The properties of the discrete atomic and molecular electronic energy levels in an exponentially shielded Coulomb potential, which is known in plasma physics as the Debye-Huckel potential and in nuclear physics as the Yukawa potential will be discussed. A Full-CI approach will be used for the calculation of the electronic structure under such an interaction potential. Some of the systems studied have been found to be Borromean in nature under appropriate shielding strength conditions, will be determined and discussed. Increasing shielding strength induces electron detachment either sequential or simultaneous. Both cases will be illustrated with examples.