Propagation of non-thermal phonons induced by alpha-particle bombardment in BaF2

We have measured the time dependence of the flux of non-thermal phonons generated by alpha particles in a BaF2 single crystal of mass 1 g using a Series Array of Superconducting Tunnel Junctions. Taking advantage of the almost perfect elastic symmetry of BaF2, we approximate the equations of quasidiffusive propagation to give a simple diffusion equation characterized by an effective diffusion coefficient D = K-8/9, where K is a material constant and L the distance between the phonon source and the point of detection. We use this model to perform pulse-shape analysis on our data and show that agreement is excellent, and highly preferred over a ballistic pulse shape. The distributions of values of K determined for different lengths L are found to overlap strongly, in support of the law D = KL8/9. We suggest that pulse-shape analysis may provide an alternative to time-difference measurements to achieve position sensitivity in a phonon-mediated detector based on a BaF2 absorber.