Batra, K

Kundliya, R

Mohan, Man

IACS Institutional Repository

1 W -  5 6 3 - 5 6 4  ( 2 0 0 2 )U P  Ban international journalT w o - p h o t o n  i o n i z a t i o n  u s i n g  p s e u d o s | i t e  s u m m a t i o n  t e c h n i q u eR  K u n d liy a , K  B a tra  an d  Ma(j M o h anDepartroant of Physics and Astrophysics, University  ^Delhi, Delhi-110 007, India E-mail : rkundliya@physics.d|.ac inAbstract : Accurate and powerful pseudostate summation technique has been used to study two-photon ionization of an atom. Results arc obtained for the two-photon ionization o f hydrogen from the ground state and the variation « f  ionization cross section on the trequency o f incident radiation is shown for both linearly and circularly polarised light.Keywords : Ionisation, pseudostateFACS No. : 32.80.RmWith the av a ilab ility  o f  w e ll d e fin e d  p o w e rfu l la s e r  so u rce s  and the recen t p ro g re ss  in th e  p h o to e le c tro n  sp e c tro sc o p y  it ha.s now  b e c o m e  p o s s ib le  to  o b s e rv e  e x p e r im e n ta lly  multiphoton io n iz a tio n  p ro c e s se s  d u r in g  th e  in te rac tio n  o f  strong e lec tro m ag n e tic  f ie ld s  w ith  a to m s. In  g en era l th e  transition p ro b a b ilitie s  a re  c o m p u te d  on  th e  b a s is  o f  A^-th order tim e-dependen t p e rtu rb a tio n  th eo ry . T h e  m a in  d ifficu lty  encountered in th e  c o m p u ta tio n  o f  tra n s itio n  am p litu d e s  o f  order N ^  2 , c o m e s  fro m  d ie  p re se n c e  o f  in f in ite  su m s extended to  th e  w h o le  a to m ic  sp ec tru m .Different a p p ro a c h e s  w e re  u se d  in  o rd e r  to  so lv e  th e  oroblem. B ebb  a n d  G o ld  [1 ] in tro d u c e d  an  a v e ra g e  fre q u en cy  ^ related to  th e  re a l e n e rg y  sp e c tru m  o f  th e  a to m  th e re b y  ^placing the  in f in ite  su m m a tio n  b y  an  a v e ra g e  te rm  an d  Jsmg closure p ro p e r ty  o f  th e  w a v e  fu n c tio n s  to  re m o v e  th e  niermediate-state tr a n s it io n s  fro m  th e  p ro b le m . G o n tie r  an d  Irahin [2 ] re la ted  d ie  in f in ite  su m m a tio n s  to  th e  n u m e ric a l ■olutions o f  a  s e t  o f  f irs t  o rd e r  d if fe re n tia l eq u a tio n s .Over the  la s t fe w  y e a rs , th e re  h a s  b e e n  c o n s id e rab le  ■'terest to  d ev e lo p  a lte rn a te  tq ip ro ach es  to  d io s e  in d ica ted  '®re. In th is  p a p er, w e  s h a l l p re s e n t c a lc u la tio n s  fo r  th e  |"* 'iiphoton io n i z a t i o n  o f  h y d r o g e n  w h ic h  in v o lv e s  •^•nation o f  su m m a tio n  o v e r  in te rm e d ia te  s ta te s . W e  h av e  ‘placed th e  in te rm e d ia te  s t t t e s  b y  a  f in ite  se t o f  p se u d o ­sta te s  w h ich  a re  ex p an d ed  in te rm s o f  a  b as is  w h ich  is d isc re te  and  co m p le te . T h e  m a in  a d v a n ta g e  o f  th e  m e th o d  is th a t it rep laces  th e  in fin ite  su m m atio n  o v e r  th e  in te n n ed ia te  sta tes  by  a fin ite  sum  o v e r th e  p se u d o  sta te s .W e inves tiga te  tw o -p h o to n  ion iza tion  o f  a to m ic  h y d ro g en  in th e  g ro u n d  sta te . T h e  p se u d o s ta te  m e th o d  b e g in s  w ith  th e  ch o ic e  o f  N  b asis  fu n c tio n s  w h ic h  a re  o f  th e  s im p le  formw here  a  = basis  p a ram e te r;/  =  an g u la r  m o m en tu m ;N  >= size  o f  basis.W e d iag o n a liz e  th e  ta rg e t H am ilto n ian  in th is  b a s is  an d  o b ta in  N  p s e u d o s ta te sT h e  p seu d o s ta te s  hav e  th e  n o rm a liza tio n  =a n d  th e  c o r ro s p o n d in g  p s c u d o s ta te  e n e rg ie s  a re  g iv e nb yT h ese  p se u d o s ta te s  a re  ta k e n  a s  th e  in te rm ed ia te  s ta te s  fo r th e  e v a lu a tio n  o f  th e  tran s itio n  am p litu d es . O u r  re su lts  fo r© 2 0 0 2 I A C S564 R Kundliya, K Batra and Man Mohanthe two-photon ionization cross sections of //(IS) are shown in Figure 1. Curves are shown for both linearly and circularlyFigure 1. Two photon ionization rates from the hydrogenic ground state : Series 1 ; liner polarisation; Series 2 ' circular polarisation.polarised light. As shown in the curves a resonance enhancement of several orders of magnitude is obtained when the frequency of incident photons corresponds to one of the intermediate states.AcknowledgmentsWe are thankful to Prof. A T Stelbovics and Prof, A K Bhatia for their useful discussions about programmes MM is thankful to UGC, DST and CSIR, India for financial help.References[I ] B H Bcbb and A Gold Phys. Rev, A43 l(~24) (1966)[2] Y Gonticr and M Trahin Phys. Rev. Ml 83(*-7) (j%8)[3] G Laplanchc, A Durricu, Y Flank, M Jaouen and A Kathman J Phys. B9 1263 (1976)[4] W Zemik Phys. Rev 135 A51 (1964)[5J W Zernik and R W Klopfenstcin J. Math Phys 6 262 (!%<i

Two-photon Ionization using Pseudostate Summation Technique

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Two-photon Ionization using Pseudostate Summation Technique

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