Collective Excitations In Nuclei Research Articles

Study of the Cross-Section for the 122Te(γ, n)121Te Reaction by the Activation Method

Relevance. The study of photonuclear reactions plays a defining role in the formation of modern ideas about highlocalized collective excitations in nuclei of the giant resonance type. The giant dipole E1-resonance (GR) is the main feature in γ-quantum absorption cross-sections of nuclei. The presence of isotopes with multiple isotopes makes it possible to trace the evolution of GR characteristics from changes in the number of neutrons in the nuclei. One such element is tellurium. Purpose. The purpose of this research is an experimental and theoretical study of the cross-section of 122Te(γ, n)121Te reaction in the region of giant E1-resonance energies. Methods. The study of the cross-section of (γ, n) reaction on 122Te isotope was performed on the bremsstrahlung γ-beam of the M-30 microtron of the Institute of Electronic Physics of the National Academy of Sciences of Ukraine. The yield curves were measured in the range of maximum gamma-quantum energies Eγmax=10-18 MeV. The reaction cross-section was calculated by the inverse matrix method. When registering the reaction products, an activation technique was used, while the gamma activity of the products was recorded by the spectrometric method. The theoretical calculations of the cross-section for the 122Te(γ, n)121Te reaction were performed using the TALYS-1.9 software package. Results. The measured experimental yield ratios of the 122Te(γ, n)121Te і 130Te(γ, n)129Te d= Yn121 /Yn129 = f (E max) reactions allowed the experimental cross-section for the 122Te(γ, n)121Te reaction to be calculated. The cross-section has a single hump shape with a maximum at an energy of ~ 15.3 MeV. It was approximated by the Lorentz curve with the parameters δ0 =(274.1±2.1) MB, Е0 (15.27±0.10) MeV, Г0 =(4.76±0.08) MeV. The cross-section obtained was compared with similar cross-sections for 126Te and 130Te isotopes, as well as with theoretical calculations according to the TALYS-1.9 program. Conclusions. The obtained cross-section for the 122Te(γ, n)121Te reaction is consistent with the evolution of the parameters of (γ, n) reaction cross-section on tellurium isotopes 130Te(γ, n)129Te with a change in the number of neutrons. The theoretical approaches used are satisfactorily consistent with the experimental data. This agreement indicates the main contribution of the statistical mechanism to the cross-section of the considered (γ, n) reaction and a relatively small contribution of semi-direct processes

A semiclassical collective response of heated, asymmetric, and rotating nuclei

The quasiparticle Landau Fermi-liquid and periodic orbit theories are presented for the semi-classical description of collective excitations in nuclei, which are close to one of the main topics of the fruitful activity of S.T. Belyaev. Density-density response functions are studied at low temperatures within the temperature-dependent collisional Fermi-liquid theory in the relaxation time approximation. The isothermal, isolated (static) and adiabatic susceptibilities for nuclear matter show the ergodicity property. Temperature corrections to the response function, viscosity and thermal conductivity coefficients have been derived, also in the long wavelength (hydrodynamic) limit. The relaxation and correlation functions are obtained through the fluctuation-dissipation theorem and their properties are discussed in connection to the static susceptibilities and ergodicity of the Fermi systems. Transport coefficients, such as nuclear friction and inertia as functions of the temperature for the hydrodynamic (heat-pole and first sound) and Fermi surface distortion zero-sound modes are derived within the Fermi-liquid droplet model. They are shown to be in agreement with the semi-microscopical calculations based on the nuclear shell model (SM) for large temperatures. This kinetic approach is extended to the study of the neutron-proton correlations in asymmetric neutron-rich nuclei. The surface symmetry binding-energy constants are presented as functions of the Skyrme-force parameters in the approximation of a sharp-edged proton-neutron asymmetric nucleus and applied to calculations of the isovector giant dipole resonance. The energies, sum rules, and transition densities of these resonances obtained by using analytical expression for these surface constants in terms of the Skyrme-force parameters are in fairly good agreement with the experimental data. An analysis of the experimental data, in particular the specific structure of these resonances in terms of a main, and some satellite peaks, in comparison with our analytical approach and other theoretical semimicroscopical models, might turn out to be of capital importance for a better understanding of the values of the fundamental surface symmetry-energy constant. The semiclassical collective moment of inertia is derived analytically beyond the quantum perturbation approximation of the cranking model for any potential well as a mean field. It is shown that this moment of inertia can be approximated by its rigid-body value for the rotation with a given frequency within the ETF and more general periodic orbit theories in the nearly local long-length approximation. Its semiclassical shell-structure components are derived in terms of the periodic-orbit free-energy shell corrections. An enhancement of the moment of inertia near the symmetrybreaking bifurcation deformations was found. We obtained good agreement between the semiclassical and quantum shell-structure components of the moment of inertia for several critical bifurcation deformations for the completely analytically solved example of the harmonic oscillator mean field.

