HAL Id: jpa-00229336
https://hal.archives-ouvertes.fr/jpa-00229336
Submitted on 1 Jan 1989
HAL is a multi-disciplinary open access
archive for the deposit and dissemination of
sci-entific research documents, whether they are
pub-lished or not. The documents may come from
teaching and research institutions in France or
abroad, or from public or private research centers.
L’archive ouverte pluridisciplinaire HAL, est
destinée au dépôt et à la diffusion de documents
scientifiques de niveau recherche, publiés ou non,
émanant des établissements d’enseignement et de
recherche français ou étrangers, des laboratoires
publics ou privés.
PREFERENTIAL TWO-ELECTRON CAPTURE
INTO SPECIFIC CORRELATED STATES
J. Nijland, M. Mack, P. Straten, A. Niehaus, J. Posthumus, R. Morgenstern
To cite this version:
PREFERENTIAL TWO-ELECTRON CAPTURE INTO SPECIFIC CORRELATED STATES
J.H. NIJLAND, M. MACK, P.V.D. STRATEN, A. NIEHAUS, J.H. POSTHUMUS* and R. MORGENSTERN
Fysisch Laboratorium, Rijksuniversiteit Utrecht Princetonplein 5, NL-3584 CC Utrecht, The Netherlands
*~ernfysisch Versneller Instituut, Rijksuniversiteit Groningen Zernikelaan 25, NL-9747 AA Groningen, The Netherlands
sum;!
Nous analysons les spectres des electrons secondaires qui sont dmis par autoionisation apres capture de deux electrons dans les systemis
c6'
+ H2 and 0" + He. La population des differents Ptats( 3C3Cr ) a kt6 etudiee en utilisant une procedure 'fit1 pour les parties correspondantes des spectres dnergetiques des Clectrons. Les valeurs thkorique des dnergies et des durees de vie recemment calculees par Ho donnent des resultats satisfaisantes. Nous trouvons une population preferentielle des etats qui ressemble beaucoup
A
celle des etats de rotation des molecules tri-atomique; c'est a dire: les deux Clectrons tournent dans la mOme direction dans une seul plan et sropposent par rapport au noyau. L'interpration a BtE! faite dans le cadre d'un modele classique.Abstract
We analyze energy spectra of secondary electrons, due to double electron capture and subsequent autoionization for the systems
c6+
+
H2and 0" + He. The population of the various (3C 3C1) states is
thoroughly investigated by means of a fit procedure for the corresponding parts of the electron energy spectra. Theoretical state energies and lifetimes, recently given by Ho yield good fits. We find a preferential population of states which to a large extent resemble rotor states of 3-atomic molecules, i.e. both electrons rotating in the same plane, in the same sense and on opposite sides about the nucleus. This is discussed in terms of a classical model.
Introduction
In atoms with two or more electrons, the electron-electron interaction plays an important role in determining the atomic properties. Recent developments treat also the role of this electron correlation in dynamical processes like charge exchange or excitation /1,2/. Collisions of fully
stripped ions on two electron targets like He and H2 form a simple system to study correlation during charge exchange. If the fully stripped ion captures
JOURNAL
DE
PHYSIQUEboth the electrons, then doubly excited states, which decay by auto-ionization, are populated. Analysis of the electron energy spectra yields information about the population of these states. Of special interest are those states, in which both electrons have the same principal quantum number, because then correlation is known to be important. Apart from the usual quantum numbers they can be characterized by correlation quantum numbers (K,T)~, which give an indication about the correlated motion of the electrons / 3 / . If a two-electron atom is compared with a three-atomic molecule, then the quantumnumbers K, T and A can be regarded as characterizing vibrational bending- and stretch- as well as rotational modes. The question now is: are there any classes of doubly excited states preferentially populated? If this is the case then from the correlation of these states, possibly more insight can be gained into the process of double electron transfer. For example one could suspect an enhanced population of states in which both electrons are "on the same side" of the nucleus, as to keep their initial vicinity they had in the target atom. Yet another suspicion would be: "on opposite side" of the nucleus, thinking about the electrons repelling each other. First results were obtained by Mack and Niehaus /4/ for the systems
c6+
+
H2 and 08++
He and by Bordenave-Montesquieu et al. /5/ for the N+'+
He system. The data of Mack are now analyzed by a fitting procedure taking into account post-collision interaction with the target ion and considering the questions: may interferences between autoionizing transitions be neglected and which of the theoretically predicted energies are most reliable?Experimental setup
Fig 1. Schematic view of the reaction center and its surroundings. The target gas flows through a conically formed ringslit towards the reaction center, which coincides with the viewing point of the cylindrical mirror analyzer.
