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Register a new userFinite Element Method for Solving the Collective Nuclear Model with Tetrahedral Symmetry
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We apply a new calculation scheme of a finite element method (FEM) for solving an elliptic boundary-value problem describing a quadrupole vibration collective nuclear model with tetrahedral symmetry. We use of shape functions constructed with interpolation Lagrange polynomials on a triangle finite element grid and compare the FEM results with obtained early by a finite difference method.
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We review the recent progress on studying the nuclear collective dynamics by solving the Boltzmann-Uehling-Uhlenbeck (BUU) equation with the lattice Hamiltonian method treating the collision term by the full-ensemble stochastic collision approach. This lattice BUU (LBUU) method has recently been developed and implemented in a GPU parallel computing technique, and achieves a rather stable nuclear ground-state evolution and high accuracy in evaluating the nucleon-nucleon (NN) collision term. This new LBUU method has been applied to investigate the nuclear isoscalar giant monopole resonances and isovector giant dipole resonances. While the calculations with the LBUU method without the NN collision term (i.e., the lattice Hamiltonian Vlasov method) describe reasonably the excitation energies of nuclear giant resonances, the full LBUU calculations can well reproduce the width of the giant dipole resonance of $^{208}$Pb by including a collisional damping from NN scattering. The observed strong correlation between the width of nuclear giant dipole resonance and the NN elastic cross section suggests that the NN elastic scattering plays an important role in nuclear collective dynamics, and the width of nuclear giant dipole resonance provides a good probe of the in-medium NN elastic cross section.
We propose a new method to solve the eigen-value problem with a two-center single-particle potential. This method combines the usual matrix diagonalization with the method of separable representation of a two-center potential, that is, an expansion of the two-center potential with a finite basis set. To this end, we expand the potential on a harmonic oscillator basis, while single-particle wave functions on a combined basis with a harmonic oscillator and eigen-functions of a one-dimensional two-center potential. In order to demonstrate its efficiency, we apply this method to a system with two $^{16}$O nuclei, in which the potential is given as a sum of two Woods-Saxon potentials.
We have developed an efficient method for quantum number projection from most general HFB type mean-field states, where all the symmetries like axial symmetry, number conservation, parity and time-reversal invariance are broken. Applying the method, we have microscopically calculated, for the first time, the energy spectra based on the exotic tetrahedral deformation in $^{108,110}$Zr. The nice low-lying rotational spectra, which have all characteristic features of the molecular tetrahedral rotor, are obtained for large tetrahedral deformation, $alpha_{32} gtsim 0.25$, while the spectra are of transitional nature between vibrational and rotational with rather high excitation energies for $alpha_{32}approx 0.1-0.2$
We have recently developed an efficient method of performing the full quantum number projection from the most general mean-field (HFB type) wave functions including the angular momentum, parity as well as the proton and neutron particle numbers. With this method, we have been investigating several nuclear structure mechanisms. In this report, we discuss the obtained quantum rotational spectra of the tetrahedral nuclear states formulating certain experimentally verifiable criteria, of the high-spin states, focussing on the wobbling- and chiral-bands, and of the drip-line nuclei as illustrative examples.
We study gauge symmetry breaking by adiabatic approximation in the adiabatic self-consistent collective coordinate (ASCC) method. In the previous study, we found that the gauge symmetry of the equation of collective submanifold is (partially) broken by its decomposition into the three moving-frame equations depending on the order of $p$. In this study, we discuss the gauge symmetry breaking by the truncation of the adiabatic expansion. A particular emphasis is placed on the symmetry under the gauge transformations which are not point transformations. We also discuss a possible version of the ASCC method including the higher-order operators which can keep the gauge symmetry.
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