Well-deformed Rare-earth Nuclei Research Articles

Photon strength functions, level densities, and isomeric ratio in Er168 from the radiative neutron capture measured at the DANCE facility

Background: The statistical approach is usually applied for the description of electromagnetic decay of the nucleus with the exception of the lowest excitation energies as well as for the calculation of the interaction of photons with nuclei, in particular the reaction cross sections. This concept employs nuclear level density (NLD) and photon strength functions (PSFs).Purpose: While PSFs and NLD of some well-deformed rare-earth nuclei were measured by several methods, sometimes with conflicting results, the PSFs of $^{168}\mathrm{Er}$ were addressed only by $(\ensuremath{\gamma},{\ensuremath{\gamma}}^{\ensuremath{'}})$ experiments. On the other hand, the low-lying levels of $^{168}\mathrm{Er}$ are well studied, including the isomeric state at 1094 keV, which enables various tests of the statistical approach.Methods: The $\ensuremath{\gamma}$ rays following radiative neutron capture on a $^{167}\mathrm{Er}$ sample were measured with the highly segmented $\ensuremath{\gamma}$-ray calorimeter Detector for Advanced Neutron Capture Experiments at the Los Alamos Neutron Science Center. The $\ensuremath{\gamma}$-ray energy spectra for different multiplicities (multistep cascade, or MSC, spectra) were gathered for many $s$-wave resonances of both possible spins. Moreover, we were able to detect the decay of the short-lived isomer and deduce the isomeric ratio for a few resonances.Results: Analysis of the MSC spectra within the statistical model enabled us to draw conclusions about dipole PSFs, in particular on the properties of the scissors mode, and NLD. The spectra can be well reproduced with phenomenological PSFs models but not with any of several models based on quasiparticle random-phase approximation (QRPA) calculations with different interactions. We showed that nonstatistical effects in feeding of the isomeric state play a role up to excitation energies of at least about 2 MeV.Conclusions: Deduced parameters of the scissors mode were found to be similar to those of neighbor well-deformed even-even Gd and Dy nuclei. Models like that of Kadmenskij, Markushev, and Furman (KMF) or like the modified generalized Lorentzian (MGLO) model provide a good description of experimental spectra. In contrast to several previous analyses of well-deformed rare-earth isotopes, we were able to match the experimental isomeric ratio with statistical model simulations.

Role of tensor terms of the Skyrme energy-density functional on neutron deformed magic numbers in the rare-earth region

The role of the tensor part of the nuclear interaction is actively investigated in recent years due to experimental advancement yielding new data in nuclei far from the $\ensuremath{\beta}$-stability line. In this article we study the effect of this part of the nuclear interaction on deformed neutron magic numbers in the rare-earth region within the Skyrme energy-density functional for various TIJ [T. Lesinski, M. Bender, K. Bennaceur, T. Duguet, and J. Meyer, Phys. Rev. C 76, 014312 (2007)] parametrizations. Two quantities signaling magic numbers are considered: two-neutron separation energies and single-particle energies. They are calculated in isotopic series involving well-deformed rare-earth nuclei ranging from $Z=64$ to $Z=72$ in the $N=100$ region. Obtained results show that, whereas the neutron-proton tensor contribution to binding energies is important to reproduce neutron subshell closure at $N=104$ in heavier rare earths $\mathrm{Yb}\phantom{\rule{0.16em}{0ex}}(Z=70)$ and $\mathrm{Hf}\phantom{\rule{0.16em}{0ex}}(Z=72)$ isotopes, like-particle tensor also plays a role in the single-particle spectrum around Fermi level and is even favored in lighter $\mathrm{Gd}\phantom{\rule{0.16em}{0ex}}(Z=64)$ and $\mathrm{Dy}\phantom{\rule{0.16em}{0ex}}(Z=66)$ rare-earth isotopes.

Investigation of excited 0+ states in 160Er populated via the (p, t) two-neutron transfer reaction

Many efforts have been made in nuclear structure physics to interpret the nature of low-lying excited 0+ states in well-deformed rare-earth nuclei. However, one of the difficulties in resolving the nature of these states is that there is a paucity of data. In this work, excited 0+ states in the N = 92 nucleus 160Er were studied via the 162Er(p, t)160Er two-neutron transfer reaction, which is ideal for probing 0+ → 0+ transitions, at the Maier-Leibnitz-Laboratorium in Garching, Germany. Reaction products were momentum-analyzed with a Quadrupole-3-Dipole magnetic spectrograph. The 0+2 state was observed to be strongly populated with 18% of the ground state strength.

Extended tests of an SU(3) partial dynamical symmetry

Background: A recent survey of well-deformed rare earth nuclei showed that B(E2) values from the γ band to the ground band could be explained rather well by a parameter-free description in terms of a partial dynamical symmetry (PDS). Purpose: Our purpose in this paper is to extend this study to deformed and transitional nuclei in the actinide and A ~ 100 regions to determine if the success of the PDS description is general in medium- and heavy-mass nuclei and to investigate further where it breaks down. Method: As with the previous study we study the empirical relative B(E2 : γ to ground) values in comparison to a pure rotor (Alaga) model and to the SU(3) PDS. Results: The data for the actinides, albeit sparser than in the rare-earth region, are reasonably well accounted for by the PDS but with systematic discrepancies. For the Mo isotopes, the PDS improves on the Alaga rules but largely fails to account for the data. Conclusions: As in the rare earths, the parameter-free PDS gives improved predictions compared to the Alaga rules for the actinides. The differences between the PDS predictions and the data are shown to point directly to specific mixing effects. Finally, inmore » the Mo isotopes, their transitional character is directly seen in the large deviations of the B(E2) values from the PDS in the direction of the selection rules of the vibrator.« less

