First direct measurements are reported of the linear reduced Stokes parameters P1,P2 for H(2p)

excited by electron impact at the benchmark energy of 54.4 eV. The results differ significantly from

previous values deduced from angular correlation measurements which are in serious conflict with all

sophisticated theoretical approaches. Our results support the trend of theoretical predictions for P2

and confirm that its value is negative at electron scattering angles above 100±, as predicted by theory

Bowe, P.

Chwirot, S.

Dziczek, D.

O'Neill, R.W.

Slevin, James A.

van der Burgt, Peter J.M.

English

MURAL - Maynooth University Research Archive Library

VOLUME 80, NUMBER 8 P HY S I CA L REV I EW LE T T ER S 23 FEBRUARY 199816Polarization Correlation Measurements of Electron Impact Excitation of Hs2pd at 54.4 eVR.W. O’Neill,1 P. J.M. van der Burgt,1 D. Dziczek,2 P. Bowe,1 S. Chwirot,2 and J. A. Slevin11Department of Experimental Physics, National University of Ireland, Maynooth, County Kildare, Ireland2Institute of Physics, Nicholas Copernicus University, Grudzia¸dzka 5-7, Pl 87100, Torun, Poland(Received 14 October 1997)First direct measurements are reported of the linear reduced Stokes parameters P1, P2 for H(2p)excited by electron impact at the benchmark energy of 54.4 eV. The results differ significantly fromprevious values deduced from angular correlation measurements which are in serious conflict with allsophisticated theoretical approaches. Our results support the trend of theoretical predictions for P2and confirm that its value is negative at electron scattering angles above 100–, as predicted by theory.[S0031-9007(98)05388-5]PACS numbers: 34.80.DpPolarization correlation measurements employ theelectron-photon delayed coincidence technique to permitmeasurements of the polarization of atomic radiativedecay corresponding to electron scattering into a welldefined direction. Coincident detection of photon andscattered electron permits a subensemble of the totalexcited atomic decay radiation to be selected for exami-nation. The polarization correlation method is intimatelyrelated to the angular correlation technique in which theintensity variation of the decay radiation correspondingto a particular electron scattering direction is mapped asa function of photon emission direction. Such detailedmeasurements provide a highly stringent test of scatteringtheories. However, despite notable recent theoreticalsuccesses in describing the scattering of electrons byhelium [1] and alkali atoms (Li, Na) [2–5], there has re-mained a very long standing discrepancy at large electronscattering angles between all sophisticated theoreticalcalculations [6–10] and the experimental measurementsof Williams [11] and Weigold et al. [12] of the angularcorrelation parameters for electron impact excitation ofH(2p) at 54.4 eV. Data at this energy have acquiredbenchmark status for the comparison of experimentwith theory at intermediate energies. Given that thehydrogenic system is the only one for which the wavefunctions are analytically known, the electron-hydrogensystem represents a prototype for calculation of morecomplex interactions. Thus any discrepancy here must beviewed as serious. It is clearly of critical importance todetermine whether this discrepancy is due to experimentalshortcomings or deficiencies in the theoretical treatment,or to a combination of both.We report in this Letter the first direct measurements ofthe linear Stokes parameters of Lyman-a decay radiation(121.6 nm) resulting from electron impact excitation atan incident energy of 54.4 eV. The primary motivationfor these measurements is to provide complementarymeasurements to those previously obtained using theangular correlation technique, and thus to shed new lighton the outstanding discrepancy between experiment andtheory at large scattering angles.30 0031-9007y98y80(8)y1630(4)$15.00The electron impact excitation of the 22Pj states of hy-drogen can be characterized by three independent parame-ters