A few questions of numerical and functional analysis for the many body problem in nuclear physics

Abstract

A major feature of nuclear physics is that the number of degrees of freedom is both too large to accommodate exactly-solvable problems in practice and too small to justify purely statistical limits. Experimental evidence in nuclear physics actually shows that the nuclear dynamics sometimes reduces to the evolution of only one (or a small number of) degree(s) of freedom, called collective, and that in some other cases no order parameter or nontrivial conserved quantity is observed. All intermediate cases between these two limits are possible and found. An essential problem of the theory thus consists in finding a systematic and sound method of reduction (or increase) of the number of degrees of freedom. In this report this question is illustrated in three ways related to numerical approximation schemes. The first way consists in deriving an infinite set of conserved quantities from the Schrödinger equation, through the moment method. The second restricts the dynamics to the manifold of Slater determinants aad yields the time-dependent way introduces the generator coordinate method to handle nuclear collisions in a microscopic formalism. It is found in all cases that a large domain of applications and progress is in order.