^{1,2,a)}, S. Yoshida

^{3}and F. B. Dunning

^{4}

### Abstract

A classical trajectory Monte Carlo approach is used to simulate the dissociation of H^{+}⋅⋅⋅F^{−} and K^{+}⋅⋅⋅Cl^{−} heavy Rydberg ion pairs induced by a ramped electric field, a technique used experimentally to detect and probe ion-pair states. Simulations that include the effects of the strong short-range repulsive interaction associated with ion-pair scattering are in good agreement with experimental results for Stark wavepackets probed by a ramped field, demonstrating that many of the characteristics of field-induced dissociation can be well described using a quasi-classical model. The data also show that states with a given value of principal quantum number (i.e., binding energy) can dissociate over a broad range of applied fields, the exact field being governed by the initial orbital angular momentum and orientation of the state.

Research supported by the National Science Foundation (NSF) under Grant No. 0964819, the Robert A. Welch Foundation under Grant No. C-0734, the U.S. Department of Energy (DOE) OBES through Contract No. ACO5-00OR22725 to ORNL managed by UT-Batelle, LLC, and the FWF (Austria) under Contract No. SFB016.

I. INTRODUCTION

II. MODEL SYSTEM

III. LARGE ANGULAR MOMENTUM STATES AND SCALING LAWS

IV. CTMC APPROACH

V. RESULTS AND DISCUSSION

VI. CONCLUSIONS

### Key Topics

- Dissociation
- 61.0
- Rydberg states
- 36.0
- Angular momentum
- 18.0
- Electric fields
- 10.0
- Photoexcitations
- 8.0

## Figures

Dissociation probabilities for H^{+}⋅⋅⋅F^{−} ion pairs in the selected *n* = 3000 |*n*ℓ*m*〉 and |*nkm*〉 initial states indicated in an applied field that rises linearly from 0 to 57 V cm^{−1} in 2.5 *μ*s. The applied field is expressed in terms of the adiabatic dissociation threshold, *F* _{ad} = 12 V cm^{−1}. The inset shows the field-free classical orbit for an ℓ = 10 *m* = 1 state over ∼9 Kepler periods. Core scattering leads to marked changes in the orientation of the orbit, i.e., to precession. The inset also includes a contour plot of the potential (−1/*r* + *zF*) showing the saddle point.

Dissociation probabilities for H^{+}⋅⋅⋅F^{−} ion pairs in the selected *n* = 3000 |*n*ℓ*m*〉 and |*nkm*〉 initial states indicated in an applied field that rises linearly from 0 to 57 V cm^{−1} in 2.5 *μ*s. The applied field is expressed in terms of the adiabatic dissociation threshold, *F* _{ad} = 12 V cm^{−1}. The inset shows the field-free classical orbit for an ℓ = 10 *m* = 1 state over ∼9 Kepler periods. Core scattering leads to marked changes in the orientation of the orbit, i.e., to precession. The inset also includes a contour plot of the potential (−1/*r* + *zF*) showing the saddle point.

Dissociation characteristics of H^{+}⋅⋅⋅F^{−}ion-pair states with *n* = 2900, ℓ = 10, *m* = 1 created in a dc field *F* _{dc} = ±1.2 V cm^{−1} and subject to a ramped field that rises linearly from 0 to 57 V cm^{−1} in 2.5 *μ*s. Both fields are applied along the *z* axis. Also included are results for *F* _{dc} = −1.2 V cm^{−1} in the presence of a small transverse stray field *F* _{stray} = *F* _{dc}/20. The ramped field is turned on following a time delay of *t* _{d} = 260 ns after photoexcitation. (a) and (b) The dissociation probability as functions of time and field, respectively, (c) the applied field, and (d) the derivative of the curves in (b).

