Extension Of Bertrand's Theorem And Factorization Of The Radial Schr\"odinger Equation

The Bertrand's theorem is extended, i.e. closed orbits still may exist for other central potentials than the power law Coulomb potential and isotropic harmonic oscillator. It is shown that for the combined potential $V(r)=W(r)+b/r^2$ ($W(r)=ar^{\nu}$), when (and only when) $W(r)$ is the Coulomb potential or isotropic harmonic oscillator, closed orbits still exist for suitable angular momentum. The correspondence between the closeness of classical orbits and the existence of raising and lowering operators derived from the factorization of the radial Schr\"odinger equation is investigated.Comment: 4 pages, 1 figug

Systematic investigation of the rotational bands in nuclei with Z≈100Z \approx 100 using a particle-number conserving method based on a cranked shell model

The rotational bands in nuclei with $Z \approx 100$ are investigated systematically by using a cranked shell model (CSM) with the pairing correlations treated by a particle-number conserving (PNC) method, in which the blocking effects are taken into account exactly. By fitting the experimental single-particle spectra in these nuclei, a new set of Nilsson parameters ($\kappa$ and $\mu$) and deformation parameters ($\varepsilon_2$ and $\varepsilon_4$) are proposed. The experimental kinematic moments of inertia for the rotational bands in even-even, odd-$A$ and odd-odd nuclei, and the bandhead energies of the 1-quasiparticle bands in odd-$A$ nuclei, are reproduced quite well by the PNC-CSM calculations. By analyzing the $\omega$-dependence of the occupation probability of each cranked Nilsson orbital near the Fermi surface and the contributions of valence orbitals in each major shell to the angular momentum alignment, the upbending mechanism in this region is understood clearly.Comment: 21 pages, 24 figures, extended version of arXiv: 1101.3607 (Phys. Rev. C83, 011304R); added refs.; added Fig. 4 and discussions; Phys. Rev. C, in pres

Nuclear superfluidity for antimagnetic rotation in 105^{105}Cd and 106^{106}Cd

The effect of nuclear superfluidity on antimagnetic rotation bands in $^{105}$Cd and $^{106}$Cd are investigated by the cranked shell model with the pairing correlations and the blocking effects treated by a particle-number conserving method. The experimental moments of inertia and the reduced $B(E2)$ transition values are excellently reproduced. The nuclear superfluidity is essential to reproduce the experimental moments of inertia. The two-shears-like mechanism for the antimagnetic rotation is investigated by examining the shears angle, i.e., the closing of the two proton hole angular momenta, and its sensitive dependence on the nuclear superfluidity is revealed.Comment: 14 pages, 4 figure

Rotation and alignment of high-jj orbitals in transfermium nuclei

The structure of nuclei with $Z\sim100$ is investigated systematically by the Cranked Shell Model (CSM) with pairing correlations treated by a Particle-Number Conserving (PNC) method. In the PNC method, the particle number is conserved and the Pauli blocking effects are taken into account exactly. By fitting the experimental single-particle spectra in these nuclei, a new set of Nilsson parameters ($\kappa$ and $\mu$) is proposed. The experimental kinematic moments of inertia and the band-head energies are reproduced quite well by the PNC-CSM calculations. The band crossing, the effects of high-$j$ intruder orbitals and deformation are discussed in detail.Comment: To appear in the Proceedings of the International Nuclear Physics Conference (INPC2013), June 2-7, 2013, Florence, Ital

A method to find unstable periodic orbits for the diamagnetic Kepler Problem

A method to determine the admissibility of symbolic sequences and to find the unstable periodic orbits corresponding to allowed symbolic sequences for the diamagnetic Kepler problem is proposed by using the ordering of stable and unstable manifolds. By investigating the unstable periodic orbits up to length 6, a one to one correspondence between the unstable periodic orbits and their corresponding symbolic sequences is shown under the system symmetry decomposition

Particle-number conserving analysis of rotational bands in 247,249Cm and 249Cf

The recently observed high-spin rotational bands in odd-$A$ nuclei $^{247, 249}$Cm and $^{249}$Cf [Tandel \textit{et al.}, Phys. Rev. C 82 (2010) 041301R] are investigated by using the cranked shell model (CSM) with the pairing correlations treated by a particle-number conserving (PNC) method in which the blocking effects are taken into account exactly. The experimental moments of inertia and alignments and their variations with the rotational frequency $\omega$ are reproduced very well by the PNC-CSM calculations. By examining the $\omega$-dependence of the occupation probability of each cranked Nilsson orbital near the Fermi surface and the contributions of valence orbitals to the angular momentum alignment in each major shell, the level crossing and upbending mechanism in each nucleus is understood clearly.Comment: 6 pages, 5 figures, to be published in Phys. Rev.