Application of the hyperspherical formalism to the trinucleon bound state problems

Ballot, J. L.; Ripelle, M. Fabre de la

doi:10.1016/0003-4916(80)90150-5

Cited by 297 publications

(148 citation statements)

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“…The hyperspherical harmonic expansion method (HHEM) is a convenient tool in many-body physics [23], where the expansion basis of the many-body wave function is the hyperspherical harmonics (HH). As the HH basis contains all possible correlations, its direct application to trapped bosons in the condensate which contains at least a few thousand bosons is an impossible task.…”

Section: N) and The Center Of Mass Throughmentioning

confidence: 99%

“…. , ζ N−1 and (N − 2) angles defining the relative lengths of these Jacobi vectors [23]. Then the Laplacian in 3N -dimensional space has the form…”

Section: N) and The Center Of Mass Throughmentioning

confidence: 99%

“…. , ζ N−1 } Jacobi vectors [23]. Thus the contribution to the grand orbital quantum number comes only from the interacting pair and the 3N -dimensional Schrödinger equation reduces effectively to a four-dimensional equation.…”

Section: N) and The Center Of Mass Throughmentioning

confidence: 99%

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Energy-level statistics of interacting trapped bosons

et al. 2012

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It is a well-established fact that statistical properties of energy-level spectra are the most efficient tool to characterize nonintegrable quantum systems. The statistical behavior of different systems such as complex atoms, atomic nuclei, two-dimensional Hamiltonians, quantum billiards, and noninteracting many bosons has been studied. The study of statistical properties and spectral fluctuations in interacting many-boson systems has developed interest in this direction. We are especially interested in weakly interacting trapped bosons in the context of Bose-Einstein condensation (BEC) as the energy spectrum shows a transition from a collective nature to a single-particle nature with an increase in the number of levels. However this has received less attention as it is believed that the system may exhibit Poisson-like fluctuations due to the existence of an external harmonic trap. Here we compute numerically the energy levels of the zero-temperature many-boson systems which are weakly interacting through the van der Waals potential and are confined in the three-dimensional harmonic potential. We study the nearest-neighbor spacing distribution and the spectral rigidity by unfolding the spectrum. It is found that an increase in the number of energy levels for repulsive BEC induces a transition from a Wigner-like form displaying level repulsion to the Poisson distribution for P (s). It does not follow the Gaussian orthogonal ensemble prediction. For repulsive interaction, the lower levels are correlated and manifest level-repulsion. For intermediate levels P (s) shows mixed statistics, which clearly signifies the existence of two energy scales: external trap and interatomic interaction, whereas for very high levels the trapping potential dominates, generating a Poisson distribution. Comparison with mean-field results for lower levels are also presented. For attractive BEC near the critical point we observe the Shnirelman-like peak near s = 0, which signifies the presence of a large number of quasidegenerate states.

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Section: N) and The Center Of Mass Throughmentioning

confidence: 99%

“…. , ζ N−1 and (N − 2) angles defining the relative lengths of these Jacobi vectors [23]. Then the Laplacian in 3N -dimensional space has the form…”

Section: N) and The Center Of Mass Throughmentioning

confidence: 99%

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Energy-level statistics of interacting trapped bosons

et al. 2012

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“…It was found that the -N potentials are the most effective part in the hypertriton binding energy as well as the separation energy B  where the -N potentials are very effective to bound or unbound the  3 H hyper nucleus. The Fabre optimal subset [27]- [29] is adopted to obtain fast and good convergence for the calculated binding energy using the renormalized Numerov method. [30], [31].…”

Section: Introductionmentioning

confidence: 99%

“…Further, the centrifugal barrier terms occurring in the set of coupled equations grow considerably with higher harmonics. One can therefore, truncate this infinite set [27]- [29] and work with a finite set (Fabre optimal subset ) of coupled differential equations or a corresponding one dimensional integral equation. The (HH) method is essentially an exact one and more reliable than other methods.…”

Section: Introductionmentioning

confidence: 99%