6,849 research outputs found
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
(), when (and only when) 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 using a particle-number conserving method based on a cranked shell model
The rotational bands in nuclei with 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
( and ) and deformation parameters ( and
) are proposed. The experimental kinematic moments of inertia
for the rotational bands in even-even, odd- and odd-odd nuclei, and the
bandhead energies of the 1-quasiparticle bands in odd- nuclei, are
reproduced quite well by the PNC-CSM calculations. By analyzing the
-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 Cd and Cd
The effect of nuclear superfluidity on antimagnetic rotation bands in
Cd and 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
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- orbitals in transfermium nuclei
The structure of nuclei with 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 ( and ) 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- 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- nuclei Cm and 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
are reproduced very well by the PNC-CSM calculations. By examining the
-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.
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