Faddeev-Yakubovsky Calculation of 4-Alpha Particle System with Realistic Alpha-Alpha Interactions

Abstract

The low-lying energy levels of ¹²C and ¹⁶O nuclei are calculated by using the Faddeev and Yakubovsky equations based on the 3- and 4-alpha models, respectively. We used two off-shell different alpha-alpha potentials which represent the Pauli exclusion property successfully. The first one is the KNFT potential which is given by Fujiwara and Tamagaki to remove the Coulomb effects from the OCM equivalent Kukulin-Neudatchin potential. The second one is the FBOM equivalent UIM potential, in which both the totally and partly Pauli forbidden states are excluded, thoroughly. In the 3-alpha calculation, almost all of the important low-lying energy levels are well reproduced with both potentials except that some spurious states appear with the KNFT potential.

It is found that not only the Coulomb force but also the three-cluster force are very important obtaining the correct order of the energy spectra as well as a good binding energy for the ground state of the ¹²C nucleus, in which we proposed a simple form of the three-cluster force. The sub-amplitudes for [3+1] as ¹²C + α system, and also for [2+2] as ⁸Be + ⁸Be system, are represented by using rank-1 and rank-2 Hilbert-Schmidt expansion methods, respectively. The convergences of the energy spectra for the low-lying 0 ⁺₁ , O ⁺₂ and 0 ⁺₃ states in the 16_O nucleus are investigated for several higher partial waves.

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