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It is shown that the density of states (DOS) proportional to the excitationenergy, the so-called polar like DOS, can arise in the odd-parity states withthe superconducting gap vanishing at points even if the spin-orbit interactionfor Cooper pairing is strong enough. Such gap stuructures are realized in thenon-unitary states, F_{1u}(1,i,0), F_{1u}(1,varepsilon,varepsilon^{2}), andF_{2u}(1,i,0), classified by Volovik and Gorkov, Sov. Phys.-JETP Vol.61 (1985)843. This is due to the fact that the gap vanishes in quadratic manner aroundthe point on the Fermi surface. It is also shown that the region of quadraticenergy dependence of DOS, in the state F_{2u}(1,varepsilon,varepsilon^{2}), isrestricted in very small energy region making it difficult to distinguish fromthe polar-like DOS.Comment: 5 pages, 3 figures, submitted to J. Phys.: Condens. Matter Lette

The polar-type density of states in a non-unitary odd-parity superconducting state with a gap with point nodes