Gamma-Ray Correlation Function in the Adiabatic Approximation

The gamma-ray correlation function following inelastic excitation of an even-$A$ nucleus by a spinless projectile has been analyzed employing only the adiabatic approximation and theorems relevant to elastic scattering. The direction making equal angles with the incident and scattered directions in the scattering plane, the adiabatic recoil direction, is a convenient axis for quantization. In particular, the intermediate (excited) nucleus is populated with only even-$M$ states, from which follows that the gamma distribution is unchanged by a rotation of $\pi$ about this axis. For a $0^{+}$-$2^{+}$-$0^{+}$ excitation de-excitation, the gamma distribution in the scattering plane reduces to the form ${sin}^2\left[2\right({\theta }_{\gamma }-{\theta }_0\left)\right]$, where ${\theta }_0$ is the adiabatic recoil axis. Comparison is made to the similar predictions of plane-wave Born approximation theories (in which the recoil direction for finite energy transfer is the symmetry axis) and to distorted-wave Born approximation calculations (for which, in general, there is no simple expression for the symmetry axis). Analysis of experiments verify the general features of the model, but further data obtained from forward scattering would be desirable to distinguish between the predictions of the adiabatic and Born approximations. Brief comments are made regarding gamma-ray polarization.