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

Background: Many nuclear-structure features have been observed in actinides in recent decades. In particular, the octupole degree of freedom has been discussed lately after the successful measurement of the $B\left(E3;0_1^{+}\to 3_1^{-}\right)$ reduced transition strength in ${}^{224}\mathrm{Ra}$. Recent results stemming from $\gamma$-spectroscopy experiments and high-resolution $(p,t)$ experiments suggested that strong octupole correlations might be observed for some positive-parity states of actinide nuclei.

Purpose: This work completes a series of $(p,t)$ experiments on actinide nuclei by adding the data on ${}^{240}\mathrm{Pu}$. The $(p,t)$ experiments allow us to study low-spin states up to $J^{\pi }=6^{+}$. Besides two-nucleon transfer cross sections, spin and parity can be assigned to excited states by measuring angular distributions, and several rotational bands are recognized based on these assignments.

Methods: A high-resolution (p,t) experiment at $E_p=24$ MeV was performed to populate low-spin states in the actinide nucleus ${}^{240}\mathrm{Pu}$. The Q3D magnetic spectrograph of the Maier-Leibnitz Laboratory (MLL) in Munich (Germany) was used to identify the ejected tritons via $dE/E$ particle identification with its focal-plane detection system. Angular distributions were measured at nine different Q3D angles to assign spin and parity to the excited states based on a comparison with coupled-channel distorted-wave Born approximation calculations.

Results: In total, 209 states have been excited in ${}^{240}\mathrm{Pu}$ up to an excitation energy of 3 MeV. Many previously known states have also been observed and their spin-parity assignments were confirmed. However, many of the populated states have been seen for the first time, e.g., 15 new and firmly assigned $J^{\pi }=0^{+}$ states. In addition, all low-spin one-octupole phonon excitations, i.e., $K^{\pi }=0^{-},1^{-},2^{-},3^{-}$, could be observed and a new candidate for the $K=3$ projection is proposed. Furthermore, the double-octupole or $\alpha$-cluster structure of the $0_2^{+}$ state in ${}^{240}\mathrm{Pu}$ has been studied in more detail. It is shown that the $0_2^{+}$ state in ${}^{230}\mathrm{Th}$ has a distinctly different structure. In addition, strongly excited $1^{-}$ states have been observed at 1.5 and 1.8 MeV in ${}^{240}\mathrm{Pu}$. The present study suggests that similar states might be observed in ${}^{230}\mathrm{Th}$.

Conclusions: At least two different and distinct structures for $J^{\pi }=0^{+}$ states are present in the actinides. These are pairing states and states with enhanced octupole correlations. We have shown that it is crucial to consider negative-parity single-particle states being admixed to some $K^{\pi }=0_2^{+}$ rotational bands to understand the $\alpha$-decay hindrance factors and enhanced $E1$-decay rates. Based on our analysis, we have identified the double-octupole or $\alpha$-cluster $K^{\pi }=0^{+}$ candidates from ${}^{224}\mathrm{Ra}$ to ${}^{240}\mathrm{Pu}$.

Figure 1

(a) ${}^{232}\mathrm{Th}(p,t){}^{230}\mathrm{Th}$, (b) ${}^{186}\mathrm{W}(p,t){}^{184}\mathrm{W}$, and [(c), (d)] ${}^{242}\mathrm{Pu}(p,t){}^{240}\mathrm{Pu}$ spectra at ${10}^{\circ }$ for the two magnetic settings which were used for the energy calibration of the focal plane detection system; see text. The overlap regions are marked by dashed lines. Some prominent peaks in ${}^{230}\mathrm{Th}$ and ${}^{184}\mathrm{W}$ are highlighted with their excitation energy in keV.

Figure 2

Excitation schemes used in the DWBA calculations. An asterisk ($*$) indicates that the intermediate states were the $2_1^{+}$ states in ${}^{242}\mathrm{Pu}$ and ${}^{240}\mathrm{Pu}$, respectively. m3a corresponds to $J_1^{\pi }=2_1^{+}$ and m4a corresponds to $J_1^{\pi }=4_1^{+}$. In most cases, it was not necessary to include all intermediate states when m3a or m4a had to be used.

