Weak-coupling Model Research Articles

The structure of 32S II. Shell model interpretation

The properties of positive-parity states in 32S are compared to predictions of shell model calculations within the complete s-d basis space using the universal s-d shell Hamiltonian. The experimental T = O spectrum is reproduced to excitation energies between 10 and 11.7 MeV, depending on the level spins. The T = 1 spectrum is known and reproduced for the first five 5 MeV in excitation in general and for the first 8 MeV in the case of Iπ = 1+ states. Altogether the excitation energies of 80 positive-parity states are reproduced with a rms deviation of 200 keV. A calculation of radiative widths and branching ratios for γ-decay which uses effective charges and free-nucleon g-factors yields good general agreement with experiment. The need for effective g-factors is felt only in the rare cases of transitions which are governed by the isovector d3/2 → d5/2 M1 matrix element. The spectrum of negative parity, T = 1 states is understood in terms of the weak-coupling model while that of the T = 0 states is comprised of octupole-quadrupole phonon multiplets. Positive-parity states from outside the s-d configuration are first observed between 9.5 and 10.5 MeV excitation energy.

Study of high- lying states in 147Eu

The high-spin states of 147Eu have been studied in the reaction 139La(13C, 5n)147Eu at a beam energy of 98 MeV. Based onthe in-beam measurements ofγ-γ-t coincidences and γ-ray angular distributions, the level scheme of 147Eu has been extended from 4174 keVup to 8137 keV in excitation energies. A zeroth-order approximation of weak coupling model was applied to explain the observed level structure of 147Eu.

Low-energy properties of regularly depleted spin ladders

We investigate a model for the regularly depleted two-leg spin-ladder systems. By using the Lieb-Schultz-Mattis theorem, it is rigorously shown that this model realizes massless excitations or, alternatively, a degenerate ground state, although the original spin-ladder system has a spin gap and a unique ground state. The ground state of the depleted model is either a spin singlet or partially ferromagnetic reflecting topological properties of the depleted sites. In order to show that the low-energy excitations are indeed massless, we proceed in our analysis in two different ways by resorting to effective field theories. We first investigate an effective weak-coupling model in terms of renormalization-group methods. Although the tendency to massless-spin excitations is seen in the strong-coupling regime, it turns out that the model is still massive for any finite coupling, implying that a conventional weak-coupling approach is not efficient to describe massless modes in our model. To overcome this difficulty, we further study low-energy properties of the depleted spin model by mapping on the nonlinear sigma model, and confirm that the massless-spin excitation indeed occurs.

Energy gap symmetry and thermal conductivity of YBa2Cu3O7

The characteristic enhancement in the heat conduction below Tc is analyzed on sintered YBa2Cu3O7 from viewpoints of both d-wave and s-wave coupling. Assuming the existence of a large energy gap Δ0(≥1.5Δ BCS ), only d-wave coupling is consistent with experimental observation. It is found that the most reasonable explanation for the enhancement is provided by the weak-coupling phonon conduction model under d-wave energy gap.

Electronic structure of the copper oxides ladder compounds La 2Cu 2O 5 and SrCu 2O 3 in a weak coupling model

We calculate the electronic structure of the ladder compounds such as La 2 − x Sr x Cu 2O 5 or SrCu 2O 3 in a simple tight binding model. By taking into account only the coupling between the d x 2 − y 2 copper orbitals and both p x and p y oxygen orbitals, which present the strongest overlap, we get an exact analytical band structure: it simply corresponds to the one of two Cu chains, coupled by an effective transfer integral t, which is mediated by the intercalated oxygen atoms. The one dimensional character of the band is very favourable to the emergence of electronic surstructures, such as spin density waves or charge density waves, which could explain why high- T c superconductivity has not been experimentally observed. It also leads to a magnetic gap in the undoped crystal, consistent with magnetic susceptibility measurements.

Finite element analysis of magneto-mechanical coupled phenomena in magnetostrictive materials

This paper presents a numerical model for the analysis of magneto-mechanical problems in magnetostrictive materials. The governing equations of these phenomena are solved simultaneously using a strong coupling model based on the finite element method. The magnetic force in magnetostrictive materials is calculated by a numerical model based on the local application of the virtual work principle. The variation of the permeability with the mechanical stress is taken into account. The strong coupling model is applied to a simple example and the results are compared with a weak coupling model.

OH vibrational modes in sillenites

Abstract High resolution (0.05 cm−1) FTIR spectroscopy in the temperature range 9-320 K is applied to study the OH and OD stretching modes in BSO, BGO, BTO and mixed BSO-BGO sillenite crystals. A model is proposed for the OH-defect responsible for the main line. The anharmonic effects are analyzed in the framework of the Morse model and compared to those reported for OH-defects in insulating materials. The temperature dependence of the line position and width fits to a weak phonon coupling model and gives the frequency of the coupled phonons.

