Green function and scattering amplitudes in many-dimensional space

Fabre de la Ripelle, M.

doi:10.1007/bf01344365

Cited by 19 publications

(20 citation statements)

References 30 publications

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“…Thus, the partial orbital momenta l 1 = l 2 = 0, and the total orbital momentum L = 0. The asymptotic part of the single-channel wave function in the hyperspherical harmonic formalism [49,50] is…”

Section: Wave Functions Of Resonance Statesmentioning

confidence: 99%

Formation and decay of resonance states in Be9 and B9 nuclei: Microscopic three-cluster model investigations

2017

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We study the nature of the low-lying resonance states in mirror nuclei 9 Be and 9 B. Investigations are performed within a three-cluster model. The model makes use of the hyperspherical harmonics, which provides a convenient description of the three-cluster continuum. The dominant three-cluster configurations α + α + n and α + α + p in 9 Be and 9 B, respectively, are taken into account. Dominant decay channels for all resonance states in 9 Be and 9 B are explored. Much attention is paid to the controversial 1/2 + resonance states in both nuclei. We study effects of the Coulomb interaction on the energy and width of three-cluster resonances in the mirror nuclei 9 Be and 9 B. We also search for the Hoyle-analog state, which is a key step for alternative ways to synthesize 9 Be and 9 B in triple collisions of clusters in a stellar environment.

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Section: Wave Functions Of Resonance Statesmentioning

confidence: 99%

Formation and decay of resonance states in Be9 and B9 nuclei: Microscopic three-cluster model investigations

2017

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“…The assumption that antisymmetrization effects between clusters are absent in the asymtptotic region is a natural one. The relative motion problem of the three clusters in the absence of a potential can then be explicitly solved in the Hyperspherical Harmonics (HH) method (see for instance [21][22][23]). It involves the transformation of the Jacobi coordinates q 1 and q 2 to the hyperradius ρ and a set of hyperangles Ω.…”

Section: A Asymptotic Solutions In Coordinate Representationmentioning

confidence: 99%

Algebraic model for scattering in three-s-cluster systems. I. Theoretical background

et al. 2001

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A framework to calculate two-particle matrix elements for fully antisymmetrized three-cluster configurations is presented. The theory is developed for a scattering situation described in terms of the Algebraic Model. This means that the nuclear many-particle state and its asymptotic behaviour are expanded in terms of oscillator states of the intra-cluster coordinates. The Generating Function technique is used to optimize the calculation of matrix elements. In order to derive the dynamical equations, a multichannel version of the Algebraic Model is presented.

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“…Mass operators of the form (2.7) satisfy all symmetry requirements and are easily diagonalized by means of hyper-spherical harmonics. [4] It is convenient to express the magnitudes r and ρ as functions of the radius R and the auxiliary variable z,…”

Section: The Confining Mass Operatormentioning

confidence: 99%

“…The mass operators considered are sums of a confining term, which depends only on the Jacobi coordinates of the 3-quark system, and a flavor and spin dependent hyperfine correction. The former provides the basic shell structure of the spectrum and is readily diagonalized by means of hyper-spherical harmonics [4]. The latter is built on the observation that a superior description of the baryon spectrum in all flavor generations may be achieved by assuming that the main hyperfine correction should have the flavor-spin structure -i<j λ i · λ j σ i · σ j , which e.g.…”

Section: Introductionmentioning

confidence: 99%

Covariant quark model for the baryons

Coester¹,

Dannbom²,

Riska³

1998

Nuclear Physics A

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A family of simply solvable covariant quark models for the baryons is presented. With optimal parameter choices the models reproduce the empirical spectra of the baryons in all flavor sectors to an accuracy of a few percent. Complete spectra are obtained for all states of the strange, charm and beauty hyperons with L ≤ 2. The magnetic moments and axial coupling constants of the ground state baryons correspond to those of conventional quark models. We construct current-density operators that are consistent with empirical nucleon form factors at low and medium energies. 0

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Green function and scattering amplitudes in many-dimensional space

Cited by 19 publications

References 30 publications

Formation and decay of resonance states in Be9 and B9 nuclei: Microscopic three-cluster model investigations

Formation and decay of resonance states in Be9 and B9 nuclei: Microscopic three-cluster model investigations

Algebraic model for scattering in three-s-cluster systems. I. Theoretical background

Covariant quark model for the baryons

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