Leading- and next-to-leading order semiclassical approximation to the first seven virial coefficients of spin-1/2 fermions across spatial dimensions

Following up on recent calculations, we investigate the leading- and next-to-leading order semiclassical approximation to the virial coefficients of a two-species fermion system with a contact interaction. Using the analytic result for the second-order virial coefficient as a renormalization condition, we derive expressions for up to the seventh-order virial coefficient $Delta b_7$. Our results at leading order, though approximate, furnish simple analytic formulas that relate $Delta b_n$ to $Delta b_2$ for arbitrary dimension, providing a glimpse into the behavior of the virial expansion across dimensions and coupling strengths. As an application, we calculate the pressure and Tans contact of the 2D attractive Fermi gas and examine the radius of convergence of the virial expansion as a function of the coupling strength.