Comparative variational studies of $0^{+}$ states in three-$\alpha$ models

Abstract

Three variational approaches, the hyperspherical-harmonics, Gaussian-basis and Lagrange-mesh methods involving different coordinate systems, are compared in studies of $0^{+}$ bound-state energies in 3$\alpha$ models. Calculations are performed with different versions of the shallow Ali-Bodmer potential (with and without Coulomb) and with the deep Buck-Friedrich-Wheatley potential. All three methods yield very accurate energies. Their advantages and drawbacks are evaluated. The implications of the disagreement between the obtained results and the experimental ${}^{12}$C energies in $3\alpha$ models with Coulomb interaction are discussed.

References in corpus (3)

• Alpha cluster condensation in 12C and 16O
• Redundant Components in the 3 alpha Faddeev Equation Using 2 alpha RGM Kernel
• Variational Calculations of the ${}^{12}C$ Nucleus Structure in a 3$\alpha$ Model Using a Deep Potential with Forbidden States

Cited by in corpus (11)

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• Faddeev calculation of 3 alpha and alpha alpha Lambda systems using alpha alpha resonating-group method kernel
• Removal of forbidden states in a three-$\alpha$ system
• Case of Almost Redundant Components in 3 alpha Faddeev Equations
• The role of the Pauli principle in three-cluster systems composed of identical clusters
• Analysing supersymmetric transformed $\alpha$-nucleus potentials with electric-multipole transitions
• Resonances in ${}^{12}$C and ${}^{24}$Mg: what do we learn from a microscopic cluster theory?
• Peculiarity of the ${}^{12}$C$(0^{+})$ and ${}^{12}$C$(2^{+})$ energy spectrum in a 3$\alpha$ model
• Spatial Structure of the ${}^{12}$C Nucleus in a 3$\alpha$ Model with Deep Potentials Containing Forbidden States