Pionic BEC--BCS crossover at finite isospin chemical potential

We study the character change of the pionic condensation at finite isospin chemical potential \mu_\mathrm{I} by adopting the linear sigma model as a non-local interaction between quarks. At low |\mu_\mathrm{I}| the condensation is purely bosonic, then the Cooper pairing around the Fermi surface grows gradually as |\mu_\mathrm{I}| increases. This q-\bar q pairing is weakly coupled in comparison with the case of the q-q pairing that leads to color superconductivity.Comment: 17 pages, 3 figures, typos in eq.(6) and refs.[37] and [41] are corrected, published in Phys. Rev.

Low-lying isovector monopole resonances

The mass difference between the even-even isobaric nuclei having the valence nucleons on the same degenerate level is attributed to a Josephson-type interaction between pairs of protons and pairs of neutrons. This interaction can be understood as an isospin symmetry-breaking mean field for a four-particle interaction separable in the two particles-two holes channel. The strength of this mean field is estimated within an o(5) algebraic model, by using the experimental value of the inertial parameter for the collective isorotation induced by the breaking of the isospin symmetry. In superfluid nuclei, the presumed interaction between the proton and neutron condensates leads to coupled oscillations of the BCS gauge angles, which should appear in the excitation spectrum as low-lying isovector monopole resonances.Comment: 16 pages/LaTex + 1 PostScript figure; related to cond-mat/9904242, math-ph/000500

Pairing and Isospin Symmetry in Proton-Rich Nuclei

Unlike their lighter counterparts, most odd-odd N=Z nuclei with mass A > 40 40 have ground states with isospin T=1, suggesting an increased role for the isovector pairing interaction. A simple SO(5) seniority-like model of this interaction reveals a striking and heretofore unnoticed interplay between like-particle and neutron-proton isovector pairing near N=Z that is reflected in the number of each kind of pair as a function of A and T. Large scale shell-model calculations exhibit the same trends, despite the simultaneous presence of isoscalar pairs, deformation, and other correlations.Comment: 8 pages + 2 postscript figures, in RevTeX. Discussion of isospin projection in HFB added. This version to appear in Phys. Lett.

Recoding and multidimensional analyses of vegetation data: a comparison

Two simulated coenoclines and a real data set were differently recoded with respect to the Braun-Blanquet coding (including presence/absence) and analysed through the most common multidimensional scaling methods. This way, we aim at contributing to the debate concerning the nature of the Braun-Blanquet coding and the consequent multidimensional scaling methods to be used. Procrustes, Pearson, and Spearman correlation matrices were computed to compare the resulting sets of coordinates and synthesized through their Principal Component Analyses (PCA). In general, both Procrustes and Pearson correlations showed high coherence of the obtained results, whereas Spearman correlation values were much lower. This proves that the main sources of variation are similarly identified by most of used methods/transformations, whereas less agreement results on the continuous variations along the detected gradients. The conclusion is that Correspondence Analysis on presence/absence data seems the most appropriate method to use. Indeed, presence/absence data are not affected by species cover estimation error and Simple Correspondence Analysis performs really well with this coding. As alternative, Multiple Correlation Analysis provides interesting information on the species distribution while showing a pattern of relevés very similar to that issued by PCA

Proton-neutron pairing in the deformed BCS approach

We examine isovector and isoscalar proton-neutron pairing correlations for the ground state of even-even Ge isotopes with mass number A=64-76 within the deformed BCS approach. For N=Z 64Ge the BCS solution with only T=0 proton-neutron pairs is found. For other nuclear systems (N>Z) a coexistence of a T=0 and T=1 pairs in the BCS wave function is observed. A problem of fixing of strengths of isoscalar and isovector pairing interactions is addressed. A dependence of number of like and unlike pairs in the BCS ground state on the difference between number of neutrons and protons is discussed. We found that for nuclei with N much bigger than Z the effect of proton-neutron pairing is small but not negligible.Comment: 24 pages, 6 figure

Neutron-proton pairing in the BCS approach

We investigate the BCS treatment of neutron-proton pairing involving time-reversed orbits. We conclude that an isospin-symmetric hamiltonian, treated with the help of the generalized Bogolyubov transformation, fails to describe the ground state pairing properties correctly. In order for the np isovector pairs to coexist with the like-particle pairs, one has to break the isospin symmetry of the hamiltonian by artificially increasing the strength of np pairing interaction above its isospin symmetric value. We conjecture that the np isovector pairing represents part (or most) of the congruence energy (Wigner term) in nuclear masses.Comment: 9 pages, RevTex, submitted to Phys. Rev.

Local Density Approximation for proton-neutron pairing correlations. I. Formalism

In the present study we generalize the self-consistent Hartree-Fock-Bogoliubov (HFB) theory formulated in the coordinate space to the case which incorporates an arbitrary mixing between protons and neutrons in the particle-hole (p-h) and particle-particle (p-p or pairing) channels. We define the HFB density matrices, discuss their spin-isospin structure, and construct the most general energy density functional that is quadratic in local densities. The consequences of the local gauge invariance are discussed and the particular case of the Skyrme energy density functional is studied. By varying the total energy with respect to the density matrices the self-consistent one-body HFB Hamiltonian is obtained and the structure of the resulting mean fields is shown. The consequences of the time-reversal symmetry, charge invariance, and proton-neutron symmetry are summarized. The complete list of expressions required to calculate total energy is presented.Comment: 22 RevTeX page

Ground state particle-particle correlations and double beta decay

A self-consistent formalism for the double beta decay of Fermi type is provided. The particle-particle channel of the two-body interaction is considered first in the mean field equations and then in the QRPA. The resulting approach is called the QRPA with a self-consistent mean field (QRPASMF). The mode provided by QRPASMF, does not collapse for any strength of the particle-particle interaction. The transition amplitude for double beta decay is almost insensitive to the variation of the particle-particle interaction. Comparing it with the result of the standard pnQRPA, it is smaller by a factor 6. The prediction for transition amplitude agrees quite well with the exact result. The present approach is the only one which produces a strong decrease of the amplitude and at the same time does not alter the stability of the ground state.Comment: 23 pages, 7 figure

The Relativistic Linear Singular Oscillator

Exactly-solvable model of the linear singular oscillator in the relativistic configurational space is considered. We have found wavefunctions and energy spectrum for the model under study. It is shown that they have correct non-relativistic limits.Comment: 14 pages, 12 figures in eps format, IOP style LaTeX file (revised taking into account referees suggestions

Algebraic approach in the study of time-dependent nonlinear integrable systems: Case of the singular oscillator

The classical and the quantal problem of a particle interacting in one-dimension with an external time-dependent quadratic potential and a constant inverse square potential is studied from the Lie-algebraic point of view. The integrability of this system is established by evaluating the exact invariant closely related to the Lewis and Riesenfeld invariant for the time-dependent harmonic oscillator. We study extensively the special and interesting case of a kicked quadratic potential from which we derive a new integrable, nonlinear, area preserving, two-dimensional map which may, for instance, be used in numerical algorithms that integrate the Calogero-Sutherland-Moser Hamiltonian. The dynamics, both classical and quantal, is studied via the time-evolution operator which we evaluate using a recent method of integrating the quantum Liouville-Bloch equations \cite{rau}. The results show the exact one-to-one correspondence between the classical and the quantal dynamics. Our analysis also sheds light on the connection between properties of the SU(1,1) algebra and that of simple dynamical systems.Comment: 17 pages, 4 figures, Accepted in PR