Two-body correlation functions in nuclear matter with npnp condensate

The density, spin and isospin correlation functions in nuclear matter with a neutron-proton ($np$) condensate are calculated to study the possible signatures of the BEC-BCS crossover in the low-density region. It is shown that the criterion of the crossover (Phys. Rev. Lett. {\bf 95}, 090402 (2005)), consisting in the change of the sign of the density correlation function at low momentum transfer, fails to describe correctly the density-driven BEC-BCS transition at finite isospin asymmetry or finite temperature. As an unambiguous signature of the BEC-BCS transition, there can be used the presence (BCS regime) or absence (BEC regime) of the singularity in the momentum distribution of the quasiparticle density of states.Comment: Prepared with RevTeX4, 5p., 4 figure

The Nucleon Spectral Function at Finite Temperature and the Onset of Superfluidity in Nuclear Matter

Nucleon selfenergies and spectral functions are calculated at the saturation density of symmetric nuclear matter at finite temperatures. In particular, the behaviour of these quantities at temperatures above and close to the critical temperature for the superfluid phase transition in nuclear matter is discussed. It is shown how the singularity in the thermodynamic T-matrix at the critical temperature for superfluidity (Thouless criterion) reflects in the selfenergy and correspondingly in the spectral function. The real part of the on-shell selfenergy (optical potential) shows an anomalous behaviour for momenta near the Fermi momentum and temperatures close to the critical temperature related to the pairing singularity in the imaginary part. For comparison the selfenergy derived from the K-matrix of Brueckner theory is also calculated. It is found, that there is no pairing singularity in the imaginary part of the selfenergy in this case, which is due to the neglect of hole-hole scattering in the K-matrix. From the selfenergy the spectral function and the occupation numbers for finite temperatures are calculated.Comment: LaTex, 23 pages, 21 PostScript figures included (uuencoded), uses prc.sty, aps.sty, revtex.sty, psfig.sty (last included

Finding and counting vertex-colored subtrees

The problems studied in this article originate from the Graph Motif problem introduced by Lacroix et al. in the context of biological networks. The problem is to decide if a vertex-colored graph has a connected subgraph whose colors equal a given multiset of colors $M$. It is a graph pattern-matching problem variant, where the structure of the occurrence of the pattern is not of interest but the only requirement is the connectedness. Using an algebraic framework recently introduced by Koutis et al., we obtain new FPT algorithms for Graph Motif and variants, with improved running times. We also obtain results on the counting versions of this problem, proving that the counting problem is FPT if M is a set, but becomes W[1]-hard if M is a multiset with two colors. Finally, we present an experimental evaluation of this approach on real datasets, showing that its performance compares favorably with existing software.Comment: Conference version in International Symposium on Mathematical Foundations of Computer Science (MFCS), Brno : Czech Republic (2010) Journal Version in Algorithmic

Deuteron life-time in hot and dense nuclear matter near equilibrium

We consider deuteron formation in hot and dense nuclear matter close to equilibrium and evaluate the life-time of the deuteron fluctuations within the linear response theory. To this end we derive a generalized linear Boltzmann equation where the collision integral is related to equilibrium correlation functions. In this framework we then utilize finite temperature Green functions to evaluate the collision integrals. The elementary reaction cross section is evaluated within the Faddeev approach that is suitably modified to reflect the properties of the surrounding hot and dense matter.Comment: 15 pages, 5 figure

Theoretical Aspects of Science with Radioactive Nuclear Beams

Physics of radioactive nuclear beams is one of the main frontiers of nuclear science today. Experimentally, thanks to technological developments, we are on the verge of invading the territory of extreme N/Z ratios in an unprecedented way. Theoretically, nuclear exotica represent a formidable challenge for the nuclear many-body theories and their power to predict nuclear properties in nuclear terra incognita. It is important to remember that the lesson learned by going to the limits of the nuclear binding is also important for normal nuclei from the neighborhood of the beta stability valley. And, of course, radioactive nuclei are crucial astrophysically; they pave the highway along which the nuclear material is transported up in the proton and neutron numbers during the complicated synthesis process in stars.Comment: 26 ReVTeX pages, 11 Postscript figures, uses epsf.sty, to be published in: Theme Issue on Science with Beams of Radioactive Nuclei, Philosophical Transactions, ed. by W. Gelletl

