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Register a new userNuclear response functions with finite range Gogny force: tensor terms and instabilities
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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.
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Recently, a new parameterization of the Gogny interaction suitable for astrophysical applications, named D1M*, has been presented. We investigate the possible existence of spurious finite-size instabilities of this new Gogny force by repeating a study that we have already performed for the most commonly used parameterizations (D1, D1S, D1N, D1M) of the Gogny force. This study is based on a fully-antisymmetrized random phase approximation (RPA) calculation of the nuclear matter response functions employing the continued fraction technique. It turns out that this new Gogny interaction is affected by spurious finite-size instabilities in the scalar isovector channel; hence, unphysical results are expected in the calculation of properties of nuclei, like neutron and proton densities, if this D1M* force is used. The conclusions from this study are then, for the first time, tested against mean-field calculations in a coordinate representation for several nuclei. Unphysical results for several nuclei are also obtained with the D1N parameterization of the Gogny force. These observations strongly advocate for the use of the linear response formalism to detect and avoid finite-size instabilities during the fit of the parameters of Gogny interactions as it is already done for some Skyrme forces.
The properties of spin polarized neutron matter are studied both at zero and finite temperature using the D1 and the D1P parameterizations of the Gogny interaction. The results show two different behaviors: whereas the D1P force exhibits a ferromagnetic transition at a density of $rho_c sim 1.31$ fm$^{-3}$ whose onset increases with temperature, no sign of such a transition is found for D1 at any density and temperature, in agreement with recent microscopic calculations.
We present a thorough analysis of the effects of the tensor interaction on the multipole response of magic nuclei, using the fully self-consistent Random Phase Approximation (RPA) model with Skyrme interactions. We disentangle the modifications to the static mean field induced by the tensor terms, and the specific features of the residual particle-hole (p-h) tensor interaction, for quadrupole (2+), octupole (3-), and also magnetic dipole (1+) responses. It is pointed out that the tensor force has a larger effect on the magnetic dipole states than on the natural parity states 2+ and 3-, especially at the mean field level. Perspectives for a better assessment of the tensor force parameters are eventually discussed.
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.
Background: The half-life of the famous $^{14}$C $beta$ decay is anomalously long, with different mechanisms: the tensor force, cross-shell mixing, and three-body forces, proposed to explain the cancellations that lead to a small transition matrix element. Purpose: We revisit and analyze the role of the tensor force for the $beta$ decay of $^{14}$C as well as of neighboring isotopes. Methods: We add a tensor force to the Gogny interaction, and derive an effective Hamiltonian for shell-model calculations. The calculations were carried out in a $p$-$sd$ model space to investigate cross-shell effects. Furthermore, we decompose the wave functions according to the total orbital angular momentum $L$ in order to analyze the effects of the tensor force and cross-shell mixing. Results: The inclusion of the tensor force significantly improves the shell-model calculations of the $beta$-decay properties of carbon isotopes. In particular, the anomalously slow $beta$ decay of $^{14}$C can be explained by the isospin $T=0$ part of the tensor force, which changes the components of $^{14}$N with the orbital angular momentum $L=0,1$, and results in a dramatic suppression of the Gamow-Teller transition strength. At the same time, the description of other nearby $beta$ decays are improved. Conclusions: Decomposition of wave function into $L$ components illuminates how the tensor force modifies nuclear wave functions, in particular suppression of $beta$-decay matrix elements. Cross-shell mixing also has a visible impact on the $beta$-decay strength. Inclusion of the tensor force does not seem to significantly change, however, binding energies of the nuclei within the phenomenological interaction.
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