Charge-independent trend of isoscalar matrix elements along the N sim Z line

Shell model calculations have been carried out using the m-scheme numerical code {\small ANTOINE} in order to elucidate the particular trend of the isoscalar matrix elements, $M_0$, for $A=4n+2$ isobaric triplets ranging from A=18 to A=42. The 2${_1^+}_{(T=1)}$ $\to$ 0${_1^+}_{(T=1)}$ transition energies, reduced transition probabilities and isoscalar matrix elements are predicted to a high degree of accuracy. The general agreement of $M_0$ between those from mirror pairs and those from $T_Z=0$ nuclides support our shell model calculations. The predicted results tie together recent experimental data, and the trend of $M_0$ strength along the $sd$ and beginning of the $fp$ shells is interpreted in terms of the dynamic shell structure. Certain discrepancies arise at A=18 and A=38 isobaric triplets, which might be explained in terms of core polarization effects and the low occupancy of the orbits at the extremes of the $sd$ shell.