Sequences of experimental ground-state energies for both odd and even $A$ 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, give numerical estim
ates 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, which always occur for the free energy and is usually present for the average energy, allows easy interpolations and extrapolations providing upper and lower bounds, respectively, to binding energies. Such bounds define an error bar for the prediction of binding energies. Finally we show how concavity and universality are related in the theory of the nuclear density functional.
We compare several definitions of the density of a self-bound system, such as a nucleus, in relation with its center-of-mass zero-point motion. A trivial deconvolution relates the internal density to the density defined in the laboratory frame. This
result is useful for the practical definition of density functionals.
The multiple scattering of high-energy particles in a thick target is fromulated in an impact parameter representation. A formalism similar but not identical to that of Moliere is obtained. We show that calculations of particle beam broadening due to
multiple Coulomb scattering alone can be given in closed form. The focus of this study is on whether or not the broadening of the Coulomb angular distribution prevents the retrieval of nuclear-interaction information from mesauring the angular distributions of charged partiles scattered from a thick target. For this purpose, we study multiple scatterings with both the nuclear and Coulomb interactions included and we do not make a small-angle expansion. Condition for retrieving nuclear infomration from high-energy protons propagating through a block of material are obtained.
