We present exact analytic results for the energy of a SU(N) repulsive Fermi gas as a function of the spin-channel occupation at second order in the gas parameter. This is an extension of an old result that now incorporates the degree of polarization of the system. Therefore, the magnetic properties of the gas can be obtained, free from numerical uncertainties. For spin 1/2 we find that second-order corrections change the itinerant ferromagnetic transition from continuous to first-order. Instead, for spin larger than 1/2 the phase transition is always of first-order type. The transition critical density reduces when the spin increases, making the phase transition more accessible to experiments with ultracold dilute Fermi gases. Estimations for Fermi gases of Yb and Sr with spin 5/2 and 9/2, respectively, are reported.

The most important parameters in the study of low-energy scattering are the s-wave and p-wave scattering lengths and the s-wave effective range. We solve the scattering problem and find two useful formulas for the scattering length and the effective range for any angular momentum, as long as the Wigner threshold law holds. Using that formalism, we obtain a set of useful formulas for the angular-momentum scattering parameters of four different model potentials: hard-sphere, soft-sphere, spherical well, and well-barrier potentials. The behavior of the scattering parameters close to Feshbach resonances is also analyzed. Our derivations can be useful as hands-on activities for learning scattering theory.

We present exact analytic results for the energy of a SU(N) repulsive Fermi gas as a function of the spin-channel occupation at second order in the gas parameter. This is an extension of previous results that now incorporates the degree of polarization of the system. Therefore, the magnetic properties of the gas can be obtained, free from numerical uncertainties. For spin 1/2 we find that second-order corrections change the itinerant ferromagnetic transition from continuous to first-order. Instead, for spin larger than 1/2 the phase transition is always of first-order type. The transition critical density reduces when the spin increases, making the phase transition more accessible to experiments with ultracold dilute Fermi gases. Estimations for Fermi gases of Yb and Sr with spin 5/2 and 9/2, respectively, are reported.