in addition to the angular differential scattering crosssection s, which have traditionally been taken asl ­kja0j2ls, R ­Reka1ap0ls, I ­Imka1ap0ls,where the brackets denote an average over unobservedelectron spins of the transition amplitudes aM for differentmagnetic substates jLMl of the excited 2Pj state. Anequivalent parametrization is the set of so-called reducedStokes parameters Pi , which describes the nascent excitedcharge cloud, i.e., immediately following instantaneousexcitation at t ­ 0. These two sets are related by [13]P1 ­ 2l 2 1, P2 ­ 22p2 R, P3 ­ 2p2 I .The reduced Stokes parameters Pi can be derived fromexperimentally measured Stokes parameters Si, providedaccount is taken of the depolarization inherent in theevolution of the excited state under the influence of internalforces over its lifetime st ­ 1.6 nsd. The experimentallymeasured Stokes parameters are operationally defined asS1 ­1«Is0d 2 Is90dIs0d 1 Is90d, S2 ­1«Is45d 2 Is135dIs45d 1 Is135d,S3 ­1«Iss2d 2 Iss1dIss2d 1 Iss1d,where Isad represents the intensity of radiation transmittedby a linear polarization analyzer whose transmission axisis oriented at an angle a degrees with respect to the quanti-zation axis provided by the direction of the electron beam.Iss1d and Iss2d represent the transmitted intensities of ra-diation characterized by helicity 11 and 21, respectively,and « is the polarization efficiency of the analyzer. Asfar as the two equivalent experimental techniques are con-cerned, measurements of angular correlations in the scat-tering plane without regard to polarization analysis of theradiation yield values for only two independent parametersl and R. A measurement of the circular polarization of theradiation is required to specify I. Such measurements of thecircular polarization have been reported by Williams [14]© 1998 The American Physical SocietyVOLUME 80, NUMBER 8 P HY S I CA L REV I EW LE T T ER S 23 FEBRUARY 1998and Nic Chormaic et al. [15]. We are concerned here withthe linear parameters P1 and P2 only.Our experimental geometry is shown in Fig. 1, the co-ordinate frame shown being the so-called collision frame.The momenta $kin, $kout of the incident primary electrons anddetected scattered electrons, respectively, define the scat-tering plane. Emitted photons are detected in a directionat 90– to $kin and at an elevation angle of 45– to the scatter-ing plane, (i.e., u ­ 90–, f ­ 135– in the collision frame).Lyman-a radiation from the discharge tube prevents posi-tioning of the polarization analyzer at the obvious positionperpendicular to the scattering plane su ­ 90–, f ­ 90–d.The general expressions relating the reduced Stokes pa-rameters Pi to experimentally measured Stokes parame-ters Si for radiation propagating in the direction su, fd canbe obtained using Eqs. (4.3.11) of Blum and Kleinpoppen[16] and conversion factors for state multipoles and inde-pendent parameters given by Anderson et al. [13]. A se-ries of purely algebraic substitutions gives two equationswhich, for the particular analysis direction specified, re-duce toP1 ­25S1 2 33s3 2 S1d, P2 ­6p23 2 S1S2 . (1)The basic apparatus used in the present experiment issimilar to that used previously in this laboratory [15]. Athermal beam of deuterium atoms produced by the dis-sociation of molecular deuterium in an rf discharge isintersected by an electron beam of energy 54.4 eV (en-ergy spread approximately 0.5 eV) and diameter ,1 mm.(Deuterium is preferred as a target in order to minimizethe small effect of the hyperfine structure, which is as-sumed to be negligible in the development of the reducedStokes parameter relations.) The discharge source pro-vides 60% dissociation and an atomic density at the in-teraction point of ,5 3 1011 cm23. Electrons scatteredat a given angle are selected for an energy loss of 10.2 eV,corresponding to n ­ 2 excitation, using two consecu-tive 127– electrostatic analyzers. The circular entranceFIG. 