A theoretical study is presented of the process of photodetachment of a negative ion by sub-threshold-frequency radiation in the presence of a simultaneous collision. Calculations are carried out for the H−-He case and the resulting cross section is compared with other competing processes, such as two-photon photodetachment and nonradiative collisional detachment

Delos, John B.

Geltman, S.

Luo, D.

English

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W&M ScholarWorks Arts & Sciences Articles Arts and Sciences 4-1-1988 Laser-induced Collisional Detachment D. Luo J. B. Delos S. Geltman Follow this and additional works at: https://scholarworks.wm.edu/aspubs  Part of the Physics Commons PHYSICAL REVIE%' A VOLUME 37, NUMBER 7Laser-induced collisional detachmentAPRIL 1, 1988D. Luo, J. B.Delos, * and S. GeltmanJoint Institute for Laboratory Astrophysics, University of Colorado and IVational Bureau ofStandards,Boulder, Colorado 80309-0440(Received 9 November 1987)A theoretical study is presented of the process of pkotodetackment of a negative ion by sub-tkreshold-frequency radiation in the presence of a simultaneous collision. Calculations are carriedout for the H -He case and the resulting cross section is compared ~itk other competing processes,such as two-photon photodetachment and nonradiative collisional detachment.I. INTRODUCTIONLaser-induced collisional processes have been studiedexperimentally and theoretically for many years. ' Allnonradiative inelastic processes such as energy andcharge transfer, Penning ionization, as we11 as associativeand dissociative versions of these, will also occur whensuitably tuned radiation is present to provide overall en-ergy conservation.In this note we would like to present a study of thelaser-induced collisional-detachment process (LICD), inwhich an electron is detached from a negative ion bymeans of the combined e8ects of the laser field and a col-lision with a gas atom, A +8+~~3 +8. An alter-nate description of this process would be collisionally in-duced photodetachment. Such a process is of interestonly if the laser photon energy is below the threshold forsingle-photon photodetachment. Then the interestingquestion, which we are presently addressing, is —howlarge is the LICD rate compared with the two-photonphotodetachment rate? These rates will be proportionalto NI and to I, respectively, where X is the atom densityand I the laser intensity. Thus it is clear that there mustbe regions of N and I where one or the other detachmentprocess predominates. Another critical process compet-ing with LICD is that of nonradiative collisional detach-ment, for which the rate is proportional to N alone.We will study in detail the system of H impacting onHe atoms. A simple estimate of the magnitude of thecross section for the process can be obtained if we assumethat during the collision the proximity of the atom 8causes a temporary lowering of the 3 photodetachmentthreshold, such that ihe electron may be detached byone-photon absorption. Based on this picture the LICDcross section estimate would beo.I -xI'w, m.R, ,where a is a mean photodetachment cross section, I' isthe laser photon Aux density, ~, is an effective collisiontime, and 8, is a mean efkctive impact parameter. Thefirst two factors, the photodetachment cross section timesthe photon Aux density, give the rate of detachment.When these are multip1ied by the time duration of a col-lision between A and 8 they give an estimate of theprobability that detachment takes place during that col-lision. That probability times the A -8 collision crosssection gives the LICD cross section. Letting ~, =8, /v,and taking t7-2X10 ' cm (Ref. 2) and R, -3ao (thischoice will be justified in a later section), we findcrt -(1.3X 10 ) I (W/cm ) cm[E (e&)]' 'In Sec. II we present a somewhat more detailed theoryand calculations. The purpose is to obtain, not high-precision results, but simple estimates, which may behelpful to experimenters who wish to examine this pro-cess.II. THEORY AND CALCULATIONSPotential energy curves for the HeH system were cal-culated by Olson and Liu using self-consistent-field-configuration-interaction (SCF-CI) methods (Fig. 1).These curves represent the lowest bound-state energiesfor the quasimolecular states 'X(HeH ) and X(HeH).%e see that the HeH curve is more strongly repulsivethan the HeH curve, so the proximity of He does indeedreduce the binding energy of the electron and the photo-detachment threshold. In fact, at R =R, =2.70QO thecurves cross, and electron detachment occurs rapidlyeven in the absence of a laser.A complete theory of LICD must include the e6'ect ofthe laser on a system that is already undergoing directcollisional electron detachment. The theory of collisionaldetachment is complicated, however (and still controver-sial besides), so we shall not attempt such a completetheory. %e will treat the system as if the electronic ener-gy of HeH were a well-defined function of 8, denotedE, (R).%'ith this approximation, one can still ask whetherE,.