Figure 3

Integrated $(p,t)$ cross sections ${\sigma }_{\mathrm{total}}$ for $0^{+},2^{+},4^{+}$, $6^{+}$, and $3^{-}$ states in ${}^{240}\mathrm{Pu}$.

Figure 4

Angular distributions of the $J^{\pi }=0^{+}$ states in ${}^{240}\mathrm{Pu}$. The angular distributions for the corresponding $L=0$ transfer calculated with the chuck3 code [32] are shown with lines. Red lines correspond to firm assignments and blue dashed lines correspond to tentative assignments, respectively. Two-neutron transfer configurations of orbitals close to the Fermi surface were chosen.

Figure 5

Same as Fig. 4 but for $J^{\pi }=2^{+},3^{+},4^{+},5^{+}$, and $6^{+}$ states in ${}^{240}\mathrm{Pu}$.

Figure 6

Angular distributions of one-phonon octupole states and of the tentatively assigned $K^{\pi }={\left(0\right)}^{-}$ band members in ${}^{240}\mathrm{Pu}$. See Sec. 3c and Fig. 4 for information about the DWBA calculations.

Figure 7

Sequences of excited states, which might belong to a common rotational band. Positive-parity $K^{\pi }=0^{+}$ (black circles), $K^{\pi }=2^{+}$ (open circles), $K^{\pi }=4^{+}$ (black triangles), and $K^{\pi }=3^{+}$ (open squares) rotational bands are shown with solid lines. Negative-parity rotational bands (open diamonds) are shown with dashed lines.

Figure 8

Running relative transfer strength for $0^{+}$ states as a function of energy up to 3 MeV. The 2QP energies are shown with solid arrows, respectively. The neutron-pairing energy ${\mathrm{\Delta }}_{\mathrm{n}}$ was calculated from the odd-even mass differences [35]. Except for ${}^{240}\mathrm{Pu}$, the data are from Refs. [19, 20, 31, 37].

Figure 9

Firmly assigned $0^{+}$, $2^{+}$, and $4^{+}$ states (Exp. with solid lines) as well as excited $0^{+}$, $2^{+}$, and $4^{+}$ states as predicted by the $spdf$ IBM. $sd$ states (solid lines) and $N_{pf}=2$, i.e., double-dipole–octupole states (red dashed lines) are shown. In addition, the 2QP energy is depicted (black dashed line), i.e., $2{\mathrm{\Delta }}_n$.

Figure 10

[(a)–(f)] $(p,t)$ cross sections for the $0_1^{+}$, $2_1^{+}$, $0_2^{+}$, $2_2^{+}$, $0_3^{+}$, and $2_3^{+}$ states as a function of boson number $N_B$ for ${}^{228,230}\mathrm{Th}$ ($N_B=10,11$) [19, 31], ${}^{232}\mathrm{U}$ ($N_B=12$) [20], and ${}^{240}\mathrm{Pu}$ ($N_B=16$). [(g)–(l)] The $B(E2;2_1^{+}\to 0_1^{+})$ values, excitation energies $E\left(0_2^{+}\right)$ and $E\left(1_1^{-}\right)$, experimental (symbols) and theoretical $B(E3;3_1^{-}\to 0_1^{+})$ values (lines) from Refs. [1, 2, 57, 58], $\alpha$-decay hindrance factors $\mathrm{HF}\left(0_2^{+}\right)$ and $\mathrm{HF}\left(1_1^{-}\right)$. If not stated otherwise, the quantities given correspond to the adopted values of Ref. [52].

Figure 11

The pairing gaps as a function of the total boson number $N_B$ in the even-even Ra, Th, U, and Pu isotopes as calculated from the odd-even mass differences [35]. (a) Twice the energy of the proton-pairing gap ${\mathrm{\Delta }}_p$. (b) The same for the neutron-pairing gap ${\mathrm{\Delta }}_n$. (c) The energy difference between the two gaps. Note that $N_B$ has been shifted by one in panel (c). These values seem to follow the evolution of $E\left(0_2^{+}\right)$ as indicated by the dashed line; compare Fig. 10.

