Cluster approach to the structure of ${}^{240}\mathrm{Pu}$

The cluster approach, which allows us to take into account both shape deformation parameters and cluster degrees of freedom, is developed to describe alternating-parity rotational bands. The important ingredient of the model is the dinuclear system concept in which the wave function of the nucleus is treated as a superposition of a mononucleus and two-cluster configurations. The model is applied to describe the multiple positive and negative parity rotational bands in ${}^{240}\mathrm{Pu}$. The observed excitation spectrum and the angular momentum dependences of the parity splitting and of the electric $E1$ and $E2$ transition moments are explained. Special emphasis is made on the investigation of the recently measured positive parity $0_2^{+}$ rotational band of reflection-asymmetric nature. The results suggest that this band might be understood as being built on the lowest excited state in the mass asymmetry degree of freedom. The $B\left(E1\right)/B\left(E2\right)$ branching ratios between the reduced transition probabilities of decay from the states of the $0_2^{+}$ band to the first negative parity band and to the groundstate band, respectively, are calculated and compared with experimental data.

Figure 1

The schematic picture of the dinuclear system with the indicated degrees of freedom used. The orientation of the vector $\mathbf{R}$ connecting the centers of nuclei is defined by the angles ${\mathrm{\Omega }}_R=({\theta }_R,{\theta }_R)$ in the laboratory frame $O{x}_R$. The orientation of the intrinsic coordinate system $O_h{x}_h$ related to the quadrupole deformed heavy fragment is defined by the angles ${\mathrm{\Omega }}_h=({\theta }_h,{\varphi }_h).$

Figure 2

Potential energy of the alpha-particle DNS as a function of angle $\epsilon$. The values calculated with (15) are shown by dots. The line represents the fit of calculated points with the expression (5).

Figure 3

Low-lying states of ${}^{240}\mathrm{Pu}$ obtained by the diagonalization of the Hamiltonian (7). They can be gathered into the rotational bands marked as $A, B, C, D$, and $E$. Using the asymptotic solution for large angular momenta (see Appendix), the approximate value of quantum number $K$ can be assigned to each band. For the bands $A$ and $D$, we get $K^{\pi }=0^{+}$, for the bands $B$ and $E, K^{\pi }=0^{-}$, and for the band $C, K^{\pi }=1^{-}$.

Figure 4

Calculated (lines) and experimental (points) values of parity splitting for ${}^{240}\mathrm{Pu}$ [see Eq. (23)]. Experimental values are taken from the data of Ref. [32].

Figure 5

Transition dipole moment $D_0$ for the transitions between the first negative-parity band $B$ and the ground-state band $B$ (a), and between the first negative parity band and the second excited $0^{+}$ band $D$ (b) as a function of the initial spin $I$.

Figure 6

Ratio of transition dipole and quadrupole moments extracted from the $E1$ and $E2$ branching ratio $B(E1,I_B^{-}\to {(I-1)}_A^{+})/B(E2,I_B^{-}\to {(I-2)}_B^{-})$ as a function of $I_B$. The experimental results are extracted from Ref. [30].