arXiv subjects

P. Schuck

Publications and source records attributed to P. Schuck.

At least 109 records · Page 6Linked to original sources

arXiv2003

Thomas-Fermi approximation to static vortex states in superfluid trapped atomic gases

We revise the Thomas-Fermi approximation for describing vortex states in Bose condensates of magnetically trapped atoms. Our approach is based on considering the hbar -> 0 limit rather than the N -> infinity limit as Thomas-Fermi approximation in close analogy with the Fermi systems. Even for relatively small numbers of trapped particles we find good agreement between Gross-Pitaevskii and Thomas-Fermi calculations for the different contributions to the total energy of the atoms in the condensate. We also discuss the application of our approach to the description of vortex states in superfluid fermionic systems in the Ginzburg-Landau regime.

cond-mat↗

arXiv2003

Spurious modes in extended RPA theories

Necessary conditions that the spurious state associated with the translational motion and its double-phonon state have zero excitation energy in extended RPA (ERPA) theories which include both one-body and two-body amplitudes are investigated using the small amplitude limit of the time-dependent density-matrix theory (STDDM). STDDM provides us with a quite general form of ERPA as compared with other similar theories in the sense that all components of one-body and two-body amplitudes are taken into account. Two conditions are found necessary to guarantee the above property of the single and double spurious states: The first is that no truncation in the single-particle space should be made. This condition is necessary for the closure relation to be used and is common for the single and double spurious states. The second depends on the mode. For the single spurious state all components of the one-body amplitudes must be included, and for the double spurious state all components of one-body and two-body amplitudes have to be included. It is also shown that the Kohn theorem and the continuity equations for transition densities and currents hold under the same conditions as the spurious states. ERPA theories formulated using the Hartree-Fock ground state have a non-hermiticity problem. A method for formulating ERPA with hermiticity is also proposed using the time-dependent density-matrix formalism.

nucl-th↗

arXiv2003

Eigenstates of the time-dependent density-matrix theory

An extended time-dependent Hartree-Fock theory, known as the time-dependent density-matrix theory (TDDM), is solved as a time-independent eigenvalue problem for low-lying $2^+$ states in $^{24}$O to understand the foundation of the rather successful time-dependent approach. It is found that the calculated strength distribution of the $2^+$ states has physically reasonable behavior and that the strength function is practically positive definite though the non-hermitian hamiltonian matrix obtained from TDDM does not guarantee it. A relation to an extended RPA theory with hermiticity is also investigated. It is found that the density-matrix formalism is a good approximation to the hermitian extended RPA theory.

nucl-th↗

arXiv2003

The Nuclear Scissors Mode in a Solvable Model

The coupled dynamics of the scissors mode and the isovector giant quadrupole resonance is studied in a model with separable quadrupole-quadrupole residual interactions. The method of Wigner function moments is applied to derive the dynamical equations for angular momentum and quadrupole moment. Analytical expressions for energies, B(M1)- and B(E2)-values, sum rules and flow-patterns of both modes are found for arbitrary values of the deformation parameter. Some predictions for the case of superdeformation are given. The subtle nature of the phenomenon and its peculiarities are clarified.

nucl-th↗

arXiv2003

Semiclassical evaluation of average nuclear one and two body matrix elements

Thomas-Fermi theory is developed to evaluate nuclear matrix elements averaged on the energy shell, on the basis of independent particle Hamiltonians. One- and two-body matrix elements are compared with the quantal results and it is demonstrated that the semiclassical matrix elements, as function of energy, well pass through the average of the scattered quantum values. For the one-body matrix elements it is shown how the Thomas-Fermi approach can be projected on good parity and also on good angular momentum. For the two-body case the pairing matrix elements are considered explicitly.

nucl-th↗

arXiv2003

Alpha-particle condensation in nuclei

A round up of the present status of the conjecture that n alpha nuclei form an alpha-particle condensate in excited states close to the n alpha threshold is given. Experiments which could demonstrate the condensate character are proposed. Possible lines of further theoretical developments are discussed.

nucl-th↗

arXiv2003

Generic Finite Size Enhancement of Pairing in Mesoscopic Fermi Systems

The finite size dependent enhancement of pairing in mesoscopic Fermi systems is studied under the assumption that the BCS approach is valid and that the two body force is size independent. Different systems are investigated such as superconducting metallic grains and films as well atomic nuclei. It is shown that the finite size enhancement of pairing in these systems is in part due to the presence of a surface which accounts quite well for the data of nuclei and explains a good fraction of the enhancement in Al grains.

cond-mat.supr-con↗

arXiv2003

Screening Effects on $^1S_0$ Pairing in Neutron Matter

The $^1S_0$ superfluidity of neutron matter is studied in the framework of the generalized Gorkov equation. The vertex corrections to the pairing interaction and the self-energy corrections are introduced and approximated on the same footing in the gap equation. A suppression of the pairing gap by more than 50% with respect to the BCS prediction is found, which deeply changes the scenario for the dynamical and thermal evolution of neutron stars.

nucl-th↗

arXiv2003

Surface behaviour of the pairing gap in a slab of nuclear matter

The surface behaviour of the pairing gap previously studied for semi-infinite nuclear matter is analyzed in the slab geometry. The gap-shape function is calculated in two cases: (a) pairing with the Gogny force in a hard-wall potential and (b) pairing with the separable Paris interaction in a Saxon-Woods mean-field potential. It is shown that the surface features are preserved in the case of slab geometry, being almost independent of the width of the slab. It is also demonstrated that the surface enhancement is strengthened as the absolute value of chemical potential $|μ|$ decreases which simulates the approach to the nucleon drip line.

