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P. Schuck

Publications and source records attributed to P. Schuck.

At least 73 records · Page 4Linked to original sources
arXiv2009

Critical Temperature for $α$-Particle Condensation within a Momentum Projected Mean Field Approach

Alpha-particle (quartet) condensation in homogeneous spin-isospin symmetric nuclear matter is investigated. The usual Thouless criterion for the critical temperature is extended to the quartet case. The in-medium four-body problem is strongly simplified by the use of a momentum projected mean field ansatz for the quartet. The self-consistent single particle wave functions are shown and discussed for various values of the density at the critical temperature.

nucl-th↗
arXiv2008

Di-neutron correlation in light neutron-rich nuclei

Using a three-body model with density-dependent contact interaction, we discuss the root mean square distance between the two valence neutrons in $^{11}$Li nuclues as a function of the center of mass of the neutrons relative to the core nucleus $^9$Li. We show that the mean distance takes a pronounced minimum around the surface of the nucleus, indicating a strong surface di-neutron correlation. We demonstrate that the pairing correlation plays an essential role in this behavior. We also discuss the di-neutron structure in the $^8$He nucleus.

nucl-th↗
arXiv2008

Nuclear Scissors with Pairing and Continuity Equation

The coupled dynamics of the isovector and isoscalar giant quadrupole resonances and low lying modes (including scissors) are studied with the help of the Wigner Function Moments (WFM) method generalized to take into account pair correlations. Equations of motion for collective variables are derived on the basis of the Time Dependent Hartree-Fock-Bogoliubov (TDHFB) equations in the harmonic oscillator model with quadrupole-quadrupole (QQ) residual interaction and a Gaussian pairing force. Special care is taken of the continuity equation.

nucl-th↗
arXiv2008

Criterion for Bose-Einstein condensation in traps and self-bound systems

The internal one-particle density matrix is discussed for Bose-Einstein condensates with finite number of particles in a harmonic trap. The outcome of the digonalization of the density matrix depends on the choice of the internal coordinates: The Pethick-Pitaevskii-type internal density matrix, whose analytical eigenvalues and eigenfunctions are evaluated, yields a fragmented condensate, while the Jacobi-type internal density matrix leads to an ideal condensate. We give a criterion for the choice of the internal coordinates: In the macroscopic limit the internal density matrix should have eigenvalues and eigenfunctions of an ideal Bose-Einstein condensate, this being a very physical condition for cases where the system is also an ideal Bose condensation in the laboratory frame. One choice fulfilling this boundary condition is given by the internal Jacobi coordinates, while the internal coordinates with respect to the center of mass do not satisfy the condition. Based on our criterion, a general definition of the internal one-particle density matrix is presented in a self-bound system, consisting of interacting bosons.

cond-mat.other↗
arXiv2008

Alpha-Particle Condensation in Nuclear Systems

The onset of quartetting, i.e. alpha-particle condensation, in symmetric nuclear matter is studied with the help of an in-medium modified four nucleon equation. It is found that at very low density quartetting wins over pairing, because of the strong binding of the alpha-particles. The critical temperature can reach values up to around 6 MeV. Also the disappearance of alpha-particles with increasing density, i.e. the Mott transition, is investigated. In finite nuclei the Hoyle state, that is the 0_2^+ of 12C, is identified as an "alpha-particle condensate" state. It is conjectured that such states also exist in heavier n alpha-nuclei, like 16O, 20Ne, etc. For instance the 6-th 0^+ state of 16O at 15.1 MeV is identified from a theoretical analysis as being a strong candidate for an alpha condensate state. Exploratory calculations are performed for the density dependence of the alpha condensate fraction at zero temperature to address the suppression of the four-particle condensate below nuclear-matter density. Possible quartet condensation in other systems is discussed briefly

nucl-th↗
arXiv2008

Alpha-particle condensation in 16O via a full four-body OCM calculation

In order to explore the 4 α-particle condensate state in 16O, we solve a full four-body equation of motion based on the 4 αOCM (Orthogonality Condition Model) in a large 4 αmodel space spanned by Gaussian basis functions. A full spectrum up to the 0_6^+ state is reproduced consistently with the lowest six 0^+ states of the experimental spectrum. The 0^+_6 state is obtained at about 2 MeV above the 4 αbreakup threshold and has a dilute density structure, with a radius of about 5 fm. The state has an appreciably large αcondensate fraction of 61 %, and a large component of α+12C(0_2^+) configuration, both features being reliable evidence for this state to be of 4 αcondensate nature.

nucl-th↗
arXiv2008

Continued fraction approximation for the nuclear matter response function

We use a continued fraction approximation to calculate the RPA response function of nuclear matter. The convergence of the approximation is assessed by comparing with the numerically exact response function obtained with a typical effective finite-range interaction used in nuclear physics. It is shown that just the first order term of the expansion can give reliable results at densities up to the saturation density value.

nucl-th↗
arXiv2008

Deformation properties of the BCP energy density functional

We explore the deformation properties of the newly postulated BCP energy density functional (EDF). The results obtained for three isotope chains of Mg, Dy and Ra are compared to the available experimental data as well as to the results of the Gogny-D1S force. Results for the fission barrier of $^{240}$Pu are also discussed.

nucl-th↗
arXiv2008

Density-induced suppression of the alpha-particle condensate in nuclear matter and the structure of alpha cluster states in nuclei

