How Are Wigner D Functions Related to Nuclear Rotor Model Wave Functions?

[patric44]

Homework Statement

Φ = ((2l+1)/8pi^2) D^{j}_{MK}

Relevant Equations

why the nuclear rotor model wave function is written in terms of Wigner D functions?

hi guys
I am recently taking a Nuclear structure course, and have a lot of questions regarding the nuclear rotor model.
in most nuclear physics books the I have, the wave function associated with the rotor model of the nucleus is written in terms of the Wigner D functions , like the expression below
$$
\bra{\theta\;\phi\;\psi}\ket{JMK} = c(D^{J}_{MK}+(-1)^{J}D^{J}_{M-K})
$$
where c is a constant, I am a little bit familiar with the rotation matrix and its representation in the angular momentum basis , isn't the Wigner D functions is just the matrix elements of the rotation matrix in 3d ? , what is the relation between D functions and the eigen functions of the rotor model?
can anyone explain how the formula above is derived, or refer to a good book or a set of lecture notes in theoretical nuclear physics.
thanks in advance.

 

[patric44]

can anyone explain what this expression mean
$$
\bra{\psi,\theta,\phi}\ket{IMK} = c D^{I}_{MK}
$$
isn't that the projection of the sate represented by IMK on the basis represented by psi,theta,phi?
why is that interpreted as the matrix elements of the rotation operator?

 

[yucheng]

I am recently taking a Nuclear structure course, and have a lot of questions regarding the nuclear rotor model.
in most nuclear physics books the I have, the wave function associated with the rotor model of the nucleus is written in terms of the Wigner D functions

Just curious, which textbooks are you referring to? $: )$