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A high-resolution $(p,t)$ experiment at $E_{p}$= 24 MeV was performed topopulate low-spin states in the actinide nucleus ${}^{240}$Pu. The Q3D magneticspectrograph of the Maier-Leibnitz Laboratory (MLL) in Munich (Germany) wasused to identify the ejected tritons via $dE/E$ particle identification withits focal-plane detection system. Angular distributions were measured at ninedifferent Q3D angles to assign spin and parity to the excited states based on acomparison with coupled-channels DWBA calculations.  In total, 209 states have been excited in $^{240}$Pu up to an excitationenergy of 3 MeV. Many previously known states have also been observed and theirspin-parity assignments were confirmed. However, many of the populated stateshave been seen for the first time. The low-spin one-octupole phononexcitations, i.e. $K^{\pi} = 0^-,1^-,2^-,3^-$, could be observed and a newcandidate for the $K = 3$ projection is proposed. Furthermore, thedouble-octupole or $\alpha$-cluster structure of the $0^+_2$ state in$^{240}$Pu has been studied in more detail. It is shown that the $0^+_2$ statein $^{230}$Th has a distinctly different structure. In addition, stronglyexcited $1^-$ states have been observed at 1.5\,MeV and 1.8\,MeV in $^{240}$Pu.The present study suggests that similar states might be observed in $^{230}$Th.  At least two different and distinct structures for $J^{\pi} = 0^+$ states arepresent in the actinides. These are pairing states and states with enhancedoctupole correlations. We have shown that it is crucial to considernegative-parity single-particle states being admixed to some $K^{\pi} = 0^+_2$rotational bands to understand the $\alpha$-decay hindrance factors andenhanced $E1$-decay rates. Based on our analysis, we have identified thedouble-octupole or $\alpha$-cluster $K^{\pi} = 0^+$ candidates from $^{224}$Rato $^{240}$Pu.

High-resolution $(p,t)$ study of low-spin states in $^{240}$Pu: Octupole excitations, $\alpha$ clustering, and other structure features