A method for semi-empirical calculation of isospin mixing probability in nuclei

A method has been proposed for an isolated two-level model calculation of isospin mixing probability in nuclei. It uses minimum experimental inputs. This method is capable of locating the unperturbed levels of an observed isospin mixed doublet. Isospin mixing probabilities, unperturbed level energies of the observed doublets and isospin mixing matrix elements are calculated for five self-conjugate isotopes of (Mg, P, S, Cl, Ar). Using experimental Gamow-Teller strength data, large isospin mixing probability ( 39.572 − 8.271 + 9.082 %) has been found in the observed doublet (1 + , 1 + ) at 9828.0 and 9965.3 keV, respectively, in 24 Mg. This is probably the largest isospin mixing ever found in a nucleus. This is much larger than that ( 20.000 − 9.904 + 9.142 %) has been found recently in non self-conjugate 26 Si sd-shell nucleus. This is also larger than that ( 27.5 + 2.5 − 2.5 %) has been measured in non self-conjugate fp-shell nucleus 55 Ni. Calculated mixing probability in 24 Mg has been used to predict the unknown Gamow-Teller strength for the transitions from the levels of 24 Al and 24 Al m to the levels in 24 Mg. The method is general enough to be applicable to other two-level model applications.