Quantitative analysis of Fermi resonances by harmonic derivatives of perturbation theory corrections

Vibrational perturbation theory has proven to be a highly accurate and efficient method for extending the harmonic approximation in the treatment of polyatomic molecular vibrations. Unfortunately, accidental near-degeneracies of the harmonic vibrational levels can lead to resonance and a breakdown of the perturbation approximation. These resonances can be resolved by the diagonalization of a small effective Hamiltonian derived from either of the usual Rayleigh–Schrödinger or van Vleck perturbation theories. However, the proper choice of states for inclusion in the effective Hamiltonian is crucial to the accuracy of the results, and is not often clearly evident. It is proposed that the analytical partial derivatives of the anharmonic vibrational correction with respect to the various harmonic frequencies, called ‘Harmonic Derivatives’ in this work, can be used as a tool to quantitatively assess the existence and strength of first-order, or Fermi, resonances. These derivatives are shown to concisely and clearly reflect the quality of the perturbation approximation and the effect of its breakdown on the computed vibrational levels.     

Quantum dimer model for trimerized kagomé antiferromagnet

Low-energy singlet states of a spin-1/2 trimerized kagomé antiferromagnet are mapped to an effective quantum dimer model on a triangular lattice. The mapping is done in the first-order of perturbation theory in a weaker coupling constant of the trimerized model. The derived quantum dimer model is dominated by kinetic energy terms (dimer resonances) on a few shortest loops of the triangular lattice.     

Analysis of E1 and E2 radiative α-capture and giant multipole resonances

Experimental data on E1 and E2 radiative α-capture are analyzed by taking account of direct and semidirect processes as well as the compound process. Observed excitation functions for these reactions are reasonably well reproduced assuming the reactions take place mainly through giant multipole resonances. It is shown that the compound process dominates in the lower energy region especially for E1 capture whereas in the higher energy region direct and semidirect captures are the major processes especially for E2 capture. Several interesting results are obtained on α-particle spectroscopic factors of target ground states and on spreading widths and isospin-mixing coefficients of the giant multipole resonance states. The data are shown to be consistent with the existence of the isoscalar giant quadrupole resonances. The applicability of direct and semidirect capture theories to α-capture is examined.     

Clusters as Many-Body Resonances

A formalism to evaluate the resonant states produced by two particles moving outside a closed shell core is presented. The two-particle states are calculated by using a single-particle representation consisting of bound states, Gamow resonances and scattering states in the complex energy plane (Berggren representation). Two representative cases are analysed corresponding to whether the Fermi level is below or above the continuum threshold. It is found that long-lived resonances are mostly determined by either bound states or by narrow Gamow resonances. However, they are significantly affected by wide resonances and the continuum background itself.     

Zeeman effect in the polarization spectroscopy of Na

The Doppler-free polarization spectrum of the D₁ line has been studied in fields of about 50 G and in zero field. Although the principal Zeeman resonances are resolved, the signals are confusing because of the very large number of cross-over resonances. Cross-over resonances also seriously distort well-resolved resonances in zero field. An interpretation is given, based on combining a first-order theory of optical pumping with the theory of Faraday rotation and dischroism.     

Higher order Gamow states with exponential decay

We derive Gamow vectors fromS-matrix poles of higher multiplicity in analogy to the Gamow vectors describing resonances from first-order poles. With these vectors we construct a density operator that describes resonances associated with higher order poles that obey an exponential decay law. It turns out that this operator formed by these higher order Gamow vectors has a unique structure.     

Dynamically generated resonances from the vector octet-baryon decuplet interaction and their radiative decays into γ-baryon decuplet

The dynamically generated resonances from vector meson-baryon decuplet are studied using La-grangians of the hidden gauge theory for vector interactions. One shows that some of the generated states can be associated with some known baryon resonances in the PDG data, while others are predictions for new states. Furthermore, we calculate the radiative decay widths of these resonances into a photon and a baryon decuplet.     

Comparison of sub-coulomb stripping and analog resonance results in Zr

The ⁹²Zr(d, p)⁹³Zr reaction, leading to states in ⁹³Zr which are parents of analog states observed in ⁹²Zr(p, p) elastic scattering, has been studied for incident deuteron energies below the Coulomb barrier. For each of the parent states the reduced normalization has been extracted, and these have been compared with the reduced normalizations calculated for the analog resonances on the basis of various analog resonance theories.     

Astrobiology: a respectable new science

Holographic quantum chromodynamics (QCD) is an extra-dimensional approach to modelling hadrons, the bound states of the strong interactions. In holographic models, the extra spatial dimension creates a waveguide for fields, and the discrete towers of modes propagating in that waveguide are interpreted as hadronic resonances. These models are motivated by the AdS/CFT correspondence, which is a duality that relates theories in different numbers of spatial dimensions. Holographic models have the potential to provide a better understanding of strongly interacting systems of quarks and gluons, as well as unconventional superconductors and other nonperturbative systems.     

