Does a proton "bubble" structure exist in the low-lying states of 34Si?

The possible existence of a "bubble" structure in the proton density of $^{34}$Si has recently attracted a lot of research interest. To examine the existence of the "bubble" structure in low-lying states, we establish a relativistic version of configuration mixing of both particle number and angular momentum projected quadrupole deformed mean-field states and apply this state-of-the-art beyond relativistic mean-field method to study the density distribution of the low-lying states in $^{34}$Si. An excellent agreement with the data of low-spin spectrum and electric multipole transition strengths is achieved without introducing any parameters. We find that the central depression in the proton density is quenched by dynamic quadrupole shape fluctuation, but not as significantly as what has been found in a beyond non-relativistic mean-field study. Our results suggest that the existence of proton "bubble" structure in the low-lying excited $0^+_2$ and $2^+_1$ states is very unlikely.Comment: 6 pages, 8 figures and 1 table, accepted for publication in Physics Letters

Low-lying states in 30^{30}Mg: a beyond relativistic mean-field investigation

The recently developed model of three-dimensional angular momentum projection plus generator coordinate method on top of triaxial relativistic mean-field states has been applied to study the low-lying states of $^{30}$Mg. The effects of triaxiality on the low-energy spectra and E0 and E2 transitions are examined.Comment: 6 pages, 3 figures, 1 table, talk presented at the 17th nuclear physics conference "Marie and Pierre Curie" Kazimierz Dolny, 22-26th September 2010, Polan

Rapid structural change in low-lying states of neutron-rich Sr and Zr isotopes

The rapid structural change in low-lying collective excitation states of neutron-rich Sr and Zr isotopes is tudied by solving a five-dimensional collective Hamiltonian with parameters determined by both relativistic mean-field and non-relativistic Skyrme-Hartree-Fock calculations using the PC-PK1 and SLy4 forces respectively. Pair correlations are treated in BCS method with either a separable pairing force or a density-dependent zero-range force. The isotope shifts, excitation energies, electric monopole and quadrupole transition strengths are calculated and compared with corresponding experimental data. The calculated results with both the PC-PK1 and SLy4 forces exhibit a picture of spherical-oblate-prolate shape transition in neutron-rich Sr and Zr isotopes. Compared with the experimental data, the PC-PK1 (or SLy4) force predicts a more moderate (or dramatic) change in most of the collective properties around N=60. The underlying microscopic mechanism responsible for the rapid transition is discussed.Comment: 10 pages (twocolumn), 10 figure

Beyond relativistic mean-field studies of low-lying states in neutron-deficient krypton isotopes

Neutron-deficient krypton isotopes are of particular interest due to the coexistence of oblate and prolate shapes in low-lying states and the transition of ground-state from one dominate shape to another as a function of neutron number. A detailed interpretation of these phenomena in neutron-deficient Kr isotopes requires the use of a method going beyond a mean-field approach that permits to determine spectra and transition probabilities. The aim of this work is to provide a systematic calculation of low-lying state in the even-even 68-86Kr isotopes and to understand the shape coexistence phenomenon and the onset of large collectivity around N=40 from beyond relativistic mean-field studies. The starting point of our method is a set of relativistic mean-field+BCS wave functions generated with a constraint on triaxial deformations (beta, gamma). The excitation energies and electric multipole transition strengths of low-lying states are calculated by solving a five-dimensional collective Hamiltonian (5DCH) with parameters determined by the mean-field wave functions. To examine the role of triaxiality, a configuration mixing of both particle number (PN) and angular momentum (AM) projected axially deformed states is also carried out within the exact generator coordinate method (GCM) based on the same energy density functional. The energy surfaces, the excitation energies of 0^+_2, 2^+_1, 2^+_2 states, as well as the E0 and E2 transition strengths are compared with the results of similar 5DCH calculations but with parameters determined by the non-relativistic mean-field wave functions, as well as with the available data...Comment: 23 pages, 10 figure

Quantum generalized Reed-Solomon codes: Unified framework for quantum MDS codes

We construct a new family of quantum MDS codes from classical generalized Reed-Solomon codes and derive the necessary and sufficient condition under which these quantum codes exist. We also give code bounds and show how to construct them analytically. We find that existing quantum MDS codes can be unified under these codes in the sense that when a quantum MDS code exists, then a quantum code of this type with the same parameters also exists. Thus as far as is known at present, they are the most important family of quantum MDS codes.Comment: 9 pages, no figure

An analysis of the inertia weight parameter for binary particle swarm optimization

In particle swarm optimization, the inertia weight is an important parameter for controlling its search capability. There have been intensive studies of the inertia weight in continuous optimization, but little attention has been paid to the binary case. This study comprehensively investigates the effect of the inertia weight on the performance of binary particle swarm optimization, from both theoretical and empirical perspectives. A mathematical model is proposed to analyze the behavior of binary particle swarm optimization, based on which several lemmas and theorems on the effect of the inertia weight are derived. Our research findings suggest that in the binary case, a smaller inertia weight enhances the exploration capability while a larger inertia weight encourages exploitation. Consequently, this paper proposes a new adaptive inertia weight scheme for binary particle swarm optimization. This scheme allows the search process to start first with exploration and gradually move towards exploitation by linearly increasing the inertia weight. The experimental results on 0/1 knapsack problems show that the binary particle swarm optimization with the new increasing inertia weight scheme performs significantly better than that with the conventional decreasing and constant inertia weight schemes. This study verifies the efficacy of increasing inertia weight in binary particle swarm optimization

Triaxially deformed relativistic point-coupling model for Λ\Lambda hypernuclei: a quantitative analysis of hyperon impurity effect on nuclear collective properties

The impurity effect of hyperon on atomic nuclei has received a renewed interest in nuclear physics since the first experimental observation of appreciable reduction of $E2$ transition strength in low-lying states of hypernucleus $^{7}_\Lambda$Li. Many more data on low-lying states of $\Lambda$ hypernuclei will be measured soon for $sd$-shell nuclei, providing good opportunities to study the $\Lambda$ impurity effect on nuclear low-energy excitations. We carry out a quantitative analysis of $\Lambda$ hyperon impurity effect on the low-lying states of $sd$-shell nuclei at the beyond-mean-field level based on a relativistic point-coupling energy density functional (EDF), considering that the $\Lambda$ hyperon is injected into the lowest positive-parity ($\Lambda_s$) and negative-parity ($\Lambda_p$) states. We adopt a triaxially deformed relativistic mean-field (RMF) approach for hypernuclei and calculate the $\Lambda$ binding energies of hypernuclei as well as the potential energy surfaces (PESs) in $(\beta, \gamma)$ deformation plane. We also calculate the PESs for the $\Lambda$ hypernuclei with good quantum numbers using a microscopic particle rotor model (PRM) with the same relativistic EDF. The triaxially deformed RMF approach is further applied in order to determine the parameters of a five-dimensional collective Hamiltonian (5DCH) for the collective excitations of triaxially deformed core nuclei. Taking $^{25,27}_{\Lambda}$Mg and $^{31}_{\Lambda}$Si as examples, we analyse the impurity effects of $\Lambda_s$ and $\Lambda_p$ on the low-lying states of the core nuclei...Comment: 15 pages with 18 figures and 1 table (version to be published in Physical Review C