why can't we have a system in analogous to an atom in which the electron is in place of a positive charge of the the same mass and charge of the electron and in the nucleus in place of the proton a negative charge is there of the same mass and same magnitude of charge of proton?( for e.g if we consider a parallel hydrogen atom?
A particle composed of an electron and a positron is a positronium. Friends of mine are doing spectriscopy on it. However, it is short lived due to the high matter antimatter anhilation propability.
When excited to Rydberg states the lifetime is much longer.
It is possible to "build" atoms consisting of a central anti-proton (negative charge, same mass as proton) and a positron (positive charge, same mass as electron). The resulting atom is called antihydrogen and there are ongoing experiments to characterize such anti-atoms (e.g. just recently at the CERN, cf. link).
http://press.cern/press-releases/2016/12/alpha-experiment-observes-light-spectrum-antimatter-first-time
Nearly for the first attempt to explain this analogy (but it fails) please check this out: https://arxiv.org/abs/cond-mat/9705012
Also you can read: http://www.nature.com/nature/journal/v405/n6789/full/405899a0.html
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