Collective pairing Hamiltonian in the GCM approximation

Using the generator coordinate method and the gaussian overlap approximation we derived the collective Schrödinger-type equation starting from a microscopic single-particle plus pairing hamiltonian for one kind of particle. The BCS wave function was used as the generator function. The pairing energy-gap parameter Δ and the gauge transformation angle ø were taken as the generator coordinates. Numerical results have been obtained for the full and the mean-field pairing hamiltonians and compared with the cranking estimates. A significant role played by the zero-point energy correction in the collective pairing potential is found. The ground-state energy dependence on the pairing strength agrees very well with the exact solution of the Richardson model for a set of equidistant doubly-degenerate single-particle levels.     

A hamiltonian with broken supersymmetry for the xenon isotopes

A hamiltonian with broken $\text{u}\text{(}\text{6}\text{2}\text{j+1)}$ supersymmetry is proposed that can describe collective excitations in nuclei with high-spin, single-j orbitals. Its bosonic part is identical with IBA, while the fermionic degrees of freedom, are characterized by the seniority quantum number. The ground state as well as excited energies of eight xenon isotopes with both odd and even mass are fairly well described by the so(6) limit of this hamiltonian with only one set of parameters.     

TDHF equations of motion for algebraic hamiltonians in a coherent state representation

Time-dependent Hartee-Fock (TDHF) equations are derived for nuclear systems with internal dynamical group U(r). The coordinates which appear in the TDHF equations are the coordinates which parameterize the U(r) coherent states. The TDHF orbits for the hamiltonian $\text{H}$ are identical with equations of motion for a classical system described by the hamiltonian function 〈$\text{H}$〉 obtained directly from the operator $\text{H}$. This quantum-classical correspondence facilitates interpretation of TDHF orbits. The phenomena of coexistence and critical elongation are discusses, as is the relation between the critical points of the function 〈$\text{H}$〉 and the spectral properties fo the operator $\text{H}$.     

Restoring of broken symmetries in the generator-coordinate method

Corrections to the potential and kinetic part of the collective hamiltonian due to particle-number projection have been derived within the generator-coordinate plus generalized gaussian-overlap (GCM + GOA) approach. The collective Schrödinger equation was constructed from the single-particle plus pairing hamiltonian using BCS generating functions. This approximation, connected with a rotation in gauge space, turns out to yield results very close to those of an exact particle-number projection. No corrections to the mass parameters were found. The GCM approach to the particle-number projection is simply generalized to restoring any broken symmetry, such as e.g. angular-momentum projection.     

$\delta$-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 (200)-zone boundary collective mode in Al within nearly-free-electron degenerate perturbation theory

The Aschroft and Sturm two-band-model on the optical properties of Al is extended for finite $\text{k}$ values and the dielectric function ?($\text{k}$,ω) is evaluated for $\text{k}$ parallel to the <100 > direction within nearly-free-electron degenerate perturbation theory. It is shown that a pair of (200) Bragg planes gives rise to another pole in the energy loss function Im[-1/?($\text{k,}$ω)] and hence to a collective mode which is of the same origin as the so-called zone boundary collective mode first proposed by Foo and Hopfield in Na. The dispersion and the strength of this (200)-zone boundary collective mode in Al are evaluated along the <100 > direction and the theoretical results agree very well with electron energy loss spectroscopy data. Comparison is also made with a numerical calculation by Singhal for some discrete $\text{k}$-values.     

Quasiparticle relaxation and phonon emission in superconducting tunnel junctions

Using SnISn tunnel junctions as generators and detectors of high frequency phonons, the temperature dependence (down to 0.3°K) of the derivative of the detected signal as a function of generator bias is reported. For T?1°K we have observed the expected BCS singularity in the signal at a generator bias of 4Δ. An additional singularity has been observed at a bias of 2Δ when the number of injected particles greatly exceeds the number thermally excited. Unlike the 4Δ peak, the temperature of occurrence of the 2Δ peak depends markedly on generator impedance, (injection rate) as expected. The data provide strong evidence that Tewordt's model (strictly valid for T = 0°K), in which an excited quasiparticle relaxes predominantly in a single step to the gap edge before recombination, is correct in the temperature range $\text{T}\text{T}{}_{\mathrm{c}}\text{< 0.3}$ and for low injection rates.     

Modified BCS treatment of pairing correlations in 240Pu at high spin and finite temperature

Strutinsky calculations are used to investigate the shape and fission stability of rotating nuclei at finite temperature. Pairing correlations are described within a modified BCS approach which allows for the inclusion of both thermal and rotational degrees of freedom. Numerical results are discussed for the case of the deformed nucleus ²⁴⁰Pu up to angular momentum $\text{I = 40}\text{h}\text{?}$. The critical temperature T which characterizes the collapse of the pairing correlations is found to be of the order of T_c ≈ 0.40 MeV, for I = 0.     

Lowest energy Cooper pairing in the presence of antiferromagnetism

Cooper pairing of electron eigenstates of an antiferromagnet involves considerable complexity in spin space and in phases of the order parameters. With a BCS interaction the pairing scheme with lowest free energy has anisotropic spin-matrix order parameter $\textcolor{red}{}\text{(}\text{k}\text{); however}\textcolor{red}{}{}^{\mathrm{+}}\text{(}\text{k}\text{)}\textcolor{red}{}\text{(}\text{k}\text{)=|△|}{}^2\textcolor{red}{}$. Magnitude of the anisotropic order parameter satisfies the simple BCS gap equation but with electron energies of the antiferromagnet eigenstates appearing instead of Bloch state energies of the nonmagnetic crystal.     

