Theory of energy-transfer collisions of excited sodium atoms: 3P+3P→3S+5S or 4D

The energy transfer between a pair of excited Na(3p) atoms leading to Na(3s)+Na(5s) and Na(3s)+Na(4d) final states is studied in a semiclassical coupled-state theory. Classical trajectories are evaluated from the average adiabatic potentials of previously calculated excited molecular states of Na₂. With this specification of average nuclear R(t) for atoms approaching in a given magnetic quantum number (mₐ,mb) substate, we solve the coupled equations for the time-dependent Schr\"odinger equation in the 21-state diabatic basis set (including 3p, 3s, 5s, and 4d) of atom pairs. The coupling terms arise from the dipole-dipole interaction. Excellent agreement is obtained with the data of the two most recent measurements of the 3s+4d and 3s+5s energy-transfer cross sections at T{~}500--600 K. Extension to low temperature shows a rising 3s+5s cross section as a result of a net attractive adiabatic potential in the (mₐ,mb)=(1,0) incident channel, as also occurs for associative ionization.