High pressure NMR study of methyl group tunnelling in dimethyl sulphide

The rotational tunnel splittings of pairs of methyl groups in dimethyl sulphide have been determined by low field proton NMR as a function of hydrostatic pressure up to 4·5 kBar. Two principal splittings are clearly observed, one being equal to 750 kHz for all pressures, the other decreasing exponentially from 100 kHz at atmospheric pressure to 40 kHz at 4·0 kBar. For the first time, tunnelling sidebands of a sideband in the NMR spectrum have been seen. The temperature dependence of the spin-lattice relaxation time has also been measured as a function of pressure and has revealed double minima at higher pressure. The results have been analysed using both weak and strong methyl coupling models.

Distribution of spin-isospin strengths in 12B and 13B

The differential cross sections of the reactions 12,13C( γ, π +) 12,13B were measured using tagged photons at the mean energy E γ = 191 MeV at five angles 35° ⩽ θ π ⩽ 145° corresponding to the momentum transfer to the nucleus 0.5 ⩽ q ⩽ 1.5 fm −1. The major transition strengths leading to various excited states in 12,13B, in both cases, are concentrated within a resonance centered at about 7 MeV excitation energy in 12,13B (about 22 MeV in 12,13C) with a full width at half maximum (FWHM) of about 12 MeV, reminiscent of the well-known electric-dipole gian resonances. The two reactions are compared in the context of the weak-coupling model.

D-wave superconductivity in high-Tc copper oxides

Abstract We study the standard d x 2 − y 2 superconductor within the weak coupling model. We show that the tunneling conductance between two superconductors is consistent with recent observations in single crystals of Bi 2 Sr 2 CaCu 2 O 8 . We predict also that the ultrasonic attenuation with the polarization vector in the a - b plane reveals the underlying symmetry of the superconducting order parameter.

Upper critical field of D-wave superconductors

Abstract Within the weak-coupling model we study the upper critical field of a dx2−y2 superconductor in a magnetic field lying in the a−b plane and tilted by an angle θ from the a−an. We find that the upper critical field exhibits four-fold symmetry and takes the maximum value when H ‖ a . The anisotropy is about 10% at T = 0 K and decreases with increasing temperature and it vanishes completely at T = Tc. We also study the effect of impurity scattering on upper critical field. We find a quasi-scaling law as found for the upper critical field in heavy fermion superconductors.

Coexistence model of anisotropic electron hole pairing and unconventional superconductivity in Heavy Fermion compounds

Various Heavy Fermion compounds exhibit unconventional superconductivity together with another electronic instability like a spin density wave or possibly a more general type of anisotropic electron-hole pairing, e.g. a spin nematic state. The coexistence behaviour of these order parameters is studied within a simple weak coupling model. It is found that depeding on the symmetry of the order parameters coexistence or phase expulsion may occur. Whereas the former case is possibly realized for theU-based superconductors, CeCu2Si2 may be an example of the second case as observed and discussed in the context of elastic constant anomalies.

Stretched proton-neutron configurations in fp-shell nuclei: (II). Systematics

The systematics of the binding energies of stretched proton-neutron configurations ( f 7 2 , g 9 2 ) 8 − , ( p 3 2 , g 9 2 ) 6 − , ( g 9 2 , p 3 2 ) 6− and ( g 9 2 ) 2 9 + are studied over a wide range of f p-shell nuclei. The effective proton-neutron interaction energies deduced from the data are nearly constant for ( p 3 2 , g 9 2 ) 6 − and ( g 9 2 ) 2 9 + states while the ( f 7 2 , g 9 2 ) 8 − configuration reveals an additional repulsive term proportional to the partial filling of the f 7 2 orbit in the target ground state. Two-body matrix elements are extracted. A crude shell model, which predicts that the excitation energy of a stretched state is equal to the sum of the single-particle energies, works well for the 6 − and 9 + states, but fails for the 8 − levels due to neglect of the additional interactions described above. The physics underlying the empirically introduced basic assumptions of the crude shell model is discussed. The binding energies are found to be linearly dependent on the mass number A and the isospin T z component and are well described by the weak-coupling model of Bansal and French. The derived parameters agree with averaged values of a similar analysis for the single-particle states in the corresponding odd-even neighbours. The data indicate a significant change of the particle-hole energies with closure of the proton f 7 2 shell.

Effect of impurity scattering on upper critical field of unconventional superconductors

The effect of Impurity scattering on upper critical fields in the axial state (P) and the hybrid state (D) is studied within weak coupling model. Unlike S-wave superconductor, impurity scattering suppresses both the transition temperature T c and upper critical field H c2(T). However, when H c2(x,T) / H c2(x,o) is plotted against T/ T c(x), the curves for different x(=0.5669 (τT c0) −1) almost collapse into a single curve. This behavior should give another test of unconventional superconductors.

