(a) The experimental excitation scheme for the case of . vuv coherent radiation excites the level of the state from the level of the ground state. The square moduli of both vibrational wave functions are shown. The tunable visible-light probe laser then excites the vibrational levels of the state. (For the intermediate state is and the levels excited are .) Vibrational levels of the state have some amplitude in the potential energy well, where they overlap with vibrational levels of the ion. (b) Fluorescence possibilities for the state of . The levels excited in the experiment are shown along with many of the vibrational levels of the lowest lying and states. On the scale of the diagram the outer wells of the and states are degenerate. The long vertical arrow indicates the reverse of the last excitation step used for , which also represents strong emission, while the short vertical arrow indicates the possibility of transitions. The ab initio electronic dipole transition moment functions for and are also shown (Ref. 30).
(a) The Born-Oppenheimer potential energy curves (solid curves) of the first three excited levels of are shown relative to the energy of the , level of . The long-dashed curves show the diabatic states: , , and . The ground electronic state of is shown by the heavy short-dashed curve. (b)–(d) show the electronic adiabatic corrections to the potential energy for the , , and states, respectively. (e) As in (a) but on a different scale and over a different range. In addition, the state of is shown, as is the ionic energy. (f) As in (b) but over a different range.
The potential energy functions of the electronic state (solid curve) and the ion (heavy curve) along with the vibrational energy levels (horizontal lines: solid for levels, short dashed for levels, and heavy for ) for , labeled by , , and . Squares of the vibrational wave functions are shown in those regions where they are non-negligible.
Squares of the state vibrational wave functions for for , with magnified views (magnification specified in each case) of their behavior in the potential energy well. specifies the number of nodes in the inner well.
Calculated rovibrational energies as a function of , labeled by ( levels, connected by solid lines), ( levels, connected by dashed lines), and ( connected by the heavy solid line). For those pairs of and levels within of each other are circled. Energies above the ionization threshold are shown by the shading. levels exhibiting strongly enhanced autoionization in experiment (Ref. 8) are flagged by rectangles and labeled “expt.” The possible approximate location of the resonance of the state is shown by the thick dashed grey line.
Calculated relative autoionization rate (top) and relative tunneling (bottom) for for the levels of the state of , plotted as a function of the energy above the related level. For each the values are normalized to 1.0 for the strongest of the eight rates shown (for ). All levels that lie within of an level with the same are circled. (For adjacent values have this property and, to simplify the diagram, share a common circle.)
The strongest emission transitions from (a) and [(b) and (c)] . The square of each of the involved vibrational wave functions is shown, as is the electronic transition dipole moment function . Going from to 16, the main lower level of emission changes from to , leading to an increased transition frequency [seen in (c)] while sampling a smaller value of [seen in (b)].
Illustration of the dissociation calculation for and 23 of the state of . The squared vibrational wave functions of these two states are shown. These levels are embedded in the dissociation continua of lower states. dissociates mainly through the state; mainly through the state. The related continuum functions at the appropriate energies are shown. The nonadiabatic coupling dominates in both cases and is shown, along with the accumulation as a function of of the integral in Eq. (21). Compared to , the accumulation for is magnified for low and for high .
The calculated rates for dissociation from to each state open to dissociation are given as a function of for for (a) and (b) . The thick grey bands show the emission rates from the same levels.
Experimental and calculated lifetimes (ns) of the rotational levels of (black) and (grey) as a function of the energies of the rovibronic levels. The vertical axis is linear for ; logarithmic for , separated by the horizontal grey bar. The energy scale for is shifted to align the potential energy barrier between the and wells for and . Experimental values (from Table I) are plotted with error bars and connected by solid lines (broken at missing levels). Calculated values are shown by black diamonds and grey squares and every fifth one is labeled by in (a). For four levels only upper or lower limits are known for the lifetimes. These are plotted by a single bar with an arrow indicating the possible range of values. (d) shows a linearized version of the data for figure from (c). For strongly enhanced tunneling increases the calculated (but not observed) predissociation. However, experimentally is seen to undergo enhanced decay (with only an upper bound known for its lifetime), which may be due to enhanced tunneling.
Experimental fluorescence lifetimes (ns) of the state of and .
References for ab initio data used in the current work.
Calculated ionization rates from the present work (Because ionization of the state depends on the details of enhanced tunneling, these calculated rates are only indicative of the possible rotational and vibrational dependencies. See the text for details.)
Calculated emission rates from the present work. [Note that Wolniewicz and Dressler (Ref. 7) accurately estimated the emission rate at equilibrium as , in agreement with the rates obtained here for .]
Calculated dissociation rates from the present work.
Calculated lifetimes (ns) from the present work.
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