Four-particle condensate in strongly coupled fermion systems

Four-particle correlations in fermion systems at finite temperatures are investigated with special attention to the formation of a condensate. Instead of the instability of the normal state with respect to the onset of pairing described by the Gorkov equation, a new equation is obtained which describes the onset of quartetting. Within a model calculation for symmetric nuclear matter, we find that below a critical density, the four-particle condensation (alpha-like quartetting) is favored over deuteron condensation (triplet pairing). This pairing-quartetting competition is expected to be a general feature of interacting fermion systems, such as the excition-biexciton system in excited semiconductors. Possible experimental consequences are pointed out.Comment: LaTeX, 11 pages, 2 figures, uses psfig.sty (included), to be published in Phys. Rev. Lett., tentatively scheduled for 13 April 1998 (Volume 80, Number 15

Space-time versus particle-hole symmetry in quantum Enskog equations

The non-local scattering-in and -out integrals of the Enskog equation have reversed displacements of colliding particles reflecting that the -in and -out processes are conjugated by the space and time inversions. Generalisations of the Enskog equation to Fermi liquid systems are hindered by a request of the particle-hole symmetry which contradicts the reversed displacements. We resolve this problem with the help of the optical theorem. It is found that space-time and particle-hole symmetry can only be fulfilled simultaneously for the Bruckner-type of internal Pauli-blocking while the Feynman-Galitskii form allows only for particle-hole symmetry but not for space-time symmetry due to a stimulated emission of Bosons

Thermodynamics of nn-pp condensate in asymmetric nuclear matter

We study the neutron-proton pairing in nuclear matter as a function of isospin asymmetry at finite temperatures and the saturation density using realistic nuclear forces and Brueckner-renormalized single particle spectra. Our computation of the thermodynamic quantities shows that while the difference of the entropies of the superconducting and normal phases anomalously changes its sign as a function of temperature for arbitrary asymmetry, the grand canonical potential does not; the superconducting state is found to be stable in the whole temperature-asymmetry plane. The pairing gap completely disappears for density-asymmetries exceeding $\alpha_c= (n_n-n_p)/n \simeq 0.11$.Comment: 7 pages, including 3 figures, uses revte

Differential flow in heavy-ion collisions at balance energies

A strong differential transverse collective flow is predicted for the first time to occur in heavy-ion collisions at balance energies. We also give a novel explanation for the disappearance of the total transverse collective flow at the balance energies. It is further shown that the differential flow especially at high transverse momenta is a useful microscope capable of resolving the balance energy's dual sensitivity to both the nuclear equation of state and in-medium nucleon-nucleon cross sections in the reaction dynamics.Comment: Phys. Rev. Lett. (1999) in pres

The damping width of giant dipole resonances of cold and hot nuclei: a macroscopic model

A phenomenological macroscopic model of the Giant Dipole Resonance (GDR) damping width of cold- and hot-nuclei with ground-state spherical and near-spherical shapes is developed. The model is based on a generalized Fermi Liquid model which takes into account the nuclear surface dynamics. The temperature dependence of the GDR damping width is accounted for in terms of surface- and volume-components. Parameter-free expressions for the damping width and the effective deformation are obtained. The model is validated with GDR measurements of the following nuclides, $^{39,40}$K, $^{42}$Ca, $^{45}$Sc, $^{59,63}$Cu, $^{109-120}$Sn,$^{147}$Eu, $^{194}$Hg, and $^{208}$Pb, and is compared with the predictions of other models.Comment: 10 pages, 5 figure