$\delta$-pairing forces and collective pairing vibrations

The collective pairing Hamiltonian is obtained in the framework of the generator coordinate method in the Gaussian overlap approximation with a slightly modified BCS function used as a generator function. The collective variable , measuring the monopole moment of the pairing field, and the gauge transformation angle are chosen as generator coordinates. The vibrational ground states are calculated by diagonalisation of the collective pairing Hamiltonian in the harmonic-oscillator basis.Received: 28 April 2003, Revised: 1 October 2003, Published online: 18 June 2004PACS: 21.30.-x Nuclear forces - 21.60.Ev Collective models     

On the moment of inertia of large nuclear systems with pairing forces

The moment of inertia of large nuclear systems with pairing forces was shown to be that of an irrotational flow byPrange. Following an argument due toThirring, we will give here a very simple derivation of this important result.     

Quadrupole pairing effects upon the structure of low lying λπ=2+ states in Zn isotopes

The influence of quadrupole pairing correlations upon quadrupole electric transitions and two nucleon transfer matrix elements is investigated. The formalism is based on the Random Phase Approximation treatment of a non-separable two body interaction. Contributions due to particle-hole and particle-particle terms of the residual interaction are explicitly calculated and the competition between them is also studied as function of the ratio of the coupling constants which define the strength of each channel. Results are shown and discussed for the case of even mass Zn isotopes, with 60 ≦A≦ 72.     

Functional approach to nuclear field theory: A schematic model with pairing and particle-hole forces

Path integral techniques in collective variables are applied to a schematic model with monopole pairing and particle-hole forces. The single-particle and collective excitation modes of the system for various kinds of phase transitions are discussed. We formulate a modified perturbation theory (loop expansion) from which, finally, nuclear field theory (NFT) is obtained. The NFT Lagrangian is strictly derived. The graphical rules of the NFT expansion come out automatically.     

pn-QRPA and higher-order approximations

The proton-neutron Quasi-particle Random Phase Approximation (pn-QRPA) is reviewed and higher-order approximations discussed with reference to the beta decay physics. The approach is fully developed in a boson formalism. Working within a schematic model, we first illustrate a fermion-boson mapping procedure and apply it to construct boson images of the fermion Hamiltonian at different levels of approximation. The quality of these images is tested through a comparison between approximate and exact spectra. Standard QRPA equations are derived in correspondence with the quasi-boson limit of the boson Hamiltonian. The use of higher-order Hamiltonians is seen to improve considerably the stability of the approximate solutions. The mapping procedure is also applied to Fermi beta operators and transition amplitudes are discussed. The range of applicability of the QRPA formalism is examined. Presented at Workshop on calculation of double-beta-decay matrix elements (MEDEX’97), Prague, May 27–31, 1997.     

Quantum entanglement and pairing correlation in the reduced BCS pairing model

Using the particle-hole version of the density-matrix renormalization-group technique, the pairing correlation and the quantum entanglement of the reduced BCS pairing model are investigated. Both of them behave smoothly from the weak to the strong coupling regimes. A convergence radius (∼1/ln Ω) of condensation energy is detected by the first order derivative of the block-block entanglement. Furthermore, the block-block entanglement in the strong coupling regime shows distinct size dependence, and a logarithmic volume law is suggested numerically.     

Quadrupole interactions in metals and alloys

The contributions of the perturbed charge density of conduction electrons due to quadrupole moments of impurity paramagnetic ions and nuclei to the electric field gradient at the nuclei in metals and alloys are analyzed. The indirect multipole interactions of nuclei in metals via the mediation of conduction electrons is investigated. The influence of these interactions on the NMR parameters is studied.     

Quadrupole moments of hadrons

We study an Abelian Higgs model in three, four and five dimensions using the mean field perturbation expansion with covariant gauge fixing. In four and five dimensions the mean field analysis shows three phases; a confined phase, a Coulomb phase with massless spin waves, and a Higgs phase in which the spin waves aquire a mass. The Higgs and confined phases are shown to be connected. In three dimensions we find a single phase.     

