucleon-nucleus potential obtained from the first-order term in the spectator expansion of the multiple scattering expansion describes experiments very well to about 60 degrees in the center-of-mass frame, which coincides roughly with the validity of the NNLO chiral interaction used to calculate both the NN amplitudes and the one-body nuclear density.

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