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We study the spin response of cold dense neutron matter in the limit of zeromomentum transfer, and show that the frequency dependence of thelong-wavelength spin response is well constrained by sum-rules and theasymptotic behavior of the two-particle response at high frequency. Thesum-rules are calculated using Auxiliary Field Diffusion Monte Carlo techniqueand the high frequency two-particle response is calculated for severalnucleon-nucleon potentials. At nuclear saturation density, the sum-rulessuggest that the strength of the spin response peaks at $\omega \simeq$ 40--60MeV, decays rapidly for $\omega \geq $100 MeV, and has a sizable strength below40 MeV. This strength at relatively low energy may lead to enhanced neutrinoproduction rates in dense neutron-rich matter at temperatures of relevance tocore-collapse supernova.

Spin Response and Neutrino Emissivity of Dense Neutron Matter