Conversion processes in light nuclei with transition energies above the e+, e- pair creation threshold are investigated within an analytical framework. In particular, we evaluate the ratio of electron transition probabilities from the negative energy continuum into the atomic K shell and into the positive energy continuum, respectively. The possible role of monoenergetic positron conversion with respect to the striking peak structures observed in e+ spectra from very heavy collision systems is examined

Greiner, Walter

Schlüter, Paul

Soff, Gerhard

English

Hochschulschriftenserver - Universität Frankfurt am Main

PHYSICAL REVIEW C  VOLUME 33, NUMBER 5  MAY 1986 Monoenergetic positron conversion in heavy ion fragments Paul Schlüter and Gerhard Soff Gesellschaft für  Schwerionenforschung,  Darrnstadr,  Germany Walter Greiner Institur für  Theoretische Physik, Johann  Wolfgang  Goethe-Universität, Frankfurt  am Main, Germany (Received 20 December 1985) Conversion processes in light nuclei with transition energies above the e+,  e-  pair creation threshold  are investigated within an analytical framework.  In particular, we evaluate the ratio of electron transition prob- abilities from the negative energy continuum  into the atomic K  shell and into the positive  energy continu- um, respectively.  The possible  role of monoenergetic positron conversion with respect  to the striking peak structures observed in  e+ spectra from very heavy collision Systems is examined. At  present,  the  positron  emission  in  elastic  and  deep- inelastic  collisions  of  very  heavy  ions  is  the  subject  of widespread  experimental  activities.'-'  Narrow  peak  struc- tures at a  kinetic  positron  energy  of  about  E + = 300  keV were  ob~erved'-~  at projectile  energies close  to the nuclear Coulomb  barrier.  Currently  there  exists  no  convincing theoretical  explanation of these puzzling cusps which repro- duces all  experimental  facts.  Conversion  processes  in  the projectile  and  target  nuclei  as  a  possible  source  of  the detected monochrornatic positrons could be ruled out exper- imentally  by  direct  measurements of the associated photon and 6-electron spectra as well as by  a line-shape analysis. In this note we study the hypothesis that a neck links the projectile  and  target  nucleus  at  the distance  of  closest  ap- proach.  In  the Course  of  Separation  a  light  ion  fragment could  be  formed  with  an excitation  energy  above the pair production threshold.  This Situation is illustrated in Fig. 1. The nuclear transition may occur by  transferring the ener- gy  to  an electron  in  the negative  energy continuum,  thus yielding  a positron.  The final state of the electron could be a  vacant  bound  state,  preferably  the K  shell, or a  positive energy  continuum  state.  The  first  of  these  conversion processes  is  associated  with  monoenergetic  positron  emis- sion.  As an example, the ratio of  the probabilities of these two different transition modes is calculated assuming a tran- sition energy of w = 2.6mec2  in a beryllium nucleus (Z  =4). The  multipolarities  EO,  El, E2, MI, and  M2 are  con- sidered.  The theoretical ingredients concerning internal pair formation  are presented  in  Refs. 8 and 9 and need not be repeated  here.  We  calculated  the  differential  conversion coefficient  dßldE for  internal  e+,e-  pair  creation  with respect to the kinetic positron energy E, which is defined by Pe +.e -  is  the probability  for  electron-positron  pair  forma- tion.  P,  denotes the photon  emission probability in  a nu- FIG.  1.  Schematic representation of  the formation of a light  ion fragment in  the neck connecting two heavy deformed nuclei. clear  transition  of  multipolarity  EL  or  ML  (L  5: 1) and transition  energy  W.  In  the  following,  Pe-  signifies  the complementary  probability  for ionizing  a  1s electron.  The corresponding  quantity  for  nuclear  E0 transitions  will  be denoted  by  dq/dE.  In  this case  Single  photon emission  is strictly forbidden. Neglecting  nuclear  size corrections and nuclear  penetration effects, one may deriveiO  in the limit Za4 0 an elementary analytical  expression  for  the  positron  spectrum  resulting from electric monopole transitions (E =  C =  mm,  = 1  ), -r,  pp'(EE1- 1) dE  2r(za)'Jo(w  +2)312 ' Here E and E' denote the energies of the positron and elec- tron  (E  +E' =  o  ), whereas p and p'  denote the correspond- ing  momenta.  The  integration  over  positron  energies  E yields with the abbreviation denotes the ratio of  the probability  for exciting a nega- tive  energy continuurn  electron  to a  vacant K  shell to  the probability  for ionizing an electron out of a completely occu- pied K shell to the positive-energy continuurn.  