Spectral density of states for ferromagnetic Fe (001) surface

We present a calculation for the spectral density of surface states at the (001) surface of ferromagnetic Fe. We employ the transfer matrix formalism for a model hamiltonian with a nine function basis ($\text{s, p}$ and $\text{d}$ orbitals). The results are presented at the special symmetry points Γ, X and M. There are bona fide surface states located above the Fermi level at point X.     

Microscopic study of the high-spin behaviour in selected A ≃ 80 nuclei

The collective and non-collective high-spin configurations in selected $\text{A ? 80}$ nuclei are analysed in detail using a shell-correction approach taking care of individual configurations and the pairing self-consistent cranking method with a non-axially-deformed Woods-Saxon potential. Shape transitions, shape coexistence, band-termination effects and alignment processes are discussed.     

Excited states of bosons and fermions in a four-Fermi quantum field theory

A scalar-pseudoscalar four-Fermi quantum field model in four dimensional space-time is considered. Introducing the scalar and pseudoscalar collective bosons, the path-integral representation for the generating functional for Green's functions in terms of the effective total action integral containing only collective bosons is expressed. Using a classcal ground-state solution for collective bosons, a new formula for the generating functional for collective boson and fermion Green functions in terms of the effective propagators is derived. It is shown by a partly nonperturbative analysis that the excited states of collective bosons do exist and form finite trajectories in the plane mass-square-spin. These trajectories for bosons are approximately linear in J, as the experimental trajectories. The existence of fermion bound or excited states depend on the value of the dynamical parameters of the model. For some values of dynamical parameters there are bound states for $\text{J =}\text{1}\text{2}$ and $\text{3}\text{2}$. However, for most of other values bound or excited fermion states do not exist.     

Spectral density of surface states: Clean W(001) surface

The transfer matrix approach is applied to calculate the spectral density of electronic states for the W(001) surface. We use a tight-binding hamiltonian with a nine function basis: 6s, 6p and 5d. Results for $\text{k}$ points along the Σ and ? symmetry lines are presented for occupied states. Both surface and bulk features of the spectral density are in good agreement with angularly resolved photoemission spectra.     

THE MICROSCOPIC CALCULATION OF THE STATISTICAL THEORY OF NUCLEAR FISSION

Based on the statistical fission theory, we have calculated the mass and kinetic energy distributions as well as other physical quantities of ²³⁵U fission induced by thermal neutron using microscopical method. That is, the quantum state densities of the fragments at scission point are calculated by means of BCS hamiltonian. The contribution of the collective deformation of fragments to the quantum state density has been taken into consideration. The potential energy of fragment is calculated by means of Strutinski procedure, and the shelling effect, pairing correlation as well as collective deformation have been taken into consideration in calculating the excitation energy at scission point. The scission point distance is treated as an adjustable parameter.Comparing with other statistical fission theories, our results give better agreement with existing experiments.     

Specific heat of superconducting Th,Sc and Th,Y alloys with Ce impurities

Measurements of the specific heat jump ΔC at the superconducting critical temperature T_c on ($\text{Th, Sc}$)Ce and ($\text{Th, Y}$)Ce Ce impurity, solid solution alloy systems indicate that the former systems obey the BCS law of corresponding states (LCS) characteristic of superconductors with non-magnetic impurities while the latter systems present deviations from the LCS linear relation between reduced parameters which are attributed to the development of localized moments at the Ce ions as the Y concentration increases.     

Elementary excitations in quadrupolar systems

We consider $\text{S ?}\text{3}\text{2}$ isotropic quadrupolar ordered systems and derive elementary excitations at low temperature. A Holstein-Primakoff type transformation and a linear approximation are used. For $\text{S =}\text{3}\text{2}$, the spectrum is made of four degenerate acoustic branches. For S ? 2, only two degenerate branches satisfy the Goldstone theorem: they describe Δm = ± 1 excitations similar to librons in molecular crystals. The two degenerate branches describing Δm = ± 2 excitations have a gap at k = 0 although the hamiltonian is isotropic. For a special $\text{S =}\text{3}\text{2}$ cubic hamiltonian, a Goldstone mode is found in the spectrum and related to a continuous degeneracy of the ground state. A comparison between $\text{S =}\text{1}\text{2}$ dipolar and $\text{S =}\text{3}\text{2}$ quadrupolar systems is presented.     

Polarization dynamics for spin 12-spin I systems with Breit-Rabi interaction

We study the full polarization dynamics of two interacting systems of spin $\text{1}\text{2}$ and spin I for the Breit-Rabi hamiltonian, the sum of contact hyperfine and Zeeman terms. We obtain the time dependence of the polarizations by solving the eigenvalue problems for the interaction hamiltonian and discuss some applications.     

N = 1 supergravity in the light-cone gauge

N = 1 supergravity is studied in a light-cone gauge. The non-linear transformations and the hamiltonian are constructed to order K in the coupling constant as a realization of the super-Poicaré algebra. The only input except the algebraic structure is the helicity content ($\text{±2, ±}\text{3}\text{2}$) and the dimensionality of the coupling constant.