Binding Energies of Multi-Deltas Systems

Abstract

Recent experimental studies on the protonproton, pion-deuteron and r-deuteron scatterings suggest the existence of several dibaryon resonances. ' ) Some of these dibaryon resonances are believed to be d* states of the Ll_N 2 ) and Ll-Ll3) systems or the J[NN 4 ) and J[J[NN 5 ) states. Although the d* model is a reasonable and interesting extension of the ordinary nuclear physics, there has been a serious objection on this model, especially on the T=O bound states of the Ll-Ll system. ) Fortunately, it has been recently shown that this objection is resolved with the employment of a one boson exchange potential (OBEP) having a tensor part as the Ll-Ll interaction.7) Therefore it is now possible to analyze dibaryon resonances as bound states of the Ll-Ll system. This kind of analysis is important not only in the study of dibaryon resonances, but also in the study of nuclear matter, because this suggests the possible existence of a new kind of nuclear matter, which is the existence of strongly bound states in many-baryons systems of one kind (especially Ll particles). Since a 2Ll's bound system has a large binding energy (BE, ~ 100 Me V), it is an interesting question whether many Ll's bound systems can have a tremendous BE (~# of bonding times I 00 MeV!!) or not. Recently Ueda has studied theoretical possibility of four Ll's bound states employing the Ll-Ll interactions derived from the Heitler-London J[J[NN model for dibaryons. ) Here we study the multi Ll's bound states within the theoretical framework used by Kamae and Fujita (K-F). In this paper, therefore, employing the Ll-Ll potential given by K-F and applying standard calculational methods of the BE of many nucleons system to many Ll's system, we calculate the BE of many Ll's bound states and discuss the possibility of strongly bound states of many Ll's system. For simplicity we discuss only bound states of the compact system of many Ll particles, and neglect the bound cluster states. The Ll-Ll potential: To calculate the BE of many ,d's bound states, we employ the nonrelativistic 5 state OBEP for the Ll-Ll potential,