Two-particle Band Research Articles

High-K multi-particle bands and pairing reduction in 254No * * Supported by the National Natural Science Foundation of China (11775112, 11535004, 11875027, 11761161001) and the Priority Academic Program Development of Jiangsu Higher Education Institutions

The multi-particle states and rotational properties of the two-particle bands in are investigated by the cranked shell model with pairing correlations treated by the particle number conserving method. The rotational bands on top of the two-particle and states and the pairing reduction are studied theoretically in for the first time. The experimental excitation energies and moments of inertia of the multi-particle states are reproduced well by the calculations. Better agreement with the data is achieved by including the high-order deformation , which leads to enlarged and deformed shell gaps. An increase of in these two-particle bands compared with the ground state band is attributed to the pairing reduction due to the Pauli blocking effect.

Microscopic Model for Feshbach Interacting Fermions in an Optical Lattice with Arbitrary Scattering Length and Resonance Width

We numerically study the problem of two fermions in a three-dimensional optical lattice interacting via a zero-range Feshbach resonance and display the dispersions of the bound states as a two-particle band structure with unique features compared to typical single-particle band structures. We show that the exact two-particle solutions of a projected Hamiltonian may be used to define an effective two-channel, few-band model for the low-energy, low-density physics of many fermions at arbitrary s-wave scattering length. Our method applies to resonances of any width and can be adapted to multichannel situations or higher-ℓ pairing. In strong contrast to usual Hubbard physics, we find that pair hopping is significantly altered by strong interactions and the presence of the lattice, and the lattice induces multiple molecular bound states.

The Low Lying Energy-Momentum Spectrum for the Lattice Four-Fermi Model

We obtain the low-lying energy-momentum spectrum for the imaginary-time lattice four-Fermi or Gross- Neveu model in d + 1 space-time dimensions (d = 1, 2, 3) and with N-component fermions. Let 0 0 the four-fermion coupling, m > 0 the bare fermion mass and take s × s spin matrices (s = 2, 4). Our analysis of the one and the two-particle spectrum is based on spectral representation for suitable two- and four-fermion correlations. The one-particle energy-momentum spectrum is obtained rigorously and is manifested by sN 2 isolated and identical dispersion curves, and the mass of particles has asymptotic value order ?ln ?. The existence of two-particle bound states above or below the two-particle band depends on whether Gaussian domination does hold or does not, respectively. Two-particle bound states emerge from solutions to a lattice Bethe-Salpeter equation, in a ladder approximation. Within this approximation, the (sN 2 ? 1)sN 4 identical bound states have O(?0) binding energies at zero system momentum and their masses are all equal, with value? ?2 ln?. Our results can be validated to the complete model as the Bethe-Salpeter kernel exhibits good decay properties. MSC 2010: 81Qxx, 81Txx, 81Vxx.

Transfer Matrix Spectrum for O(N) High Temperature Lattice Classical Ferromagnetic Spin Systems and Staggering Transformations

We obtain the low-lying energy-momentum spectrum for the imaginary-time lattice quantum field model associated with d-dimensional lattice ferromagnetic classical N-component vector spin systems at high temperature (0 < β << 1). Each system is characterized by a single site a priori spin probability distribution. The energy-momentum spectrum exhibits isolated dispersion curves which are identified as single particles and multi-particle bands. Our two-particle bound state analysis is restricted to a ladder approximation of the Bethe–Salpeter equation, and the existence of bound states depend on whether or not Gaussian domination for the four-point function is verified. It is known that two-particle bound states appear below the two-particle band if Gaussian domination does not hold. Here, we show that two two-particle bound states appear above the two-particle band if Gaussian domination is verified. We also show how the complete two-particle spectral pattern for these models can be understood by making a correspondence between the Bethe–Salpeter equation and a two-particle lattice Schrödinger Hamiltonian operator with attractive or repulsive spin-dependent delta potentials at the origin. A staggering transformation is used to relate the attractive and repulsive potential cases, as well as their associated Hamiltonians spectrum and eigenfunctions.