(R) should be the HeH energy calculated by Olsonand Liu. The presence of the crossing between boundand free states suggests that Olson and Liu have obtaineda partially "diabatic" representation, since the complete-ly "adiabatic" representation is one in which the HeHand HeH curves avoid crossing. In such a completelyadiabatic representation, the HeH curve ~ould mergeinto the HeH+e continuum from below; therefore theenergy gap would be zero inside some radius close to R, .37 2361 Qc1988 The American Physical SocietyD. LUO, J. B.DELOS, AND S. GELTMANHere a;k is the probability amplitude for 6nding the elec-tron in the free state with energy EI, E—&+(k /2) afterthe collision. 4,- k are the electronic wave functions, E;and EI are the 'X(HeH ) and X(HeH) curves in Fig. I,and Ek(R ) =E/(R )+(k /2). Also, the rotating-wave ap-proximation is used in (3) and Eo is the laser electric fieldstrength amplitude. The dipole moment operatorp(R)= f dr@k(r, R) gz 4, (r,R)Jis a complicated function of R when evaluated with thefull CI forms for 4, and 4I, even with the simplifying as-sumption that the ejected electron will not appreciablydistort 4I, i.e.,C/((1 R) —@f(r,, ri, R)g„(ri)R (units of a& )FIG. 1. Potential curves for the lowest states of HeH andHeH as evaluated by Olson and Liu.It is not clear which representation would provide thebetter starting point for a first-order calculation of LICD.We chose an adiabatic representation. However, we notethat the issue is academic, since we will show below thatat the energies for which collisional detachment is al-lowed, it swamps the LICD cross section. ThereforeLICD can only be seen at those collision energies suchthat the atoms do not enter the region of crossing oravoided crossing of the curves so the problem of "diabat-ic" or "adiabatic" representation does not arise.The transition amplitude between the discrete and con-tinuurn states of HeH caused by the radiation field canbe calculated using first-order perturbation theory andthe rotating-wave approximation. The result (in atomicunits) isa,k— f dt f drat', (r, R)Xz, @;(r,R)2 oor~ exp i f —dt '[E„(R) —E, (R )+co](3)The asymptotic form of p(R ) is the atomic negative ionbound-free matrix element, which is very well knownfrom many theoretical studies on the photodetachmentof H, and which is in good agreement with experiment.The departure of p(R ) at smaller R from its asymptoticvalue would arise from an efFective decrease in the bind-ing energy of an electron to an H atom in the presence ofa He atom as reflected in the energy curves in Fig. 1. Wemake the initial simplification that p, (R ) —=p( oo ). The ex-treme values of p(R) are p( oo ) corresponding to H andthe united ion p(0) corresponding to Li . The calcula-tion of Ref. 5 showed that the maximum value of thephotodetachment cross section of Li is about twice thatof H . Thus we can be reasonably confident that our ap-proximation p(R)=—p, ( oo ) will at worst lead to LICDcross sections which are low by 5 50%. Further, weevaluate p( ao ) in the negative ion model' where the radi-al bound-free matrix element for H is expressed asD(k)= f dr r PQ,„,where Po and X,k are the radial wave functions as definedin Ref. 5, and we neglect any inner-shell contributions tothe bound-free process. The resulting LICD probabilityat the end of a classical collision is2E,'P(p)= 1 dk D (k) f dt exp[ i f dt' co ——37? 0 Qc 02(E E)below the photodetachment threshold, there is no5( k —k o ) part present, and all of the Fourier transformsin (7) are well defined. They have been evaluated numeri-cally.%'e have evaluated the cross-section diAerential inejected electron energy and the total cross section for thetwo relative kinetic energies, 0.7 and 10 eV, and for alaser photon energy of 0.55 eV. The lower kinetic energycorresponds to an energy below the free negative ion de-The forms we use for E;(R) and E&(R) are the curvesglvell ill Fig. I foi R )R~, but wltll E; (R ) =E/(R ) fofR & R, . We have carried out the t ' integral in (7) analyti-cally after fitting EI{R) —E; (E. ) for R «8, to the formC4 C6 C8+ + +0.0271 .In Fig. 2 we show D (k) corresponding to R = ao. Itshould be noted that for ~ «E&( ~ ) E, (~ ), i.e., — .LASER-INDUCED COLLISIGNAL DETACHMENT4Q3,0I.5IQ0.500 0. l 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 l. Gk (Unl~S Or ao' jFIG. 2. Variation of the square of the bound-free radial ma-trix element with ejected electron momentum.tachment threshold of 0.75 eV and hence radiationlesscollisional detachment may not occur. The latter processbecomes very probable for energies where the curvecrossing between E; and Ef can be reached (this occursat & 1.3 eV). S1nce the two atotnlc bodtes may not ap-proach one another more closely than 3.2ao at 0.7 eV ki-netic energy, we assume specular reflection from a hardsphere of this radius to describe the trajectories of smallerimpact parameters. For the higher energy (10 eV) all im-pact parameters are treated by straight-line paths. Fig-ure 3 shows I'(p) (integrated over all electron momenta)and Fig. 4 shows the difFerential cross section in k (in-tegrated over the impact parameter).The total LICD cross sections are 1. 