Saxsena, Sachin

Srivastava, Rajesh

IACS Institutional Repository

\lnJ,anJ. Phys. 76B (4), 519-522 (2002)U P  Ban international JournalSuperelastic electron scattering fr^m potassium atomsR ajesh  S riv a s tav a  and  S ach in  f a x e n a  Department o f Physics, University o f Roorkcc, H|porkec-247 667, India li-mail ; sasasdph@isc.rurkiu.er^t inAbstract : We have carried out distorted wave (DW) calculations for the electron impact 4 *5-4 *P resonance excitation o f  potassium. The results for alignment and orientation parameters arc obtained and compared with the very recent superclastic electron scattering measurements from the laser excited 4 */* states o f potassium. The validity of DW method is commented upon.kerwards . l:lectrons, excitation, Stokes parameters, alignment and orientationPACS No. ; 34.80.DpI. IntroductionIhcie has been  n u m b e r  o f  th e o re tic a l in v e s tig a tio n s  to  s tu d y  resonance ex c ita tio n  in p o ta s s iu m  b y  im p ac t o f  e le c tro n s  *1 These h a v e  in c lu d e d  d is to r te d  w a v e  m e th o d s  an d  close coupling c a lc u la tio n s . D u e  to  lim ited  a v a ila b ility  o f  cspcrimcntal d a ta  th e  m e th o d s  seem  to  w o rk  su cce ss fu lly  only in certa in  e n e rg y  ra n g e  as d e m o n s tra te d  by  S to ck m an  <' i'/ [4] th ro u g h  th e  c o m p a r iso n  o f  th e ir  m e a su re m e n ts  on  potassium fo r S to k e s  p a ra m e te rs  a t th e  e le c tro n  e n e rg ie s  o f  10 and 54.4 eV .Very recen tly  S to c k m a n  e t  a !  f5 ] h a v e  th e re fo re  ex ten d e d  ilieir experim ental s tu d y  in th e  w id e  en e rg y  ran g e  u p  to  1 0 0  for certa in  e le c tro n  sc a tte r in g  a n g le s  in  o rd e r  to  p ro v id e  testing o f  th e  s u i t a b i l i t y  o f  d i f f e r e n t  t h e o r e t i c a l  approximations fo r  th e  re s o n a n c e  e x c ita tio n  in p o tass iu m . They m easured a n g u la r  d e p e n d e n c e  o f  th e  S to k e s  p a ra m e te rs  and alignm ent a n d  o r ie n ta tio n  p a ra m e te rs  fo r  th e  4  s ta te  tn potassium u s in g  su p e re ia s tic  te c h n iq u e . In  th e ir  e x p e rim en t ® collimated b e a m  o f  p o ta s s iu m  a to m s  in te rsec ts  a  b eam  o f  electrons in th e  s c a t te r in g  p la n e , w h ic h  is d e f in e d  b y  th e  'icident and  s c a tte re d  e le c tro n  m o m e n tu m  d ire c tio n s . T h e  vertically d ire c te d  la s e r  b e a m  o f  w a v e le n g th  766 .701  nm  crosses the a to m  a n d  e le c tro n  b e a m s  n o rm a l to  th e  sca tte r in g  P*®ne. The la se r  ra d ia tio n  e x c ite s  th e  p o ta ss iu m  a to m s from  ground 4  ^5  s ta te  to  th e  4  s ta te  h a v in g  ex c ita tio nen e rg y  eq u a l to  1.6  eV . T h o se  e lec tro n s  th a t g a in  1 .6  eV  in e n e rg y , th e  su p ere ia s tic  e lec tro n s , in th e  co llis io n  w ith  th e  ex c ited  a to m s, a re  d e te c te d  a t se lec ted  s c a tte r in g  an g le s  fo r s ix  d if fe re n t la s e r  p o la r iz a t io n  s ta te s . T h e  in te n s i ty  o f  su p e re ia s tic  e le c tro n s  d e tec ted  a t each  s c a tte r in g  a n g le  an d  th e  p o la r iz a tio n  o f  th e  d ecay  f lu o re scen ce  a n a ly z e d  in  th e  sca tte r in g  p lan e  is u sed  to  d e te rm in e  th e  re d u c e d  S to k