Resonance states of the continuous spectrum of a bounded crystal near the critical points of volume bands

The conditions for the existence of resonance electronic states near the critical points of volume bands are obtained. It is shown that resonances of this type are qualitatively different from surface resonances associated with states induced by an image potential. The manifestation of such “volume” resonances in the scattering of very slow electrons by a TiS₂ surface is studied. Fiz. Tverd. Tela (St. Petersburg) 40, 2003–2007 (November 1998)     

Multipole-based modal analysis of gate-defined quantum dots in graphene

A new numerical method based on the multipoles of the Dirac equation is presented for rigorous and fast analysis of electron scattering from gate-defined structures in graphene. The new method is used to study the strongly bound states and the weakly bound states of a circular quantum dot. The accuracy of the obtained results is then verified by the T-matrix method. Furthermore, we characterize the resonances of elliptical gate-defined quantum dots and compare these resonances with the strongly bound states of circular dots. The effects of coupling between two quantum dots are also investigated.     

Understanding the Meson States and Non-qq States

By studying the behavious of Regge trajectories of the boson resonances and comparing with the predictions from quark model, we understand more the existing scalar, tensor, pseudoscalar particles and non-quark-antiquark states. One can find some resonances are non-qq states.     

Bound states in photonic Fabry-Perot resonator comprised of two nonlinear off-channel defects

Two off-channel nonlinear defects coupled to the photonic waveguide constitute the Fabry-Perot interferometer (FPR). The defects are made from a Kerr-like nonlinear material. For the linear case such a FPR can support the bound states in the form of standing waves between the defects if the distance between them is quantized. For the nonlinear case the bound states appear for arbitrary distance between the defects however for an quantized electromagnetic intensity. For the transmission through FPR we reveal new resonances and show these are a result of coupling of the bound states with incident wave because of nonlinearity of the defects. The resonances are spaced at the eigen frequencies of bound states.     

New method for extracting quasi-bound states from the continuum

A new parameter-free method is proposed for treatment of single-particle resonances in the real-energy continuum shell model. This method yields bound states embedded in the continuum, the anamneses of resonances, which provide a natural generalization of weakly bound single-particle states.     

2-Particle asymptotic completeness and bound states in weakly coupled quantum field theories

Rigorous results on poles of the 2- and 4-point functions, which yield 2-particle asymptotic completeness and give information on the presence or absence of 2-particle bound states and resonances, are presented for weakly coupled even and non-even-field theories with mass gap in space-time dimensiond=2, 3 (and for related hypothetical theories in dimension 4). Methods used are more convenient and more general than those used previously (with more limited results) forP()₂ theories.     

Effects of mean-field and pairing correlations on the Bogoliubov quasiparticle resonance

The quasiparticle resonances are investigated by examining three kinds of quasiparticle spectra, i.e., the density of quasiparticle states, the occupation number density, and the pair number density in the continuum Skyrme Hartree-Fock-Bogoliubov theory with the Green's function method. Taking the weakly bound nucleus ~(66)Ca as an example, the quasiparticle resonant energies and widths extracted from these three kinds of quasiparticle spectra are compared. For the narrow resonances, the extracted resonant energy and the width are consistent with each other. However, it is difficult to use the density of quasiparticle states to identify the broad resonances due to the background of nonresonant continuum. By switching off the pairing potential and/or the Hartree-Fock(HF) potential respectively in the calculation of these quasiparticle spectra, the roles of HF mean-field and pairing correlations in the quasiparticle resonances are demonstrated clearly. It turns out that all the quasiparticle resonances corresponding to the deeply bound, weakly bound and positive-energy single-particle resonant states, are mainly contributed by the HF potential. The pairing potential helps to slightly increase the resonant energy and the width. However, the pairing potential is important to make the nucleons occupy the low-lying nonresonant continuum states near the threshold and take part in the pairing correlations here,especially for the partial waves with small angular momentum ?.     

The response of two-degree-of-freedom systems with quadratic and cubic non-linearities to multifrequency parametric excitations

The response of two d.o.f. systems with quadratic and cubic non-linearities to multi-frequency parametric excitations is determined by using the method of multiple scales. Four first-order ordinary differential equations are derived to describe the modulation of the amplitudes and the phases when principal parametric resonances of both modes and combination resonances of the additive and difference type occur simultaneously. In all cases the steady state solutions and their stability are determined. Numerical results depicting the various resonances are presented.     

The damping of the giant resonances in heavy and medium-heavy nuclei

The damping of the giant resonances in heavy and medium-heavy nuclei can be described by thermalization and cooling-off processes. The direct emission of particles, which is strongly inhibited by Coulomb and centrifugal barriers is neglected here. In the damping process, which begins with the thermalization, the 1p-1h giant resonance states induced by the incoming electromagnetic field are scattered inelastically due to the presence of two-body residual forces into other 1p-1h and 2p-2h states. In heavy nuclei there exist, at the energy of the giant resonance, several hundreds of such 2p-2h states. The 1p-1h dipole and quadrupole basis states for the diagonalization of the Hamiltonian are obtained from a spherical Nilsson potential. The density of the 2p-2h states obtained from the same potential are then used to determine the energy dependence of the widths of the giant resonances.