Dynamical adiabatic theory of atomic collisions: The global structure of dynamical adiabatic potential energy curves

The concept of dynamical adiabatic states, originally proposed to describe one-electron atom(ion)-ion collision systems is developed and the properties of the corresponding dynamical adiabatic potential energy curves are studied for a complete range of internuclear separations $R$. The advantages of a dynamical adiabatic basis are threefold. First, it is compatible with the boundary conditions, whereas in standard adiabatic two-Coulomb center basis we have nonvanishing inelastic transitions when internuclear distance $R\to \infty$. Second, rotational transitions are transformed into radial transitions via a type of hidden crossings in contrast with the standard adiabatic basis, where these transitions could only be included by numerical close-coupling calculations. And third, the ionization process can be described using a basis of the complete discrete orthogonal wave packets, which is much more satisfactory for the process compared with the standard adiabatic approach where the continuum states which have no direct physical meaning are employed. Results of the calculation for the (HeH)${}^{2+}$ quasimolecular system are presented and discussed. Comparison is made with previous results derived by perturbation theory in the united-atom and separated atoms limits.

Figure 1

The 90 lowest eigenvalues (DAPEC and “ghosts”) for symmetric (${\pi }_3=1$) states of the (HeH)${}^{2+}$ collision system ($Z_A=1,Z_B=2$) as functions of the internuclear separation $R$ for $\omega =1$ a.u. [solid (black) curves] and the lowest 20 DAPEC for $\omega =0$ [dashed (blue) curves].

Figure 2

Magnification of the region of small internuclear separations from Fig. 1. Spurious eigenvalues are labeled as “ghosts.”

Figure 3

The lowest ($N=0$) manifold from Fig. 2 at very small internuclear separations [solid (black) lines] together with the predictions of the perturbation theory Eq. (40) [dashed (red) lines].

Figure 4

Moduli $|{\Phi }_{\gamma }(q,{\theta }_3,{\varphi }_3;R)|$ of the first 12 eigenfunctions as functions of ${\varphi }_3$ at the fixed values of $q=2,{\theta }_3=\pi /4$, $R=0.01$ for (a) $\omega =1$ and (b) $\omega =0.2$. Spurious eigenstates are labeled as “ghosts.”

Figure 5

Scaled (divided by $R^2$) DAPEC from Fig. 1.

Figure 6

Segment of low-lying scaled DAPEC from Fig. 5 represented in terms of “effective united atom principal quantum number” Eq. (42) [solid (black) curves]. Also shown [dashed (blue) curves] are the standard PEC of the (HeH)${}^{2+}$ molecular ion labeled by united-atom quantum numbers. The inset shows enlarged region of the avoided crossing between two DAPEC located around ($R=1.493$, $N_{\mathrm{UA}}=3.088$).

Figure 7

Same as described in the legend of Fig. 6 but for antisymmetric (${\pi }_3=-1$) states.

Figure 8

Numerically calculated expression $\Delta E(R,\omega )=E(R,\omega )+(1/2)R^2+1/R$ for the DAPEC corresponding to $\omega =1$ [solid (black) curves], which approaches the asymptote [dashed-dotted (black) curve] given by Eq. (46). Dashed (blue) curve corresponds to the $\omega =0$ case and doted (blue) curve to the asymptote given by Eq. (47).