39,355 research outputs found
Practical Calculation Scheme for Generalized Seniority
We propose a scheme or procedure for doing practical calculations with
generalized seniority. It reduces the total computing time by calculating and
storing in advance a set of intermediate quantities, taking advantage of the
memory capability of modern computers. The requirements and performance of the
algorithm are analyzed in detail
Accuracy of the new pairing theory and its improvement
Recently I proposed a new method for solving the pairing Hamiltonian with the
pair-condensate wavefunction ansatz based on the Heisenberg equations of motion
for the density matrix operators. In this work an improved version is given by
deriving the relevant equations more carefully. I evaluate both versions in a
large ensemble with random interactions, and the accuracy of the methods is
given statistically in terms of root-mean-square derivations from the exact
results. The widely used variational calculation is also done and the results
and computing-time costs are compared
A Number-Conserving Theory for Nuclear Pairing
A microscopic theory for nuclear pairing is proposed through the generalized
density matrix formalism. The analytical equations are as simple as that of the
BCS theory, and could be solved within a similar computer time. The current
theory conserves the exact particle number, and is valid at arbitrary pairing
strength (including those below the BCS critical strength). These are the two
main advantages over the conventional BCS theory. The theory is also of
interests to other mesoscopic systems
Random Phase Approximation without Bogoliubov Quasi-particles
A new version of random phase approximation is proposed for low-energy
harmonic vibrations in nuclei. The theory is not based on the quasi-particle
vacuum of the BCS/HFB ground state, but on the pair condensate determined in
Ref. [4]. The current treatment conserves the exact particle number all the
time. As a first test the theory is considered in two special cases: the
degenerate model (large pairing limit) and the vanished-pairing limit
Generalized Seniority on Deformed Single-Particle Basis
Recently we proposed [62] a fast computing scheme for generalized seniority
on spherical single-particle basis. This work redesigns the scheme to make it
applicable to deformed single-particle basis. The algorithm is applied to the
rare-earth nucleus Gd for intrinsic (body-fixed frame)
neutron excitations under the low-momentum {\emph{NN}} interaction
. By allowing as many as four broken pairs, we compute the
lowest intrinsic states of several multipolarity. These states converge
well to the exact ones, showing generalized seniority is very effective in
truncating the deformed shell model. Under realistic interactions, the picture
remains approximately valid that the ground state is a coherent pair
condensate, and the pairs gradually break up as excitation energy increases
Solving for the Particle-Number-Projected HFB Wavefunction
Recently we proposed a particle-number-conserving theory for nuclear pairing
[Jia, Phys. Rev. C 88, 044303 (2013)] through the generalized density matrix
formalism. The relevant equations were solved for the case when each
single-particle level has a distinct set of quantum numbers and could only pair
with its time-reversed partner (BCS-type Hamiltonian). In this work we consider
the more general situation when several single-particle levels could have the
same set of quantum numbers and pairing among these levels is allowed (HFB-type
Hamiltonian). The pair condensate wavefunction (the HFB wavefunction projected
onto good particle number) is determined by the equations of motion for density
matrix operators instead of the variation principle. The theory is tested in
the simple two-level model with factorizable pairing interactions and the
semi-realistic model with the zero-range delta interaction
Particle-Hole Symmetry in Generalized Seniority, Microscopic Interacting Boson (Fermion) Model, Nucleon-Pair Approximation, and Others
The particle-hole symmetry (equivalence) of the full shell-model Hilbert
space is straightforward and routinely used in practical calculations. In this
work we show that this symmetry is preserved in the subspace truncated at a
certain generalized seniority, and give the explicit transformation between the
states in the two types (particle and hole) of representations. Based on the
results, we study the particle-hole symmetry in popular theories that could be
regarded as further truncations on top of the generalized seniority, including
the microscopic interacting boson (fermion) model, the nucleon-pair
approximation, and others
Generalized-Seniority Pattern and Thermal Properties in Even Sn Isotopes
Even tin isotopes of mass number are calculated with
realistic interactions in the generalized-seniority approximation of the
nuclear shell model. For each nucleus, we compute the lowest ten thousand
states ( of each parity) up to around MeV in excitation energy, by
allowing as many as four broken pairs. The lowest fifty eigen energies of each
parity are compared with the exact results of the large-scale shell-model
calculation. The wavefunctions of the mid-shell nuclei show a clear pattern of
the stepwise breakup of condensed coherent pairs with increasing excitation
energy. We also compute in the canonical ensemble the thermal properties --
level density, entropy, and specific heat -- in relation to the thermal pairing
phase transition
The FWHM of local pulses and the corresponding power-law index of gamma-ray burst FRED pulses
The FWHM of gamma-ray burst (GRB) pulses is known to be related with energy
by a power-law. We wonder if the power-law index is related with the
corresponding local pulse width . Seven FRED (fast rise and exponential
decay) pulse GRBs are employed to study this issue, where six of them were
interpreted recently by the relativistic curvature effect (the Doppler effect
of fireballs) and the corresponding local pulses were intensely studied. A
regression analysis shows an anti-correlation between and with a slope of . This suggests that, for the class of
the GRB pulses which are consequences of the curvature effect, the difference
of the local pulse width might lead to the variation of the power law index,
where the smaller the width the larger the value of . Since the number
of sources employed in this analysis is small, our result is only a preliminary
one which needs to be confirmed by larger samples.Comment: 14 pages, 2 figures. accepted by ApJ
Equivalent Representations of Collective Hamiltonian and Implication on Generalized Density Matrix Method
We discuss equivalent representations of the collective/bosonic Hamiltonian
in the form of Taylor expansion over collective coordinate and momentum.
Different expansions are equivalent if they are related by a transformation of
collective variables. The independent parameters in the collective Hamiltonian
are identified, which are much less in number than it appears. In this sense,
the microscopic generalized density matrix method fixes the collective
Hamiltonian completely, which seems to solve the old problem of microscopic
calculation of the collective Hamiltonian.Comment: 2 page
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