Neutron star structure and collective excitations of finite nuclei

We study relationships between properties of collective excitations in finite nuclei and the phase transition density $n_t$ and pressure $P_t$ at the inner edge separating the liquid core and the solid crust of a neutron star. A theoretical framework that includes the thermodynamic method, relativistic nuclear energy density functionals and the quasiparticle random-phase approximation is employed in a self-consistent calculation of $(n_t,P_t)$ and collective excitations in nuclei. The covariance analysis shows that properties of charge-exchange dipole transitions, isovector giant dipole and quadrupole resonances and pygmy dipole transitions are correlated with the core-crust transition density and pressure. A set of relativistic nuclear energy density functionals, characterized by systematic variation of the density dependence of the symmetry energy of nuclear matter, is used to constrain possible values for $(n_t,P_t)$. By comparing the calculated excitation energies of giant resonances, energy weighted pygmy dipole strength, and dipole polarizability with available data, we obtain the weighted average values: $n_t = 0.0955 \pm 0.0007$ fm$^{-3}$ and $P_t = 0.59 \pm 0.05$ MeV fm$^{-3}$.

A Semiclassical Collective Response of Heated, Asymmetric, and Rotating Nuclei

The Landau Fermi-liquid and extended Gutzwiller periodic-orbit theories are presented for the semiclassical description of collective excitations in nuclei, which are close to main topics of the fruitful activity of S.T. Belyaev. Static susceptibilities show the ergodicity of Fermi liquids. Transport coefficients (nuclear friction and inertia) as functions of the temperature for the hydrodynamic and zero-sound modes are derived within the response theory by using the Fermi-liquid droplet model, in agreement with the shell model for large temperatures. The surface symmetry binding-energy constants are obtained as functions of Skyrme force parameters in the approximation of a sharp edged proton-neutron asymmetric nucleus.The energies and sum rules of the isovector dipole giant resonances are in fairly good agreement with the experimental data. An analysis of the specific structure of these resonances in terms of a main, and satellite peaks, in comparison with the experimental data and microscopic theoretical models, might turn out to be of importance for a better understanding of the values of the surface symmetry-energy constant. The semiclassical collective moment of inertia is derived analytically beyond the quantum perturbation approximation of the cranking model for any potential well as a mean field. It is shown that this moment of inertia can be approximated by its rigid-body value for the rotation with a given frequency within the ETF and more general periodic orbit theories in the nearly local long-length approximation. Its semiclassical shell-structure components are derived in terms of the periodic-orbit free-energy shell corrections. We obtained good agreement between the semiclassical and quantum shell-structure components of the moment of inertia for several critical bifurcation deformations for the harmonic oscillator mean field.

Time scales in nuclear giant resonances

We propose a general approach to characterise fluctuations of measured cross sections of nuclear giant resonances. Simulated cross sections are obtained from a particular, yet representative self-energy which contains all information about fragmentations. Using a wavelet analysis, we demonstrate the extraction of time scales of cascading decays into configurations of different complexity of the resonance. We argue that the spreading widths of collective excitations in nuclei are determined by the number of fragmentations as seen in the power spectrum. An analytic treatment of the wavelet analysis using a Fourier expansion of the cross section confirms this principle. A simple rule for the relative life times of states associated with hierarchies of different complexity is given.

