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We calculate the axial form factor in the chiral quark soliton (semibosonized Nambu - Jona-Lasinio) model using the semiclassical quantization scheme in the next to leading order in angular velocity. The obtained axial form factor is in a good absolute (without additional scaling) agreement with the experimental data. Both the value at the origin and the -dependence of the form factor as well as the axial m.s.radius are fairly well reproduced.

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