Addition of an arbitrary number of different spins

Volume 76A, number 3,4

PHYSICS LETTERS

31 March 1980

The general proof of formula (4) is concluded by the verification of the fact that the numbers Qm satisfy the relations (6). We do not give this proof in view of

plement the results of ref. [2] and, in particular, ref. [4], in which recurrence relations, generating functions and nonexplicit expressions for P1 and Qm were

the compressed stile of a letter, We can mention that the multiplicities P1 and satisfy simple relations [2,4,5]:

given for the case r =2 More details wifi be given elsewhere.

Qm

References

—

/ Qm Qm+iIm=j~ (7) The correctness of relation (7) for (3) and (4)is easily established with the help of the relation for binomial coefficients —

/a\

~,b)

ía —

-~

~ b

1~ Ia I =

— i\ —

i)

The basic result of this letter is constituted by the explicit expressions (3), (4). They generalize and sup-

230

[1] P.W.

Atkins and ToP. Lambert, Mol. Phys. 32 (1976) 1151. [2] V.V. Mikhaiov, J. Phys. AlO (1977) 147. [31 M.A. Rashid, J. Phys. AlO (1977) L135. [41 J. Katriel and R. Pauncz, mt. J. Quantum. Chem. 12, Suppi. 1(1977)143. [5] V.V. Mikhailov, J. Phys. A12 (1979). [6] C. Pelagalli, V.S. Zamiralov and A.Ja. Rothvain, preprint, Bologna Univ. (1978).