Leptodermous expansion of finite-nucleus incompressibility

Abstract

Abstract:We consider the influence of higher-order terms in the leptodermous expansion used to extract the incompressibility K, of infinite nuclear matter from data on the breathing mode of finite nuclei. The terms we calculate are the curvature term Z&A -2'3, the surface-symmetry term Z& Z2A-"3, the quartic volume-symmetry term Z&Z+', and a Coulomb-exchange term. Working within the framework of the scaling model we derive expressions for their coefficients in terms of quantities that are defined for infinite and semi-infinite nuclear matter. We calculate these coefficients for four different Skyrme-type forces, using the extended Thomas-Fermi (ETF) approximation. With the same forces we also calculate the incompressibility K(A, I) for a number of finite nuclei, fit the results to the leptodetmous expansion, and thereby extract new results for the same coefficients. The comparison of the two calculations shows that the leptodermous expansion is converging rapidly. Of the new terms, the term K,Z4 is quite negligible, the curvature term should be included, and we discuss to what extent the other higher-order terms are significant.

Giant resonances inTi46,48

“…The GMR energy in 40 Ca is in agreement with the calculation by Nayak et al [7] using the SkM * interaction, whereas that in 58 Ni is about 1 MeV higher than the calculation. Consequently we have studied the giant resonances in 46,48 Ti which lie between 40 Ca and 58 Ni in the mass region.…”

“…Figure 6 shows the mass dependence of E GMR in 46,48 Ti, 40 Ca and 58 Ni together with theoretical calculations obtained in the scaling model using the leptodermous expansion of the finite-nucleus incompressibility K A . Non-relativistic calculations using the extended Thomas-Fermi (ETF) approximation with the SkM * Skyrme interaction (K NM = 216.6 MeV) by Nayak et al [7] and relativistic calculations using the relativistic mean-field (RMF) theory with the NLC interaction (K NM = 224.5 MeV) by Chossy and Stocker [32] are also shown in Fig. 6.…”

“…The E GMR was obtained from the theoretical finite nucleus incompressibility K A using the rms charge radius, which is available from experiments, rather than the rms matter radius. [7] and solid squares show results obtained using the relativistic mean-field (RMF) theory with the NLC interaction [32]. The lines are added to guide the eye.…”

Isoscalar giant resonances for nuclei with mass between 56 and 60

“…However, this is somewhat lower than K NM ∼ 231 MeV, suggested by energies for a number of other nuclei [3]. The nonrelativistic parametrization set SkM * reproduce the GMR energy in 40 Ca [29], but not the relativistic parametrization set NL1 [30], and both of the calculations miss the energy of 90 Zr. The experimental value of GMR energy in 58 Ni is more than 1.2 MeV higher than in 56 Fe and 60 Ni, but both calculations fail to predict this feature.…”

“…12. (Color online) GMR energies calculated with the relativistic mean-field parametrization [30] and the nonrelativistic parametrizations [29] are compared to the experimental energies shown by solid circles. The error bars on the data include systematic errors.…”