Parity mixing of electron states should be extremely strong for heliumlike uranium. We calculate its size and discuss whether it could be determined experimentally. We analyze one specific scheme for such an experiment. The required laser intensities for two-photon spectroscopy of the 23P0–2 1S0level splitting is of the order of 1017 W/cm2. A determination of parity mixing would require at least 1021 W/cm2

Greiner, Walter

Indelicato, Paul

Müller, Berndt

Schäfer, Andreas

Soff, Gerhard

English

Hochschulschriftenserver - Universität Frankfurt am Main

PHYSICAL REVIEW A  VOLUME 40, NUMBER 12  DECEMBER 15, 1989 Prospects for an atomic parity-violation experiment in ugDf A. Schäfer* and G. Soff Gesellschaft für Schwerionenforschung, Postfach 11 05  52, 6100 Darmstadt, West Germany P. Indelicato National Institute of Standards and Technology, Gaithersburg, Maryland 20899 and Laboratoire de  Physique Atomique et Nucleaire, Tour 12-22 Troisfeme  Etage, Universite Pierre et Marie Curie, 4 place Jussieu, F- 75252 Paris CEDEX 05, France B. Müller and W. Greiner Institut für Theoretische Physik, Postfach 11 1932, 6000 Frunkfurt, West Germany (Received 30 May 1989) Parity mixing of electron states should be extremely strong for heliumlike uranium.  We calculate its size and discuss whether it could be determined experimentally. We analyze one specific scheme for  such  an  experiment.  The  required  laser  intensities  for  two-photon  spectroscopy  of  the 2 3~o-2  's,  level splitting is of  the order of  10"  W/cm2.  A determination of  parity mixing would require at least 10''  W/cm2. One of the most important tests of the standard model of particle physics is the measurement of parity-violating effects in atoms.  The highest experimental and theoreti- cal precision has now been reached for cesi~m'~~  and al- lows one to test radiative corrections to the Weinberg an- gle.  (Other Systems under investigation are, e.g., thalli- um and bismuth.)  Due to the parity-violating exchange of Z bosons, every electron state has a small admixture of a wave  function with  opposite parity, e.g., an sl,,  state has  a  small  P,,, component  giving  the  M1  transition in cesium, an E1 admixture.  Due to the ex- tremely small size of this component the influence of the parity-violating  transition  amplitude  can  only  be  ob- served on a large collection of atoms, by studying the re- fractive properties of the vapor. The size of parity mixing depends on two factors:  (1) the overlap of  the electron wave functions with  the nu- clear charge distribution and (2)  the energy difference be- tween  adjacent  states  of  opposite  parity.  Heliumlike uranium is a very interesting system because the nuclear overlap of  the electron wave  functions is  large and two states of opposite parity but identical total spin happen to be almost degenerate, namely, 3~0(  ls,  2p  1 and 'so(  ls,  2s ), which are separated by about 1 eV out of a total binding energy  of  165  ke~.~  An  experiment  using  u9''  has, however, to differ  in many respects from an experiment using  cesium.  Heliumlike uranium  is  only  available  in ion beams, and thus the experiment requires techniques of beam-foil spectroscopy.  The 2 3~0  state is metastable, but still decays with a lifetime of about  10"  s, which is just long enough to extract the beam.  Figure 1 shows the level  scheme of  u9'+.  With new  accelerators presently under construction, a production of  a beam of  107/s of monoenergetic u90f ions in the 3~o  state appears to be possible in the near future. Precision  experiments  can  be  done best  with  optical photons.  Thus a parity experiment in u9'+  has to focus on the transition 2 3~o-2  'so, which is an EI-M1 transi- tion with a small, parity-violating 2E1 component.  Our idea is to try to induce this two-photon transition with an intense la~er.~  The different  two-photon  transitions  re- quire photons with different polarizations.  For an EI-M1 transition  the two  photons  are polarized  orthogonally, while  for 2E1 and 2M1 transitions both have the Same polarization.  Thus by  using  polarized  light  the rate of 2E1  transitions  could  be  extracted  from  the  measure- ments.  If both photons come from the Same laser beam, the EI-M1 transition rate is actually Zero for a 0--0+ transition  because,  first,  within  the coherence  time  all photons  have  the  same  polarization  and,  second,  the relevant  matrix  element  is  proportional  to (k,  -  k,).(~~  Xe2)  where k„k,  and E~,E,  are the momen- tum and polarization  vectors of  the two photons,  such that it vanishes for kl=k2. If  a transition  occurs, the 'so  state decays nearly  in- stantaneously  to  the  ground  state,  emitting  two  high- FIG. 1.  Level structure of u90f  according to Ref. 4. 7362  @ 1989 The American Physical Society BRIEF REPORTS  7363 /I  Y  detector 11  Y  detector FIG. 2.  Schematic view of the proposed experiment. energy  photons with  a  combined  energy of  about  96.3 keV, which can be used  for detection.  Figure 2 shows a schematic view of the proposed experiment.  