Measurement of the relative sign of neutron and proton transition matrix elements of the 2⁺ states in ³⁰Si

Measurement of the inelastic alpha scattering cross sections for the first two 2⁺ states in ³⁰Si shows unambigously that the relative sign of the neutron and proton transition matrix elements for both 2⁺ states are positive. For the first 2⁺ state, this is consistent with its collective nature. For the second 2⁺ state, the result is consistent with recent lifetime measurements for the corresponding transition in ³⁰P but is in contradiction with the prediction of shell-model calculations.