Studies of exotic nuclei with advanced radiation detectors

An analytic phenomenological shell model mass formula for light nuclei is constructed., The formula takes into account the non locality of the self consistent single particle potential and the special features of light nuclei, namely: a) charge and mass distributions are closer to a Gaussian shape than to the shape characteristic in medium and heavy nuclei; b) the central charge and mass densities are larger than, and decrease towards, the "asymptotic" values that are the reference parameters for nuclear matter; and c) after a shell closure, the next level has a larger orbital angular momentum and a noticeably larger mean square radius. Only then a good numerical fit is obtained with parameters consistent with optical model analysis and empirical spin-orbit couplings. A correlation between the "skin effect" and the symmetry dependence of the optical potential is established. Towards the neutron drip line the potential well depth, the spin-orbit splitting of the single particle levels and the gap between major shells decrease, as has been observed. The ensuing shift and contraction of the single particle level scheme may lead to: a) to strong configuration mixing and new magic numbers, and b) the onset of the halo effect, to avoid the expulsion of single particle levels to the continuum.

A shell model mass formula for exotic light nuclei

The general scepticism and loss of faith on the predictive ability of different mass formulae, arising out of the divergence of their predictions in unknown regions taken with respect to a reference mass formula, is successfully dispelled. When the result of relativistic mean field (RMF) theory with a Lagrangian common for all nuclei is taken as reference, the divergence disappears, and clear trend with strong correlation appears restoring our faith in general on the predictions of mass formulae, qualifying them as useful guideline for theoretical and experimental studies of nuclear phenomena. Mass formulae occupy the centre stage in the research in nuclear physics. The first model of the nucleus is a mass formula proposed by Bethe and Weiszackar in mid 1930s, soon after the discovery of the neutron unravelling the composition of the nucleus. It defined some of the key concepts and parameters for the first time for the description of nuclear phenomena, and laid the foundation for their future exploration. Our inability to predict the masses of nuclei starting from first principle, and our present experimental incapability to produce large majority of them in the laboratory, warrants reliable mass formulae of nuclei for understanding many phenomena, most notably, the nucleosynthesis and stellar evolution. Therefore the development of nuclear mass formulae has been all along a core theme of nuclear physics which has implicitly sustained and nourished the research in diverse areas of nuclear structure and nuclear reactions. Over the last 70 years, about a dozen of mass formulae have been proposed. With the advent of heavy-ion reactions, the prospect of the exploration of the "terra incognita" is very much in the realm of possibility. To the already known about 2000 nuclei, another 5000 to 7000 nuclei will be added in future by their synthesis in the laboratory for which unprecedented activity in different laboratories is underway. Therefore the predictive ability of differnt mass formulae is under serious scrutiny. Figure 1 represents an often quoted result (1-3) on the comparison of the predictions of different mass models with experiment on the Tin isotopes. Here the difference of the binding energy of various models and experimental results with respect to the predictions of the model of Duflo and Zuker (4), taken as reference, is plotted for the chain of isotopes of Sn with neutron number varying between 45 and 110. There is unanimity of all the mass models on good agreement with experiment in the known region close to stability, however, the predictions diverge as one moves away to unknown

https://arxiv.org/pdf/nucl-th/0504063.pdf

Sachivalaya Marg

Papers

Consistency of nuclear mass formulae