Time scales in nuclear giant resonances

Abstract

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 selfenergy 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.PACS numbers: 24.30. Cz, 24.60.Ky, 24.10.Cn Nuclear Giant Resonances (GR) have been the subject of numerous investigations over several decades [1]. Some of the basic features such as centroids and collectivity (in terms of the sum rules) are reasonably well understood within microscopic models [2,3]. However, the question how a collective mode like the GR disseminates its energy is one of the central issues in nuclear structure physics.According to accepted wisdom, GRs are essentially excited by an external field being a one-body interaction. It is natural to describe these states as collective 1p-1h states. Once excited, the GR disseminates its energy via direct particle emission and by coupling to more complicated configurations (2p-2h, 3p-3h, etc). The former mechanism gives rise to an escape width, while the latter yields spreading widths (Γ ↓ ). An understanding of lifetime characteristics associated with the cascade of couplings and scales of fragmentations arising from this coupling (cf [4,5,6,7]) remains a challenge. A recent highresolution experiment of the Isoscalar Giant Quadrupole Resonance (QR) [8,9,10] provides new insight for this problem.It has been shown by Shevchenko et al. [8] that the fine structure of the QR observed in (p, p ′ ) experiments is largely probe independent. Furthermore, a study of the fine structure using wavelet analysis [11,12,13] reveals energy scales [9,10] in the widths of the fine structure displaying a seemingly schematic pattern, as can be seen in Fig.2. This pattern varies with the structure of the nucleus being studied. While the physical meaning of the results of such an analysis is still being debated, we try here to offer a general explanation. However, we do not embark on a specific microscopic analysis, but rather make use of general and well-established techniques of many-body theory. Gross effects due to nuclear deformation and coupling to the continuum [5] are not discussed; we rather focus on the decay of the QR into configurations of various complexity.To proceed we use the Green's function approach. A central role is played by the self-energy whose finer structure is imparted upon the Green's function via the solution of Dyson's equation which reads [14]where we assume G 0 (ω) = ...

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