[en] The neutron balance equation in the age approximation is proposed as an additional condition imposing restrictions on form of the neutron spectrum for a unique solution of the improper problem of reconstructing a neutron spectrum. The solution is not limited to the range of application of the age approximation and can be extended to a medium containing water. The geometric parameter and a number of other quantities that appear in the expression for the neutron spectrum are determined from the condition for best agreement between the measured and calculated activation integrals