Jha, L K

Roy, B N

Shrivastava, S K

IACS Institutional Repository

Indian J .  P hys. 67B (3) 237 -  244 (1993)Antiproton and proton excitation of atomic shell electronL K Jha, S K Shhvastava and B N R oyDcpartmicnl of Physics, Univcrsiiy of Bihar, Muzaffarpur-842 001, Lidia Received 12 April 1993, accepted 4 May 1993Abstract We have invesiigaied ihe dependence of sign of projectile charge on anUproionand pioton impact A 'shcll ionisation cross sections of atoms using the Binary Encounter Approximaiion. ILc effects of Coulomb atiraclion/rcpulsion and dccrcase/increase in binding of A- shcll electron have been incorporated in respective cases The Hartrcc-Fock veltKiiy distribution for the atomic A-shell electrons has been used throughout the calculations. Aniiproion cross sections arc larger by a factor of about 2 than proton cross sections at I MeV and the factor mcrcascs with decrease in impact energy.K eyw ords Aniiproion and proton exciialiori, A -shell ionisation. Coulomb  altraction/rcpulsion. increase/decrcasc in binduig, binary encounter approiumaiion, Martruc-Fodc velocity distribution.PACS No. 34.50.Fa1. IntroductionA convenient and com petent method required for d isclosing the various m echanism s that cause atomic excitation in ion-atom collision is to investigate the dependence of relevant cross sections on the projectile charge. With the establishment o f low  energy amiproton beam at CERN [1-4J, it is now  possib le to test charge scaling for atom ic co llis ion  through a comparison betw een cross section induced by antiproton and proton. Such a com parison  constitutes an excellent basis for the exploration o f  charge dependent cross sections since  antiproton and proton differ only by their different signs o f  charge, so far atom ic collision  process is concerned.Andersen eta l [1,2] have found experimentally that antiproton impact multiple (double and triple) ionisation cross sections for multielectron atomic system s (N e and Ar) are larger Dy a factor o f  2 and 4 in cases o f  double and triple ionisation, respectively, than those for proton in the energy range 0 .5-5  M cV. This is in sharp contrast to the case o f  single  ionisation in which proton and antiproton crOwSs sections are equal. Andersen et al pointed out that despite various m echanism s contributing to multiple ionisation, inner-shell ionisation appreciably enhances the m ultiple ionisation cross sections, especia lly  in case o f  many electron system s. They emphasized that at low  energy (0.5 M eV), the AT-shell ionisation cross section o f  N e may be charge dependent. Antiprotons due to Coulomb attraction, the decreased binding effect and the increased speed near the target nucleus, may produce more AT-shell238 L  K  J h a , S  K  S h riv a s ia va  a n d  B  N  R o yholes than protons do and thus contribute more to double and triple ionisiition. So our iiim in this paper, is to investigate the effect o f  change in sign ol charge o f  antiproton and proton on inner shell ionisation o f  atoms. Antiprotons, accelerated by nuclear positive charge, are sijppo.scd to penetrate atoms more deeply and hence would excite the inner shell clecirons with higher probabilities than protons do under the same physical conditions (see [5J).In quantiil approximations, usually scaled resull5  for various projectiles and targets are available in literature. These .scalings arc supposed to incorporate various m echanism s contributing the inner-shell ionisation. H ow ever, the.se scalings do not incorporate, in particuhir, the effect o f  wave function representing the target electron under consideration. And in general, the theoretical binding energy corrections being different for different targets ainnot be incorporated correctly in scalings ([6 J and references therein). On the other hand, we have found that the BEA calculations incor|X)raiing all these mechanisms give a very gcx)d account of cxpcnmenLil observations [7,8). Keeping the above m entioned facts m v ie ^ , w e  luivc considered it worthw'hilc to calculalc K -shell ionisation cross sections o f atom s due to impact o f proton and antiproion in the BEA. \'iWe have taken Vricns [9] expressions for ionisation cross section to calculate K  -.