Adopted values for the reduced electric quadrupole transition probability, B(E2)↑, from the ground state to the first-excited 2+ state of even–even nuclides are given in Table I. Values of τ, the mean life of the 2+ state; E, the energy; and β, the quadrupole deformation parameter, are also listed there. The ratio of β to the value expected from the single-particle model is presented. The intrinsic quadrupole moment, Q0, is deduced from the B(E2)↑ value. The product E×B(E2)↑ is expressed as a percentage of the energy-weighted total and isoscalar E2 sum-rule strengths.

Table II presents the data on which Table I is based, namely the experimental results for B(E2)↑ values with quoted uncertainties. Information is also given on the quantity measured and the method used. The literature has been covered to November 2000.

The adopted B(E2)↑ values are compared in Table III with the values given by systematics and by various theoretical models. Predictions of unmeasured B(E2)↑ values are also given in Table III.

Transition probability from the ground to the first-excited 2^+ state of even-even nuclides

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 $2.3\phantom{\rule{0.3em}{0ex}}\text{MeV}$, 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.

0 + states in deformed actinide nuclei by the (p,t) reaction

The excitation spectra in the deformed nucleus {sup 230}Th were studied by means of the (p,t) reaction, using the Q3D spectrograph facility at the Munich Tandem accelerator. The angular distributions of tritons are measured for about 200 excitations seen in the triton spectra up to 3.3 MeV. Firm 0{sup +} assignments are made for 16 excited states by comparison of experimental angular distributions with the calculated ones using the CHUCK code. Additional assignments are possible, with assignments for four states relatively firm and another four tentative. Assignments up to spin 6{sup +} are made for other states. Sequences of the states are selected that can be treated as rotational bands and as multiplets of excitations. Experimental data are compared with interacting boson model (IBM) and quasiparticle-phonon model (QPM) calculations.

Spectroscopy of 230 Th in the ( p,t) reaction

Octupole states have been studied systematically in the deformed actinide nuclei ${}^{230}\mathrm{Th},$ ${}^{234,236,238}\mathrm{U},$ ${}^{240}\mathrm{Pu},$ ${}^{246}\mathrm{Cm},$ and ${}^{250}\mathrm{Cf}$ using the interacting boson approximation 1. Parameters for the positive parity cores were set by reproducing data from the ground state and \ensuremath{\gamma}-vibration bands with the extended consistent-$Q$ formalism. A prescription for setting the parameter ${\ensuremath{\epsilon}}_{f}$ systematically was adopted for the calculations of the octupole bands. The ordering of the ${K}^{\ensuremath{\pi}}{=0}^{\ensuremath{-}},$ ${1}^{\ensuremath{-}},$ and ${2}^{\ensuremath{-}}$ bands and the behavior of many $E1$ and $E3$ transitions are well reproduced with a narrow range of parameters, particularly when the existence of a $N=164$ subshell gap is assumed. It is predicted that in ${}^{246}\mathrm{Cm}$ and ${}^{250}\mathrm{Cf}$ the ${K}^{\ensuremath{\pi}}{=3}^{\ensuremath{-}}$ octupole states built on the ground state are located above 6 MeV and are strongly fragmented.

Octupole states in deformed actinide nuclei with the interacting boson approximation

The (p, t) reaction was studied at 22 MeV proton energy using targets of230,232Th and234,236,238U. In228Th we observed in addition to the 832 keV first-excited 0+ level a second-excited 0+ level at 939 keV populated with 5% of the ground-state strength. A 0+ level proposed recently in232U at 927 keV was not observed in the (p, t) reaction, with an upper limit for its excitation of 0.2% of the ground-state strength. In234U a level at 1045 keV, assigned in the literature as second-excited 0+ level, is weakly populated in the (p, t) reaction but does not show the angular distribution characteristic for single-stepL=0 transfer. In236U we observed a level at 1036 keV with an angular distribution suggesting that it might be a doublet composed of a known 3− level and a new 0+ level. The properties of the first two excited 0+ bands in228Th,232U and234U are compared and discussed.

Study of low-lying 0+ excitations in228Th and232,234,236U in the (p, t) reaction

Nuclear levels in230Th have been investigated in theβ decay of230Pa, the230Th(d, pnγ) reaction and the232Th(p, t) reaction. TheKπ=01+, 21+, and 22+ bands with band heads at 635, 781, and 1010 keV were observed up to the 8+, 9+, and 7+ levels, respectively. A second excited 0+ level was identified at 1297 keV which might be interpreted as the usualβ shape-oscillation. The branching ratios of theE2 transitions from the 01+, 21+, and 22+ bands are explained in the framework of the rotational model by taking into account the coupling of these bands with the ground-state band, and the coupling between the 01+ and 21+ band. A strong enhancement ofE2 transitions from the 21+ to the 01+ band reported earlier is not confirmed. For the octupole vibrations withKπ=0−, 1−, and 2− theE1 branching ratios are analyzed in terms of the Coriolis coupling of these bands. An almost complete experimental set ofE1 transition moments from these negative-parity bands to the 0g+, 01+, and 21+ bands was obtained. It is suggested that octupole correlations might be important in explaining theseE1 moments.

Experimental investigation of vibrational excitations in 230 Th

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Experimental investigation of vibrational excitations in 230 Th