Determination of the Difference Potential from Resonant Charge-Exchange Total Cross Sections: Analysis of RB+-Rb andCs

Abstract

Within a two-state formalism, a systematic procedure is developed for deriving the difference between the gerade and ungerade state potentials from resonant charge-exchange total cross sections. It is shown that three potential constants may be derived from (i) the relative monotonic velocity dependence of the cross sections, (ii) the absolute scaling factor, and (iii) the frequency of the interference oscillations. The method is applied to the Rb -Rb and Cs + -Cs experimental cross-section measurements of Perel, Vernon, and Daley. The difference potential for Rb + -Rb is found to exhibit a maximum at 5.6 a.u. with a magnitude of 3.0 eV. The Cs + -Cs data are likewise analyzed and a maximum of 2.3 eV is located at 6.5 a.u. In both cases, the error estimates are about ±25%. INTRODUCTION THEORYWithin the boundaries of the validity of the twostate approximation and in the low-keV energy region, it is well established that the difference potential between the gerade and ungerade ground states of a symmetric system controls the resonant charge-exchange total cross sections. 1 Experimental measurements, such as those by Perel, Vernon, and Daley on the Rb and Cs systems, 2 may hence be used to deduce information about this difference potential.In the above experimental observations, the cross sections were found to obey the general relationship Q 1/2 =a -blnv.The most interesting aspect, however, was an oscillatory structure that was seen superimposed upon this monotonic velocity dependence. This oscillatory structure may be interpreted by a two-state stationary phase argument 3 that predicts its occurrence whenever the difference potential between the gerade and ungerade states exhibits a maximum. This same concept has been used to predict that oscillations would also appear in the cross sections of the Li -Li system. 4 The object of this work is to provide a convenient method for analyzing the resonant chargeexchange cross sections. A systematic procedure is set up for determining three parameters of the difference potential from (i) the relative monotonic velocity dependence of the cross sections, (ii) the absolute scaling factor, and (iii) the frequency of the interference oscillations. A hypothetical test case is examined and explained. Then, using the methods described within, the Rb -Rb and Cs + -Cs experimental cross sections 2 are analyzed. A check is also made by retrieving the difference potential from Li -Li theoretical cross sections 4 which were calculated by an independent method.In the two-state region of validity, the resonant charge-exchange total cross section is given by 1Here k is the wave number of the colliding system, we have k = \xv/H as usual, and 77 j are the phase shifts for the gerade and ungerade states. Except at small impact parameters b and at low velocities, the difference in phase shifts may be approximatedwhere the semi classical relation b = (Z 4-- §)/& has been utilized. If the difference potential V (r)-V~(r) possesses a maximum or a minimum, interference effects will arise from co...

Cooling and stabilization by collisions in a mixed ion–atom system

“…The ions are evolved in the experimental potential 6 , from a random initial position distribution, which is much bigger than the extent of the atomic distribution, for elastic only and the elastic with RCx collisions. All collisions are instantaneous and the ion-atom binary interaction potential 20,21 determines the specifics of the scatter ing event. The number of RF cycles between collisions is sampled from a Poisson distribution with a mean of 20 RF cycles and the exact instant of collision within the chosen cycle is randomized uniformly.…”

“…= 0.43 mm) of atoms about the ion trap centre. Elastic 15,20 and RCx 21,22 collisions are both incorporated in the simulation. The ions are evolved in the experimental potential 6 , from a random initial position distribution, which is much bigger than the extent of the atomic distribution, for elastic only and the elastic with RCx collisions.…”

“…At higher energies, the charge exchange is active outside the centrifugal barrier and we can define a critical impact parameter for charge exchange b cx such that when b ≤ b cx , the average probabil ity for RCx is 1/2 and for b > b cx the probability of RCx rapidly falls to zero. The value of b cx is determined from the Rb + -Rb molecu lar potential 21,22 . The two critical impact parameters b cel and b cx are plotted in Fig.…”

High-accuracy Rb$_{2}^+$ interaction potentials based on coupled cluster calculations

“…For Rb 2 + , initial experiments date back to the 1960s to 1980s and have been performed in Rb vapor with densities of 2.69 • 10 19 atoms cm −3 [15]. Corresponding measurements range from associative photoionization [15,16] to rough estimates based on the analysis of charge exchange cross sections [17] to multiphoton ionization of Rb 2 and subsequent dissociation of dimer ions by one or more additional photons [18]. More recent experiments [1][2][3][4][5][6] used the same technique as described for Li 2 + .…”

Oscillatory patterns in angular differential ion-atom charge exchange cross sections: The role of electron saddle swaps

“…During the last 50 years, charge exchange studies of atom-atom [1], ion-alkali [2,3] and ion-Rydberg collisions [4] at the total cross section level have systematically indicated the presence of oscillatory structures which were either interpreted as due to a region of stationary phase in the difference between the incident and outgoing channels or, in a classical picture, the number of swaps the electron undergoes across the potential saddle before it is captured by the projectile [5]. A more detailed inspection of the physical mechanisms responsible for those oscillations was experimentally prohibitive in those days while the limited computational facilities also restricted the theoretical capabilities to further refine our understanding of those collision processes at the highly differential level.…”