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Register a new userThe $alpha-alpha$ fishbone potential revisited
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The fishbone potential of composite particles simulates the Pauli effect by nonlocal terms. We determine the $alpha-alpha$ fishbone potential by simultaneously fitting to two-$alpha$ resonance energies, experimental phase shifts and three-$alpha$ binding energies. We found that essentially a simple gaussian can provide a good description of two-$alpha$ and three-$alpha$ experimental data without invoking three-body potentials.
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The fishbone potential of composite particles simulates the Pauli effect by nonlocal terms. We determine the $n-alpha$ and $p-alpha$ fish-bone potential by simultaneously fitting to the experimental phase shifts. We found that with a double Gaussian parametrization of the local potential can describe the $n-alpha$ and $p-alpha$ phase shifts for all partial waves.
Two body data alone cannot determine the potential uniquely, one needs three-body data as well. A method is presented here which simultaneously fits local or nonlocal potentials to two-body and three-body observables. The interaction of composite particles, due to the Pauli effect and the indistinguishability of the constituent particles, is genuinely nonlocal. As an example, we use a Pauli-correct nonlocal fish-bone type optical model for the $alpha-alpha$ potential and derive the fitting parameters such that it reproduces the two-$alpha$ and three-$alpha$ experimental data.
We carry out Faddeev calculations of three-alpha (3 alpha) and two-alpha plus Lambda (alpha alpha Lambda) systems, using two-cluster resonating-group method kernels. The input includes an effective two-nucleon force for the alpha alpha resonating-group method and a new effective Lambda N force for the Lambda alpha interaction. The latter force is a simple two-range Gaussian potential for each spin-singlet and triplet state, generated from the phase-shift behavior of the quark-model hyperon-nucleon interaction, fss2, by using an inversion method based on supersymmetric quantum mechanics. Owing to the exact treatment of the Pauli-forbidden states between the clusters, the present three-cluster Faddeev formalism can describe the mutually related, alpha alpha, 3 alpha and alpha alpha Lambda systems, in terms of a unique set of the baryon-baryon interactions. For the three-range Minnesota force which describes the alpha alpha phase shifts quite accurately, the ground-state and excitation energies of 9Be Lambda are reproduced within 100 - 200 keV accuracy.
Cross sections of $^{120}$Sn($alpha$,$alpha$)$^{120}$Sn elastic scattering have been extracted from the $alpha$ particle beam contamination of a recent $^{120}$Sn($^6$He,$^6$He)$^{120}$Sn experiment. Both reactions are analyzed using systematic double folding potentials in the real part and smoothly varying Woods-Saxon potentials in the imaginary part. The potential extracted from the $^{120}$Sn($^6$He,$^6$He)$^{120}$Sn data may be used as the basis for the construction of a simple global $^6$He optical potential. The comparison of the $^6$He and $alpha$ data shows that the halo nature of the $^6$He nucleus leads to a clear signature in the reflexion coefficients $eta_L$: the relevant angular momenta $L$ with $eta_L gg 0$ and $eta_L ll 1$ are shifted to larger $L$ with a broader distribution. This signature is not present in the $alpha$ scattering data and can thus be used as a new criterion for the definition of a halo nucleus.
We calculate Lambda alpha, Sigma alpha and Xi alpha potentials from the nuclear-matter G-matrices of the SU6 quark-model baryon-baryon interaction. The alpha-cluster wave function is assumed to be a simple harmonic-oscillator shell-model wave function. A new method is proposed to derive the direct and knock-on terms of the interaction Born kernel from the hyperon-nucleon G-matrices, with explicit treatments of the nonlocality and the center-of-mass motion between the hyperon and alpha. We find that the SU6 quark-model baryon-baryon interactions, FSS and fss2, yield a reasonable bound-state energy for 5 He Lambda, -3.18 -- -3.62 MeV, in spite of the fact that they give relatively large depths for the Lambda single-particle potentials, 46 -- 48 MeV, in symmetric nuclear matter. An equivalent local potential derived from the Wigner transform of the nonlocal Lambda alpha kernel shows a strong energy dependence for the incident Lambda-particle, indicating the importance of the strangeness-exchange process in the original hyperon-nucleon interaction. The Sigma alpha and Xi alpha potentials are repulsive with the attractive isospin I=1/2 (Sigma alpha) and I=0 (Xi alpha) components and the repulsive I=3/2 (Sigma alpha) and I=1 (Xi alpha) components.
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