We obtain,I0 in the limit Za4 0,  the simple result qj;)=x312  , independent of Z.  For w = 2.6 and Z =  4 this leads to In  consequence,  monoenergetic  positron  E0 conversion  is 33  1816  -  @ 1986 The American Physical Society BRIEF REPORTS  1817 FIG. 2.  Differential conversion coefficient  dT/dE  in  l/keV for an electric  monopole transition  in  beryllium with  w = 1329 keV  vs the kinetic positron energy in keV.  Solid line:  Analytical result derived in the limit Za -  0.  Dashed line:  Numerical result employing rela- tivistic Coulomb wave functions. strongly suppressed in  light  nuclei,  which  is reflected in  the factor  (Za  )-3.  In completely  stripped  low-Z ions, nuclear E0  transitions predominantly  occur  via  electron  transitions to  the  positive-energy  continuum  leading  to  a  continuous e+ spectrum.  In  principle,  two-photon  emission is  also al- lowed.  The positron  distribution drl/dE  is displayed in  Fig. 2.  A broad and flat spectrum  (solid line) is obtained, being FlG. 3.  Differential  conversion  coefficient  dßldE in  l/keV for electric  dipole  transitions  in  beryllium  with  w= 1329  keV  vs  the kinetic positron energy in keV.  Solid line:  Analytical result derived within  the  Born  approximation  (Z  = 0). Dashed  line:  Result  em- ploying relativistic Coulomb wave functions. TABLE I.  Total conversion coefficients ß and a( '  )  for w = 1329 keV  in  beryllium  and  various  multipolarities.  Asymptotic  expres- sions  valid  for  Zu- 0  are  used  in  the  computations.  (XE  -n denotes X x 10-"). E 1  E 2  M 1  M 2 ß  1.42E  -4  3.47E  -5  2.348-5  6.39E  -6 a(  +  I  8.69E-8  2.16E-8  1.558-8  3.58E-9 u(-I  2.416-7  4.588  -7  3.286-7  5.81E-7 typical  for  results  derived  within  the  Born  approximation (Z  =0).  For  the  integrated  conversion  ratios  it  follows 2  87 and T,!:'  2  0.047. For comparison,  the dashed line shows the calculated  positron  spectrum employing relativis- tic electron wave functions for the Coulomb potential of an extended  nucleus.  Small  Coulomb  distortion  effects  are visible. Now we turn the discussion to nuclear  EL  and ML  transi- tions  with  L L  1.  In  contrast  to  electric  monopole transi- tions,  here  single  photon  emission  evidently  represents  a competing  process.  The  ratio  of  the  electron  transition probability  from  the negative-energy  continuum  into  a va- Cant  K shell and the photon  emission probability  P,  will  be denoted  by  a"'.  Similarly,  the  quantity  a'-'  determines the ordinary K -shell conversion from the completely  occu- pied  bound  state to the positive-energy  continuum.  Thus, a"'  is  correlated  with  monoenergetic  positron  production, whereas a'-' corresponds to monoenergetic  electron emis- sion.  Again, in the limit Za4 0,  we can deduce the handy expressions a'-'(ML  )  as  well  as  a'-'(EL  ),  for  the  limiting  cases w-  0 and w -  W, agree with the results of Ref. 11. Considering  continuum-continuum  transitions,  we  eval- uated  the positron  spectrum  dßldE resulting  from  electric dipole transitions.  In Fig.  3  we compare the outcome (solid line)  of  Born  approximation  calculations  (Z  = 0)  with  nu- merical  data, employing Coulomb  wave  functions  (dashed line).9  Again, both distributions are very similar and exhibit no striking structures.  Table I provides the total conversion coefficients  ß  and  U.(  ' for  various  multipolarities.  Here the absolute positron production probabilities are suppressed by  about  four  orders of  magnitude  compared  with  the al- lowed  photon  emission  probability.  The  monoenergetic e+-production  mode  is  additionally  suppressed  by  about three orders of magnitude.  Consequently, there should be a strongly  enhanced  photon  peak  associated  with  a  possible line structure in the positron distribution. Based  on  these  intensity  arguments,  we  may  conclude that the pronounced  e+-peak structure detected in collisions of  very  heavy ions most likely  is not correlated  with mono- energetic positron conversion in light ion fragments. We  are  grateful  for  enlightening  discussions  with H. Backe,  who brought the idea concerning the investigated conversion mode to our attention. 1818  BRIEF REPORTS  -  33 'E.  Berdermann.  F.  Bosch,  M. Clemente, F. Güttner,  P.  Kienle, W.  Koenig,  C. Kozhuharov,  B.  Martin,  B.  Povh,  H. Tsertos, W.  Wagner,  and  Th.  Walcher,  Gesellschaft  für  Schwerionen- forschung,  Darmstadt,  Report  No.  GSI-81-2,  ISSN  0174-0814, 1980, P. 128. lM. Clemente, E.  Berdermann,  P. Kienle,  H. Tsertos, W. Wagner, C. Kozhuharov,  F. Bosch, and W. Koenig,  Phys.  Lett. 137B,  41 (1984). 'H.  Tsertos,  E.  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Monoenergetic positron conversion in heavy ion fragments

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