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We present the analytical results at the mean-field level for theasymmetrical fermion system with attractive contact interaction at the zerotemperature. The results can be expressed in terms of linear combinations ofthe elliptic integrals of the first and second kinds. In the limit of small gapparameter, we discuss how the asymmetry in fermion species affects the phasesof the ground state. In the limit of large gap parameter, we show that twocandidate phases are competing for the system's ground state. The Sarma phasecontaining a pure Fermi fluid and a mixed condensate is favored at large degreeof asymmetry. The separated phase consisting of a pure Fermi fluid and a bosoncondensate supports the system at smaller degree of asymmetry. The two phasesare degenerate in the limit of infinite pairing gap.Comment: 23 pages, no figur

Analytical results for cold asymmetrical fermion superfluids at the mean-field level