Changes

a_{L S}^{J}

a_{L S}^{J}

</math>

</math>

where <math>\lambda=\lambda_1-\lambda_2</math>,and the double-stacked symbols are Clebsh-Gordon coefficients.  The product of CG coefficients in the second brackets on the right-hand side represent the overlap between the basis vectors in the helicity and ''L,S'' basis, which turns out to be independent of ''m'', as required by rotational invariance.  This overlap integral is somewhat lengthy to calculate, but the result turns out to be fairly simple, as shown above.  This expression holds regardless of what axis is used to define the quantization direction for m, but whatever choice is made must server as the z-axis of the reference frame in which the plane wave direction <math>\Omega</math> is defined.

where <math>\lambda=\lambda_1-\lambda_2</math>,and the double-stacked symbols are Clebsh-Gordon coefficients.  The product of CG coefficients in the second brackets on the right-hand side represent the overlap between the basis vectors in the helicity and ''L,S'' basis, which turns out to be independent of ''m'', as required by rotational invariance.  This overlap integral is somewhat lengthy to calculate, but the result turns out to be fairly simple, as shown above.  This expression holds regardless of what axis is used to define the quantization direction for m, but whatever choice is made must serve as the z-axis of the reference frame in which the plane wave direction <math>\Omega</math> is defined.

=== Isospin Projections ===

=== Isospin Projections ===