Spectra and their analysis
Energy spectra of electrons from 60 keV 13c6+
+
H2 collisions and from 96 keV 180'++
He collisions are presented infigures 2 and 3 respectively.
The spectra are properly corrected for the energy dependent transmission of the CMA and transformed to the emitter energy scale. There is a kinematical broadening of the peaks, but the narrowest peak, having a width of 300 meV indicates that this is of minor importance. Shapes and widths are mainly determined by the so called Post Collision Interaction (PCI); the autoionization occurs still in the vicinity of the now ionized target atom. PC1 induces a shift of the peak maximum to a lower energy, and causes a broadening of the peak with an asymmetrical shape, all being strongly dependent on the lifetime of the state, but also on the emission angle of the electrons /8,9/.2
1
electron energy (eV) - ~
I . . .
20 30
JOURNAL
DE
PHYSIQUEThe peaks of fig 2 and 3 are assigned by "+'L"(K,T). The correlation number A is omitted, because it is always 1 when both electrons have the principal quantum number n=3. Triplet states are not taken into account. It was discussed before by Mack /lo/ that a spin change is very unlikely in the double electron capture. Several authors - Lipsky et al./ll/, Bachau /12,5/, Abu-Salbi and Callaway /13/, Oza /14,15/, Ho /16-19/ and Martin et a1./20/:
-
have calculated the energies and lifetimes of these states, all leading to the same identification of the peaks but nevertheless differing enough to allow a test by comparison with our spectra.The first fits were made with the following formula for the intensity:
in which fL(&) stands for the PC1 amplitude, and the A=($) contain the population amplitudes, the spherical harmonics YLM and the reduced matrix elements /21/. In these "incoherent fits", interference between the transitions is neglected. Taking the energies E~ and widths TL from theory, the population amplitudes are left as fit parameters. In fig 2, for
c6+
+
H2, the solid line indicates the fit results, taking the most recent theoretical values of Ho /19/ as given in table 1; except for the values of Abu-Salbi and Callaway /13/ that are much alike, the ones from the other authors all lead to unsatisfactory results. The rather good reproduction of the spectrum strongly supports their values for the energies and lifetimes of the correlated states discussed here. For 0 8 ++
He the fit result is indicated by the solid line in fig 3. Now also the energies eL were taken as free parameters as the ones calculated by Ho and by Abu-Salbi and Callaway did not satisfy completely. Nevertheless we show them in table 1, becausethey best approximate the experimental values.
06+(31,3f')
' ~ ' ( 2 . 0 ) . ' D ~ ( I , I ) l ~ a ( ~ , l )
-
-
-
I electron energy (eV)1 1 1 1 1 1 1 1 1 1 1
Energies are given with respect to the n=2 level, i.e. the final state in the autoionization /4/. For 06+ the experimental values as calculated in the fits are also given. The last column gives the relative populations (in %) of the various states following from the fits shown in fig 2 and 3.
The next step is to allow for interferences in the calculation of the STATE ENERGY WIDTH POPULATION
?lo Ho % :S (2,O) 21.42 0.130 2 D (2,O) 22.51 0.177 6 ~ ~ ( 1 1 ) 23.39 0.381 3 ~ ~ ( 1 , l ) 23.82 0.0084 5 :D (0,2) 25.31 0.310 12 S(0,O) 25.51 0.523
-
'G(2,O) 26.96 0.620 5 5 '~'(1,l) 27.22 0.316 8 :D~(o,o) 28.90 0.0789 6 P ( - 1 , 29.82 0.106 2 'S (-2,O) 32.88 0.0078 1fits. Interferences have proven to be of major importance in the electron spectra measured coPncident with the projectiles/22,23,24/. In the noncolncident spectra presented here, several effects may attenuate or wash out interference structures: the analyzer integrates over all azimuthal detection angles 9 and projectile scattering angles
.
This causes ae~
smoothing due to variable kinematical shifts and could directly wipe out any interference structures dependent on one of those angles. On the other hand
8 is small and interfences should not be excluded beforehand.
