Enhancement of the electron electric dipole moment in gadolinium 3+

There have been recent suggestions for searching for the electron electric dipole moment, using solid state experiments with compounds containing Gd 3+ ions. These experiments could improve the sensitivity compared to present atomic and molecular experiments by several orders of magnitude. The analysis of the problem requires a calculation of the enhancement coefficient K for the electron electric dipole moment in the Gd 3+ ion. In this work we perform this calculation. The result is K = -4.9 +- 1.6. Limitations of the accuracy of the calculation are mainly due to the lack of data on Gd 3+ excitation spectra. We formulate which quantities have to be measured and/or calculated to improve the accuracy.