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 $\mathrm{\ensuremath{\Delta}}{b}_{7}$. Our results at leading order, though approximate, furnish simple analytic formulas that relate $\mathrm{\ensuremath{\Delta}}{b}_{n}$ to $\mathrm{\ensuremath{\Delta}}{b}_{2}$ 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 Tan's contact of the two-dimensional attractive Fermi gas and examine the radius of convergence of the virial expansion as a function of the coupling strength.