Dissociation characteristics of H^{+}⋅⋅⋅F^{−}ion-pair states with *n* = 2900, ℓ = 10, *m* = 1 created in a dc field *F* _{dc} = ±1.2 V cm^{−1} and subject to a ramped field that rises linearly from 0 to 57 V cm^{−1} in 2.5 *μ*s. Both fields are applied along the *z* axis. Also included are results for *F* _{dc} = −1.2 V cm^{−1} in the presence of a small transverse stray field *F* _{stray} = *F* _{dc}/20. The ramped field is turned on following a time delay of *t* _{d} = 260 ns after photoexcitation. (a) and (b) The dissociation probability as functions of time and field, respectively, (c) the applied field, and (d) the derivative of the curves in (b).

Time evolution of *L* _{ z } for six random initial trajectories corresponding to H^{+}⋅⋅⋅F^{−}ion-pair states with *n* = 2900, ℓ = 10, *m* = 1 created in the presence of a dc field *F* _{dc} = −1.2 V cm^{−1} and a small transverse stray field *F* _{stray} = *F* _{dc}/20 and then subject, following delay times *t* _{d} of (a) 290 and (b) 200 ns, to a ramped field applied along the +*z* axis that rises from 0 to 57 V cm^{−1} in 2.5 *μ*s. The corresponding distributions in *L* _{ z } 500 ns after the ramped field is turned on are shown in (c) and (d).

Time evolution of *L* _{ z } for six random initial trajectories corresponding to H^{+}⋅⋅⋅F^{−}ion-pair states with *n* = 2900, ℓ = 10, *m* = 1 created in the presence of a dc field *F* _{dc} = −1.2 V cm^{−1} and a small transverse stray field *F* _{stray} = *F* _{dc}/20 and then subject, following delay times *t* _{d} of (a) 290 and (b) 200 ns, to a ramped field applied along the +*z* axis that rises from 0 to 57 V cm^{−1} in 2.5 *μ*s. The corresponding distributions in *L* _{ z } 500 ns after the ramped field is turned on are shown in (c) and (d).

(a) Dissociation probabilities and (b)–(f) dissociation probabilities per unit time for the delay times *t* _{d} indicated and the same field conditions as in Fig. 3.

(a) Dissociation probabilities and (b)–(f) dissociation probabilities per unit time for the delay times *t* _{d} indicated and the same field conditions as in Fig. 3.

Dissociation probabilities for K^{+}⋅⋅⋅Cl^{−} ion pairs (solid lines) with *n* = 5000 and H^{+}⋅⋅⋅F^{−} ion pairs (dashed lines) with *n* = 3000 as a function of applied field. (a) Comparison of results for K^{+}⋅⋅⋅Cl^{−}and H^{+}⋅⋅⋅F^{−} ion pairs in well defined |*n*ℓ*m*〉 initial states with the values of ℓ indicated and ℓ = *m*. (b) Comparison of results for a microcanonical distribution of K^{+}⋅⋅⋅Cl^{−} and H^{+}⋅⋅⋅F^{−} states, together with the prediction for a pure Coulomb potential. The applied field slew rates used for H^{+}⋅⋅⋅F^{−} and K^{+}⋅⋅⋅Cl^{−} ion pairs are 23 V cm^{−1}/*μ*s and 5 kV cm^{−1}/*μ*s, respectively. The angular momentum is expressed in scaled units ℓ*/n*.

Dissociation probabilities for K^{+}⋅⋅⋅Cl^{−} ion pairs (solid lines) with *n* = 5000 and H^{+}⋅⋅⋅F^{−} ion pairs (dashed lines) with *n* = 3000 as a function of applied field. (a) Comparison of results for K^{+}⋅⋅⋅Cl^{−}and H^{+}⋅⋅⋅F^{−} ion pairs in well defined |*n*ℓ*m*〉 initial states with the values of ℓ indicated and ℓ = *m*. (b) Comparison of results for a microcanonical distribution of K^{+}⋅⋅⋅Cl^{−} and H^{+}⋅⋅⋅F^{−} states, together with the prediction for a pure Coulomb potential. The applied field slew rates used for H^{+}⋅⋅⋅F^{−} and K^{+}⋅⋅⋅Cl^{−} ion pairs are 23 V cm^{−1}/*μ*s and 5 kV cm^{−1}/*μ*s, respectively. The angular momentum is expressed in scaled units ℓ*/n*.

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