Regge poles in the collective model of the nuclear giant multipole resonances

Giant nuclear resonance states, of higher multipolarity than dipole, have recently been observed in hadron and electron scattering. They may possibly be described by the collective Goldhaber-Teller model as extended to the higher multipolarity case, and as generalized to include spin-isospin vibrations and spin waves. Based on such a model, we show that the multipole resonances, together with the conventional dipole resonances, can be generated by the motion of a few basic Regge poles through the complex angular momentum plane. This viewpoint unifies all the resonances with a given spin-isospin character but arbitrary value of the multipolarity, and suggests the existence of the higher-multipole resonances as a consequence of the existence of the dipole resonance. We also analyze these Regge poles in terms of collective surface waves (“creeping waves”) circumnavigating the nucleus, and we determine their phase velocities and attenuations. Finally, the giant resonances them selves are explained as a resonant reinforcement of phase-matched surface waves.     

Two-fluid model description of isovector giant resonances in fast rotating nuclei

Isovector giant resonances of arbitrary multipolarity in fast rotating nuclei are studied by solving the inviscid two-fluid equation of relative motion in a rotating frame of reference. Both Coriolis and centrifugal forces are taken into account. The resulting expressions display in a quite simple way general features of giant multipole resonances of fast rotating nuclei, in addition to a good agreement with other calculations for the giant dipole resonance. Typical values for the resonance energies and their fragmentation due to nuclear deformation and rotation are given. In particular, enormously large resonance splitting should occur in the superdeformed states.     

A Study of Giant Monopole an. d. Quadrupole States in the Relativistic Thomas-Fermi Approximation

The isoscalar giant monopole and quadrupole states in finite nuclei are studied in a relativistic δ-ω model by making use of a local Lorentz boost and scaling method, and the nuclear surface and the density distribution are treated in the relativistic Thomas-Fekmi approximation.The excitation energies of the giant resonances are self-consistently calculated. It is found that the excitation energies of giant monopole arehbasically in agreement with experimental data for all nuclei and those of giant quadrupole for light nuclei. Coupling constants and δ-meson mass in the theory are chosen to fit static properties of nuclear matter.     

Microscopic description of giant resonances in highly excited nuclei

Giant resonances of general multipolarity in highly excited nuclei, which are produced in compound nuclear and deep inelastic heavy ion reactions, are described microscopically in the finite temperature linear response formalism. The linear response function is calculated in the finite temperature (FT) quasi-particle RPA approximation (FT-HFB-RPA) and is based on the corresponding self-consistent quasi-particle basis (FT-HFB). The theory is derived from the small amplitude limit of FT-TDHFB. The inclusion of cranking constraints allows the investigation of giant resonances in nuclei with large intrinsic excitation energy and high spin. A schematic model for the FT-HFB-RPA is developed and applied to the isovector giant dipole resonance in hot spherical nuclei. It is shown that the energy of the resonance depends only weakly on temperature in these systems. The experimentally observed lowering of the giant mode in highly excited nuclei is to be attributed to different effects. The descritpion of resonance damping lies beyond the scope of the random phase approximation. Possible extensions in this direction and qualitative features of the width of giant resonances at finite temperature are discussed.     

Dynamics of single-particle and collective excitations in heavy nuclei

The propagation of single-particle and small-amplitude collective excitations in a heavy nucleus is considered. We calculate perturbatively corrections to the mean-field approximation induced by the coupling of one-particle and collective motion via the residual particle-hole interaction. Special attention is paid to the energy variation of the quasiparticle effective mass near Fermi energy. We conclude from the calculation that particles and holes excited in low multipolarity giant resonances have average effective masses of the order of 0.8 m rather than m. The mechanism for the decrease is provided by the enforced decoupling of the quasiparticles from surface oscillations due to the high frequency of the giant resonances. We also study the role of surface modes in the decay of giant resonances. Considerable reduction of the damping into 2p-2h states expected from the absorptive part of the optical potential is found. The correlated particle-hole pairs interact with each other by exchanging surface oscillations which adds a destructive interference term to the decay widths of giant resonances. The reduction depends on the multipolarity of the mode and is only large for low angular momenta.     

