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 $^{ 28}_{ 8}O_{ 20}$.
Categories: nucl-th