^hell ionisation cross section o f  atom s. The e ffects o f  C oulom b aiiraction /rcpu lsion  and dccrcase/incrcasc in binding o f the A -shell electrons have been incorporated in the prc.scnt calculations. Quantum mechanical Hartrec-Fock velocity distribution for the bound electrons o f the atoms have been used throughout the calculations.2 , TheortM ical co n sid era tio n sVricns [9] expressions for ionisation cross section o f  atom by heavy chiirged particle impact have been used with modifications incorporating the effects o f Coulom b repulsion/attraciion o f the incident proton/aniiproton in the nuclctir field o f  the Uirgct and the increase/dccrease in binding o f the uirgei elecu-on in thepre.scnce o f prolon/antiproion. Vricns [9] expressions for ionisation cross section lor the heavy particle impact can be given in terms o f  dim ensionless variables .v and t (see [ 1 0 ])Q(s.O =sHjI2 2 1 + —31(;ra^). \ < 4 s ( s - t )4(.r 4 I)4.9 (5 ■ /)<  1 < 4 i ( j  + 0= 0, 1 > 4s (i + 0- (1)The effects of Coulomb repulsion of incident proton have been incorporated along the line suggested by Thomas and Garcia [11], (see also [10]). The effects of Coulomb repulsion can be introduced analytically through the relationAnuprolon and proton excitation of atomic K-shell electron 239o(E,) = 1 1---- 4------2 2 1- ,2 X To(E 'i) is the ionisation cross section at the reduced impact energyQlk(2)(3)where Q ta is the radius of the atomic /^-shcll. Z2  and Sjjt arc the nuclearcharge o f  the target and the screening constant for the shell, respectively. In case of antiproton, the Coulomb attraction has been taken into account by considering cq. (2 ) at increased impact energy= (4)The effect of ihc increase in the binding o f the uirget electron in the presence of the proton has been included following the method suggested by Brandt and Lapicki [12],The effect o f the increase in the binding energy o f the target electron can be incorporated in ihe ionisation expression, if tlic unperturbed binding energy of the atomic /f-shcll IS replaced by V^ = f/2jfcC, where 1!  ^ is the corrected binding energy and e is a correction factor given byHere, Gy is Ihe reduced binding energy and (or ihe /C-shcll electron, it is given by Vu(5)02* = 4t(13.6)The factor g is a velocity dependent term and for the AT-shell it is given by (sec 113J)8 =(1 ^ 5x 7 .1 4 jc^  + 4 .27x^  -k 0 .9 4 7 jc^ )(1 ^x)(6)(7)whereX  == 1 1^ - (?•)2 ®2it V2*The decrease in binding energy o f /^-shell electron in the presence of antiproton has been incorporated in the ionisation expression by assuming the correciion factorThe ionisation cross sections have been obtained by integrating Vriens expressions incorporating the two m odifications mentioned above over the Harirce-Fock velocity  distribution for the target electron. The momentum distribuiion function for the target electron has been constructed using the Hartree-Fock radial functions given by Clcmcnti and Roctli [14]. The binding energies o f the target electrons have been taken fmm tlic table of L ou  [15J. For the shell radii o f  atoms, the quantum mechanical values of the points o f maximum radial240 L  K  Jh a , S K  S h riva.m va  and B  N  R o yprobability density reported by Dcsclaux [16] have been used. The  screening constant for the A'-shell has been taken to be cquiil to 0.3. As the relativistic nature of AT-sheli electron and the polarisation o f  the A'-shcil orbit would identically affect tbc proton and antiproton A’-sheJJlonis^ition cross scx'ijon, wc have not incorjx^rjlcd ihcir effects in our c<3lcuiot^ on^ s,3 . R esu lts  and  d iscussionWe have calculated proton and annpmlon impaci -shell ionisation cross sections for atomic system s O, Mg, Al,  Cu and Zn following the method outlined in Section 2. Our proton cross .scction.s have been compared widi .some experimental observations. In order to maintain the ’ clarity o f the figures, we have not plotted other theoretical calculations which were discussed m detail in our previou.s publications 16,71. We could not compare our antiproton cross ions widi cxpc;rimcnuil data due to non-availability of the .same. The experimental values? r ; = : r : “ : r  ™where CD* IS the nuorc.scciicc yield o f th e /C-shfii Th/. i,..i . r .■under consideration have, been taken from Kraii.se 117 |.Our calculated cross .sections for atomic oxygen have been pre.semed m the Figure 1 . 'I’rauni for oxygen Curve A ■K l a l i r r  C o » Resent L« k u U  on.f<>rprou,n,mpacl.ncludmg.heXrof binam f  ^A  only, Curve* D i  K : P„,em1181 for proton, a : ExperimenUl cn»s «ciio„* „ /Y„ A  n ^ o r ' ^ Z ”Antiproum and proton excitation q f atomic K-shelt electronProton impact X-ray production cross sections have been taken from Hart etcU [18] and Yu et at [19] to obtain the expoimental X-shell ionisation cross sections. Our proton cross sections are in very good agreement with the experimental observations and are always within a factor 1.3 of the experimental values. The calculated antiproton cross section is larger by a factor of 1.6 than the calculated proton cross section at 1 MeV and the factor is 6 at 0.1 MeV. There is a change of an order of magnitude in the two cross sections at still lower energies. The two cross sections identically converge at 10 MeV impact energy.The theoretical and experimental cross sections for Mg have been shown in the Figure 2. The experimental proton ionisation cross sections have been obtained from AT-shell X-ray production cross sections of Khan el d  [20] and Yu rto/ [ 19]. The calculated cross sections due to impact of protons agree well with the experimental results and are always within a factor of 1.4 of the experimental cross