Dynamic theory of vibronic spectra of charge transfer excitons

The vibronic spectra of charge transfer excitons (CTE) in a molecular chain are treated in the framework of a dynamic approach (which neglects the thermal excitation of the excitons and of the intramolecular vibration). The model includes two mechanisms of coupling between CTEs and vibrational quanta, generalizes in this way the simple CTE Hamiltonian as well as the vibronic Hamiltonian of Frenkel excitons and allows to study the vibronics of CTEs. The linear optical susceptibility is calculated in the vibronic regime (one CTE plus one vibrational quantum). A double splitting of the vibronics of CTEs is established: (1) a splitting connected with the location of the intramolecular vibration on donors or on acceptors and (2) a splitting connected with the symmetry of the vibronic states (in the degenerate case, realized in the absence of an external electric field). The investigation of the general structure of the vibronic spectra of CTEs, which includes two-particle bands and bound CTE-phonon states, allows to model the optical absorption spectra in two cases: (1) without proper transfer of a vibrational quantum between neighboring molecules and (2) with transfer of a vibrational quantum between donor and acceptor molecules.

Charge transfer excitons: dynamic theory of vibronic spectra

The vibronic spectra of charge transfer excitons (CTE) in a molecular one-component or alternatingly ordered two-component chain are treated in the framework of a dynamic approach (neglecting thermal excitations of the intramolecular vibrations). The model introduces two mechanisms of coupling between CTEs and vibrational quanta: (1) shift of the equilibrium positions of the nuclei in the ionized donor or acceptor; (2) change of the vibrational frequency in the ionized molecule. This model allows to generalize the simple CTE Hamiltonian and the vibronic Hamiltonian of Frenkel excitons. The linear optical susceptibility is calculated in the vibronic region (one CTE and one vibrational quantum). The double splitting of vibronics of CTEs was analyzed: (1) the splitting connected with the location of the intramolecular vibration on the donors or on the acceptors; (2) the splitting connected with the symmetry of the vibronic spectra (in the degenerate case). The general structure of the vibronic spectra of CTEs is established. It contains structureless absorption lines, which correspond to two-particle bands (the phonon is excited on a neutral molecule neighboring the donor or the acceptor) and Lorentz-type lines of one-particle states, which correspond to the bound propagation of the CTE and the phonon.

Excitation spectrum and staggering transformations in lattice quantum models.

We consider the energy-momentum excitation spectrum of diverse lattice Hamiltonian operators: the generator of the Markov semigroup of Ginzburg-Landau models with Langevin stochastic dynamics, the Hamiltonian of a scalar quantum field theory, and the Hamiltonian associated with the transfer matrix of a classical ferromagnetic spin system at high temperature. The low-lying spectrum consists of a one-particle state and a two-particle band. The two-particle spectrum is determined using a lattice version of the Bethe-Salpeter equation. In addition to the two-particle band, depending on the lattice dimension and on the attractive or repulsive character of the interaction between the particles of the system, there is, respectively, a bound state below or above the two-particle band. We show how the existence or nonexistence of these bound states can be understood in terms of a nonrelativistic single-particle lattice Schrödinger Hamiltonian with a delta potential. A staggering transformation relates the spectra of the attractive and the repulsive cases.

Interband spectrum of weakly coupled stochastic lattice Ginzburg-Landau models.

We analyze the excitation spectrum of the generator associated with the relaxation rate to equilibrium in weakly coupled stochastic Ginzburg-Landau models on a spatial lattice Z(d). The spectrum has a quasiparticle interpretation. Depending on d and on the specific interaction, by solving the Bethe-Salpeter equation in the ladder approximation, we show the existence of a stable particle above the upper envelope of the two-particle band, possessing a concave dispersion curve. This result furthers our knowledge about the spectrum of the stochastic dynamics generator.

Characterization of energy levels in the nucleus170Lu

Configuration assignments are derived for the observed energy levels in the odd-odd deformed nucleus170Lu99 based on the calculations of the two-particle band head energies for a zero range residual interaction, the beta-feeding characteristics, and the observed features for similar bands in the neighbouring nuclei. In particular, specific assignments are given for theJπ=1+ levels at 198.4 keV, 349.0 keV and 785.5 keV. The ambiguities with respect to the assignments for theKπ=3− bands are discussed. A new isomer withJπ=7+ and half-life of several seconds is predicted around (225±25) keV and experiments are suggested to identify it.

