Collective Properties of Low-lying Octupole Excitations in   $^{208}_{82}Pb_{126}$, $^{60}_{20}Ca_{40}$ and $^{28}_{8}O_{20}$
  The octupole strengths of $\beta$-stable nucleus $^{208}_{82}Pb_{126}$, a neutron skin nucleus $^{60}_{20}Ca_{40}$ and a neutron drip line nucleus $^{28}_{8}O_{20}$ are studied by using the self-consistent Hartree-Fock calculation plus the random phase approximation (RPA) with Skyrme interaction. The collective properties of low-lying excitations are analyzed by using particle-vibration coupling. The results show that the lowest isoscalar states above threshold in $^{60}_{20}Ca_{40}$ and $^{28}_{8}O_{20}$ are the superpositions of collective excitations and unperturbed transitions from bound state to nonresonance states. 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. It is found that, for $^{208}_{82}Pb_{126}$, the ratios are equal to $(\frac{N-Z}{A})^2$ in good accuracy, while for $^{60}_{20}Ca_{40}$ and $^{28}_{8}O_{20}$, the ratios are much larger than $(\frac{N-Z}{A})^2$. This results from the excess neutrons with small binding energies in $^{60}_{20}Ca_{40}$ and $^{28}_{8}O_{20}$. 
X. R. Zhou, E. G. Zhao, B. G.Dong, X. Z. Zhang and G. L. Long