sections. Antiproton cross sections are largerF ig u re  2. Cross secuons for magnesiuin. Curves A, B, C . D, E : Same as in Figure I; •  ; Experimcnial cross sections of Khan el at [201 fur proton, ▲ : Expeiimcnul cross sections d  Y uelat [19] for proton.by a factor of 1.8 than the proton cross sections at 1 MeV impact energy. With decrease in impact energy, the factor increases and is about 10 at 0.1 MeV. Cross sections induced by antiprotons and protons converge at the impact energy 12 MeV.242 L  K  J h a , S K  Shriviisiava a n d  B  N  R o yWc have ploiiccl the antiproion and proion impact ionisation cross sections for Al in die Figure 3 The AT-shell X-ray production cross sections o f Basbas e ta l  [13 | and Yu c ta l  [19| have been taken to obtain the experimental proton ionisation cross sections. Our cross sections show a very good agreement with experim ents lying within a factor o f 1 . 3  from cxpcrimentiil values. The antiproton impact cross sections are larger by a factor o f 1.84 than proion cross sections al I M eV impact energy. At impact energy 0.1 M eV , the antiproion cross section is ahoiii ten times larger than proton cross section. The two cross .section curves conveige ideiuically al 20 M eV.Figure 3. Cross secuons for aluminium. Curves A , B, C, D, E ; Same as in Figure 1 ; •  : Expcnmenial results of Basbas et al [13] for proion. ▲ ; lixpcrimenial results of Yu el a/ [19] for proton.CYoss Scciions lor Cu and Zn have been shown in the Figures 4  and 5. For both the atoms, the cxpcrimcnuil proion induced ionisaiion cross sections have been obuined  from the /f-shcll X-i..y production cros" sections o f  Lopes e i a l  (21]. The calculated proion cros.s sections are in excellent agrectr.cni with the experim ental observations. The antiproion induced cross sections arc larger by a lacior o f 2.1 than the proion cross sections al I MeV  impact energy. There is a change o f an order o f  magnitude in antiproion cross section  compared to proton cross s a i io n  al 0.1 MeV impact energy. In case o f  Cu and Zn, the two  cross .scciiorr curves identically converge at 30 MeV impact energy.Anliproion and proton excitation of atomic K-shell electron 243From a close inspection of the curves presented in the Figures 1 -fi, u is obvious thai ihc energy range for the convergence of anliproion and proton cross scciions shills lowards higher values as the atomic number of the Uirgci increases. This uend implies dial anliproion cross sections remain larger than those for proton upio higher impaci energies with ihc increase in atomic number of target atom. This may be ailribulcd to the lad that the energy range of persistence of Coulomb aliradion/rcpulsion and dccrcase/increasc in binding of the target clccUon shifts lowards higher values as the atomic number ol the target atom increases which is physically justified. It is also noticed that die anliproion cross .sections arc larger by a factor at about 1.6 in O, 1.8 in Mg. 1.84 in Al and 2.1 in Cu and Zn than prolon cross scciions at 1 MeV impaci energy.Fi(»urL' 4. Results For copper Curves A, H, C, D, h : Same as in Figure 1; •  ; lixpcrimcnial cross sccijon of Ijopcs et a l  \ 2 \  \ for prolon.Fi^u^e 5. Result for zinc Curves A» li, C. D, I* Same as in Figure 1; •  KxpcnmeiUal results ol Uipcs e t a l  (21 ] for prolon.Al low impact energies due to physical prcKCSscs considered there is an appreciable decrease in prolon cross sections and an appreciable increase in anliproion cross scciions causing a large difference between the two.244 /, K  J h a . S K  S h riv a s itm i a n d li  N  R o yA ck n o w led ^ fm en lsOne o f us (SKS) IS graiefiil lo Council o fS cicn iilic  & Incliisirial Research, N ew  D elh i, India Tor awardini: a Research AsscK iaieship.Kurcrenersn i L il Anderson. P Ilvdplund, II Knudsen, S P Moller, K lilsener, K G Rcnsfclt and E Uggerhoj 1986 Phys Rfv U u  57 2147f2| L H Andersen, P Hvclplund. II Knudsen, S P Mollcr. A H Sorensen, K Elscncr, K G Rcnsfell and E Uggerhoj Phys Rev A36 3612n i L H Andersen, P llvelplund, H Knuden, S P Mollcr, J 0  P Pedersen, E Uggerhoj, K Elscncr and E Morcn/oni 1989 Phy.\ Rev Lett 62 1731|4 ] R Medcnwaldl, S P Mollci, E Uggerhoj, T Worm, P llvelplund, II Knudsen, E Elscncr and E Morenzoni 1991 Phys U tt  A155 15515) W Brandi and G BaNbas 1983 Phys Rev A27 578|6 | S K Shnvaslava «nd B N Roy 1986 Physica C138 219 ;|7| S K Minvdslfiva, A Kumar and H N Roy 1984 Phy\ua  ('124 12/|S| V Kumar, S K Shnvaslava and H N Roy 1990 Vtatnana-J Phys 35 485|9| L Vnens P>()7 I’rot Phys Sor 90 935|10| A Kumar and H N Kov 1978 ,/ Phys It 11 1435111 j H K Jhomas and J I ) (uirc i.i 19()9 Phys R rv A 179 9 1 11 W Brandi arrd (. 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Antiproton and Proton Excitation of Atomic K-Shell Electron

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Antiproton and Proton Excitation of Atomic K-Shell Electron

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