Spectroscopic Factors: Observability and Measurability

Spectroscopic factors that are actively used in the analysis of nuclear reactions are discussed. It is emphasized that spectroscopic factors are absent in the rigorous theory of nuclear reactions. They arise only within the standard version of the distorted-wave Born approximation. The accuracy of the spectroscopic factors extracted from the experimental data is low. Spectroscopic factors are off-shell quantities which are not determined by the $$S$$ matrix unlike on-shell quantities, such as phase shifts, binding energies, and asymptotic normalization coefficients. Spectroscopic factors are non-invariant under the unitary transformations of nuclear forces conserving the $$S$$ matrix. The conclusion is that they are non-observables which can only be defined within a special convention, like a particular form of the nuclear Hamiltonian which is used to derive or calculate them.

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