Evolution of 2+ γ wave functions and gamma-stiffness in well-deformed rare-earth nuclei

The evolution of the structure of the gamma-vibrational band head 2+ γ in well-deformed rare-earth nuclei is studied within the framework of RPA calculations using a quasiboson approximation based on the Nilsson model. The obtained evolution of the quasiparticle structure of the gamma-vibrational band head is shown to correlate well with the evolution of the same nuclei within the IBA symmetry triangle when described in the extended consistent-Q formalism. An empirical relation is presented that links the IBA parameter χ with the quasiparticle structure of the gamma-vibrational band head.

Moments of inertia of nuclei in the rare earth region: A relativistic versus nonrelativistic investigation

A parameter-free investigation of the moments of inertia of ground-state rotational bands in well-deformed rare-earth nuclei is carried out using cranked relativistic Hartree-Bogoliubov (CRHB) and nonrelativistic cranked Hartree-Fock-Bogoliubov (CHFB) theories. In CRHB theory, the relativistic fields are determined by the nonlinear Lagrangian with the NL1 force and the pairing interaction by the central part of a finite-range Gogny D1S force. In CHFB theory, the properties in particle-hole and particle-particle channels are defined solely by Gogny D1S forces. Using an approximate particle number projection before variation by means of the Lipkin-Nogami method improves the agreement with the experimental data, especially in CRHB theory. The effect of the particle number projection on the moments of inertia and pairing energies is larger in relativistic than in nonrelativistic theory.

Blocking effect and odd-even differences in the moments of inertia of rare-earth nuclei

A phenomenological analysis of the experimental odd-even differences in the moments of inertia, \ensuremath{\delta}J/J, of well-deformed rare-earth nuclei is reviewed, which reveals that there exist large fluctuations in \ensuremath{\delta}J/J with the blocked levels in odd-A nuclei. A calculation using the particle-number conserving treatment shows that the odd-even difference in the moments of inertia is a pure quantum mechanical interference effect and the experimental strong fluctuations in \ensuremath{\delta}J/J with the blocked level can be reproduced satisfactorily. The calculated value of \ensuremath{\delta}J/J depends sensitively on the energetic location and Coriolis response of the blocked level and the underlying physics is discussed. Particularly, \ensuremath{\delta}J/J is especially large if the blocked orbital is a high-j intruder orbital near the Fermi surface. In contrast, if the blocked orbital is of normal parity with low j and high \ensuremath{\Omega} (e.g., proton [404] 7/2, [402]5/2), \ensuremath{\delta}J/J almost vanishes.

Coriolis attenuation in the A

The particle-rotor model has been applied to calculate the band structure in a number of highly neutron deficient odd-A rare-earth nuclei in the A\ensuremath{\simeq}130--150 region. Several transitional nuclei are also included in the study. The only adjustable parameter, used in the calculation, is the Coriolis attenuation coefficient. However, it is seen that the observed band structures in these nuclei can be reproduced practically without any ad hoc reduction of the Coriolis matrix elements. The systematics of the Coriolis attenuation in the neutron-deficient, transitional, and well-deformed rare-earth nuclei are discussed in the light of the present work and several theoretical studies, made earlier. The importance of the pairing interaction in the Coriolis attenuation study is emphasized.

Effects of inelastic multistep processes on (p, t) reactions in a transition region between rare-earth nuclei and double-magic 208Pb

Effects of inelastic multistep processes on (p, t) reactions in a transition region between well-deformed rare-earth nuclei and the double-magic 208Pb have been investigated by the 188Os(p, t) 1860s, 194, 196Pt(p, t) 192, 194Pt and 200, 202Hg(p, t) 198, 200Hg reactions at E p = 51.9 MeV. The observed ground 0 +, first excited 2 + and 4 + angular distributions together with those for the 206, 208pb(p, t) 204, 206pb reactions have been compared with CCBA and DWBA calculations, using transfer form factors based on the Nilsson, vibrational and shell models. It is found that the inelastic multistep processes play a very important role in reproducing both the shapes and magnitudes of the observed first excited 2 + angular distributions, contrasting to small contributions in the ground-state 0 + transitions. The effects of the inelastic multistep processes on the first excited 4 + transitions are also considered to be important.

Spin alignment in the particle-rotor and cranking models

It is shown that the cranking model normally gives a smaller rotation-aligned spin for an odd quasiparticle than the particle-rotor model, especially at low rotational frequencies. The basic reason is found to be that the rotational frequency vector of the cranking model is “sharp”. This is an unphysical model property, and in the presence of a particle whose rotational motion is partly decoupled from the rotational motion of the average field its consequences become serious. A “sharp” rotational frequency corresponds to a neglect of the recoil effect that establishes coherence between the motion of the decoupled nucleon and the other nucleons and therefore is a prerequisite for the conservation of angular momentum. In conclusion the cranking model cannot be invoked to explain the so-called “Coriolis attenuation”, relative to the particle-rotor model, that is observed experimentally. Particle-rotor calculations are carried out into the backbending region of some well-deformed rare-earth nuclei, and the results indicate that the “Coriolis attenuation” effect is weak or absent at high rotational frequencies. However, the experimental i 13 2 , unfavoured band of 167Yb is found to exhibit an anomalous “downbending” behaviour.