P
The following simple formula was used for "coherent fits": ENERGY WIDTH POPULATION Ho Exp Bo % 34.68 34.80 0.138 1 36.15 36.69 0.176 4 37.40 37.66 0.381 8 37.94 38.19 0.0084
3
40.01 40.06 0.329 14 40.36-
0.569-
42.41 42.21 0.708 48 42.82 42.59 0.362 9 45.09 44.51 0.114 12 46.46 45.52 0.118 1 50.64-
0.069 -with aL(&) = arg(fL(&)) and pL(+)= arg(AL(9)). The moduli (AL/ and the phases
BL
were used as fit parameters, 22 in total. A more accurate treatment also would have to take the population amplitudes for magnetic sublevels into account seperately, but this would lead to 66 free parameters which is more than desireable. In spite of the increased number of fit parameters, the fits could not significantly be improved for any of the energy and lifetime sets.Discussion
C1-346 JOURNAL
DE
PHYSIQUEN ' + + H ~ collisions. This highest L state has many sublevels but statistically one would expect a population of no more than 20 X ! The state '6(2,0) is one which is characterized by a highly correlated motion of the two electrons on opposite sides of the nucleus ( K=2 ), in the same plane
( T=O ) and rotating in the same sense ( L=4 ).
Classically one can explain the preference for this state within the framework of the extended classical barrier model /25/ which states, among other things, that an electron can pass from the target to the projectile as soon as the Coulomb barrier between the cores is sufficiently low. The first electron then transfers at R = 7.4 a.u. The barrier for the second electron should allow a transition at R = 5.0 a.u. if screening by the first electron is neglected. A complete screening, reducing the charge of the projectile core by one, would yield R2= 4.7 a.u. Due to the motion of the first electron there is a screening which varies as a function of time, leading to a periodical raising and lowering of the potential barrier and thus causing an over-barrier transition preferentially when the first electron is "behind" the nucleus of the projectile. To give more significance to this classical picture we note that several electron-revolutions occur between R and R2, and that the tunneling probabilities for the electrons are small at these internuclear distances. Finally it is interesting to realize that also the angular momenta of the exchanged electrons can be understood within a classical picture: according to the model described by Burgdgrfer et a1 /26/ the average angular momementum for each exchanged electron should be !=2 for the cases considered here.
Conclusions
The electron spectra of (3!3tt) autoionizing states can well be fitted, using proper theoretical values for the energies and lifetimes such as the ones of Ho /19/ or Abu-Salbi and Callaway /13/. Interferences were not found to play any significant role. The fits show a clear preference for the population of the highly correlated state 1~(2,0). This can be understood by picturing the capture process with the aid of the classical barrier- model /25/ and a strong correlation during the double electron capture process.
Acknowledgement
This work is part of the research program of the Stichting voor Fundamentel Onderzoek der Materie (FOM) with financial support of the Nederlandse organisatie voor Wetenschappelijk Onderzoek (NWO).
References
1. N. Stolterfoht, C.O.Havener, R.A.Phaneuf, J.K.Swenson, S.,M.Shafroth, F.W.Meyer; Phys.Rev.Lett.
2
14 (1986)2. H. Winter, M. Mack, R. Hoekstra, A. Niehaus, F.J. de Heer; Phys.Rev.Lett,
2
957 (1987)R. Geller, B. Jacquot; Nucl.Instr. and Meth.
202
399 (1982)M. Mack, A. Niehaus; Nucl.Instr. and Meth. in Phys.Res. B23 291 (1987) P. v.d. Straten, R. Morgenstern; J. Phys. 1361 (1986)
P.W. Arcuni; Phys.Rev.
A33
105 (1986)M. Mack; Nucl.Instr. and Meth. in Phys.Res. 23 74 (1987) L. Lipsky et al.; At .Data Nucl.Data Tables E127 (1977) H. Bachau; 3. Phys. B17 1771 (1984)
N. Abu-Salbi, ~ . ~ a l l = y ; Phys Rev
e,
2372 (1981) D.H. Oza; Phys.Rev. A33 824 (1986)D.H. Oza; J. Phys, = ~ 1 3 (1987) Y.K. Ho; J.Phys.
B12
387 (1979) Y.K. Ho; Phys.Lett.79A
44 (1980) Y.K. Ho; Phys.Rev.A35
2035 (1987) Y.K. Ho; Private communication 1988F.Martin, O.Mo, A.Riera,M.Yanez; Europhys.Lett.4 799 (1987) P.v.d.Straten and R-Morgenstern; Phys.Rev. A34 4482 (1986)
P.v.d.Straten and R.Morgenstern, Comments onX.Mol.Phys.
