VOLUME 68, NUMBER 11 P H YSICAL REVI EW LETTERS 16 MARCH 1992 Nonperturhative Study of the Damping of Giant Resonances in Hot Nuclei F. V. De Blasio, ' W. Cassing, M. Tohyama, P. F. Bortignon, ' and R. A. Broglia ' ' ' 'Di partimento di Fisica, Unit ersi ta di Milano, Milano, Italy ' 'Institut fiir Teoretische Physik, Universitat GiessenG, iessenG, ermany ' School of MedicineK, yorin University, Tokyo, Japan Dipartimento di Ingegneria lVucleare, Politecnico di Milano, Milano, Italy "'Istituto W'azionale di Fisica Nucleare, sezione di Milano, Milano, Italy '"'The Niels Bohr Institute, University of Copenhagen, CopenhagenD, enmark (Received 5 September 1991) The damping of dipole and quadrupole motion in ' 0 and Ca at zero and finite temperature is stud- ied including particle-particle and particle-hole interactions to all orders of perturbation. We find that the dipole dynamics in these light nuclei is well described in terms of mean-field theory (time-dependent Hartree-Fock), while the quadrupole motion is strongly damped through the coupling to more compli- cated configurations. Both the centroid and the damping width of the quadrupole and dipole giant reso- nances show a clear stability with temperature as a consequence of the weakening of the interaction, which contrasts with the increase of the phase space. PACS numbers: 24. 30.Cz, 21.60.Jz, 24.60. Ky Giant resonances are the nuclear zero sounds. Once excited it takes a few periods before the oscillation re- laxes. Empirical evidence from excited nuclei testifies to the fact that the properties of these resonances are re- markably stable with temperature. In fact, the centroid seems not to change with excitation energy, while the conspicuous changes observed in the damping width as a function of temperature can be mainly attributed to de- formation effects induced by the fast rotation of the hot nucleus [I]. A variety of studies have identified the coupling to the nuclear surface as the main damping mechanism [2]. Ul- timately, this coupling can be traced back to collisions among the nucleons. However, central questions remain unanswered concerning the nature of these processes, the most pressing being its temperature dependence. In what follows we shall address this question in a systematic way. It will be concluded that theory provides a simple ex- planation of the observations based on the fact that the progressive loss of definition of the Fermi surface as a function of temperature is accompanied by a progressive loss in the definition of the nuclear surface. While the first phenomenon makes collisions more prolific, the sec- ond makes each of them less effective. The Hartree-Fock approximation provides a natural description of the single-particle motion in atomic nuclei. Its time-dependent extension (TDHF) constitutes a powerful tool to study collective motion in many-body systems, and also for going beyond the collisionless re- gime. A general formulation of mean-field theories supple- mented by collisions has been given in Refs. [3,41, result- ing in a set of coupled equations for the one-body density matrix p(l, I';t) and the two-body correlation function c~(12, 1'2';t). Because of technical limitations these equa- tions can, at present, only be solved accurately for small- amplitude nuclear motion. In this case one can expand both p and c2 in terms of single-particle states y, ful- filling the TDHF equations, i h — h(l ) vt. (l, t) =0, I according to p(1, 1', t ) =g n. t(Vtt( (I ', t ) Ilt. (I, t ), a, p and c~(1, 2, I ', 2';t ) (2) C. p. a(t)Vt. (l, t)ytt(2, t)Vt. *(l', t)Vtt((2', t) . a, pa', p' (3) ih n. It=a [Crst( (a(T)v(yb') — C.s„(yo)( (Pb')] (I yb~ and (s) i A Capa'p = Bapa'p'+ Papa'p'+ Hapa'p' at where The quantity h(i) =t(i)+U(i) is the one-body Hamil- tonian, i.e. , the sum of a kinetic-energy term and the mean field U(i;t) =Tr2-2 [v(i2)A;2p(22';t)] . The quantity ( (12) is the two-body interaction acting among nucleons while Aiq=l — P~q, where P(q denotes the permutation operator between nucleons. The equations of motion for the occupation matrix n tt(t) and C, t( t((t) are B, t(, i( = g (k ~ A ~ ~ v ~ k P 4) ~ [(8 (, , — n (, , ) (Bt(q, — ntj(„, ) n(„,, n(, it — n, („,ntt(, , (b'(„, , — n(, , ) (h(„,t( — n(, t( ) ] A, I A, 2A. 3A.4 (7) 1992 The American Physical Society 1663