1. Schematic diagram of the experimental geometry.aperture of the electron energy analyzer subtends a solidangle at the interaction region of 0.002 sr. Lyman-a pho-tons emitted in the direction u ­ 90–, f ­ 135– are col-lected by a VUV polarization analyzer and detected bya channel electron multiplier coated with CsI, which en-hances the Lyman-a detection efficiency. The linear po-larization analyzer [17] consists of a quartz (fused silica)reflector whose degree of polarization was measured as83.5 6 0.5%, using a polariscope arrangement. The po-larization analyzer was preceded by a LiF lens of fo-cal length 10 mm at 121.6 nm which increases the solidangle subtended by the analyzer at the point of intersec-tion of the beams (focal point of lens) to 0.6 sr. Thelarge collection solid angle of the polarization analyzerrequires that Eqs. (1) be modified to account for this.This was done using the procedure of Goeke et al. [18],by integrating the analytical expressions for the relevantStokes parameters over the acceptance angle of the detec-tor su 6 d, f 6 d, with d ­ 22.5–d to obtainP1 ­25S1 2 2.873s2.87 2 0.86S1d, P2 ­8.552.87 2 0.85S1S2 .(2)This change amounts to a correction of at most 5%for the parameters measured. An important experimentalcheck is that measurements at small electron scatteringangles (up to 20–) were made both with and without theuse of the LiF lens. Without the lens the acceptancesolid angle of the polarization analyzer was restrictedto 0.008 sr. Good agreement in both sets of measuredStokes parameters was obtained, thus giving confidencethat the lens does not spuriously affect the measuredpolarizations.An experimental measurement consists of a series ofconsecutive measurements at each of the four polarizerorientations. Measurements at low electron scatteringangles can be completed to reasonable statistical accuracyin a matter of hours, while the results at high scatteringangles are the result of approximately eight weeks of dataaccumulation at each angle. This is a direct consequenceof the sharp decrease in the angular differential crosssection for H(2p) excitation. As is standard practice, allmeasured photon intensities are normalized to the scatteredelectron count rate to account for possible variations inelectron beam intensity and target density over the courseof a run.As a matter of course in these measurements it is alsopossible to measure approximately the corresponding non-coincident Stokes parameters (i.e., Stokes parameters forthe decay radiation averaged over all electron scatteringangles) simultaneously with the coincident parameters.This provides an important experimental check of system-atics, in particular, of any system misalignment. The non-coincident S1 parameter is required to be zero by virtueof the axial symmetry of the measurement. All measure-ments reported here were supported by a noncoincident S2measurement within the range 60.03. The noncoincident1631VOLUME 80, NUMBER 8 P HY S I CA L REV I EW LE T T ER S 23 FEBRUARY 1998S1 parameter is also routinely measured and comparedwith the established experimental value of 0.12 6 0.02[19], but less reliance is placed on this check as our mea-surement is subject to molecular contamination (,20% ofthe total photon flux originates from molecular excitation)and atomic cascade contributions. Nonetheless, we typi-cally recorded values in the range 0.11–0.15. These val-ues are also corrected to account for the large acceptancesolid angle of the polarization analyzer.Standard consistency checks have also been satisfied.The electron and photon count rates and the coincidencerate were linear with electron beam intensity and targetdensity. The possibility of Lyman-a resonance trappingwas tested at low electron scattering angles by reducingthe atomic target density by a factor of 3 and lookingfor variation in the measured Stokes parameters. Nosignificant variation was observed. The possibility of anypolarization sensitivity of the channeltron photon detectorwas also excluded after a systematic search for any sucheffect.Directly measured Stokes