nucl-th↗

arXiv2003

Analysis of previous microscopic calculations for second $0^+$ state in $^{12}$C in terms of 3-alpha particle Bose-condensed state

The wave function of the second $0^+$ state of $^{12}$C which was obtained long time ago by solving the microscopic 3$α$ problem is shown to be almost completely equivalent to the wave function of the 3$α$ condensed state which has been proposed recently by the present authors. This equivalence of the wave functions is shown to hold in two cases where different effective two-nucleon forces are adopted. This finding gives strong support for interpreting the second $0^+$ state of $^{12}$C which is the key state for the synthesis of $^{12}$C in stars ('Hoyle' state), and which is one of the typical mysterious $0^+$ states in light nuclei, as a gas-like structure of three $α$ particles, Bose-condensed into an identical s-wave function.

nucl-th↗

arXiv2003

Pair Fluctuations in Ultra-small Fermi Systems within Self-Consistent RPA at Finite Temperature

A self-consistent version of the Thermal Random Phase Approximation (TSCRPA) is developed within the Matsubara Green's Function (GF) formalism. The TSCRPA is applied to the many level pairing model. The normal phase of the system is considered. The TSCRPA results are compared with the exact ones calculated for the Grand Canonical Ensemble. Advantages of the TSCRPA over the Thermal Mean Field Approximation (TMFA) and the standard Thermal Random Phase Approximation (TRPA) are demonstrated. Results for correlation functions, excitation energies, single particle level densities, etc., as a function of temperature are presented.

nucl-th↗

arXiv2002

Random Phase Approximation and Extensions Applied to a Bosonic Field Theory

An application of a self-consistent version of RPA to quantum field theory with broken symmetry is presented. Although our approach can be applied to any bosonic field theory, we specifically study the $ϕ^4$ theory in 1+1 dimensions. We show that standard RPA approach leads to an instability which can be removed when going to a superior version,i.e. the renormalized RPA. We present a method based on the so-called charging formula of the many electron problem to calculate the correlation energy and the RPA effective potential.

hep-ph↗

arXiv2002

Self-Consistent Quasi-Particle RPA for the Description of Superfluid Fermi Systems

Self-Consistent Quasi-Particle RPA (SCQRPA) is for the first time applied to a more level pairing case. Various filling situations and values for the coupling constant are considered. Very encouraging results in comparison with the exact solution of the model are obtained. The nature of the low lying mode in SCQRPA is identified. The strong reduction of the number fluctuation in SCQRPA vs BCS is pointed out. The transition from superfluidity to the normal fluid case is carefully investigated.

nucl-th↗

arXiv2002

The Pairing interaction in nuclei: comparison between exact and approximate treatments

As a model for a deformed nucleus the many level pairing model (picket fence model with ~100 levels) is considered in four approximations and compared to the exact solution given by Richardson long time ago. It is found that, as usual, the number projected BCS method improves over standard BCS but that it is much less accurate than the more sophisticated many-body-approaches which are Coupled Cluster Theory (CCT) in its SUB2 version or Self-Consistent Random Phase Approximation (SCRPA).

nucl-th↗

arXiv2002

Mass Number Dependence of Nuclear Pairing

Large scale Hartree-Fock-Bogoliubov (HFB) calculations with the finite-range Gogny force D1S have been performed in order to extract the corresponding theoretical average mass dependence of the nuclear gap values. Good agreement with experimental data from the three-point filter $Δ^{(3)}$(N) with N odd has been found for both the neutron and proton gaps. The study confirms earlier findings [W. Satula, J. Dobaczewski, and W. Nazarewicz, Phys. Rev. Lett. 81 3599 (1998)] that the mass dependence of the gap is much weaker than the so far accepted 12/$\sqrtA$ MeV law.

nucl-th↗

arXiv2001

Alpha cluster condensation in 12C and 16O

A new $α$-cluster wave function is proposed which is of the $α$-particle condensate type. Applications to $^{12}$C and $^{16}$O show that states of low density close to the 3 resp. 4 $α$-particle threshold in both nuclei are possibly of this kind. It is conjectured that all self-conjugate 4$n$ nuclei may show similar features.

nucl-th↗

arXiv2001

Transition from BCS pairing to Bose-Einstein condensation in low-density asymmetric nuclear matter

We study the isospin-singlet neutron-proton pairing in bulk nuclear matter as a function of density and isospin asymmetry within the BCS formalism. In the high-density, weak-coupling regime the neutron-proton paired state is strongly suppressed by a minor neutron excess. As the system is diluted, the BCS state with large, overlapping Cooper pairs evolves smoothly into a Bose-Einstein condensate of tightly bound neutron-proton pairs (deuterons). In the resulting low-density system a neutron excess is ineffective in quenching the pair correlations because of the large spatial separation of the deuterons and neutrons. As a result, the Bose-Einstein condensation of deuterons is weakly affected by an additional gas of free neutrons even at very large asymmetries.

nucl-th↗

arXiv2001

A Class of Exactly Solvable Pairing Models

We present three classes of exactly solvable models for fermion and boson systems, based on the pairing interaction. These models are solvable in any dimension. As an example we show the first results for fermion interacting with repulsive pairing forces in a two dimensional square lattice. Inspite of the repulsive pairing force the exact results show attractive pair correlations.

cond-mat.supr-con↗