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Register a new userEffective Nucleon-Nucleon Interaction and Fermi Liquid Theory
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A. Schwenk SUNY Stony Brook
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We present two novel relations between the quasiparticle interaction in nuclear matter and the unique low momentum nucleon-nucleon interaction in vacuum. These relations provide two independent constraints on the Fermi liquid parameters of nuclear matter. Moreover, the new constraints define two combinations of Fermi liquid parameters, which are invariant under the renormalization group flow in the particle-hole channels. Using empirical values for the spin-independent Fermi liquid parameters, we are able to compute the major spin-dependent ones by imposing the new constraints as well as the Pauli principle sum rules.
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Low-energy nuclear structure is not sensitive enough to resolve fine details of nucleon-nucleon (NN) interaction. Insensitivity of infrared physics to the details of short-range strong interaction allows for consistent, free of ultraviolet divergences, formulation of local theory at the level of local energy density functional (LEDF) including, on the same footing, both particle-hole as well as particle-particle channels. Major difficulty is related to parameterization of the nuclear LEDF and its density dependence. It is argued that structural simplicity of terminating or isomeric states offers invaluable source of informations that can be used for fine-tuning of the NN interaction in general and the nuclear LEDF parameters in particular. Practical applications of terminating states at the level of LEDF and nuclear shell-model are discussed.
We discuss renormalization group approaches to strongly interacting Fermi systems, in the context of Landaus theory of Fermi liquids and functional methods, and their application to neutron matter.
We present a calculation of low energy magnetic states of doubly-closed-shell nuclei. Our results have been obtained within the random phase approximation using different nucleon-nucleon interactions, having zero- or finite-range and including a possible contribution in the tensor channel.
The $Lambda N$ and $Sigma N$ interactions are considered at next-to-leading order in SU(3) chiral effective field theory. Different options for the low-energy constants that determine the strength of the contact interactions are explored. Two variants are analysed in detail which yield equivalent results for $Lambda N$ and $Sigma N$ scattering observables but differ in the strength of the $Lambda N to Sigma N$ transition potential. The influence of this difference on predictions for light hypernuclei and on the properties of the $Lambda$ and $Sigma$ hyperons in nuclear matter is investigated and discussed. The effect of the variation in the potential strength of the $Lambda N$-$Sigma N$ coupling (also called $Lambda -Sigma$ conversion) is found to be moderate for the considered $^3_Lambda rm H$ and $^4_Lambda rm He$ hypernuclei but sizable in case of the matter properties. Further, the size of three-body forces and their relation to different approaches to hypernuclear interactions is discussed.
Some form of nonperturbative regularization is necessary if effective field theory treatments of the NN interaction are to yield finite answers. We discuss various regularization schemes used in the literature. Two of these methods involve formally iterating the divergent interaction and then regularizing and renormalizing the resultant amplitude. Either a (sharp or smooth) cutoff can be introduced, or dimensional regularization can be applied. We show that these two methods yield different results after renormalization. Furthermore, if a cutoff is used, the NN phase shift data cannot be reproduced if the cutoff is taken to infinity. We also argue that the assumptions which allow the use of dimensional regularization in perturbative EFT calculations are violated in this problem. Another possibility is to introduce a regulator into the potential before iteration and then keep the cutoff parameter finite. We argue that this does not lead to a systematically-improvable NN interaction.
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