  The idea of treating the trinucleon systems as elementary entities in the
elementary particle model (EPM) as an Effective Field Theory has been a success
in explaining the weak charge-changing processes in nuclei. The EPM results are
found to be as good as those obtained from nuclear microscopic models using
two- and three-body forces. We extend this concept to investigate the validity
of the elemental nature of $A=3$ nuclei through studies of nuclear structure of
neutron-rich nuclei. By treating neutron-rich nuclei as primarily made up of
tritons as its building blocks, we extract one- and two-triton separation
energies of these nuclei. Calculations have been performed here within
relativistic mean field (RMF) models with latest interactions. Clear evidence
arises of a new shell structure with well-defined predictions of new magic
nuclei. These unique predictions have been consolidated by standard one- and
two-neutron separation energy calculations. The binding energy per nucleon
plots of these nuclei also confirm these predictions. We make unambiguos
prediction of six magic nuclei: $_{\:\:8}^{24}{\rm O}_{16}$, $_{20}^{60}{\rm
Ca}_{40}$, $_{\:\:35}^{105}{\rm Br}_{70}$, $_{\:\:41}^{123}{\rm Nb}_{82}$,
$_{\:\:63}^{189}{\rm Eu}_{126}$ and $_{\:\:92}^{276}{\rm U}_{184}$.