18g 10I (W/cm ) cm for 10 eV and 1.28X10 I (W/cm )cm for 0.7 eV. Our simple estimate in (2) comes fortui-tously close to these values in giving 4. 1X10 ' I (W/cm ) cm at 10 eV and 1.6X10-I (W/cm ) cm at 0.7 eV. The full calculated values donot follow the E '/ dependence in (2) because the use ofa hard sphere for the lower-energy trajectories reducesthe cross section (see Fig. 3).III. COMPARISON KITH OTHER PROCESSESAs mentioned briefly in Sec. I, any attempt to experi-mentally measure LICD cross sections mould have to sortthem our from the competing processes of two-photonphotodetachmentH +2fi~~H+eand nonradiative collisional detachmentH +He~H+He+e .The latter process has been studied theoretically" and ex-perimentally with good quantitative agreement. Thistheoretical work was also based on the potential curves ofOlson and Liu, ' and requires the conversion of kineticenergy of relative motion into electronic energy in attain-ing the transition from initial to final state. This meansthat it has zero cross section for kinetic energies belowthe 0.75-eV threshold, and hence this process will notcompete with LICD at 0.7 eV, but will do so at 10 eV. Amore decisive threshold for this process will be at themerging or apparent crossing of the curves, and to reachthis point requires about 1.3 eV. The calculated andmeasured cross sections at 10 eV areo. &- -= 11ao —3. 1 & 10 ' cm%'e may make a reasonable estimate of the two-photonphotodetachment cross section on the basis of severaltheoretical evaluations. The values found by these au-thors at A~v=0. 55 eV for this generalized cross sectiono'2' are0.7 F10-"Cm4Sfrom Crance and Aymar;0.9&10 cm sfrom Fink and Zoller; and1.0g10-4' cm'sfrom Arrighini eI. al. %e take the average value ofx i042 5.022,5—200—l 7.5—l 5,0I 2.5l 0.0C45.Q25—0 l0 0.5 I.G l 5 2.0 2.5 3.0 3.5 4.0 4.5 5.0 5.5 6.0l 7.5—l 5.0—IQQ—0QFIG. 3. Variation of total LICD probability (P/Eo) with im-pact parameter. The dashed curve shows the 0.7-eV result foruninterrupted straight-line paths.FIG. 4. Variation of LICD diAerential cross section[(do. /dk)/E&~)] with ejected electron momentum.2364 D. LUG, J. B.DELOS, AND S. GELTMAN 370.9X10 cm s for use in estimating the magnitude ofthe detachment rate due to this mechanism.%'e combine the above cross sections to obtain the fol-lowing rates for electron detachment. For LICD~ ( )) 0.59 (at 0.7 eV)~1()2. 1 (at 10 eV)XI ( W/cm )X (Torr ),for nonradiative collisional detachmentWN(s ).5 4 (at 10 ev) x 10 lV (Torr)0(at07eV)and for two-photon photodetachmentfV (s ')=(1X10 ' )[I (W/cm )]From these rates it is clear that for 10-eV collisions 8'Land 8'z will be comparable in magnitude only at the veryhigh laser intensity of —10' W/cm . At such an intensi-ty and reasonable gas densities W2 will be much largerthan either of these collisional rates. This means there isno chance in practice of observing LICD as isolated fromnonradiative collisional detachment for any kinetic ener-gies above the detachment threshold.On the other hand, for collisional energies belowthreshold, only 8'I and Wz need be compared, and wesee that for lV(Torr)=100 the LICD process will dom-inate at I (W/cm ) g4. 0&&10, which is a reasonablerange of intensities to work with. It is hoped that suchmeasurements with slow negative ions may be performedas a demonstration of laser-induced collisional detach-ment.D. L. has received support from National ScienceFoundation (NSF) Grant No. AST82-16481. J. B. D. ac-knowledges support from the Joint Institute for Labora-tory Astrophysics. All computations have been carriedout on the JILA VAX/8600, and have been supported byNSF Grant No. PHY86-04504 to the University ofColorado.'Permanent address: Department of Physics, College of VA'lli-am and Mary, %ilhamsburg, VA 23185.'Reviews have been given by P. R. Herman and E. J. Robinson,in Photon-Assisted Collisions and Related Topics, edited by N.K. Rahman and C. Guidotti (Hardwood, Chur, 1982), p. 15; R.S. Berry, in Physics ofElectronic and Atomic Collisions, editedby S. Datz (North-Holland, Amsterdam, 1982), p. 413; F.Roussel, Comments At. Mol. Phys. 15, 59 (1984); J. %einer,ibid. 16, 89 (1985).~L. M. Branscomb and S. J. Smith, Phys. Rev. 98, 1028 {1955)'„S.J. Smith and D. S. Burch, ibid. 116, 1125 (1959).3R. E. Olson and B. Liu, Phys. Rev. A 22, 1389 (1980).4See for example, S. Geltman, Astrophys. J. 136, 935 {1962).5S. Geltman, Phys. Rev. 104, 346 (1956).6R. D. Taylor and J. B.Delos, Proc. R. Soc. London Ser. A 379,209 (1982)."M. S. Huq, L. D. Doverspike, R. L. Champion, and V. Esau-lov, J. Phys. B 15, 951 (1981).SM. Crance and M. Aymar, J. Phys. B 18, 3529 (1985); M. G. J.Fink and P. Zoller, ibid. 18, L373 (1985); G. P. Arrighini, C.Guidotti, and N. Durante, Phys. Rev. A 35, 1528 (1987).

Laser-induced Collisional Detachment

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Laser-induced Collisional Detachment

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