es  param eters  [6 ,7]. T hus such  m easu rem en ts  p ro v id e  a  co m p le te  s e t  o f  th e  fo u r  sp in  a v e ra g e d  p a ra m e te r s  w h ic h  fu lly  ch a rac te riz e  th e  e le c tro n  im p ac t ex c ita tio n  o f  th e  4  ^iS-4 tran s itio n .In th e  ligh t o f  th e  e x p e rim e n t o f  S to ck m an  e t  a l  [5 ] w e  h av e  ca rr ied  o u t d is to rted  w av e  a p p ro x im a tio n  ca lc u la tio n s  fo r  e le c tro n  im p ac t ex c ita tio n  o f  th e  4  ^5^-4 ^P  tra n s itio n  in p o tass iu m  an d  p re sen t c o m p a riso n  o f  o u r  re su lts  w ith  th e  e x p e rim e n t fo r  th e  red u c e d  S to k es  p a ra m e te rs  a n d  a lig n m e n t an d  o rien ta tio n  p a ram e te rs . In o rd e r  to  b e  b rie f , h e re , w e  o u tlin e  th e  th eo re tic a l co n s id e ra tio n s  an d  re p o r t o u r  Selected  re su lts  o n ly . T h e  e x te n s iv e  p re se n ta tio n  w ith  fu ll d e ta ils  w ill b e  g iv en  in o u r  la te r  p u b lic a tio n .2. Theoretical considerations2.1. D is to r te d  w a v e  th e o ry  :W e tre a t th e  p o ta ss iu m  a to m  a s  o n e  e le c tro n  sy s te m  a n d  c o n s id e r  th e  d e c tr o n  im p a c t 4  ^S -A  ^P  e x c ita tio n  as d u e  to0 2 0 0 2  lA C S520 Rajesh Srivastava and Sachin Saxenae x c ita tio n  o f  th e  v a le n c e  4 ;  e le c tro n  to  th e  Ap  o rb ita l. In  th is  p ro c e s s  e f fe c t o f  c o re  e le c tro n  is tak en  th ro u g h  th e  c o re  p o te n tia l . T ra n s itio n  m a tr ic e s  fo r  e le c tro n  im p ac t ex c ita tio n  o f  p o ta s s iu m  fro m  in itia l s ta te  ( 0  to  a  fin a l s ta te  ( /) , fo r  th e  s in g le t (s )  a n d  tr ip le t ( /)  m o d es  can  b e  w ritte n  a s*iJM ~  ^  UJK4‘iJM i^JKf(s in g le t m o d e ) ( 1)( tr ip le t m o d e )  (2 )w h e re  7 ^  a n d  a re  th e  sp in  a v e ra g e d  d ire c t  a n d  e x c h a n g e  m a tr ic e s  in d is to r te d  w a v e  ap p ro x im a tio n . M  = 0 ,  ±  1 re fe rs  to  th e  m a g n e tic  c o m p o n e n ts  o f  th e  e x c ite d  4  s ta te . T h ese  c an  b e  fu r th e r  w ritten  as(3)a n d  T ^ = { F - { k j , r i ] ^ j ^ ( r , ) \ V - U f { r , ) \(4)w h e re  V  is th e  to ta l in te rac tio n  p o te n tia l b e tw e e n  th e  ta rg e t p o ta s s iu m  a to m  a n d  th e  p ro je c ti le  e le c tro n  a n d  can  b e  e x p re ssed  asr  =  - ± + _ Ln  U - ,r +  F '" ® ( ;^ ) (5)(6 )H ere  is  th e  d is to r tio n  p o te n tia l fo r  th e  in itia l ( f in a l)  c h an n e l a n d  c h o se n  asTJ ^ . ^exch C7)where is the sta tic po ten tia l in  the in itia l (fin a l) channel and is obtained from  the in itia l (fin a l) state o f the potassium  atom(8 )T lie  fo llo w in g  e x p re s s io n  fo r  e x c h a n g e  p o te n tia l inth e  in itia l ( f in a l)  c h a n n e l is ta k e n  [8 ]i/exch _  J .  J f  J .  