Simple scattering theory would say that the state of the whole system is
|Psi> = a |P>|T> + b |P*>|T*>
and the reduced density matrix for P has non-zero off-diagonal terms which only disappear after the measurement is made by the detectors.
However, I suspect that if the nuclei are large enough (i.e., have enough internal degrees of freedom) then the collision itself will decohere the superposition.
So, which is the correct picture? Presumably there is a "quantum-classical" crossover as the nuclei get heavier? Are there smoking gun experiments (e.g., Mott scattering of identical particles) to distinguish the two pictures?
Nuclear topology and reactions appear through detectors, yet the research validity of an atomic topological function with high data density will exceed SEM/AFM optical imaging by application in software modeling with interactive animation based on relative quantum wavefunction physics. Recent advancements in quantum science have produced the picoyoctometric, 3D, interactive video atomic model imaging function, in terms of chronons and spacons for exact, quantized, relativistic animation. This format returns clear numerical data for a full spectrum of variables. The atom's RQT (relative quantum topological) data point imaging function is built by combination of the relativistic Einstein-Lorenz transform functions for time, mass, and energy with the workon quantized electromagnetic wave equations for frequency and wavelength.
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Next, the correlation function for the manifold of internal heat capacity energy particle 3D functions is extracted by rearranging the total internal momentum function to the photon gain rule and integrating it for GT limits. This produces a series of 26 topological waveparticle functions of the five classes; {+Positron, Workon, Thermon, -Electromagneton, Magnemedon}, each the 3D data image of a type of energy intermedon of the 5/2 kT J internal energy cloud, accounting for all of them.
Those 26 energy data values intersect the sizes of the fundamental physical constants: h, h-bar, delta, nuclear magneton, beta magneton, k (series). They quantize atomic dynamics by acting as fulcrum particles. The result is the exact picoyoctometric, 3D, interactive video atomic model data point imaging function, responsive to keyboard input of virtual photon gain events by relativistic, quantized shifts of electron, force, and energy field states and positions.
Images of the h-bar magnetic energy waveparticle of ~175 picoyoctometers are available online at http://www.symmecon.com with the complete RQT atomic modeling manual titled The Crystalon Door, copyright TXu1-266-788. TCD conforms to the unopposed motion of disclosure in U.S. District (NM) Court of 04/02/2001 titled The Solution to the Equation of Schrodinger.