ABSTRACT
In (17.33) or (17.46) the two nucleon interaction is expressed in terms of its matrix elements. In Sections 10 and 12 we saw how such an interaction can be expressed in terms of the coefficients Fk of an expansion in scalar products of irreducible tensors. We will now obtain the analogous expansion in the formalism of second quantization. Before doing that, we transform (17.33) into a form that clearly displays the fact that it is a scalar (rotationally invariant) operator. Recalling the definition (17.12) we can express A(jj′ JM) by: () A ( j j ′ J M ) = − ( 1 + δ j j ′ ) − 1 / 2 ∑ m m ′ ( j , − m j ′ , − m ′ | j j ′ J M ) a j , − m a j ′ , m ′ = − ∑ m m ′ ( 1 + δ j j ′ ) − 1 / 2 ( − 1 ) j + j ′ − J + j + m + j ′ + m ′ × ( j m j ′ m ′ | j j ′ J , − M ) a ˜ j m a ˜ j ′ m ′ = − ( 1 + δ j j ′ ) − 1 / 2 ( − 1 ) J + M ( a ˜ j × a ˜ j ′ ) − M ( J ) https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9780203739716/ff034a11-a369-4bc6-a470-f8cf1794dcb5/content/eq1427.tif"/>
