I. INTRODUCTION In the even-even isotopes of actinides and also in the heavy Ba and Ce isotopes the low-lying negative parity states are observed together with the usually presented collective positive-parity states combined into rotational or quasirotational ground-state bands. The formation of the positive-parity rotational or quasirotational bands are connected in general to the quadrupole collective motion, while the lowering of the negative-parity states is a signature of the presence of the reflection asymmetric collective mode. There are several approaches to treat the collective motion related to the reflection asymmetric degrees of freedom. One of them is based on the concept of the nuclear mean field [1] which has a static mirror asymmetric deformation or is characterized by a large amplitude of reflection asymmetric vibrations around the equilibrium shape. Another approach is based on the assumption that the reflection asymmetric shape is a consequence of the α -clustering in nuclei [2]. It is also known from the Nilsson-Strutinsky type calculations for light nuclei that nuclear configurations corresponding to the minima of the potential energy contain particular symmetries which are related to certain cluster structures [3, 4]. Several calcula- tions performed for heavy nuclei [5–7] have shown that configurations with large equilibrium quadrupole deformations and low-lying collective negative parity states are strongly related to clustering. We mention also a different approach to description of the properties of the alternating parity bands which is based on the idea of the aligned octupole phonons [8, 9] The main idea of the cluster model developed in [7, 10, 11] is that a dynamics of a reflection asymmetric collective motion can be treated as a collective motion of nucleons between two clusters or as a motion in a mass-asymmetry coordinate. Such collective motion simultaneously creates deformations with even and odd-multipolarities. Among different cluster configurations only α -cluster system $^{A}$Z → ( A − 4) ( Z − 2)+ $^{4}$He gives a significant contribution to the formation of the low-lying nuclear states. Within this approach the existing experimental data on the angular momentum dependence of the parity splitting and multipole transition moments (E1,E2,E3) of the low-lying alternating parity states in odd and even actinides 220 − $^{228}$Ra, 223 , 225 , $^{227}$Ac, 222 − 224 , 226 , 228 − $^{232}$Th, $^{231}$Pa, 232 − 234 , 236 , $^{238}$U and 240 , $^{242}$Po and the medium mass nuclei 144 , 146 , $^{148}$Ba, 151 , $^{153}$Pm, 146 , $^{148}$Ce 153 , $^{155}$Eu and 146 , $^{148}$Nd are well described. The perfect agreement between the calculated results and experimental data supplies the proof of the cluster features of reflection-asymmetric states. However, 2