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2(2lj

+ 1)(2lj + 3)

Kh

- mj +

- 1)(lj + mj + 1)

(lj + mj - 1)(lj + mj) 2(2lj - 1)(2lj + 1) (lj - mj)(lj + j

This shows that in the emission of a photon, hts, three independent polarizations appear in which the transitions occur between states that fulfill that lj, lj ± 1.

After substitution of Eqs. (189) and (195) into Eqs. (3) we will have that

X l1n1 l'1nl1,n2 m1,m2

(ês

ê+)Om

,m1+1

for

p

=1

(es

ê-)Om

,m1-1

for

p

=2 (199)

(ês

ê z)Om1

,m1

for

p

X l1n1 l'1nl1,n2 m1,m2

it + P [(Xln )2 - Xn2 )2] + iSa l' n' 1 Il2n2 T 2 O ,

(ês

ê+)Omf2 ,m2+1

for

p

=1

(ês

ê-)Om'2 ,m2-1

for

p

=2

(ê3

ê z)Om'2 ,m2

for

p

=3

After substitution of Eqs. (199) and (200) into Eqs. (2) and (1) we obtain dQ, dts

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