Giant first-forbidden resonances

Recent experimental data on first-forbidden charge-exchange resonances are discussed in the framework of a schematic model. We also evaluate the screening of the weak coupling constants induced by both the giant resonances and the Δ-isobar. It is shown that the last effect does not depend on the multipolarity of the one-particle moment. Due to the same reason, the fraction of the reaction strength pushed up into the Δ-resonance region is always the same regardless of the quantum numbers carried by the excitation. Simple expressions are derived for the dependence of the excitation energies of the first-forbidden giant resonances on the mass number and isospin of the target. The model reproduces consistently both the Gamow-Teller and the first-forbidden resonances.     

Nuclear forward scattering for high energy mössbauer transitions

We have studied nuclear forward scattering of synchrotron radiation for the 67.41 keV resonance of 61Ni using a silicon crystal monochromator with low-index reflections and a multielement detector. This approach can be extended to other high-energy M?ssbauer transitions and does not pose any restrictions on the sample environment. Under conditions of large sample thickness and short nuclear lifetime, typical for work with high-energy nuclear resonances, the nuclear decay follows a universal dependence where both thickness effects and hyperfine interactions are taken into account by time scaling.     

Excitation of isovector giant resonances by inelastic scattering of positive pions on90Zr at 226 MeV

We studied the region of giant resonances with positive pions of 226 MeV scattered inelastically on⁹⁰Zr. Two groups of resonances were seen: the first structure between 12 and 19 MeV excitation energy is explained as a sum of the isoscalar quadrupole resonance at 14 MeV, the isovector dipole resonance at 16.5 MeV and possibly some E₀ strength. The second group between 24 and 34 MeV excitation energy also corresponds to more than a simple multipolarity and may be described as a sum of a monopole and a quadrupole isovector resonance.     

A Chiral Breaking Field Theory for Giant Multipole States of Nuclei

The isoscalar giant monopole and quadrupole states of finite nuclei are studied in a relativistic chiral breaking field theory by making use of local Lorentz-boost and scaling method. The nudear surface effect and the density distribution are treated in the relativistic Thomas-Fermi approximation. The excitation energies of the giant resonances are self consistently calculated. The numerical results for the excitation energies are in agreement with experimental data for all nuclei.     

Role of the nuclear surface in a unified description of the damping of single-particle states and giant resonances

The damping widths of single-particle states and of giant resonances are estimated in spherical nuclei, based on the excitation of surface modes.A Skyrme III interaction with an effective mass consistent with that resulting from infinite nuclear matter calculations with “realistic” forces $\text{(m}{}^1\text{/m = 0.76)}$, was utilized. The single-particle basis needed to construct the unperturbed nuclear response function for each multipolarity was obtained, treating this force in the Hartree-Fock approximation. Diagonalizing a schematic interaction in this basis, the surface modes were calculated. They are used to dress the single-particle and single-hole states and to renormalize the vertex interaction, taking into account the proper energy dependence of the couplings.The essential new feature of the present calculation as compared to the calculations reported in ref.¹) is that the energy dependence of the real and imaginary part of the self-energy is taken into account. This is done utilizing a strength function model.About 70 % of the damping widths arise from the coupling to specific intermediate states containing one low-lying collective surface vibration. The rest, from the coupling to many nonspecific states.Qualitative agreement is found with the experimental data for spherical nuclei throughout the mass table for both the single-particle states and the giant resonances. The model seems however to predict widths which are smaller than those experimentally observed.     

Stochastic modeling of resonance collisions and the hypothesis of local ergodicity

In application to nuclear reactions in the domain of weakly overlapping resonances, a principle of local egodicity of cross sections is formulated. For a number of the simplest examples, estimates are obtained of the energy interval of local ergodicity.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 3, pp. 66–72, March, 1989.     

Classical scaling theory of quantum resonances

The quantum resonances occurring with delta-kicked particles are studied with the help of a fictitious classical limit, establishing a direct correspondence between the nearly resonant quantum motion and the classical resonances of a related system. A scaling law which characterizes the structure of the resonant peaks is derived and numerically demonstrated.     

