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Register a new userNuclear response Functions with Realistic Interactions
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H.S. Kohler
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Linear density response functions are calculated for symmetric nuclear matter of normal density by time-evolving two-time Greens functions in real time. The feasability and convenience of this approach to this particular problem has been shown in previous publications. Calculations are here improved by using more realistic interactions derived from phase-shifts by inverse scattering. Of particular interest is the effect of the strong correlations in the nuclear medium on the response. This as well as the related energy weighted sum rule, dependence on mean field and effective mass are some of the main objects of this investigation. Comparisons are made with the collision-less limit, the HF+RPA method. The importance of vertex corrections is demonstrated.
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A fully-antisymmetrized random phase approximation calculation employing the continued fraction technique is performed to study nuclear matter response functions with the finite range Gogny force. The most commonly used parameter sets of this force, as well as some recent generalizations that include the tensor terms are considered and the corresponding response functions are shown. The calculations are performed at the first and second order in the continued fraction expansion and the explicit expressions for the second order tensor contributions are given. Comparison between first and second order continued fraction expansion results are provided. The differences between the responses obtained at the two orders turn to be more pronounced for the forces including tensor terms than for the standard Gogny ones. In the vector channels the responses calculated with Gogny forces including tensor terms are characterized by a large heterogeneity, reflecting the different choices for the tensor part of the interaction. For sake of comparison the response functions obtained considering a G-matrix based nuclear interaction are also shown. As first application of the present calculation, the possible existence of spurious finite-size instabilities of the Gogny forces with or without tensor terms has been investigated. The positive conclusion is that all the Gogny forces, but the GT2 one, are free of spurious finite-size instabilities. In perspective, the tool developed in the present paper can be inserted in the fitting procedure to construct new Gogny-type forces.
Linear response functions are calculated for symmetric nuclear matter of normal density by time-evolving two-time Greens functions with conserving self-energy insertions, thereby satisfying the energy-sum rule. Nucleons are regarded as moving in a mean field defined by an effective mass. A two-body effective (or residual) interaction, represented by a gaussian local interaction, is used to find the effect of correlations in a second order as well as a ring approximation. The response function S(e,q) is calculated for 0.2<q<1.2 fm^{-1}. Comparison is made with the nucleons being un-correlated, RPA+HF only.
Linear density response functions are calculated for symmetric nuclear matter of normal density by time-evolving two-time Greens functions in real time. Of particular interest is the effect of correlations. The system is therefore initially time-evolved with a collision term calculated in a direct Born approximation as well as with full (RPA) ring-summation until fully correlated. An external time-dependent potential is then applied. The ensuing density fluctuations are recorded to calculate the density response. This method was previously used by Kwong and Bonitz for studying plasma oscillations in a correlated electron gas. The energy-weighted sum-rule for the response function is guaranteed by using conserving self-energy insertions as the method then generates the full vertex-functions. These can alternatively be calculated by solving a Bethe -Salpeter equation as done in some previous works. The (first order) mean field is derived from a momentum-dependent (non-local) interaction while $2^{nd}$ order self-energies are calculated using a particle-hole two-body effective (or residual) interaction given by a gaussian it local rm potential. We present numerical results for the response function $S(omega,q_0)$ for $q_0=0.2,0.4$ and $0.8 {rm fm}^{-1}$. Comparison is made with the nucleons being un-correlated i.e. with only the first order mean field included, the HF+RPA approximation. We briefly discuss the relation of our work with the Landau quasi-particle theory as applied to nuclear systems by Sjoberg and followers using methods developped by Babu and Brown, with special emphasis on the induced interaction.
Basic issues of the time-dependent density-functional theory are discussed, especially on the real-time calculation of the linear response functions. Some remarks on the derivation of the time-dependent Kohn-Sham equations and on the numerical methods are given.
The longitudinal response function of 4He is calculated with the Argonne V18 potential. The comparison with experiment suggests the need of a three-body force. When adding the Urbana IX three-body potential in the calculation of the lower longitudinal multipoles, the total strength is suppressed in the quasi-elastic peak, towards the trend of the experimental data.
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