The spectroscopic factor has long played a central role in nuclear reaction theory. However, it is not an observable. Consequently it is of minimal use as a meeting point between theory and experiment. In this paper the nature of the problem is explo
red. At the many-body level, unitary transformations are constructed that vary the spectroscopic factors over the full range of allowed values. At the phenomenological level, field redefinitions play a similar role and the spectroscopic factor extracted from experiment depend more on the assumed energy dependence of the potentials than on the measured cross-sections. The consistency conditions, gauge invariance and Wegmanns theorem play a large role in these considerations.
A generalization of the Hohenberg-Kohn theorem proves the existence of a density functional for an intrinsic state, symmetry violating, out of which a physical state with good quantum numbers can be projected.
Sequences of experimental ground-state energies are mapped onto concave patterns cured from convexities due to pairing and/or shell effects. The same patterns, completed by a list of excitation energies, can be used to give numerical estimates of the
grand potential $Omega(beta,mu)$ for a mixture of nuclei at low or moderate temperatures $T=beta^{-1}$ and at many chemical potentials $mu.$ The average nucleon number $<{bf A} >(beta,mu)$ then becomes a continuous variable, allowing extrapolations towards nuclear masses closer to drip lines. We study the possible concavity of several thermodynamical functions, such as the free energy and the average energy, as functions of $<{bf A} >.$ Concavity, when present in such functions, allows trivial interpolations and extrapolations providing upper and lower bounds, respectively, to binding energies. Such bounds define an error bar for the prediction of binding energies. An extrapolation scheme for such concave functions is tested. We conclude with numerical estimates of the binding energies of a few nuclei closer to drip lines.
The nature of the scientific method is controversial with claims that a single scientific method does not even exist. However the scientific method does exist. It is the building of logical and self consistent models to describe nature. The models ar
e constrained by past observations and judged by their ability to correctly predict new observations and interesting phenomena. The observations exist independent of the models but acquire meaning from their context within a model. Observations must be carefully done and reproducible to minimize errors. Models assumptions that do not lead to testable predictions are rejected as unnecessary.