Excitation of deformation vibrations by radiationless muonic transitions

An investigation is carried out for selected doubly even nuclei in the rare-earth and actinide regions for possible resonances between pairs of muonic levels of the appropriate quantum numbers and certain nuclear collective states. Such resonances can lead to the excitation of the particular nuclear state involved, and could be used as an alternate means of nuclear excitation. Electric monopole excitations were found which can result in the excitation of the nuclear 0⁺ level of the β-band. The muonic states involved, however, are such that the probability of nuclear excitation may be small. An electric quadrupole resonance in ¹⁸²W involving the excitation of the 2⁺ state of the β-band is found to be a very likely candidate. Dipole and octupole resonances were also investigated; however no possible resonances were found. Also unsuccessful was the search for quadrupole excitations of the 2⁺ state in the γ-band. The matrix elements involved in the EO and E2 resonances are calculated, the nuclear contribution being computed using the nuclear collective model of Davydov and Chaban. The probability for nuclear excitation in the E2 resonance in ¹⁸²W is computed.     

A note on the absence of resonances for Schrödinger operators

A simple proof of the absence of resonances for Schrödinger operators in the semiclassical limit is given under a generalized scaling and nontrapping (or virial) condition. The method of local distortion due to Hunziker is employed and a pseudo-differential operator calculus is used to construct the parametrix. The result is primarily intended for applications to the shape resonance, but can be also applied to various models including Stark effect and periodic potentials.Dedicated to Professor Tosihusa Kimura on his 60th birthday.     

Excitation of nuclei by photon beams carrying orbital angular momentum

A drop in the efficiency of nuclear excitation through transitions of high multipolarity is related to the increase in the angular momentum difference between the nuclear states involved in the excitation transition. Such transitions need photons with a high angular momentum. It is well known that photon beams carrying a well-defined and arbitrarily high value of angular momentum about the beam axis can be produced. We discuss some features in the excitation of nuclei with the beams.     

Isovector quadrupole resonance observed in the 60Ni(13C,13N)60Co reaction at E/A=100 MeV

The charge-exchange reaction 60Ni(13C,13N)60Co at E/A=100 MeV has been studied to locate isovector (deltaT=1) non-spin-flip (deltaS=0) giant resonances. Besides the giant dipole resonance at E(x)=8.7 MeV, another resonance has been observed at E(x)=20 MeV with a width of 9 MeV. Distorted-wave Born approximation analysis on the angular distribution clearly indicated the L=2 multipolarity, attributing the E(x)=20 MeV state to the giant isovector quadrupole resonance.     

Resonances and wave propagation velocity in the subglottal airways

Previous studies of subglottal resonances have reported findings based on relatively few subjects, and the relations between these resonances, subglottal anatomy, and models of subglottal acoustics are not well understood. In this study, accelerometer signals of subglottal acoustics recorded during sustained [a:] vowels of 50 adult native speakers (25 males, 25 females) of American English were analyzed. The study confirms that a simple uniform tube model of subglottal airways, closed at the glottis and open at the inferior end, is appropriate for describing subglottal resonances. The main findings of the study are (1) whereas the walls may be considered rigid in the frequency range of Sg2 and Sg3, they are yielding and resonant in the frequency range of Sg1, with a resulting ~4/3 increase in wave propagation velocity and, consequently, in the frequency of Sg1; (2) the "acoustic length" of the equivalent uniform tube varies between 18 and 23.5 cm, and is approximately equal to the height of the speaker divided by an empirically determined scaling factor; (3) trachea length can also be predicted by dividing height by another empirically determined scaling factor; and (4) differences between the subglottal resonances of males and females can be accounted for by height-related differences.     

Quark-hadron duality of nucleon spin structure function

Bloom-Gilman quark-hadron duality of nuclear spin structure function is studied by comparing the integral of g₁ from perturbative QCD prediction in the scaling region to the moment of g₁ in the resonance region. The spin structure function in the resonance region is estimated by the parametrization forms of non-resonance background and of resonance contributions. The uncertainties of our calculations due to those parametrization forms are discussed. Moreover, the effect of the (1232)-resonance in the first resonance region and the role of the resonances in the second resonance region are explicitly shown. Elastic peak contribution to the duality is also analyzed.     

Calculation of Wannier-Bloch and Wannier-Stark states

The paper discusses the metastable states of a quantum particle in a periodic potential under a constant force (the model of a crystal electron in a homogeneous electric field), which are known as the Wannier-Stark ladder of resonances. An efficient procedure to find the positions and widths of resonances is suggested and illustrated by numerical calculations for a cosine potential, which are in excellent agreement with complex scaling resonance energies. Received: 27 April 1998 / Revised: 21 July 1998 / Accepted: 3 August 1998