parameters and the reducedStokes parameters derived from these using Eqs. (2) arepresented in Table I. Each value represents a leastsquares combination of several independent experimen-tal measurements. Errors here represent statistical uncer-tainties combined with the uncertainty in the measuredpolarization efficiency «, and are quoted at one standarddeviation. Figure 2 compares our measured values for thereduced Stokes parameter P1 with the values derived fromthe angular correlation measurements of Williams [11]and Weigold et al. [12]. Also shown are the results ofvarious recent theoretical calculations. Figure 3 displaysthe same comparisons for P2.The theoretical approaches considered fall into oneof two categories: nonperturbative close-coupling cal-culations [6–9] or perturbative distorted-wave approxi-mations [10]. The various close-coupling calculationsdiffer mainly in their treatment of the continuum viathe use of pseudostates, the most ambitious of this typebeing the 36 state convergent close-coupling calculation1632TABLE I. Directly measured Stokes parameters S1, S2 at electron scattering angles ue , andreduced Stokes parameters P1, P2 derived from these using Eqs. (2). Numbers in bracketsrepresent statistical uncertainty in the least significant digits expressed as 1s.ue S1 S2 P1 P22– 0.259(015) 20.053s014d 0.459(048) 20.169s045d4– 0.192(014) 20.174s015d 0.244(047) 20.553s048d6– 0.131(009) 20.242s009d 0.052(029) 20.748s030d8– 0.078(016) 20.249s018d 20.115s052d 20.762s056d10– 20.013s019d 20.229s021d 20.369s061d 20.681s068d15– 20.054s009d 20.266s010d 20.480s030d 20.780s030d20– 20.039s019d 20.221s021d 20.445s062d 20.681s068d30– 0.075(029) 20.223s028d 20.120s090d 20.680s090d90– 0.153(032) 0.055(033) 0.115(100) 0.170(102)110– 0.118(038) 20.055s036d 0.010(114) 20.169s113d120– 0.162(057) 20.062s060d 0.143(175) 20.194s189dof Bray and Stelbovics [6]. The single distorted-wavecalculation of Madison et al. [10] is exact to second orderand includes a treatment of second-order exchange. Itcan be seen that all of these sophisticated calculations arein broad agreement as to the values of P1 and P2 over theentire electron scattering range.Measurements at low electron scattering angles (up to30–) were undertaken mainly in order to establish thatour experimental technique is free of any significant sys-tematic errors, since previous experiment and theory arein reasonable agreement over this range. Indeed, duringthe long accumulation times required at higher electronscattering angles (,2 months integration), we regularly re-measured small angle values to ensure against any system-atic changes in the apparatus. Our measurements of P1are in fair agreement with the previous angular correlationresults over the entire angular range measured and confirmthat there exists a minimum in the electron scattering rangeof 90––120–which is deeper than that predicted by any re-cent calculation.It is in values for P2 above 90– that the discrepancy be-tween previous experiment and theory is most pronounced,and this has been the primary motivation for this experi-ment. As can be seen in Fig. 3, the various theoreticalapproaches all predict negative values for P2 in the scat-tering range above 90–, falling to a minimum of ,20.6 at,130–, while both sets of angular correlation data recordonly positive mean values in this angular range. In thecase of Williams’ results [11], the possibility of negativevalues is strongly rejected on the basis of his reported sta-tistical uncertainties. The current polarization correlationresults at 110– and 120– strongly contradict the trend ofthe angular correlation data and qualitatively support thetheoretically predicted variation of P2. Error bars on thecurrent data are unfortunately too large to be entirely con-clusive; however, on the assumption that the uncertaintiesare normally distributed, the datum at 110– expresses a93% probability, and the datum at 120– an 85% proba-bility, that P2 is negative in value at these scatteringangles. At 