Collective properties of low-lying octupole excitations in ²⁰⁸₈₂Pb₁₂₆, ⁶⁰₂₀Ca₄₀ and ²⁸₈O₂₀

The octupole strengths of three nuclei: β-stable nucleus ²⁰⁸₈₂Pb₁₂₆, neutron skin nucleus ⁶⁰₂₀Ca₄₀ and neutron drip line nucleus ²⁸ ₈O₂₀ are studied by using the self-consistent Hartree-Fock calculation with the random phase approximation. The collective properties of low-lying excitations are analyzed by particle-vibration coupling. The results show that there is the coexistence of the collective excitations and the decoupled strong continuum strength near the threshold in the lowest isoscalar states in ⁶⁰₂₀Ca₄₀ and ²⁸₈O₂₀. For these three nuclei, both the low-lying isoscalar states and giant isoscalar resonance carry isovector strength. The ratio B(IV)/B(IS) is checked and it is found that, for ²⁰⁸₈₂Pb₁₂₆, the ratio is equal to ((N-Z)/A)² in good accuracy, while for ⁶⁰₂₀Ca ₄₀ and ²⁸₈O ₂₀, the ratios are much larger than ((N-Z)/A)². The study shows that the enhancement of the ratio is due to the excess neutrons that have small binding energies in ⁶⁰₂₀Ca₄₀ and ²⁸₈O ₂₀.