Freeze-out at constant energy density and spin polarization in heavy-ion collisions

Using the local equilibrium density operator, we develop a geometry-informed linear response theory that takes into account the parametrization of the freeze-out hypersurface before the gradient expansion is carried out. Assuming local equilibrium on an iso-energy density hypersurface, we study the <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"><a:mi mathvariant="normal">Λ</a:mi></a:math> hyperon spin polarization, and compute corrections to the isothermal case due to finite density. We argue that corrections to isothermal freeze-out should be small, and that even in heavy ion collisions with energy as low as <d:math xmlns:d="http://www.w3.org/1998/Math/MathML" display="inline"><d:msqrt><d:msub><d:mi>s</d:mi><d:mrow><d:mi>N</d:mi><d:mi>N</d:mi></d:mrow></d:msub></d:msqrt><d:mo>=</d:mo><d:mn>11.5</d:mn><d:mtext> </d:mtext><d:mtext> </d:mtext><d:mi>GeV</d:mi></d:math> they constitute at most a 10% effect. They may, however, become relevant for local polarization observables.