  A methodology is worked out to retrieve the numerical values of all the main
parameters of the six-dimensional adiabatic potential energy surface (APES) of
a polyatomic system with a quadratic T-term Jahn-Teller effect (JTE) from
ultrasound experiments. The method is based on a verified assumption that
ultrasound attenuation and speed encounter anomalies when the direction of
propa- gation and polarization of its wave of strain coincides with the
characteristic directions of symmetry breaking in the JTE. For the SrF2:Cr
crystal, employed as a basic example, we observed anomaly peaks in the
temperature dependence of attenuation of ultrasound at frequencies of 50-160
MHz in the temperature interval of 40-60 K for the wave propagating along the
[110] direction, for both the longitudinal and shear modes, the latter with two
polarizations along the [001] and [110] axes, respectively. We show that these
anomalies are due to the ultrasound relaxation by the system of non-interacting
Cr2+ JT centers with orthorhombic local distortions. The interpretation of the
ex- perimental findings is based on the T2g (eg +t2g) JTE problem including the
linear and quadratic terms of vibronic interactions in the Hamiltonian and the
same-symmetry modes reduced to one interaction mode. Combining the experimental
results with a theoretical analysis we show that on the complicated
six-dimensional APES of this system with three tetragonal, four trigonal, and
six orthorhombic extrema points, the latter are global minima, while the former
are saddle points, and we estimate numerically all the main parameters of this
surface, including the linear and quadratic vibronic coupling constants, the
primary force constants, the coordinates of all the extrema points and their
energies, the energy barrier between the orthorhombic minima, and the tunneling
splitting of the ground vibrational states.
