Geometric Duality for Convex Vector Optimization Problems

Geometric duality theory for multiple objective linear programming problems turned out to be very useful for the development of efficient algorithms to generate or approximate the whole set of nondominated points in the outcome space. This article extends the geometric duality theory to convex vector optimization problems.Comment: 21 page

Nonstandard limit theorem for infinite variance functionals

We consider functionals of long-range dependent Gaussian sequences with infinite variance and obtain nonstandard limit theorems. When the long-range dependence is strong enough, the limit is a Hermite process, while for weaker long-range dependence, the limit is $\alpha$-stable L\'{e}vy motion. For the critical value of the long-range dependence parameter, the limit is a sum of a Hermite process and $\alpha$-stable L\'{e}vy motion.Comment: Published in at http://dx.doi.org/10.1214/07-AOP345 the Annals of Probability (http://www.imstat.org/aop/) by the Institute of Mathematical Statistics (http://www.imstat.org

Nuclear shape coexistence : a study of the even-even Hg isotopes using the interacting boson model with configuration mixing

Background: The Po, Pb, Hg, and Pt region is known for the presence of coexisting structures that correspond to different particle-hole configurations in the shell model language or equivalently to nuclear shapes with different deformation. Purpose: We intend to study the configuration mixing phenomenon in the Hg isotopes and to understand how different observables are influenced by it. Method: We study in detail a long chain of mercury isotopes, Hg172-200, using the interacting boson model with configuration mixing. The parameters of the Hamiltonians are fixed through a least-squares fit to the known energies and absolute B(E2) transition rates of states up to 3 MeV. Results: We obtained the IBM-CM Hamiltonians and we calculate excitation energies, B(E2)'s, quadrupole shape invariants, wave functions, isotopic shifts, and mean-field energy surfaces. Conclusions: We obtain a fairly good agreement with the experimental data for all the studied observables and we conclude that the Hamiltonian and the states we obtain constitute a good approximation to the Hg isotopes

Exactly solvable models of nuclei

In this paper a review is given of a class of sub-models of both approaches, characterized by the fact that they can be solved exactly, highlighting in the process a number of generic results related to both the nature of pair-correlated systems as well as collective modes of motion in the atomic nucleus.Comment: 34 pages, 8 figures accepted for publication in Scholarpedi

A focus on shape coexistence in nuclei

The present collection of articles focuses on new directions and developments under the title of shape coexistence in nuclei, following our 2011 Reviews of Modern Physics article (K Heyde and J L Wood)

Thermodynamical properties of a mean-field plus pairing model and applications for the Fe nuclei

A mean-field plus pairing model for atomic nuclei in the Fe region was studied using a finite-temperature quantum Monte-Carlo method. We present results for thermodynamical quantities such as the internal energy and the specific heat. These results give indications of a phase transition related to the pairing amongst nucleons, around temperatures of 0.7 MeV. The influence of the residual interaction and of the size of the model space on the nuclear level densities is discussed too.Comment: 23 pages, including 17 eps figure

Disentangling the nuclear shape coexistence in even-even Hg isotopes using the interacting boson model

We intend to provide a consistent description of the even-even Hg isotopes, 172-200Hg, using the interacting boson model including configuration mixing. We pay special attention to the description of the shape of the nuclei and to its connection with the shape coexistence phenomenon.Comment: To appear in CGS15 conference proceedings (EPJ Web of Conferences

Quest of shape coexistence in Zr isotopes

Background: The mass region with A approximate to 100 and Z approximate to 40 is known to experience a sudden onset of deformation. The presence of the subshell closure Z = 40 makes it feasible to create particle-hole excitations at a moderate excitation energy and, therefore, likely intruder states could be present in the low-lying spectrum. In other words, shape coexistence is expected to be a key ingredient to understand this mass region. Purpose: The aim of this work is to describe excitation energies, transition rates, radii, and two-neutron separation energies for the even-even Zr94-110 nuclei and, moreover, to obtain information about wave functions and deformation. Method: The interacting boson model with configuration mixing will be the framework to study the even-even Zr nuclei, considering only two types of configurations: 0particle-0hole and 2particle-2hole excitations. On one hand, the parameters appearing in the Hamiltonian and in the E2 transition operator are fixed trough a least-squares fit to the whole available experimental information. On the other hand, once the parameters have been fixed, the calculations allow to obtain a complete set of observables for the whole even-even Zr chain of isotopes. Results: Spectra, transition rates, radii, rho(2)(E0), and two-neutron separation energies have been calculated and a good agreement with the experimental information has been obtained. Moreover, a detailed study of the wave function has been conducted and mean-field energy surfaces and deformation have been computed too. Conclusions: The importance of shape coexistence has been shown to correctly describe the A approximate to 100 mass area for even-even Zr nuclei. This work confirmed the rather spherical nature of the ground state of Zr94-98 and its deformed nature for Zr100-110 isotopes. The sudden onset of deformation in Zr-100 is owing to the rapid lowering of a deformed (intruder) configuration which is high-lying in lighter isotopes

The influence of intruder states in even-even Po isotopes

We study the role of intruder states and shape coexistence in the even-even $^{190-206}$Po isotopes, through an interacting boson model with configuration mixing calculation. We analyzed the results in the light of known systematics on various observable in the Pb region, paying special attention to the unperturbed energy systematics and quadrupole deformation. We find that shape coexistence in the Po isotopes behaves in very much the same way as in the Pt isotopes, i.e., it is somehow hidden, contrary to the situation in the Pb and the Hg isotopes.Comment: Contribution to the Nuclear Structure and Dynamics 2015 (Portorose, Slovenia) proceeding