The Mass Determination in Relation to Nuclear Structure and to the Theory of Nuclear Matter

Abstract

The experimental determination of nuclear masses throughout the periodic table yields — as one of the most important consequences — a well defined value for the binding energy of Nuclear Matter (Bethe, Swiaticki). In the same time the corresponding density was determined through extended measurements of nuclear radii and nuclear charge distributions (Hofstaedter). On the other hand, a comparison of these quantities with the results from a numerical calculation based on general theoretical principles (Bethe-Brueckner theory) represents a decisive test of microscopic theories of nuclear matter and hence of nuclear structure. It is, however, well-known for many years (compare F. Coester, Phys.Rev. Cl, 1970, 769) that all calculations based on any expression for the fundamental nuclear forces, which,in turn,is in reasonable agreement with the experimental scattering phases of the 2-nucleon problem, will not yield simultaneously the right experimental values for binding and density of nuclear matter (i.e. for reasonable binding values the density is too high and vice versa). Even using the (otherwise satisfactory) description of the nuclear force based on a boson exchange model (compare as an example K. Holinde,K.Erkelenz, R. Alzetta, Nucl.Phys. A 194 1972, 161), a characteristic discrepancy remains. The main purpose of this short contribution is to give some general reasons for this disturbing fact: 1) Any explicite expression for the nuclear force, which is determined through the boson exchange in between two free nucleons, is changed in a characteristic way (by the order of magnitude of a few percents) if the nucleons in question are embedded into nuclear matter. This fact is mainly due to a typical displacement of some relevant intermediate nucleon states which occur during the exchange process. In this way the boson theory of nuclear forces is — in principle — able to lift the characteristic discrepancy (apparent already in the 3-body problem) between the forces to be used in the two-body (scattering) problem and the nuclear matter properties. In order to calculate this new effect, bosonic variables must be introduced explicitely in the entire calculation (compare D. Schutte, Nucl.Phys. A221, 1974, p. 450–460, and K. Kotthoff, Doctor Thesis, Bonn, 1974). While this fundamental enlargement of nuclear theory yields corrections of the order of a few percents to all relevant nuclear properties, it might yield large changes in the case of extremely high nuclear densities which occur in Neutron Stars where this method will lead in a natural way to the so-called boson condensation. 2) Apart from the introduction of the additional bosonic variables, it appears of fundamental importance to include also the inner degrees of freedom of the nucleons themselves. This means that the virtual excitation (through boson absorption) of the nucleons into their various higher lying resonance states must also be considered. For numerical reasons only the first state — the so-called ∆ -resonance (1236 Mev) — must be considered. This kind of ‘polarisation’ is in fact inevitable and yields a most important contribution to the middle-range attractive part of nuclear forces (compare A.M. Green and P. Haapakoski “The effect of the ∆(1236) resonance,” reprint from Research Inst.f.Theor.Phys., Helsinki) and is thus — to a large extent - responsible for nuclear binding. (In addition it replaces the “unphysical” scalar σ-boson which had so far been used in most boson-theoretical deductions of nuclear forces). The contribution from the virtual ∆ -excitation to the nuclear force is,again, different in the cases of free and of “embedded” nucleons. While the introduction of bosonic variables leads to a needed increase of nuclear binding, the effect of the ∆-resonance yields an important adjustment (decrease) of nuclear density through its characteristic strongly repulsive short-range contribution to the nucleon-nucleon interaction.(There remains, however, the still unsolved problem of a numerical evaluation of the effect due to a characteristic change of the mesonic self-energies of nucleons when embedded into nuclear matter).