Magnetic quadrupole transition probabilities for the beryllium isoelectronic sequence

The magnetic quadrupole transition probabilities for the $1s^{2}2s2p$ ${}_{}{}^3{}_{}{}^{}P_2^{}{}_{}{}^{}-1\mathrm{}{s}^{2}2s^2$ ${}_{}{}^1{}_{}{}^{}S_0^{}{}_{}{}^{}$ and $1s^{2}2s2p$ ${}_{}{}^3{}_{}{}^{}P_2^{}{}_{}{}^{}-1\mathrm{}{s}^{2}2p^2$ ${}_{}{}^1{}_{}{}^{}S_0^{}{}_{}{}^{}$ transitions of elements of the beryllium isoelectronic sequence are calculated using eigenfunctions obtained by the $Z$-expansion method. Matrix elements are presented for $Z=6-30\mathrm{}$ and transition probabilities are obtained for all elements with $Z\ge 6$ for which excitation energies are available. Good agreement is obtained with other calculations when common values for the transition energies are used.