Limiting Value for the Width Controlling the Coupling of Collective Vibrations to the Compound Nucleus

Abstract

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. PACS numbers: 24.30.Cz, 21.60.Jz, 24.60.LzThe question concerning the variety of mechanisms at work in the damping of collective motion of many-body systems is a fascinating one, and central in a variety of fields ranging from condensed matter to atomic nuclei. An example is provided by the nuclear isovector giant dipole resonance (GDR), that is, the collective vibration of protons against neutrons. Once excited, the mode will relax its energy and angular momentum either by particle emission or by coupling to the complicated intrinsic motion of the nucleons, the compound nucleus. The relaxation of the resonance is recognized by the width of the associated bell-shaped strength function P(E), which is the probability distribution for finding the resonance at the excitation energy E.

Quantum chaos and thermalization in isolated systems of interacting particles

“…For a more generic model (2.2) with a finite perturbation range (corresponding, for example, to the inter-particle interaction), the form of the SF changes with increasing V and eventually approaches the standard semicircle with the radius R = 2v √ 2b [11,12,13,14,80,22] determined by the specific interaction V and the width b of the band. As a result, one can conclude that, generically, the limiting form of the SF (when increasing the perturbation strength) is given by the density of states defined by the perturbation V only.…”

“…Having the same quantum numbers, the original state and the newborn collective mode repel each other and form the two peaks predicted in (3.16) which concentrate the significant fraction of the total strength [in the limit (3.16) the whole strength is evenly divided between the two peaks]. If the coherent interactions responsible for the excitation of collective modes are absent and the system is close to chaoticity, the corresponding limit of the SF will be a semicircle with radius R ≈ σ k , where σ 2 k is again the average second moment (3.6) and the effective spreading width is Γ = 2 √ 3 σ k [1,80]. As it usually happens, realistic atoms and nuclei are typically between the two limits, and the shape of the SF evolves from the Breit-Wigner behavior at the center to the Gaussian behavior with faster decreasing wings.…”

Single-Particle Self-Energy in Many-Body Systems at Finite Temperature

“…where * is the multipolarity of the surface vibration and with the typical values of the averaging parameter 'r0.5 MeV, which approximately takes into account the coupling to more complex states than the doorways here considered [19] in the hierarchy of the intermediate states [21]. It is noted that, for both graphs in Figs.…”

Erratum: Multiscale fluctuations in the nuclear response [Phys. Rev. C60, 064307 (1999)]

“…To do so, the coherence should be kept and the width should fulfill equation (9). However, we will often neglect the energy dependence of the width Γ µ in the analytical expressions.…”