Pure electronic, vibronic, and two-particle surface excitons on the anthracene crystal. II. Experimental study and analysis of the (0,1) region

In this second part, we present the experimental and theoretical study concerning vibronic surface transitions for the vibration modes 390 and 1400 cm−1. We begin by a theoretical discussion of the different limiting cases of exciton-vibration coupling. In the experimental part, evidence of the surface character for the observed structures in surface emission excitation spectra is provided by their shifts upon surface coating. A general smilarity of the surface states with the previously described bulk states, including a translational equivalence (δ̄=206 cm−1), is established. The observed structures are assigned to interacting single particle (vibron) resonances and two-particle bands. However, some slight discrepancies between surface and bulk band structures lead us to question the complete validity of their translational equivalence. Finally, our observations show that the surface two-particle excitation profile (peak shaped) is quite different from the surface two-particle absorption profile (stepwise threshold profile). We propose a model mechanism of the surface excitations relaxation which accounts qualitatively for this specific surface excitation profile.

Two-particle vibrational excitations in molecular crystals

In this paper we utilize a two-particle band model to describe cooperative vibrational excitations and vibrational overtones in molecular crystals of diatomic molecules. The cooperative vibrational excitation involves a two-vibron continuum, while the overtone corresponds to a two-vibron bound state. The problem of two-particle vibrational excitations was shown to be equivalent to the perturbation of a band by a local potential, whose strength is determined by the intramolecular anharmonicity. Model calculations were performed for a three-dimensional, semicircular density of states, resulting in transparent expressions for the energetics and intensities, which were utilized subsequently to provide a self-consistent analysis of the available experimental results. In all these cases, the local perturbation is sufficiently strong to ensure the appearance of a bound overtone state outside the two-particle band. Finally, we consider the effects of structural disorder on two-vibron states, which provide a diagnostic tool for the identification of two-particle bound states and of two-particle continua.

Temperature effects in two-phonon spectra

Abstract A number of vibrational spectra peculiarities in crystals are predicted in this paper, which appear at high temperatures ( kT ⪆ ℏω ) in the summation and difference tones of vibrations. It is shown that the anharmonic interaction between the phonons grows with temperature, which leads to splitting of levels of both summation and difference biphonons from the two-particle bands. The dielectric permittivity of the crystal for the above spectral regions is calculated.

Bound and many-particle states in polariton Raman spectra of NH 4Cl crystals

The properties of polariton Raman spectra for the internal vibration region of NH 4Cl crystal are discussed. These spectra have been recorded by means of a copper laser ( λ = 5105 and 5782 A ̊ ) for sample temperature T=80 and 10°K. According to the theory a polariton singularities in the region of a polar bound state has been obtained. The two-particle bands have been studied and a very complicate structure inside of these bands has been revealed. Moreover, multiphonon singularities at polariton curves have been observed. The experimental polariton law has been compared to the theory and a conclusion has been made as to the necessity of a further development of the theory.

Vibronic Coupling in the Exciton States of the Rigid-Lattice Model of Molecular Crystals

The vibrational structure of the Frenkel exciton states of a molecular crystal is investigated by a variational technique using a rigid-lattice-model Hamiltonian. The spirit of the weak coupling formalism is strictly adhered to by constructing crystal wavefunctions from products of isolated molecule wavefunctions so that the only parameters of the theory are Franck—Condon factors and vibrational frequency shifts. The basis set consists of all vibronic, i.e., single particle, states belonging to the same electronic state transforming according to a given wave vector, plus a set of two-particle states in which vibronic and ground vibrational excitation occupy different sites. Interactions between single-particle states are treated in detail, as are interactions between one- and two-particle states. However, part of the interaction between certain two-particle states is neglected and this makes the treatment progressively less accurate for higher vibrational states and stronger coupling. Electron exchange effects, coupling of excitons to photons, higher electronic states, and ion-pair states are not considered. It is shown how each element of the conventional weak coupling energy matrix is supplemented by terms which account for the interaction between one- and two-particle states as well as interactions among the two-particle states. For a given wave vector each single-particle state is accompanied by a family of two-particle bands which rapidly increases in size for higher vibrational states. In the weak coupling limit the families are widely separated, while intermediate coupling corresponds to two-particle bandwidths comparable with the vibrational spacing. The onset of strong coupling corresponds to overlapping of adjacent families.