A partial-wave expansion of the finite rotation operator

✍ Scribed by W Happer

• Publisher: Elsevier Science
• Year: 1968
• Tongue: English
• Weight: 539 KB
• Volume: 48
• Category: Article
• ISSN: 0003-4916
• DOI: 10.1016/0003-4916(68)90146-2

✦ Synopsis

We discuss a useful expansion of the finite rotation operator, exp(-ipA *J), into partial waves. This expansion is analogous to Rayleigh's expansion of a plane wave, exp(ik * r), into spherical harmonics and spherical Bessel functions. A close relationship exists between these two expansions in the limit of large angular momenta. The partialwave expansion of the finite rotation operator is particularly useful in angular correlation problems involving external magnetic fields, since it allows one to use standard Racah algebra to obtain the solutions of many problems without writing out matrix elements.