A sum rule description of giant resonances at finite temperature

Abstract

A generalization of the sum rule approach to collective motion at finite temperature is presented. The m 1 and m-1 sum rules for the isovector dipole and the isoscalar monopole electric modes have been evaluated with the modified SkM force for the 2°spb nucleus. The variation of the resulting giant resonance energies with temperature is discussed.Recent experimental developments in the domain of light projectile induced reactions (e.g. P3' [ 1] ) as well as heavy ion reactions [2] make it important to quantitatively describe the behaviour of nuclear giant resonances when increasing the excitation energy. As a natural extension of the zero excitation energy case one may describe relevant strength functions in the statistical approximation through finite temperature RPA calculations. This has been performed for the dipole mode in the schematic force model and recently with more realistic forces but within a non fully selfconsistent approach [3]. The technical difficulties associated with such RPA calculations provide an incentive to develop a tractable yet sufficiently accurate method to grasp the bulk of the phenomenon under study.In the zero temperature case the sum rule approach has been shown to be well suited to that purpose (see e.g. ref.[4] ). Moreover it has appeared that a semiclassical determination of some sum rules, such as the inverse energy weighted sum rule, yielded very good 0.031-9163/83/$ 03.00 © Elsevier Science Publishers B.V. (North-Holland Physics Publishing Division) approximations to quantal (i.e. Hartree-Fock) results [5,6]. The finite temperature generalisation of such an approach implies an extension of some basic results to the non zero excitation energy case. It is the aim of this letter to discuss such a generalisation and to provide some illustrations of the methods in the particular cases of isovector dipole and isoscalar monopole electric modes.For a statistical mixture defined by its density matrixn whose dynamics is governed by a hamiltonian H with eigenvectors In) and eigenvalues En, the kth order moment of the strength function associated to a given operator Q may be defined as mk(a)= ~ I(nlOlP)12Pn(Ep -En) k . (2) n,p¢nFor all moments which can be expressed in the pure 279

Electric multipole response of the halo nucleus 6He

“…This value can be compared with the non energy weighted sum rule calculations for monopole strength, that gives about 2800f m 4 , using formulas of Ref. [54], giving a very good agreement. …”

A density variational approach to nuclear giant resonances at zero and finite temperature

“…(2.36), even at finite temperatures (see also Refs. [ 10,46,47,72,1093). This corresponds, on the microscopic level, to the neglect of the higher continuum states of the nucleons in HF caIculations [393, which was shown [ 1151 to be a good approximation up to temperatures of ~4 MeV.…”

“…As a natural generalization [46,47,50,743 of the strength function one defines (2.23) and accordingly the moments…”

Nuclear collective states at finite temperature

“…Continuum TRPA calculations of the whole nuclear response function for selected spin and parity modes are already available r19, 20], as well as others of shell model TRPA type mostly concentrated in the giant resonance region of the nuclear spectrum [21][22][23][24]. Other methods, essentially based on the calculation of TRPA sum rules, either with RPA accuracy [25] or using semiclassical approximations have also been applied to giant resonances [26][27][28][29][30].…”