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 $^{158}_{~64}$Gd$_{94}$ for intrinsic (body-fixed frame) neutron excitations under the low-momentum {\emph{NN}} interaction $V_{{\rm{low}}-k}$. By allowing as many as four broken pairs, we compute the lowest $300$ 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 $A = 108 \sim 124$ 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 ($5000$ of each parity) up to around $8$ 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 $\alpha$ is related with the corresponding local pulse width $FWHM_0$. 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 $log \alpha$ and $log FWHM_0$ with a slope of $-0.37\pm0.13$. 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 $\alpha$. 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