Yes! We run PCRs to define V and J gene usage and diversity for humans and mice.
You may check following references, most recent are essentially on alpha chain repertoires:
Thuderoz, F., M.A. Simonet, O. Hansen, N. Pasqual, A. Dariz, T.P. Baum, V. Hierle, J. Demongeot, P.N. Marche, and E. Jouvin-Marche. 2010. Numerical Modelling Of The V-J Combinations Of The T Cell Receptor TRA/TRD Locus. PLoS Comput Biol 6:e1000682.
Jouvin-Marche, E., P. Fuschiotti, and P.N. Marche. 2009. Dynamic aspects of TCRalpha gene recombination: qualitative and quantitative assessments of the TCRalpha chain repertoire in man and mouse. Adv Exp Med Biol 650:82-92.
Human alpha
Fuschiotti, P., N. Pasqual, V. Hierle, E. Borel, J. London, P.N. Marche, and E. Jouvin-Marche. 2007. Analysis of the TCR alpha-chain rearrangement profile in human T lymphocytes. Mol Immunol 44:3380-3388.
Mouse alpha
Pasqual, N., M. Gallagher, C. Aude-Garcia, M. Loiodice, F. Thuderoz, J. Demongeot, R. Ceredig, P.N. Marche, and E. Jouvin-Marche. 2002. Quantitative and qualitative changes in V-J alpha rearrangements during mouse thymocytes differentiation: implication for a limited T cell receptor alpha chain repertoire. J Exp Med 196:1163-1173.
Human beta / CDR3
Vigan, I., E. Jouvin-Marche, V. Leroy, M. Pernollet, E. Delachanal, M. Colomb, J.P. Zarski, and P.N. Marche. 2003. T lymphocytes infiltrating the liver during chronic hepatitis C infection express a broad range of T cell receptor beta chain diversity. J. Hepatology 38:651-659.