Few nucleon systems

M. Rosina, A lower bound on the ground state energy of some few-nucleon systems, in Report of the Density Matrix Seminar (A. J. Coleman and R. M. Erdahl, eds.), Queen s Press, Kingston, Ontario, 1969, p. 82. 

Abstract In this chapter, four topics are treated. (1) Fundamental constituents and interactions of matter and the properties of nuclear forces (experimental facts and phenomenological and meson-field theoretical potentials). (2) Properties of nuclei (mass, binding energy, spin, moments, size, parity, isospin, and characteristic level schemes). (3) Nuclear states and excitations and individual and collective motion of the nucleons in the nuclei. Description of basic experimental facts and their interpretation in the framework of shell, collective, interacting boson, and cluster models. The recent developments, few nucleon systems, and ah initio calculations are also shortly discussed. (4) In the final section, the a- and P-decays, as well as the special decay modes observed far off the stability region are treated. 

Recently, major advances have been obtained in the microscopic description of few nucleon systems. Starting from realistic NN-, as well as NNN -interactions (see O Sects. 2.1.2.1 and O 2.3.1.3), many properties of 3 < A < 8 nuclei (energies of ground and excited states, radii, electromagnetic moments, etc.) have been described in agreement with experimental results. These calculations have three different frameworks ... 

The procedure can be applied also for quantal systems. For example, if one wants to know the ground state energy of a few nucleon system, one may start from a trial wave function P c(, where a denotes variational parameters to be optimized. The expectation value of the Hamiltonian with the trial wave function gives an estimate for the energy of the ground state ... 

The success of ab initio calculations goes far beyond the reproduction of the properties of few-nucleon systems. The methods can be applied also to hadrons, exotic 4-6 quark states, and hypernuclei (nuclei containing, e.g., s-quarks). In these cases the methods are similar, only the basis states and, of course, the interactions are different. 

In this chapter we review the recent history of and evidence for collective, moleculelike behavior of valence electrons in atoms and indicate some of the questions that will have to be explored in order to resolve the question of how well the electrons in atoms are described by independent-particle or collective models. We then turn the question around and ask whether atoms in a molecule could, under suitable circumstances, display independent-particle behavior, with their own one-particle angular momenta behaving like nearconstants of the motion. The larger question that emerges is then one of whether few-body systems—the valence electrons of an atom, the atoms that constitute a small polyatomic molecule, and perhaps others such as the nucleons in a nucleus, all of which have heretofore seemed nearly unrelated— share characteristics to the extent that we can devise a unifying picture of the dynamics of few-body systems that will expose their commonalities as well as their obvious differences. 

From the viewpoint of the image resolution and the slice thickness, the ECT systems are most certainly inferior to their nucleonic counterparts. Typical spatial resolution is 5-10% of vessel diameter with the electrode height of a few centimetres. Their advantage lies in fast imaging capabilities - e.g. for the IMIST system 200 frames per second, which outperforms most of the nucleonic systems used so far. 

The vantage point that will be maintained for the bulk of this chapter is that the atomic nucleus can be viewed as a two-component quantum fluid, i.e., the degrees of freedom are those associated with nucleons. Despite the quantum nature of the systems, classical analogs can be of great heuristic value. Leading this list of analogs is that of a charged two-component liquid drop. Here, the quantum aspects are buried in a few well-chosen coefficients of a physical expansion. 

The industrial process tomography systems can be based on a number of measurement principles, including nucleonic, optical, acoustic, microwave, NMR and electrical methods [21] - each of them usually having a number of distinctive variants. From the practical point of view only a few are routinely used for investigating fluidised beds. This chapter will concentrate therefore on nucleonic transmission tomography (x-ray and y-ray tomography) and electrical capacitance tomography (ECT). 

There are a number of many-body systems which exhibit quantum effects on a macroscopic scale. These include liquid and crystal states of both He-3 and He-4, the electron gas, and neutron matter which probably constitutes the interior of pulsors. In addition, "nuclear matter" - a hypothetical extensive system of nucleons has been studied for the insight one may gain into the nature of finite nuclei. The theoretical studies of these systems have by now a long history, but are by no means concluded. In the last few years, significant advances have been made. This has come in part from the maturity of and gradual unification of many-body theory, in part from the development and application of powerful new expansion procedures, especially varieties of hypernetted-chain equations (3 ) and finally to the growing power of computer simulation methods for quantum systems. This article is intended as a review of some recent development in computational methods for extensive quantum systems, and of the relation between results so obtained to the evolution of other theoretical work. 

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