Spreading Widths Of Giant Resonances Research Articles

Reply to “Comment on ‘Spreading widths of giant resonances in spherical nuclei: Damped transient response’ ”

We demonstrate that our approach [Phys. Rev. C 95, 061305(R) (2017)PRCHCD2469-998510.1103/PhysRevC.95.061305] serves as a useful tool to describe the gross structure of the spreading widths of the giant resonances of the doubly magic heavy nuclei. It reduces significantly the computational efforts implementing the ideas of random matrix distribution of the coupling between one-phonon and two-phonon states and generating the energies of the two-phonon states by means of the Gaussian orthogonal ensemble distribution. We show that the Comment misrepresents our paper and fails to provide plausible arguments against the description of the gross structure with the aid of the random matrix theory.

Comment on “Spreading widths of giant resonances in spherical nuclei: Damped transient response”

We argue whether the physics of the general approach of Severyukhin et al. [Phys. Rev. C 95, 061305(R) (2017)] is appropriate.Received 30 June 2017DOI:https://doi.org/10.1103/PhysRevC.97.059801©2018 American Physical SocietyPhysics Subject Headings (PhySH)Research AreasCollective modelsElectromagnetic transitionsEnergy levels & level densitiesNuclear many-body theoryNuclear structure & decaysResonance reactionsStatistical phenomena & chaosNuclear Physics

Spreading widths of giant resonances in spherical nuclei: Damped transient response

We propose the universal approach to describe spreading widths of monopole, dipole and quadrupole giant resonances in heavy and superheavy spherical nuclei. Our approach is based on the ideas of the random matrix distribution of the coupling between one-phonon and two-phonon states generated in the random phase approximation. We use the Skyrme interaction SLy4 as our model Hamiltonian to create a single-particle spectrum and to analyze excited states of the doubly magic nuclei $^{132}$Sn, $^{208}$Pb and $^{310}$126. Our results demonstrate that the universal approach enables to describe gross structure of the spreading widths of the considered giant resonances.

The spreading width calculation of giant resonances with a semi-microscopic approach

We have proposed a semi-microscopic approach to calculate the two particles - two holes (2p - 2h) spreading width of giant resonances. Our proposal has been based in a hybrid method that implements the statistical multistep compound theory of Feshbach, Kerman and Koonin (FKK), widely and successful used in nuclear reactions mechanisms, in order to include relevant informations about the microscopic structure obtained by the Random Phase Approximation (RPA) calculations. This method is an approximative calculation to avoid the intrinsic numerical difficulties of those microscopic calculations that incorporate more complex structure than one particle - one hole (1p - 1h) excitations. Unlike the reaction context, the residual interaction was adjusted in RPA calculation to reproduce the lowest energy levels of the studied nuclei. The feasibility and the efficiency of the approach has been tested in giant dipole resonances in 208Pb and neutron-rich calcium isotopes, 48Ca and 60Ca.

Contribution of density fluctuations to the damping of giant resonances

A generalized kinetic equation of Lennard-Balescu type is derived with retardation effects. By explicit consideration of the density-density fluctuations we give the contribution of fluctuations to the spreading width of giant resonances besides the collisional part. For small frequencies and long wavelengths, approximate formulas for the damping of giant resonances are derived. The density fluctuations couple the equation of state to the damping rate and give rise to an overall enhancement factor. This density and temperature dependent factor can reproduce the experimental values of the damping. Inside the spinodal region the factor turns out to be negative, indicating unstable modes. Explicit comparisons are made with the experimental values of giant monopole and dipole resonances. It is shown that the experimental widths can be described assuming finite nuclei since surface effects are important for the influence on density fluctuations. The recently reported saturation of the dipole width with increasing energy is explained as a transition between zero and first sound. Within this treatment we find an overcritical range of fluctuations, above which the nucleus is destroyed and no collective behavior is possible at all. {copyright} {ital 1996 The American Physical Society.}

Analysis of the spreading width of the particle-hole giant resonances.