Neutron-proton pairing

The two topics discussed here are the treatment of neutron-proton pairing and the problem of phase transitions in systems of neutrons and protons. The conclusions are based on exact calculations, possible in simplified situations, and the exact results are compared with the BCS treatment. QRPA, and many of its modifications, which are the most popular approaches to double beta decay, involve the quasiparticle transformation as a decisive first step. It is therefore imperative to understand its strengths and limitations. Presented at Workshop on calculation of double-beta-decay matrix elements (MEDEX’97), Prague, May 27–31, 1997. The work reported here is based on Refs. 3, 4, and 5. The credit for it belongs to my collaborators, in particular to Osvaldo Civitarese, Jonathan Engel, and Stuart Pittel. This work was supported by the U.S. Department of Energy under Grant. No. DE-FG03-88ER-40397.     

Nuclear Quadrupole Interactions in Nuclear Quadrupole Resonance Detection of Energetic and Controlled Materials: Theoretical Study

There has been a growing interest in nuclear quadrupole resonance (NQR) techniques useful for the detection of explosives and drugs in solid state systems. This paper uses the first-principles one-electron Hartree?CFock theoretical method to study the nuclear quadrupole interaction parameters e ² qQ and ?? for the ¹⁴N nuclei in the explosives RDX and ??-HMX as well as the drugs cocaine and heroin. It has been found in our earlier published investigations reviewed here that there is very good agreement for our calculated e ² qQ and ?? for ¹⁴N, for all these four systems, and experiment. We also present our unpublished theoretical results for cocaine with an HCl molecule attached. We successfully explain quantitatively the drastic decrease in e ² qQ in going to cocaine-HCl from cocaine-free base as well as the observed substantial increase in ?? and discuss the implications of these dramatic changes for NQR detection in general.     

Quadrupole interactions in lithium borodeuteride

Polycrystalline samples of lithium borohydride and borodeuteride, LiBH₄ and LiBD₄, are studied by ²H, ⁷Li, and ^10,11B NMR in 7.04 T and 9.35 T magnetic fields in the temperature range 116–580 K. The ^10,11B NMR line shape of the orthorhombic phase of LiBH₄ and LiBD₄ suggests that first-order quadrupole interaction takes place. The quadrupole coupling constant (QCC) χ _q and asymmetry parameter η of the electric field gradient tensor for ¹¹B are described by linear temperature dependences: χ _q (¹¹B) = 177 ? 0.24T and η = 0.043 + 0.0014T. The electric field gradient at the positions of boron nuclei is created by external charges, primarily lithium cations. In the range of 388–391 K, the ⁷Li NMR line shape reflects the coexistence of two phase modifications of LiBH₄ and LiBD₄ and the occurrence of a reversible first-order phase transition. In the temperature range of 390–530 K, the ⁷Li NMR line shape represents a first-order quadrupole perturbed spectrum with zero asymmetry parameter and a weakly temperature dependent ⁷Li QCC. The spin-lattice relaxation time and the NMR line shape of ²H are interpreted in terms of the reorientation of the BD ₄ ^? anion about their proper symmetry axes C₂ and C₃.     

Quadrupole interactions in pionic and kaonic atoms

We discuss the quadrupole hyperfine structure in mesonic atoms for nuclei with spin I 1. The optical potential is expanded in terms of the non-spherical density contributions. Examples are given for the hyperfine splitting of peripheral and deeper-lying states in pionic and kaonic atoms.     

A semiclassical approach to pairing vibrations and pairing correlation effects on giant resonances

We extend the semiclassical approaches to the dynamics of nuclear collective motions, based on the Wigner transform of quantum mean field theories, to the inclusion of pairing correlation effects. We develop simple analytic equations for the contributions to giant resonance frequencies, which are in general quite small. We are able also to study pairing vibrations, related to oscillations of the superfluid part. Hydrodynamics-like solutions are obtained, without distortion of the Fermi surface, corresponding to low energy excitations.     

Quadrupole Radiation of Ion-Acoustic Waves

An experiment to measure the radiation of ion-acoustic waves from a quadrupole antenna is described. The quadrupole consists of 4 hemispherical grids located at the corners of a square structure. The results are contrasted with those obtained from an antenna with the 4 hemispheres excited in phase and compared with a fluid model prediction. Electrostatically coupled excitation of ion-acoustic waves from 3 hemispheres when only the fourth is excited is also observed in this experiment.