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Register a new userCalculation of strongly-coupled rotational bands in terms of the tilted axis cranking model
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Recently observed strongly-coupled rotational bands associated with the $ u [505]{11/2}^-$ quasiparticle state are studied by means of a microscopic tilted axis cranking (TAC) model. The results of calculation for the routhians and the $B(M1)/B(E2)$ ratios are investigated in the light of other existing models, i.e. the strong-coupling model and the conventional cranking model. It is demonstrated that only the TAC model can successfully reproduce these two observables at the same time. The reason of the success is clarified by making connections between these models.
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The selfconsistent cranking approach is extended to the case of rotation about an axis which is tilted with respect to the principal axes of the deformed potential (Tilted Axis Cranking). Expressions for the energies and the intra bands electromagnetic transition probabilities are given. The mean field solutions are interpreted in terms of quantal rotational states. The construction of the quasiparticle configurations and the elimination of spurious states is discussed. The application of the theory to high spin data is demonstrated by analyzing the multi quasiparticle bands in the nuclide-s with $N=102,103$ and $Z=71,72,73$.
We report the results of recent measurements of the spectroscopic quadrupole moments of high-spin isomers. For the K=35/2- five-quasiparticle isomer in 179W we measured Q_s=4.00(+0.83)(-1.06)eb. It corresponds to a smaller deformation compared to the ground states of the W isotopes and is in disagreement with the current theoretical predictions. We also measured the quadrupole moment of the I=11- isomer in 196Pb, Q_s=(-)3.41(66)eb. It has the same proton s(-2)1/2 h9/2 i13/2 configuration as the one suggested for the I=16- magnetic bandhead which allows to deduce the quadrupole moment of the 16- state as Q_s=-0.316(97)eb. This small value proves the near sphericity of the bandhead.
A collective bands of positive and negative parity could be composed of the vibrations and rotations. The rotations of the octupole configurations can be based either on the axial or the non-axial octupole vibrations. A consistent approach to the quadrupole-octupole collective vibrations coupled with the rotational motion enables to distinguish between various scenarios of disappearance of the E2 transitions in negative-parity bands. The here presented theoretical estimates are compared with the recent experimental energies and transition probabilities in and between the ground-state and low-energy negaive-parity bands in $^{156}$Dy. A realistic collective Hamiltonian contains the potential energy term obtained through the macroscopic-microscopic Strutinsky-like method with particle-number-projected BCS approach and deformation-dependent mass tensor defined in vibrational-rotational, nine-dimensional collective space. The symmetrization procedure ensures the uniqueness of the Hamiltonian eigensolutions with respect to the laboratory coordinate system. This quadrupole-octupole collective approach may also allow to find and/or verify some fingerprints of possible high-order symmetries (e.g. tetrahedral, octahedral,...) in nuclear collective bands.
By employing the angular momentum projection technique we propose a method to reliably calculate the quantum spectrum of nuclear collective rotation. The method utilizes several cranked mean-field states with different rotational frequencies and they are superposed in the sense of the configuration mixing or the generator coordinate method, after performing the projection; the idea was originally suggested by Peierls-Thouless in 1962. It is found that the spectrum as a result of the configuration mixing does not essentially depend on chosen sets of cranking frequencies if the number of mean-field states utilized in the mixing is larger than a certain small value. We apply this method to three examples employing the Gogny D1S effective interaction and show that it is useful to study high-spin rotational bands by means of the angular momentum projection method.
Structure of eight superdeformed bands in the nucleus 151Tb is analyzed using the results of the Hartree-Fock and Woods-Saxon cranking approaches. It is demonstrated that far going similarities between the two approaches exist and predictions related to the structure of rotational bands calculated within the two models are nearly parallel. An interpretation scenario for the structure of the superdeformed bands is presented and predictions related to the exit spins are made. Small but systematic discrepancies between experiment and theory, analyzed in terms of the dynamical moments, J(2), are shown to exist. The pairing correlations taken into account by using the particle-number-projection technique are shown to increase the disagreement. Sources of these systematic discrepancies are discussed -- they are most likely related to the yet not optimal parametrization of the nuclear interactions used.
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