The excitation spectra in the deformed nucleus 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 + 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: relatively firm for 4 states and tentative also for 4 states. Assignments up to spin 6 + are made for other states. Sequences of the states are selected which can be treated as rotational bands and as multiplets of excitations. Experimental data are compared with interacting boson model (IBM) and quasiparticlephonon model (QPM) calculations.

The intensities and reduced probabilities of the E1, E2, M1 and M2 transitions between excited states in 168Er are calculated within the quasiparticle-phonon nuclear model. The intensities and reduced probabilities are in reasonably good overall agreement with experimental ones. It is shown that the contribution of the two-phonon configuration to the wavefunction of excited states with energy below 2 MeV is small. The wavefunction of the first Knu pi =41+ state contains the largest double-gamma vibrational term equal to 30%. The dominance of the decay from the first excited 01+ state to the gamma vibrational state over that to the ground state band is in agreement with the experimental data. The specific features of the calculated B(E1), B(E2) and B(M1) values and the relative intensities of the gamma-ray transitions are discussed.

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Recent high resolution (p, t) experiments have established the existence of a large number of low-lying excited 0 + levels in the deformed 158 Gd [1] and, later on, in some actinide nuclei [2] and 168 Er [3]. The number of 0 + states detected in 168 Er is particularly large, the levels below 4 MeV amounting to about 22 [4]. The distribution pattern of the two-nucleon transfer transition strengths shows that one single 0 + state is strongly populated in all nuclei, with the exception of 168 Er where the strength is fragmented into several small peaks.All theoretical studies performed so far have been confined to 158 Gd. The first was a phenomenological investigation [5], which shows that the extended (sdpf ) interacting boson model (IBM) can account for a large fraction of the detected 0 + states. The (sdpf ) IBM analysis points out the importance of the octupole degrees of freedom.In order to account for all detected states and to gain a detailed information on their properties, it is necessary to adopt microscopic approaches. The first calculation of this kind was performed in the framework of the projected shell model (PSM) [6] adopting a restricted space spanned by two and four quasiparticle states. Including the latter states was crucial for covering the whole spectrum. The calculation reproduces well all the energy levels and yields very small E2 decay strengths for the corresponding states.An extensive study of the 0 + states in 158 Gd was carried out recently [7], within the quasiparticle-phonon model (QPM) [8]. Energies, E2 and E0 transition strengths as well as two-nucleon transfer spectroscopic factors were computed and investigated. It came out that an appreciable fraction of the 0 + states in 158 Gd has large or dominant twophonon components, mostly built out of collective octupole phonons, in agreement with the IBM results [5]. The calculation has also confirmed the PSM prediction [6] of very weak quadrupole collectivity for all 0 + states. In fact, the 0 + one-phonon states came out to be linear combinations of several pairing correlated two-quasiparticle qq components. These, however, add coherently only in one state. Such a 0 + pairing collective state is strongly populated in (p, t) two-nucleon transfer reactions, in agreement with experiments.In [9] we extend the QPM study to 168 Er and some Th and U isotopes. All these nuclei were explored in the latest (p, t) experiments [2,3,4]. We intend to test if the QPM can account for the huge number of 0 + levels observed in 168 Er [4] and is able to offer a consistent picture of the properties of the 0 + states in deformed nuclei of different regions.Our study shows that it is necessary to go beyond the mean field approximation (RPA) in order to account for the large number of 0 + levels observed in 168 Er. RPA, in fact, generates only 15 0 + states be low 4 MeV. Moreover, according to our QPM calculation, several levels, specially above 3 MeV, correspond to states with appreciable, often dominant, two-phonon components. A few of these states carry to...

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The centroid energies of the two-phonon states in doubly even deformed nuclei are calculated within the quasiparticle-phonon nuclear model taking into account the Pauli principle in the two-phonon components of the wave functions. It is shown that the collective two-phonon energies are shifted by t-2 MeV to higher energies due to the Pauli principle. A strong fragmentation of the two-phonon collective states over many nuclear levels occurs at the excitation energies of 3-4MeV. It is concluded that the two-phonon states cannot exist in deformed nuclei. The analysis of the available experimental data on the two-phonon states shows that the experimental data do not contradict the results of these calculations.