Giant Resonance Overtones: Compression Modes of the Nucleus

Giant resonances are high-frequency collective excitations of atomic nuclei, the occurrence of which is a typical phenomenon in many-body quantum systems confined in a potential well [1]. In hydrodynamic models, giant resonances can be described as density and shape oscillations around the ground-state density distribution and shape. Such collective excitations of a nucleus may, similarly to other media with given boundary conditions, exhibit standing wave oscillations with a discrete series of frequencies as solutions of the applied wave equations. In this simple picture, most of the giant resonances studied extensively so far can be associated with the lowest energy, leading-order solutions (main tone). Giant resonances corresponding to higher-order solutions (overtones) have not been identified, except for the special cases of the isoscalar giant monopole (ISGMR) and isoscalar giant dipole (ISGDR) resonances, where excitation of the main-tone components is physically forbidden. Strong evidence for the overtone mode of the isoscalar giant quadrupole resonance, which is denoted as ISGQR2, has been found in our experiments [2,3], which is highly supported by predictions of recent RPA calculations [4]. Moreover, the microscopic structures of high-energy isoscalar giant resonances have been studied through measurements of direct particle decay, and in the case of the ISGDR for the first time in our measurements of such branching ratios.

Low-lying collective excitations of nuclei as a semiclassical response

For the low-lying multipole collective excitations in nuclei, the transport coefficients of the response function theory, such as the inertia and the friction, are derived within the periodic orbit theory in the lowest orders of semiclassical expansion corresponding to the extended Thomas-Fermi approach with the surface and the curvature corrections. The collective vibrations near the spherical shape are described in the mean-field approximation through the spherical edgelike potential by using a statistical averaging of the transport coefficients. It is shown that the inertia of the collective motion is significantly larger than that of irrotational hydrodynamical flow. For large enough particle numbers in the nucleus, the mean energies of quadrupole and octupole low-lying collective vibrations, their sum rule contributions, and reduced transition probabilities are in reasonable agreement with experimental data.

Semiclassical inertia of nuclear collective dynamics

For the low-lying collective excitations in nuclei, the transport coefficients, such as the stiffness, the inertia, and the friction, are derived within the periodic-orbit theory in the lowest orders of semiclassical expansion corresponding to the extended Thomas—Fermi approach. The multipole vibrations near the spherical shape are described in the mean-field approximation through the infinitely deep square-well potential and Strutinsky averaging of the transport coefficients. Owing to the consistency condition, the collective inertia for sufficiently increased particle numbers and temperatures is substantially larger than that of irrotational flow. The average energies of collective vibrations, reduced friction, and effective damping coefficients are in better agreement with experimental data than those found from the hydrodynamic model.

Collective excitations of nuclei in the Monte-Carlo shell model

Collective excitations of nuclei in the Monte-Carlo shell model

Microscopic description of E2 and E3 giant resonances in deformed and superdeformed nuclei.

The vibrating potential model, which represents a self-consistent version of the random-phase approximation (RPA) with a separable residual interaction, is generalized to the description of E\ensuremath{\lambda} collective excitations in nuclei with any even-multipole static deformation. The model is used to study the isoscalar E2 and E3 giant resonances in deformed and superdeformed $^{154}\mathrm{Sm}$ and $^{152}\mathrm{Dy}$. The importance of the nuclear self-consistency is shown. The model provides a satisfactory description of the isoscalar E2 and E3 giant resonances in deformed $^{154}\mathrm{Sm}$, predicting a considerable washing out of these resonances, especially the octupole one, in superdeformed $^{152}\mathrm{Dy}$. The latter result means that the experimental observation of the isoscalar giant resonance in superdeformed nuclei can encounter serious troubles. \textcopyright{} 1996 The American Physical Society.

Limiting value for the width controlling the coupling of collective vibrations to the compound nucleus.

