9 Be Low-Lying Spectrum Within a Three-Cluster Model

Filikhin, I.; Suslov, V. M.; Vlahović, Branislav

doi:10.1007/s00601-010-0135-3

Cited by 11 publications

(7 citation statements)

References 17 publications

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“…This new αn potential was proposed in Ref. [10]. The parameters of the potential were obtained by modification of the potential given in Ref.…”

Section: Modelmentioning

confidence: 99%

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Modeling of 6ΛHe hypernucleus within configuration space Faddeev approach

Filikhin¹,

Suslov²,

Vlahović³

2014

Math. Model. Geom.

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The cluster 4 He + Λ + n model is applied to describe the 6 Λ He hypernucleus. The consideration is based on the configuration space Faddeev equations for a system of non-identical particles. A set of the pair potentials includes the OBE simulating (NSC97f) model for the Λn interaction and the phenomenological potentials for the αΛ and αn interactions. We calculated energies of spin (1 − ,2 − ) doublet. For the 2 − excitation energy, the obtained value is 0.18 MeV. The hyperon binding energy of the bound 1 − state is less than the experimental value, which may be an evidence for violation of the exact three-body cluster structure.

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“…This new αn potential was proposed in Ref. [10]. The parameters of the potential were obtained by modification of the potential given in Ref.…”

Section: Modelmentioning

confidence: 99%

“…We use the potentials proposed for the αn and Λn interactions in Refs. [10,11] to evaluate energies of the (1 − , 2 − ) spin doublet. The model does not include the ΛN-ΣN coupling that may be strong, as it was indicated in [12].…”

Section: Introductionmentioning

confidence: 99%

Modeling of 6ΛHe hypernucleus within configuration space Faddeev approach

Filikhin¹,

Suslov²,

Vlahović³

2014

Math. Model. Geom.

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“…We have found a broad resonance in the channel Λ + n + n. The results of the calculations are presented in figure 1a). The method of analytical continuation in the coupling constant is used to calculate the parameters of the resonance [6]. The coupling constant is the coefficient γ which scales triplet component of the ΛN potential.…”

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confidence: 99%

Λnnbound state with three-body potential

Filikhin

Suslov

Vlahović

2016

EPJ Web of Conferences

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Abstract. Formalism of the configuration-space Faddeev equations is applied to analyze the bound state problem of ΛNN system. The simulated NSC97f potential for ΛN interaction and semi-realistic NN potentials are used for calculations. We predict a broad Λnn resonance near threshold. A spin dependent three-body ΛNN potential has been proposed to explain experimental evidence for 3 Λ n bound state. The potential is defined by a Gaussian function of a hyper-radius. It was found that such potential with appropriate spin dependence does not support a bound state of 3 Λ n. A short range form of the potential generates non-physical solutions of the Faddeev equations.The HypHI Collaboration has recently reported evidence for a bound state of Λ + n + n system [1]. However, the bound 3 Λ n state has not been found under theoretical analysis (see for instance [2]). In the present work we construct a phenomenological three-body ΛNN potential with spin dependence that forms a bound state in the channel Λ + n + n (T =1, S =1/2). Such potential does not affect the ground state energy of 3 Λ H hypernucleus fixed by the experimental value of 0.13(5) MeV for the hyperon separation (or binding) energy Formalism of the configuration-space Faddeev equations was applied for Λ + n + n and Λ + n + p systems within an s-wave approach. The simulated NSC97f potential [3] for ΛN interaction and MT-I-III semi-realistic NN potential [4] were used for calculations. This model reproduces well the hyperon binding energy for 3 Λ H, with the value of 0.14 MeV (see also Ref.[5]). We have found a broad resonance in the channel Λ + n + n. The results of the calculations are presented in figure 1a). The method of analytical continuation in the coupling constant is used to calculate the parameters of the resonance [6]. The coupling constant is the coefficient γ which scales triplet component of the ΛN potential. The complex value of the Pade approximant calculated by set of negative energies (circles in figure 1a) for γ=1 gives the energy and width of resonance: E(γ = 1) = E r − i Γ 2 . Our result for the energy of the resonance is 0.2 MeV, that agrees with [7]. Within the presented model, the three-body ΛNN potential is treated as a perturbation of the Hamiltonian. It is defined as one range Gaussian: V 3b f (ρ) = −δ exp(−αρ 2 )S (s Λ , s NN ), where ρ is the hyper-radius: ρ 2 = x 2 + y 2 , with x, y the mass scaled Jacobi coordinates. The function S (s Λ , s NN ) depends on the spin variables of a hyperon (s Λ ) and NN pair (s NN ). Two free parameters δ and α have to be adjusted. We assume the ratio S (1/2, 1)/S (1/2, 0) to be equal 1 or 1/3 [2]. The calculations for α=0.1 fm −2 are shown in figure 1b). The three-body ΛNN potential resulted in a bound state of 3 Λ n generates Λnp over-bound states for S =1/2 and 3/2. The spin dependence, which provides a bound state of 3 Λ n and keeps the 3 Λ H ground state energy, cannot be considered as realistic. It was found that the short range form (when α>0.1 fm −2 ) of the potential generates non-physical ...

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“…A variant of this method with an additional nonphysical three-body potential is employed. The strength parameter of this potential is considered as a variational parameter (coupling constant) for the analytical continuation of the bound state energy into the complex plane [14]. The structure of the 6 Λ He spectrum is studied within the three-body…”

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confidence: 99%

“…The set of potentials for the models includes the simulated NSC97f potential [12] for ΛN interaction, the TH αΛ potential taken from [13] and αn potential proposed in Ref. [14]. For nucleon-nucleon interaction we used the Malfliet-Tjon potential (MT-I-III) corrected by Friar et al [15].…”

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confidence: 99%