$0^{+}$ states in deformed actinide nuclei by the $(p,t)$ reaction

By means of the $(p,t)$ reaction we study the excitation spectra of $0^{+}$ states in the deformed nuclei ${}^{228}\mathrm{Th}$, ${}^{230}\mathrm{Th}$, and ${}^{232}\mathrm{U}$, using the Q3D magnetic spectrograph facility at the Munich tandem accelerator. At small reaction angles the $0^{+}$ transfer angular distributions have steeply rising cross sections which allow us to identify these states in otherwise very complicated and dense spectra. For each of these nuclei we resolve typically about ten excited states with safe $0^{+}$ assignments. The studied excitation energies range up to 2.5, 2.7, and $2.3\text{MeV}$, respectively, and the summed transfer strengths add to more than $60\%$ of the ground state strength. As in a recent study of ${}^{158}\mathrm{Gd}$ we compare with interacting boson approximation (IBA) calculations in the $spdf$ boson space. This highly schematic collective model description, including octupole collectivity, but neglecting other relevant degrees of freedom, gives numbers of excited $0^{+}$ states in these actinide nuclei that are rather close to the observed ones.

Figure 1

Schematic presentation of the different kinds of excitations in deformed nuclei, yielding excited $K^{\pi }=0^{+}$ states: Positive parity two-quasiparticle excitations (of collective and of noncollective nature), two-phonon excitations, and monopole pairing excitations.

Figure 2

Spectrum for the ${}^{230}\mathrm{Th}(p,t){}^{238}\mathrm{Th}$ reaction $\left(E_{\mathrm{p}}=25\text{MeV}\right)$ at a detection angle of $7.5°$ in logarithmic scale, in the energy range beginning with the first excited $0^{+}$ state. Some levels are labeled with their excitation energy in keV. States assigned as $0^{+}$ are marked with an asterisk.

Figure 3

Complete spectrum for ${}^{232}\mathrm{Th}(p,t){}^{230}\mathrm{Th}$ $\left(E_{\mathrm{p}}=25\text{MeV}\right)$ in logarithmic scale for a detection angle of $7.5°$. Some levels are labeled with their excitation energy in keV. States assigned as $0^{+}$ are marked with an asterisk.

Figure 4

Spectrum for ${}^{234}\mathrm{U}(p,t){}^{232}\mathrm{U}\left(E_p=25\text{MeV}\right)$ in logarithmic scale for a detection angle of $7.5°$, in the energy range beginning with the first excited $0^{+}$ state. Some levels are labeled with their excitation energy in keV. States assigned as $0^{+}$ are marked with an asterisk.

Figure 5

Angular distributions of assigned $0^{+}$ states in ${}^{228}\mathrm{Th}$. The lines are drawn to guide the eyes and have no further meaning.

Figure 6

Angular distributions of assigned $0^{+}$ states in ${}^{230}\mathrm{Th}$. The lines are drawn to guide the eyes and have no further meaning.

Figure 7

Angular distribution of assigned $0^{+}$ states in ${}^{232}\mathrm{U}$. The lines are drawn to guide the eyes and have no further meaning.

Figure 8

Angular distributions of the first excited $1^{-}$, $2^{+}$, $3^{-}$, $4^{+}$, and $6^{+}$ states. In the shaded area we compare the angular distributions of the ${}^{232}\mathrm{U}$ $0^{+}$ ground state and the $927.3\text{keV}$ excited state. This angular distribution does not allow for a firm $0^{+}$ assignment proposed by Ardisson et al. [59]. The lines are drawn to guide the eyes and have no further meaning.

Figure 9

Ground state transition data with DWBA fits. The spectroscopic factors $S={(d\sigma ∕d\Omega )}^{\text{expt}}∕{(d\sigma ∕d\Omega )}^{\text{CHUCK3}}$ are given.

Figure 10

DWBA calculations of cross sections of excited $0^{+}$ states at $7.5°$ normalized to the ground state cross section (calculated with CHUCK3 using the input files of Fig. 15).

Figure 11

Incremental plot of the transfer strengths to excited $0^{+}$ states in ${}^{158}\mathrm{Gd}$, ${}^{228}\mathrm{Th}$, ${}^{230}\mathrm{Th}$, and ${}^{232}\mathrm{U}$. The ${}^{158}\mathrm{Gd}$ data are derived from Ref. 30.

Figure 12

Lowest negative parity bands in ${}^{228}\mathrm{Th}$, ${}^{230}\mathrm{Th}$, and ${}^{232}\mathrm{U}$, comparing the $spdf$-IBA calculation with known excitation energies from the NDS [33, 34, 35] and Ref. 28. Left side experimental, right side calculated levels.

Figure 13

Lowest positive parity bands in ${}^{228}\mathrm{Th}$, ${}^{230}\mathrm{Th}$, and ${}^{232}\mathrm{U}$, comparing the $spdf$-IBA calculation with known excitation energies from the Nuclear Data Sheets (NDS) [33, 34, 35] and Ref. 28. For ${}^{228}\mathrm{Th}$ we show two $0^{+}$ bands. According to the schematic IBA calculation the octupole two-phonon band is the one with the lower excitation energies. In reality the two bands are expected to mix.

Figure 14

Excitation energies of all safely assigned excited $0^{+}$ states in ${}^{228}\mathrm{Th}$, ${}^{230}\mathrm{Th}$, and ${}^{232}\mathrm{U}$, compared with $spdf$-IBA calculations. OTP states are marked by a dot. The shadowed areas indicate the upper range of the experimental evaluation. The positions of the $1_1^{-}$ states are indicated, too.

Figure 15

CHUCK3 input files for the discussed $(p,t)$ reactions.