At low densities, with decreasing temperatures, in symmetric nuclear matter alpha-particles are formed, which eventually give raise to a quantum condensate with four-nucleon alpha-like correlations (quartetting). Starting with a model of alpha-matter, where undistorted alpha particles interact via an effective interaction such as the Ali-Bodmer potential, the suppression of the condensate fraction at zero temperature with increasing density is considered. Using a Jastrow-Feenberg approach, it is found that the condensate fraction vanishes near saturation density. Additionally, the modification of the internal state of the alpha particle due to medium effects will further reduce the condensate. In finite systems, an enhancement of the S state wave function of the c.o.m. orbital of alpha particle motion is considered as the correspondence to the condensate. Wave functions have been constructed for self-conjugate 4n nuclei which describe the condensate state, but are fully antisymmetrized on the nucleonic level. These condensate-like cluster wave functions have been successfully applied to describe properties of low-density states near the n alpha threshold. Comparison with OCM calculations in 12C and 16O shows strong enhancement of the occupation of the S-state c.o.m. orbital of the alpha-particles. This enhancement is decreasing if the baryon density increases, similar to the density-induced suppression of the condensate fraction in alpha matter. The ground states of 12C and 16O show no enhancement at all, thus a quartetting condensate cannot be formed at saturation densities.

nucl-th↗
arXiv2008

Khon-Sham Density Functional Inspired Approach to Nuclear Binding

A non-relativisitic nuclear density functional theory is constructed, not as usual, from an effective density dependent nucleon-nucleon force but directly introducing in the functional results from microscopic nuclear and neutron matter Bruckner G-matrix calculations at various densities. A purely phenomenological finite range part to account for surface properties is added. The striking result is that only four to five adjustable parameters, spin-orbit included, suffice to reproduce nuclear binding energies and radii with the same quality as obtained with the most performant effective forces, containing on the order of ten parameters. In this pilot work, for the pairing correlations, simply a density dependent zero range force is adopted from the literature. Possible future extensions of this approach are pointed out.

nucl-th↗
arXiv2007

Boson-Fermion pairing in Bose-Fermi mixtures on 1D optical lattices

Boson-fermion pairing is considered in a discrete environment of bosons and fully spin-polarized fermions, coupled via an attractive Bose-Fermi Hubbard Hamiltonian in one dimension. The results of the T-matrix approximation for particles of equal mass and at double half filling are compared with the results of exact diagonalization and with Quantum Monte Carlo results. Satisfactory agreement for most quantities is found. The appearance of a stable, weak-coupling pairing mode is also confirmed.

cond-mat.other↗
arXiv2007

Coexistence of BCS and BEC-like pair structures in halo nuclei

We investigate the spatial structure of the two-neutron wave function in the Borromean nucleus $^{11}$Li, using a three-body model of $^9$Li $+n+n$, which includes many-body correlations stemming from the Pauli principle. The behavior of the neutron pair at different densities is simulated by calculating the two-neutron wave function at several distances between the core nucleus $^9$Li and the center of mass of the two neutrons. With this representation, a strong concentration of the neutron pair on the nuclear surface is for the first time quantitatively established for neutron-rich nuclei. That is, the neutron pair wave function in $^{11}$Li has an oscillatory behavior at normal density, while it becomes a well localized single peak in the dilute density region around the nuclear surface. We point out that these features qualitatively correspond to the BCS and BEC-like structures of the pair wave function found in infinite nuclear matter.

nucl-th↗
arXiv2007

Nuclear Scissors Mode with Pairing

The coupled dynamics of the scissors mode and the isovector giant quadrupole resonance are studied using a generalized Wigner function moments method taking into account pair correlations. Equations of motion for angular momentum, quadrupole moment and other relevant collective variables are derived on the basis of the time dependent Hartree-Fock-Bogoliubov equations. Analytical expressions for energy centroids and transitions probabilities are found for the harmonic oscillator model with the quadrupole-quadrupole residual interaction and monopole pairing force. Deformation dependences of energies and $B(M1)$ values are correctly reproduced. The inclusion of pair correlations leads to a drastic improvement in the description of qualitative and quantitative characteristics of the scissors mode.

nucl-th↗
arXiv2007

Random phase approximation for the 1D anti-ferromagnetic Heisenberg model

The Hartree-Fock-RPA approach is applied to the 1D anti-ferromagnetic Heisenberg model in the Jordan-Wigner representation. Somewhat contrary to expectation, this leads to reasonable results for spectral functions and sum rules in the symmetry unbroken phase. In a preliminary application of Self-Consistent RPA to finite size chains strongly improved results are obtained.

cond-mat.str-el↗
arXiv2006

Evidence for an alpha cluster condensed state in 16O(alpha,alpha') at 400 MeV

Inelastic $α$ scattering on 16O is studied at 400 MeV by using an ice target. Near the 4-alpha breakup threshold of 14.4 MeV, a broad peak is observed at an excitation energy of 13.6+/-0.2 MeV with a width of 0.6+/-0.2 MeV. The spin-parity is estimated to be 0+ from the momentum-transfer dependence. The observed width is significantly larger than those of the neighboring 0+ states indicating a state with a well-developed alpha cluster structure. The magnitude of the cross section is sensitive to the density distribution of the constituent alpha clusters. The observed cross section is consistent with the theoretical prediction for the alpha cluster condensed state characterized by its dilute density distribution with a large root-mean-square radius of about 4.3 fm.

nucl-ex↗