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Register a new userTowards symmetry-unrestricted Skyrme-HFB in coordinate-space representation: the example of rotational bands of the octupole-deformed nucleus $^{222}$Th
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We report on cranked Skyrme-HFB calculations of rotational bands of the octupole-deformed nucleus $^{222}$Th. A sudden change in configuration is observed, with the shape of the yrast state jumping from large octupole deformation at low spin to small octupole deformation at high spin.
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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.
In the light of recent experimental developments, increasing attention is devoted to nuclear phenomena related to rotational excitations of exotic intrinsic nuclear configurations that often lack symmetries present in the majority of nuclei. Examples include configurations with a non-vanishing octupole moment. In order to describe this kind of states, we have developed a new computer code to solve the self-consistent mean-field equations, able to use most of todays effective Skyrme interactions and working in coordinate-space. We report on the development of MOCCa, a code based on the same principles as EV8, but offering the user individual control on many symmetry assumptions. In addition, the HF+BCS pairing treatment of EV8 has been generalised to the full machinery of Hartree-Fock-Bogoliubov transformations. We discuss as example the static fission barrier of $^{226}$Ra, prefacing extended studies in the region, using the recent series of Skyrme parameterizations SLy5s1 through SLy5s8.
We describe the first version (v1.00) of the code HFBRAD which solves the Skyrme-Hartree-Fock or Skyrme-Hartree-Fock-Bogolyubov equations in the coordinate representation within the spherical symmetry. A realistic representation of the quasiparticle wave functions on the space lattice allows for performing calculations up to the particle drip lines. Zero-range density-dependent interactions are used in the pairing channel. The pairing energy is calculated by either using a cut-off energy in the quasiparticle spectrum or the regularization scheme proposed by A. Bulgac and Y. Yu.
The survey of different configurations near Fermi surface of 138Nd results in 12 lowest configurations, at both positive- and negative-deformations. These are calculated to be the energetically lowest configurations. The results show that, for both EDFs, the rotational states based on positive-minimum, which is at gamma~35, are lower than the respective configurations with negative-deformation. The general trends of the spin-versus-omega curve, and the energy-versus-spin curve reproduce well those of the experimental data. Further, for the observed bands `T1-T8, the calculated results using SLy4L allows the configurations of the observed bands to be assigned. The calculations predict transitional quadrupole moments, which can be used to compare with future experimental data. The current cranked self-consistent mean-field calculations of the near-yrast high-spin rotational bands in 138Nd reproduce well the experimental data. The results suggest that the experimentally observed bands can be assigned to the calculated bands with various configurations at the positive-deformation. The predictions of the current calculations are complementary to that of the well-know macroscopic-microscopic calculations, both of which await future experiment to verify.
A Reflection ASymmetric Relativistic Mean Field (RAS-RMF) approach is developed by expanding the equations of motion for both the nucleons and the mesons on the eigenfunctions of the two-center harmonic-oscillator potential. The efficiency and reliability of the RAS-RMF approach are demonstrated in its application to the well-known octupole deformed nucleus $^{226}$Ra and the available data, including the binding energy and the deformation parameters, are well reproduced.
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