We evaluate the spreading width of the giant resonances using the discontinuity in the second derivative of the propagator of the vibrational phonon. This allows us to isolate the processes that contribute to the spreading width in terms of the Feynman diagrammatic expansion of the full boson propagator. Utilizing for classification purposes the nuclear field theory perturbative treatment of the one-phonon state, we obtain a very simple expression for the spreading width in the lowest (nonvanishing) order of perturbation theory.

Single and multiple giant resonances: Counterplay of collective and chaotic dynamics

The damping of collective states is a subject of broad interest, especially in finite manybody systems. We present a model to explain the saturation of the spreading widths of giant resonances in hot nuclei and the spreading widths of multiphonon states in terms of the chaotic dynamics governing the coupling of collective motion to incoherent degrees of freedom.

Landau's collision term in time-dependent density matrix formalism

Landau's expression for the spreading widths of giant resonances is derived, based on the small-amplitude limit of the time-dependent density-matrix theory. It is pointed out that a consistent treatment of the groundstate correlations is essential to obtain the expression.

Landau's collision term in the memory function approach to the nuclear response function and the spreading width of giant resonances

A straightforward derivation of Landau's collision term within linear response theory using the memory function approach to correlation function is presented. The relation with recent works in nuclear physics on the subject of the damping of collective modes is shown. It is discussed by means of the equations of motion method. In particular, we point out that the second RPA yields results at variance with Landau's expression. Arguments are advanced that the latter is (still) the correct one.

A microscopic phenomenological approach to the spreading widths of giant resonances

Spreading widths of giant resonances are calculated in the framework of an extended response function HF-RPA theory in which nucleon self-energy corrections for the particle and hole are introduced. These are obtained from phenomenological nucleon-optical potentials. It is argued that in addition to the self-energies a consistent account of the coupling of 1p-1h states to more complicated configuration requires the introduction of a renormalized ph interaction containing an imaginaary term. This interaction is parameterized in terms of a zero-range density-dependent interaction. A prescription to determine the form of this induced imaginary interaction is suggested. The isoscalar monopole and quadrupole as well as the isovector monopole and dipole giant resonances are treated numerically.

Spreading width of giant resonances in fluid-dynamical approximation

On the basis of a semiclassical argument a fluid-dynamical expression is derived for the coupling matrix element between a giant multipole state and a two-phonon state responsible for the spreading width. Significance of effective three-body forces originating from the density-dependent potential energy functional is pointed out in the description of the coupling.

Collisional spreading of small amplitude nuclear vibrations

We present a microscopic treatment of the spreading widths of giant resonances — a collisional RPA (with complex frequencies,z=iω+γ) which turns out to have a very simple analytical form. Its essential ingredients are:a) The usual mean field contribution, which reproduces the frequencies of the collisionless RPA andb) non-unitary (collision) contributions which arise from the inclusion of quantum correlation effects in the weak coupling approximation. This collisional RPA equation can be easily put to quantitative use in realistic nuclear structure problems.

Spreading width of giant resonances and the attenuation of zero sound

It is shown that the RPA plus perturbation approach which is commonly used to calculate microscopically the spreading width of Giant Resonances is equivalent to Landau's suggestion that the damping width of zero sound at temperatureT=0 can be obtained by multiplying the classical collision result with an energyω- andT-dependent correction factor [1+(ω/2πkT)2] withT→0.

Spreading widths of giant resonances inC12andO16

The $E2$ and $E4$ resonances in $^{12}\mathrm{C}$ and $^{16}\mathrm{O}$ are calculated within the core-coupling-random-phase approximation.NUCLEAR STRUCTURE $^{12}\mathrm{C}$; $^{16}\mathrm{O}$; calculated electric giant resonance energies and $B(\mathrm{EL})$ values. Core-coupling RPA.