120– there is only a 2% probability that theVOLUME 80, NUMBER 8 P HY S I CA L REV I EW LE T T ER S 23 FEBRUARY 1998FIG. 2. Reduced Stokes parameter P1 as a function of elec-tron scattering angle. The reported polarization correlationmeasurements (d) are compared with those deduced from theangular correlation measurements of Williams shd [11] andWeigold et al. sed [12]. Error bars represent statistical un-certainties quoted at 1 standard deviation. Also shown are theresults of recent calculations viz., 36 state convergent close-coupling results of Bray and Stelbovics (—) [6], 17 stateclose-coupling calculation of Wang et al. (? ? ??) [7], multipseu-dostate close-coupling calculation of van Wyngaarden and Wal-ters s– · · · –d [8], intermediate energy R matrix calculation ofScholz et al. s– ? –d [9], and the second-order distorted wavecalculation of Madison et al. (- - - - -) [10].value of P2 is as high as the mean value reported byWilliams. It is equally clear, however, that the currentdata are not in accord with theory. Indeed, the probabilityFIG. 3. Reduced Stokes parameter P2 as a function ofelectron scattering angle. Symbols are the same as in Fig. 2.of a P2 value of 20.5 at 120– is estimated to be only5%. There seems little point, therefore, in discussingthe extent of disagreement with the individual theoreticalapproaches.It is our conclusion that the angular correlation experi-ments of both Weigold et al. and Williams were in errorin their measurements of the correlation parameter R, andthat the resulting discrepancy between experiment andtheory, while still not satisfactorily resolved, has beensignificantly diminished by the polarization measurementsreported here. Further experimental effort will be requiredto confirm this conclusion.This work was carried out with the support of For-bairt (Ireland) and the EU Human Capital and Mobilityprogram.Note added—Since the submission of this Letter,Yalim et al. [20] have published important and directlyrelevant angular correlation data for electron impactexcitation of H(2p) at 54 eV and at scattering angles of10–, 30–, and 100–. Their measurement at 100– is ingood agreement with theory, and, like the present work,strongly suggests that the earlier angular correlation dataof Weigold et al. [12] and Williams [11] is in error. Thenew data from both Yalim et al. and our own groupprovide strong evidence of the essential validity of currenttheories.[1] D. V. Fursa and I. Bray, Phys. Rev. A 52, 1279 (1995).[2] D. H. Madison, R. P. McEachran, and M. Lehmann,J. Phys. B 27, 1807 (1994).[3] V. Karaganov et al., Phys. Rev. A 54, R9 (1996).[4] I. Bray, Phys. Rev. A 49, 1066 (1994).[5] D. H. Madison, K. Bartschat, and R. P. McEachran,J. Phys. B 25, 5199 (1992).[6] I. Bray and A. Stelbovics, Phys. Rev. A 46, 6995 (1992).[7] Y. D. Wang, J. Callaway, and K. Unnikrishnan, Phys. Rev.A 49, 1854 (1994).[8] W. L. van Wyngaarden and H.R. J. Walters, J. Phys. B 19,929 (1986).[9] T. T. Scholz et al., J. Phys. B 24, 2097 (1991).[10] D. H. Madison, I. Bray, and I. E. McCarthy, J. Phys. B 24,3861 (1991).[11] J. F. Williams, J. Phys. B 14, 1197 (1981).[12] E. Weigold, L. Frost, and K. J. Nygaard, Phys. Rev. A 21,1950 (1980).[13] N. Andersen, J.W. Gallagher, and I. V. Hertel, Phys. Rep.165, 1 (1988).[14] J. F. Williams, Aust. J. Phys. 39, 621 (1986).[15] S. Nic Chormaic, S. Chwirot, and J. Slevin, J. Phys. B 26,139 (1993).[16] K. Blum and H. Kleinpoppen, Phys. Rep. 52, 203 (1979).[17] S. Chwirot et al., Appl. Opt. 32, 1583 (1993).[18] J. Goeke, G. F. Hanne, and J. Kessler, J. Phys. B 22, 1075(1989).[19] W. R. Ott, W. E. Kauppila, and W.L. Fite, Phys. Rev. A1, 1089 (1970).[20] H. A. Yalim, D. Cvejanovic, and A. Crowe, Phys. Rev.Lett. 79, 2951 (1997).1633

Polarization Correlation Measurements of Electron Impact Excitation of Hs2pd at 54.4 eV

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Polarization Correlation Measurements of Electron Impact Excitation of Hs2pd at 54.4 eV

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