Determination of $M1-E2\mathrm{}$ Mixing Amplitudes in ${\mathrm{Mg}}^{25}$, ${\mathrm{Al}}^{27}$, ${\mathrm{Si}}^{29}$, and ${\mathrm{P}}^{31}$

A method of analyzing gamma-ray angular distribution and direction-polarization data to yield values for the relative amplitudes of mixed multipole gamma-ray transitions is described. The analysis of the data does not demand a knowledge of the mechanism of formation of the gamma-emitting level. Measurements are reported on some mixed $M1-E2\mathrm{}$ de-excitation gamma rays from low-lying levels in ${\mathrm{Mg}}^{25}$, ${\mathrm{Al}}^{27}$, ${\mathrm{Si}}^{29}$, and ${\mathrm{P}}^{31}$; these levels were excited by inelastic proton scattering. The following results were obtained: