| Summary: | The H^{+}+H and D^{+}+D collisions represent the simplest examples of collisions involving identical fermions and bosons, respectively. We report a study of these collisions in the range of energies corresponding to 0–40 K at a resolution of 100 mK based on a half-collision approach. Using the technique of pulsed-field-ionization zero-kinetic-energy photoelectron spectroscopy (PFI-ZEKE-PES), which relies on the pulsed field ionization of nonpenetrating Rydberg states of very high principal quantum number (n≥250), we have measured the positions and widths of all low-lying shape resonances of this collision and compare them with the results of ab initio calculations that consider nonadiabatic, relativistic, and radiative corrections to the Born-Oppenheimer energies. Excellent agreement between calculated and measured widths and positions is found except for the X^{+}(v^{+}=25,N^{+}=8) shape resonance, the width of which is calculated to be narrower than observed. Comparison with similar observations made for the H^{+}+H collision [Beyer and Merkt Phys. Rev. Lett. 116, 093001 (2016)PRLTAO0031-900710.1103/PhysRevLett.116.093001] indicates that the shape resonances measured by PFI-ZEKE-PES are broadened by the effects of the localization of the charge of the dissociating ion core arising from a nonadiabatic coupling between ion core and Rydberg electron. A simple model is presented that enables one to predict which shape resonances are likely to be affected and to correct for the resulting broadening. Two shape resonances of D_{2}^{+}, the X^{+}(v^{+}=26,N^{+}=5) and the A^{+}(v^{+}=0,N^{+}=5) resonances, have electric-dipole-allowed transitions to bound states of D_{2}^{+} and are shown to facilitate the radiative association at low temperature. The results are used to determine the elastic cross sections of the H^{+}+H and D^{+}+D collisions for partial waves up to N^{+}=11 and the radiative-association cross sections and rate constants in the range between 10 mK and 100 000 K.
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