1.2 _  K**** 1  —f f  JL _l^**** 1” 2 \ U  j  [ U- 8 otA ( / ) ] ' ^ |  (9 )Pi(^ is spherica lly averaged charged density o f the potassi atom  in the in itia l ( fin a l) channel and r  is taken -t-] and respective ly fo r s ing le t and trip le t modes [9 ],The sca tte ring  a m p litude  am  is  re la ted to the i  tran s ition  m a trix  through the fo llo w in g  re lationw h e re  r j  a n d  rz  a re  re sp e c tiv e ly  th e  p o sitio n  co -o rd in a te s  o f  th e  ta rg e t an d  p ro je c ti le  e le c tro n s  w ith  re sp e c t to  th e  ta rg e t n u c leu s . T h e  co re  p o te n tia l o f  th e  p o ta ss iu m  a to m  is tak en  as d e fin e d  in re fe re n c e  [ 1 ].in itia l (f in a l) ch an n e l p ro jec tile  e lec tron  d is to r te d  w av e  w ith  th e  w a v e  v e c to r  kup  an d  sa tis f ie s  th e  fo llo w in g  d if fe re n tia l e q u a tio nF in a lly , th e  sp in -a v e ra g e d  a m p litu d e  is gjb y{ ^ K f  .< ** /)=  2 (2 S ,  + 1 1  S ^ 2 5  +  l ) f lJ / .a J ^w h e re  5 , is th e  a to m ic  sp in  in  th e  in itia l s ta te  and S  is to ta l sp in  o f  th e  sy s tem  i.e . S  = 0  fo r  s ing le t mode S’ =  I fo r  tr ip le t m o d e .2.2 . S to k e s  p a r a m e te r s  a n d  a l ig n m e n t  a n d  oriental p a ra m e te r s  :F u rth e r , th e  p o la r iz a t io n  o f  th e  l ig h t e m itte d  from d e c a y  o f  th e  e x c ite d  4  s ta te  in a  p a rticu la r direc c a n  b e  c o m p le te ly  d e s c r ib e d  b y  th e  fo l lo w in g  Sto p a ram e te rsP, / ( 0 ° ) - / ( 9 0 ° )/ ( 0 ‘’ )  + /(9 0 “ )P - 7 f 4 5 ° ) - ; ( 1 3 5 ° ) ^ / ( O - j  +  f f lS S * )^  / ( R H C ) - / ( L H C ) ^ / ( R H C )  +  / ( L H C )w h e re  / ( ^ )  is  th e  in te n s i ty  o f  l ig h t  w ith  polarizai v e c to r  in th e  ^  d ire c tio n  w ith  re sp e c t to  in c id en t eleci d ire c tio n  a n d  /(R H C )  a n d  /(L H C )  a re  re sp ec tiv e ly  in ten s itie s  o f  th e  r ig h t an d  le ft c irc u la r ly  po larized  I c o m p o n e n ts .T h ese  S to k es  p a ra m e te r  P x -P z  c an  b e  re la ted  to e x c ita tio n  am p litu d e s  th ro u g h  th e  fo llo w in g  re la tio n , say th e  d e c a y  L  - *  L j= j - j ’ ‘ nj y \ L  L LzJi ^ J j G 2 ( L ) ( r ( L ) ^ } - G 2 ( L ) ( r ( L ) ^ 2 }i  ^ } [ 2 G . ( ^ ) { n i ) 5 i > ]=  1  ^ } [ 2 f G i ( i ) { r ( i ) r i > ]Superelcatic electron scattering from potassium atoms 521j 9 2 j ^ { T ( L r ^ )  + G ,{ L ) { T ( L ) )  ( ,g )The depolarization coeffic ien t G k(L )  can be w ritten asGAr(^) =  ( 2 5 + i ) Z ^ ^ ‘^ '^ * ^ ^ { 7  L ^ :}  0 ^ )|,?is the electronic spin  and J  =  I  +  5  is the  total angular [jfthc atom. The GifJL) are norm alized  such that G o(I) = 1 for all value o f  i .  { T ( L ) k q )  is the state m ultipolcs o f  the lexcited state w ith angu lar m om entum  L  are related  to  the omplex scattering am plitude as( n D h ) -" { m ' - m(2 0 ).0 describe the alignm ent and orientation o f  the charge l^oud of the excitation 4 state o f  potassium , w e use the indcrsen param eters [10] w hich are related  to the Stokes irameters by the fo llow ing relationsy = ^ a r g ( /* i+ / f ’2 ) (21 )(2 2 )L i = - P i (23)P* = +  P ^  +  P ^ (24)perfect over all agreem ent w ith the experim ent. For ^  param eters, ou r both the calculations are in satisfactory agreem ent fo r energies above 30 eV  o f  energy, although the nature observed for the experim ental data is reproduced. Finally, f o | param eter, both the calculations are in goodElectron energy (cV)Figure 1* The reduced Stokes parameters P\> A and h  Tor electron impact 4 S^-A excitation in potassium at a fixed scattering angle of 45 degree. The electron energy refers to the energy of the superelastic electrons. Solid circles arc experimental data from Stockman et al [5]. The dashed and solid lines respectively