content_image/441775.jpg content_image/441776.jpg
<img src='content_image/441775.jpg'>

where the Wigner and Clebsch-Gordan coefficients are introduced. 

<img src='content_image/441776.jpg'>

[1] Stenger, J., Inouye, S., Stamper-Kurn, D. M., Miesner, H.-J., Chikkatur, A. P., Ketterle, W.: Spin domains in ground-state Bose-Einstein condensates. Nature (London) 396 , 345 (1998). 

[2] Barrett, M. D., Sauer, J. A., Chapman, M. S.: All-Optical Formation of an Atomic Bose-Einstein Condensate. Phys. Rev. Lett. 87 , 010404 (2001). 

[3] W¨ urtz, P., Langen, T., Gericke, T., Koglbauer, A., Ott, H.: Experimental Demonstration of Single-Site Address- ability in a Two-Dimensional Optical Lattice. Phys. Rev. Lett. 103 , 080404 (2009). 

[4] Li, Z. B., Chen, Z. F., He, Y. Z., Bao, C. G.: Evaluation 

of the $^{52}$Cr − $^{52}$Cr interaction via repeating collisions of a pair of atoms in a trap. preprint, arXiv:0908.2929v1. 

[5] Tobocman, W.: A generalized Talmi-Moshinsky transfor- mation for few-body and direct interaction matrix ele- ments. Nucl. Phys. A. 357 , 293 (1981). 

[6] M. Baranger, M., Davies, K. T. R.: Oscillator brackets for Hartree-Fock calculations. Nucl. Phys. 79 , 403 (1966). 

[7] Brody, T. A., Moshinski, M.: Table of Transformation Brackets. Monografias del Instituto de Fisica, Universidad Nacional Autonoma de Mexico (1960). 