Variation of self-energy and exciton-phonon coupling in KI and RbI with pressure.

We measured the 1s exciton energies in KI and RbI versus temperature at three different pressures via three-photon-excitation spectroscopy. The observed excitations display a Lorentzian line shape, which can be viewed as evidence that excitons and phonons in KI and RbI are only weakly coupling. Using the weak-coupling model we were able to find values for the real part of the temperature-dependent self-energy of the 1s exciton (peak-shift parameter \ensuremath{\Delta}). We find that the absolute value of \ensuremath{\Delta} and the strength of the exciton-phonon coupling increase with pressure. We also studied the behavior of the linewidth of the 1s exciton-polariton resonance with pressure and temperature and found that it decreases with pressure. However, we do not think that the linewidth parameter \ensuremath{\Gamma} of the polariton can be rigorously interpreted as the imaginary part of the exciton self-energy.

Fulde-Ferrell state in heavy-fermion superconductors.

Within the weak-coupling model we study the upper critical field of S-wave and D-wave superconductors in the clean limit close to the Chandrasekhar-Clogston limit. We find for parameters derived from ${\mathit{dH}}_{\mathit{c}2}$(T)/${\mathit{dT}}_{\mathit{T}=\mathit{T}\mathit{c}}$ of a single crystal of the recently discovered heavy-fermion superconductor ${\mathrm{UPd}}_{2}$${\mathrm{Al}}_{3}$ that the Fulde-Ferrell (FF) state is possible for the S-wave and one of the D-wave superconductors of ${\mathit{D}}_{6\mathit{h}}$ symmetry but not for the hybrid state. Indeed, choosing a g factor slightly less than 2, we can describe the temperature dependence of ${\mathit{H}}_{\mathit{c}2}$(T) for both H\ensuremath{\parallel}Rc and H\ensuremath{\parallel}a extremely well. On the other hand the D-wave model predicts the transition into the FF state at T/${\mathit{T}}_{\mathit{c}}$=0.29 in sharp contrast to the experimental observation T/${\mathit{T}}_{\mathit{c}0}$=0.8.

Rotational evolution of solar-type stars with core-envelope decoupling

The anomalously rapid decrease in the surface rotation rates of G dwarfs between the ages of the α Persei and Pleiades clusters has been attributed by some authors to the temporary decoupling of the convective envelope from the radiative interior. We investigate the implications of this suggestion for the evolution of the rotational velocity distributions in open clusters using a parametrized model of standard magnetic braking with varying strength of core-envelope coupling. We find that for solar-type stars only a weak coupling model, in which little of the angular momentum stored in the core of a fast rotator has been transferred to the envelope by the age of the Hyades, can provide a reasonable fit to the observed rotational distributions at the ages of the α Per, the Pleiades and the Hyades clusters

Upper critical field of unconventional superconductors.

Limiting ourselves to the weak-coupling model and neglecting the Pauli paramagnetism and the spin-orbit coupling, we determine the upper critical field of the axial (${\mathit{E}}_{1\mathit{u}}$) and the hybrid (${\mathit{E}}_{1\mathit{g}}$) state numerically. When the external field H is parallel to the symmetric axis (the c axis), the solution proposed by Luk'yanchuk and Mineev is analyzed. When H is perpendicular to the c axis, we find the exact solution for the axial state, while we construct approximate solutions for the hybrid state.

Three-quasiparticle states analysis in odd-mass lead isotopes.

Three quasiparticle excitations for odd-even lead isotopes in the mass region 197[le][ital A][le]203 are calculated using a realistic two-body interaction. The analysis is performed in a correlated basis constructed by the tensor product of one times two quasiparticle states. Good agreement with available experimental data is found. The one phonon approximation of the weak coupling model is also analyzed.

SINGLE PARTICLE GREEN'S FUNCTION AND QUANTUM MAGNETIC OSCILLATION IN VORTEX STATE OF UNCONVENTIONAL SUPERCONDUCTORS

Within weak-coupling model we construct the superconducting order parameter in the vortex states of the axial and hybrid wave function. In terms of these order parameters the quasi-particle Green's function in the vortex state in the vicinity of upper critical field is constructed. In general the most important modification on the quantum oscillation in the vortex state is increase of the damping constant (or the Dingle temperature). However, since this extra term is proportional to the average of | f |2 over the electron orbit at the belly or neck of the Fermi surface, we find that this exrtra term vanishes for the hybrid state for both [Formula: see text] and [Formula: see text], while it vanishes in the axial state only for [Formula: see text]. This should provide a unique probe to the nature of the superconducting wave functions.