Abstract
Zero-range effective interactions are commonly used in nuclear physics to describe a many-body system in the mean-field framework. If they are employed in beyond- mean-field models, an artificial ultraviolet divergence is generated by the zero-range of the interaction. We analyze this problem in symmetric nuclear matter with the t0-t3 Skyrme model. In this case, the second-order energy correction diverges linearly with the momentum cutoff. After that, we extend the work to the case of nuclear matter with the full Skyrme interaction. A strong divergence related to the velocity-dependent terms of the interaction is obtained. Moreover, a global fit can be simultaneously performed for both symmetric and nuclear matter with different neutron-to-proton ratios. These results pave the way for applications to finite nuclei in the framework of beyond mean-field theories.
Highlights
Contact interactions are reasonable approximations for the real finite-range forces that can be employed in cases where the interaction range is much smaller than the typical lengthscale for the inter-particle distance
Zero–range effective interactions are commonly used in nuclear physics to describe a many-body system in the mean-field framework
Two examples of commonly adopted contact interactions are the zero-range effective Skyrme forces which are used in nuclear physics [1,2] and the contact interactions with coupling strengths depending on the s-wave scattering length which are employed for dilute atomic gases [3]
Summary
Contact interactions are reasonable approximations for the real finite-range forces that can be employed in cases where the interaction range is much smaller than the typical lengthscale for the inter-particle distance. To summarize, when phenomenological zero-range interactions are used, two issues have to be addressed if beyondmean-field theories are adopted: 1) Choosing a strategy to handle the ultraviolet divergence associated to the use of a contact force; 2) Deciding at which level the fitting procedure of the parameters has to be done and which constraints have to be included. The equation of state with the simplified Skyrme interaction V(r1, r2) at the mean-field level for symmetric nuclear matter is calculated by considering the first-order diagram (plus the exchange term) displayed in the first line of figure 1. The second-order correction in symmetric nuclear matter with the simplified Skyrme interaction diverges linearly with the momentum cutoff Λ [10, 11].
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