Stability of the chiral soliton with the Skyrme term that is quantized by taking account of breathing modes in addition to the spin-isospin rotation is examined on the basis of a family of trial functions for the profile function of the hedgehog ansatz. It is shown that when the effects of the Skyrme term are sufficiently strong (small Skyrme term constant $e$), the eigenstates of lower spin-isospin are stable, having finite contributions both from the rotational and breathing modes. On the other hand when the effects of the Skyrme term are weak ($e>\mathrm{}5\mathrm{}$), the spin-isospin rotational and the breathing modes are completely frozen and all states tend to infinitely degenerate states labeled by the constant SU(2) matrices.

• Received 1 April 1991

DOI:https://doi.org/10.1103/PhysRevD.44.1578