Figure 12

Comparison of the experimentally well-established ground state and $K^{\pi }=0_1^{-}$ rotational bands [52] (solid lines) with the predictions of the $spdf$ IBM (dashed lines). In addition, possible negative-parity bands are compared to the corresponding bands of the IBM. Note that the $5^{-}$ and $6^{-}$ state of the $K^{\pi }=1_{\mathrm{IBM}}^{-}$ band are nearly degenerate. The $4^{-}$ state of the $K^{\pi }=2^{-}$ band has not been observed experimentally. Unlike all other negative-parity bands in the figure, one of the $K^{\pi }=0_{\mathrm{IBM}}^{-}$ bands shown here has a $N_{pf}=3$ structure (right part of the figure). The other negative-parity bands correspond to one-octupole phonon excitations. The one-octupole phonon $K=3$ projection is predicted at an energy of 2013.5 keV. The present $K^{\pi }=3^{-}$ assignment to the state at 1550 keV might therefore not be unambiguous.

Figure 13

(a) Possible running sum of experimental $B(E1;0_1^{+}\to 1_i^{-})$ strength in ${}^{240}\mathrm{Pu}$ (black solid line) between 2 and 4.5 MeV [69]. No parities were determined in Ref. [69]. Thus, some of the $J=1$ states will likely have a positive-parity assignment. For comparison, the experimentally determined running sum of $B(E1;0_1^{+}\to 1_i^{-})$ strength of firmly assigned $J^{\pi }=1^{-}$ states in ${}^{238}\mathrm{U}$ up to 4.5 MeV (blue dashed line) is also presented [70]. No clearly resolved strength is observed above this energy since the level density is too high. Missing strength of about $60\times {10}^{-3}$ ${\mathrm{e}}^2{\mathrm{fm}}^2$ up to the neutron-separation threshold was estimated. The $E1$ strength predicted by the IBM is shown as well (fine-dashed red line). (b) The $n_p/n_f$ ratios as predicted by the $spdf$ IBM. States with $n_p/n_f>1$ correspond to dominant $\alpha$-cluster $1^{-}$ states [71].

Figure 14

(a) $(p,t)$ cross sections ${\sigma }_{(p,t)}$ depicted as a function of excitation energy for the $J^{\pi }=1^{-}$ states observed in ${}^{228,230}\mathrm{Th}$ [19, 31], ${}^{232}\mathrm{U}$ [20], and ${}^{240}\mathrm{Pu}$. (b) Centroid energies calculated from the excitation energies and ${\sigma }_{(p,t)}$ of the $J^{\pi }=1^{-}$ states as a function of the boson number $N_B$.

Figure 15

${}^{242}\mathrm{Pu}(p,t){}^{240}\mathrm{Pu}$ spectrum detected at ${10}^{\circ }$ as a function of the residual triton energy. Some prominent excited states of ${}^{240}\mathrm{Pu}$ are marked with their excitation energy given in keV. In addition, the expected triton energies for the ground as well as first excited state of ${}^{237}\mathrm{Pu}$ (green), ${}^{238}\mathrm{Pu}$ (red), ${}^{242}\mathrm{Pu}$ (purple), and ${}^{236}\mathrm{U}$ (blue) are marked with dashed lines and symbols, respectively. The first $J^{\pi }=1/2^{+}$ state of ${}^{237}\mathrm{Pu}$ has been added as well, since it would be excited via a $l=0$ transfer in the ${}^{239}\mathrm{Pu}(p,t){}^{237}\mathrm{Pu}$ reaction. In addition, the expected triton energies for the $J^{\pi }=0_2^{+}$ state in ${}^{236}\mathrm{U}$ and ${}^{242}\mathrm{Pu}$ are highlighted. The spectra in the right panels are enlarged in the regions of interest to identify or exclude possible contaminants.