  A new method has been proposed for isolated two-level model to calculate
isospin mixing probability in nuclei overcoming common limitations of usual
shell model results with isoscalar nuclear Hamiltonian. The method is based on
locating the unperturbed levels of the mixed doublet before mixing.
Experimental and shell model level energies, electromagnetic/Gamow-Teller
transition matrix elements associated with a doublet or two doublet pairs in a
nucleus are used to calculate isospin mixing probability in seven
self-conjugate nuclei. The four self-conjugate nuclei (P, S, Cl, Ar) considered
here show large isospin mixing matrix elements and large unperturbed
energy-gaps of the observed isospin-mixed doublet pairs. Large isospin mixing
(31.40-48.76 %) is found in the observed doublet ($1^{+},1^{+}$) at 9828.11 and
9967.19 keV, respectively, in $^{24}Mg$. This is probably the largest isospin
mixing ever found in a nucleus. This is much larger than that
$({20}_{-9.904}^{+9.142}$%) has been found recently in $^{26}$Si. The method is
general enough to be applicable to other two-level/multi-level mixing problems
and in particular, might be useful for consideration of isospin mixing in the
context of Fermi beta decay also.
