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Register a new userPure Collective Precession Motion of High-Spin Torus Isomer
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We investigate the precession motion of the exotic torus configuration in high-spin excited states of $^{40}$Ca. For this aim, we use the three-dimensional time-dependent Hartree-Fock (TDHF) method. Although the high-spin torus isomer is a unique quantum object characterized by the alignment of angular momenta of independent single-particle motions, we find that the obtained moment of inertia for rotations about an axis perpendicular to the symmetry axis is close to the rigid-body value. We also analyze the microscopic structure of the precession motion using the random-phase approximation (RPA) method for high-spin states. In the RPA calculation, the precession motion of the torus isomer is generated by coherent superposition of many one-particle-one-hole excitations across the sloping Fermi surface that strongly violates the time-reversal symmetry. By comparing results of the TDHF and the RPA calculations, we find that the precession motion obtained by the TDHF calculation is a pure collective motion well decoupled from other collective modes.
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We systematically investigate the existence of exotic torus isomers and their precession motions for a series of $N=Z$ even-even nuclei from $^{28}$Si to $^{56}$Ni. We analyze the microscopic shell structure of the torus isomer and discuss why the torus shape is generated beyond the limit of large oblate deformation. We use the cranked three-dimensional Hartree-Fock (HF) method with various Skyrme interactions in a systematic search for high-spin torus isomers. We use the three-dimensional time-dependent Hartree-Fock (TDHF) method for describing the precession motion of the torus isomer. We obtain high-spin torus isomers in $^{36}$Ar, $^{40}$Ca, $^{44}$Ti, $^{48}$Cr, and $^{52}$Fe. The emergence of the torus isomers is associated with the alignments of single-particle angular momenta, which is the same mechanism as found in $^{40}$Ca. It is found that all the obtained torus isomers execute the precession motion at least two rotational periods. The moment of inertia about a perpendicular axis, which characterizes the precession motion, is found to be close to the classical rigid-body value. The high-spin torus isomer of $^{40}$Ca is not an exceptional case. Similar torus isomers exist widely in nuclei from $^{36}$Ar to $^{52}$Fe and they execute the precession motion. The torus shape is generated beyond the limit of large oblate deformation by eliminating the $0s$ components from all the deformed single-particle wave functions to maximize their mutual overlaps.
Finite-dimensional Lie algebras of vector fields determine geometrical collective models in quantum and classical physics. Every set of vector fields on Euclidean space that generates the Lie algebra sl(3, R) and contains the angular momentum algebra so(3) is determined. The subset of divergence-free sl(3, R) vector fields is proven to be indexed by a real number $Lambda$. The $Lambda=0$ solution is the linear representation that corresponds to the Riemann ellipsoidal model. The nonlinear group action on Euclidean space transforms a certain family of deformed droplets among themselves. For positive $Lambda$, the droplets have a neck that becomes more pronounced as $Lambda$ increases; for negative $Lambda$, the droplets contain a spherical bubble of radius $|Lambda|^{{1/3}}$. The nonlinear vector field algebra is extended to the nonlinear general collective motion algebra gcm(3) which includes the inertia tensor. The quantum algebraic models of nonlinear nuclear collective motion are given by irreducible unitary representations of the nonlinear gcm(3) Lie algebra. These representations model fissioning isotopes ($Lambda>0$) and bubble and two-fluid nuclei ($Lambda<0$).
We investigate the possibility of the existence of the exotic torus configuration in the high-spin excited states of $^{40}$Ca. We here consider the spin alignments about the symmetry axis. To this end, we use a three-dimensional cranked Skyrme Hartree-Fock method and search for stable single-particle configurations. We find one stable state with the torus configuration at the total angular momentum $J=$ 60 $hbar$ and an excitation energy of about 170 MeV in all calculations using various Skyrme interactions. The total angular momentum J=60 $hbar$ consists of aligned 12 nucleons with the orbital angular momenta $Lambda=+4$, +5, and +6 for spin up-down neutrons and protons. The obtained results strongly suggest that a macroscopic amount of circulating current breaking the time-reversal symmetry emerges in the high-spin excited state of $^{40}$Ca.
The general problem of dissipation in macroscopic large-amplitude collective motion and its relation to energy diffusion of intrinsic degrees of freedom of a nucleus is studied. By applying the cranking approach to the nuclear many-body system, a set of coupled dynamical equations for the collective classical variable and the quantum mechanical occupancies of the intrinsic nuclear states is derived. Different dynamical regimes of the intrinsic nuclear motion and its consequences on time properties of collective dissipation are discussed.
The status of the macroscopic and microscopic description of the collective quadrupole modes is reviewed, where limits due to non-adiabaticity and decoherence are exposed. The microscopic description of the yrast states in vibrator-like nuclei in the framework of the rotating mean field is presented.
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