Unitary correlation in nuclear reaction theory: Separation of nuclear reactions and spectroscopic factors

Future exact many-body theory will allow us to calculate nuclear reactions based on the adopted $\mathit{NN}$ and many-body nuclear potentials. But $\mathit{NN}$ potentials are not observable and there are an infinite number of the phase-equivalent $\mathit{NN}$ potentials related via finite-range unitary transformations. We show that asymptotic normalization coefficients, which are the amplitudes of the asymptotic tails of the overlap functions, are invariant under finite-range unitary transformations but spectroscopic factors are not. We prove also that the exact amplitudes for the $(d,p),(d,\mathit{pn})$, and $(e,e^{\prime }p)$ reactions determining the asymptotic behavior of the exact scattering wave functions in the corresponding channels, in contrast to spectroscopic factors, are invariant under finite-range unitary transformations. Moreover, the exact reaction amplitudes are not parametrized in terms of the spectroscopic factors and nuclear reactions in the exact approach cannot provide a tool to determine spectroscopic factors which are not observable.