We show that the damping of nuclear collective excitations in the regime of chaotic intrinsic dynamics is well described by the coupling to doorway states. Subsequent collision processes which eventually lead the system into the compound nucleus eigenstates do not increase the damping width. We also argue that the damping width of collective excitations in nuclei does not increase without bounds as the excitation of the nucleus is increased, but acquires a limiting value.

Studies of [formula omitted] reactions and electromagnetic currents in rotational nuclei

The general formalism is presented for electron scattering studies involving excitation of a discrete state followed by the emission of any number of real photons which are detected in coincidence with the scattered electron. Special limited situations are discussed in which only a single real photon is emitted and in which one multipole dominates in the γ-decay. The formalism is applied in a treatment of low-lying collective excitations in nuclei. Observables which become accessible from measurements of angular distributions in the (e, e′γ) reaction permit the determination of transverse multipole matrix elements through sensitivity to transverse/longitudinal interferences, and so yield information on intrinsic nuclear electromagnetic current distributions where heretofore in almost all cases only charge distribution information has been available. Illustrative examples of vibrational and rotational excitations are presented to help elucidate the degreee of sensitivity to the nature of the current flow. Detailed results are given for rotational bands described within the context of the deformed Hartree-Fock method (using projected Hartree-Fock and cranking approximations, and using several effective forces) applied to two selected nuclei, a light nucleus, 20Ne and a rare-earth nucleus, 166Er.

A hamiltonian with broken supersymmetry for the xenon isotopes

A hamiltonian with broken u( 6 2 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.

Collectivity and geometry. III. The three-dimensional case in the Sp(6)⊇Sp(2)×𝒪(3) chain for closed shells

As was indicated in previous papers, general Hamiltonians for systems of n particles in three-dimensional space can be formulated in the enveloping algebra of the symplectic group Sp(6n). This group admits, among others, the subgroup Sp(6)×O(n) and, as has been noticed by many authors, collective Hamiltonians can be formulated in the enveloping algebra of Sp(6), so that their eigenstates can be characterized by a definite irreducible representation (irrep) of this group. The mathematical problem is then to determine the matrix elements of the generators of Sp(6) in a basis characterized by irreps of this group as well as of appropriate subgroups. In the present series of papers the subgroups chosen where Sp(2)×𝒪(3) as the Casimir operator of Sp(2) when n → ∞ is formally related to the Bohr–Mottelson vibrational Hamiltonian (BMVH), while 𝒪(3) gives the angular momentum of the state. We give an algorithm for determining these states that closely parallels the procedure followed for the BMVH. Programs are being developed to convert our algorithm into a computational tool for determining collective excitations in nuclei.

A study of the weak coupling limit of the pseudo SU(3) scheme

The usefulness of the pseudo SU(3) weak coupling limit for the study of even-even nuclei for which the protons and neutrons fill different major oscillator shells is examined. The content of proton and neutron configurations in the total wave function of the coupled space is estimated in order to understand their relative importance. The structure of 144Ba is investigated in detail. Our calculations show that both proton and neutron configurations are important to study the collective excitations in nuclei and perhaps the strong coupling limit is more appropriate for nuclei such as those considered in this work.

Collective excitations of nuclei in a relativistic mean-field theory

Collective excitations of finite nuclei are discussed in a model relativistic baryon-meson field theory. Eigenvalue equations for small amplitude motion about the static mean-field solutions assuming irrotational flow are derived. Variational estimates of the lowest modes are obtained.

Spurious states in calculations of collective excitations in nuclei

Spurious states in calculations of collective excitations in nuclei

Relation between many-body and single-particle aspects in nuclei

The process by which certain types of collective excitations in nuclei are built up from single-particle excitations through the nucleon-nucleon interaction is described. Analogies in the methods used to those employed in describing other Fermi systems are shown. Among the types of collective excitations are the dipole state and vibrational motion. A schematic model formulated in the language of the many-body theory and designed to handle the main qualitative features of a finite system is described. It was found that taking ground-state correlations meant doubling the order of the matrix in shell- model calculations. The ground-state correlations enhanced the transition probability for vibrational states where E << epsilon and cut it dow. for plasma oscillations. (M.C.G.)