arc our DWE and DW calculations.1-P 3 are the reduced S tokes param eters w hich m ay be btained by using the sam e relations (eqs.15 -17) as for |^ »easured Stokes param eters P\ - /^3 bu t w ith all Gj({L)\3ktx\ s unity.Results an d  d iscussionJtockman et a l  [5] m easured  the reduced Stokes param eters electron scattering  angles o f  45, 60 and 90 degrees, ‘spectively. T he energy  o f  the incident electrons w as up to eV, which corresponds to  1 0 0  eV  fo rthesupere lastica ly  ‘^ ered electrons. In Figure I , we com pare their experim ental i for reduced Stokes param eters a t 45 degree o f  scattering ‘ with our d istorted  w ave calculations. In order to  sec effect o f  e lec tron  exchange effec t in the d isto rtion  l^ential we p resen t ou r tw o types o f  calculations l e .  with ^change potential (D W E ) and witiiout (DW ). From the figure, ‘ find that fo r ^  param eter, the D W E results are in theFigure 2. The reduced Stokes parameurs K  h  and h  for electron impact 4 5^ -4  excitation in potassium for superelastic electron energy of 80 cV. The captions arc as in Figure 1.522 Rajesh Srivastava and Sachin Saxenaagreement with experiment. We also observe as expected that the DWE calculations can be said to be better than the DW. Results at odier scattering angles are not compared and discussed in this paper.As an additional study Stockman e t a l [5] also measured the angular dependence of the Stokes parameters at an incident electron energy of 78.4 eV i.e. superelastic electron energy of 80 eV. We compare in Figures 2 and 3, their experimental results for reduced Stokes parameters J\, Pj,Scattering angle (deg)F igure 3. The Pi, y  (degrees) and P* parameters for the electron impact excited 4 '^ P state o f potassium for superelastic electron energy o f 80 eV. The captions are as in Figure I.P^  and a lignm ent and orien ta tion  param eters {viz. y,P^  on ly , as L j ^ = - P ^ )  w ith  ou r d istorted wave calculation, W e fin d  th a t o u r D W E  c a lc u la tio n s  reproduce th experim ental results exce llen tly . Bem g h igh energy the DW] and D W  calcu la tions are also very close,4. C onclusionThe present study suggests that D W  theory can describ the 4 ^S-A ^P excita tion  in potassium  atom  fo r a wide rant o f incident electron energies as it  sa tis fac to rily  reproduu the recent experim ental results.Acknow ledgm entThe authors are thankfu l to  BR NS, Departm ent o f Aionn Energy, fo r the finan c ia l assistance to  th is  w ork.R eferen ces(I J S Venna and R Srivastava J  Phys B28 4823 (1W5)(21 J Mitroy J. Phys. B26 2201 (1993)[3J V Zeman, R P McEachran and A D Stauffer F.nr Phrs 1)1! (1998)|4 ] K A Stockman, V Karaganov, I Bray and P J O fciibncrj iv.i B3I L867 (1998)[5] K A Stockman, V Karaganov, I Bray and P J O Teubm-t J Ph B34 (2001) (In pre$.s) [private communication)[6] P M Farrell, W R McGillivary and M C Standaga/Vma A44 1828 (1991)[7] X K Mcng, W R McGillivary adm M C Standage Phys R a V 1767 (1992)[8] J B Furness and 1 F, McCarthy J. Phys. B . At Mol Phys (i 22i (1973)[9] S Vucic, R M Potvlige and C J Joachain J. Phys B20 3i' (1987)(10] N Anderson, J W Gallagher and 1 V Hartel Phys Rep K>.^(1994)

Superelastic Electron Scattering from Potassium Atoms

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Superelastic Electron Scattering from Potassium Atoms

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