The crucial question is whether the stimulation of such a two-photon transition is at all feasible with presently available lasers. The calculation of the required laser intensity is the pur- Pose of this work. To analyze the prospects for the proposed experiment, the first number we need is the size of the parity admix- ture 7, which should be given  to very  good approxima- tion in first-order perturbation theory by We  have  calculated  7  using  a  relativistic  multi- configuration Hartree-Fock (MCHF)  Computer program6 developed  by  Desclaux  following  a  method  derived  in Refs. 7 and 8.  Table I shows the results we obtained for the binding energies.  The results  agree quite well  with those obtained by Drake with a completely different tech- nique.  The corresponding energies for thorium are also given.  The uncertainties for the energy difference AE be- tween the 3~o  and 's,  states are comparable to its value. To  illustrate this point let us note that already the uncer- tainty  of  the uranium nuclear radius leads to uncertain- ties of the order 0.5 eV for AE.  We have used the extra- polated value given in Ref. 10.  Using, e.g., the value re- cently  derived  by  de Vries,  de  Jager,  and  de ~ries" changes AE by  +0.37  eV. - The value of AE is crucial for our scheme.  If it would turn out to be, e.g., 2 eV, an optical laser could be used. (The photon  energy  w  has to be  AE/2.  Note that the Doppler effect  can be used  to adjust the laser frequency to the resonance frequency.) If the required photon ener- gy  would  be  substantially  smaller,  no  suitable  laser  is available.  If  it  would  be  much smaller, a  maser  would have to take the place of the laser.  We shall See, howev- er, that enormous intensities are required, which can only be achieved by strongly focusing a powerful laser.  Either uranium or thorium will  have a  AE  in the eV range so (23~,/(~F/2~~)(1-4sin28,-N/Z)p,,y,~2'~,)  that is not likely to be a problem. -  -  In principle, the energy difference could also be adjust- E(~~P,)-E(~  'so)  ed by  choosing an appropriate isotope.  It has recently (1)  been  shown that isotope-dependent nuclear polarization effects induce shifts of the order of  1 eV in inner-shell s G, is  Fermi's  constant,  8,  the Weinberg  angle, N  the  states in uranium. l2  It should, therefore, be possible to neutron number, Z the proton number, and p,,  the elec-  find  a  uranium (or thorium) isotope where the 3~o-1~o tric charge density (normalized to Z).  energy difference is about 1 eV.  It is, however, very ques- TABLE I.  Contributions to the binding energies (in eV) of the 'P,  and 'So  states.  Also cited are the results from Ref. 9. ~90  +  ~h~~+ Level  'so(  ls,2s)  'P,( ls,2p)  'So(  ls,2s)  'P0(  ls,2p) Coulomb energy  -  165 494.025  -  165 524.083  -  157 170.891  -  157 195.784 Magnetic energy  66.55 1  152.318  61.381  140.227 Retardation  4.945  -  10.043  4.524  -  9.492 Mass  polarization  0.000  -  0.04  1  0.000  -  0.040 Electric correlation  -0.528  -0.332  -  0.432  -0.319 Magnetic correlation  -0.615  -0.517  -0.590  -0.480 Self-energy  418.380  362.660  382.406  33 1.435 Self-energy screening correction  -4.280  -  1.018  -  3.903  -0.921 Vacuum  polarization first order  -  109.299  -  96.465  -96.539  -  85.224 Vacuum  polarization correction, higher order  4.466  4.021  3.823  3.440 Total  -  165 114.406  -  165 113.500  -  156 820.220  -  156817.158 7364  BRIEF REPORTS  40 tionable  whether sufficiently  strong beams  of  such iso- topes can be produced. Using the MCHF wave functions 7  turns out to be For AE=  1 eV this number is about six orders of magni- tude larger than for cesium. Let  us  next  calculate  the  laser  intensity  needed  to stimulate  the 2E1 transition.  Using  the lowest  MCHF wave  functions,  comprising  the  configurations  (ls,  2s 1, (ls,2p), ( ls,3s), ( ls,3p), and  ( ls, 3d), we  calculated  the 2E1 matrix  element  approximately.  Using  the notation of Ref.  13, the transition rate for two-photon absorption at resonance, assuming  that  the  width  of  the levels  is much larger than the energy spread of the photons, is where is  the  photon  density  and I is  the  laser  intensity  in w/cm2.  r is the total width of the initial and final state including the laser width.  It is dominated by the 'so  de- cay width.  Inserting the decay width from Ref. 4 and our MCHF wave functions we get for the transition rate for the parity-violating 2E1 transition Since the two-photon decay to the ground state from the 3~o  and 'so  states cannot be distinguished experimental- ly, the rate (5) must at least be comparable to the spon- taneous decay rate W? -  lO/ns  of the 3~o  state, requir- Po ing a laser intensity I of order 102' w/cm2. The strong- est  tabletop  lasers  available  today  reach  10'~-10'' w/cm2.  In view of the rapid development of laser tech- nology, however, the required intensity-optimally  com- bined with picosecond pulsing-does  not appear to be en- tirely utopian. To induce the normal EI-M1 transition one has to use two lasers or one has to split the laser beam and arrange for a  path  difference  of  the two beams larger than the coherence length.  The probability is substantially larger than for the 2E1 transition where we  have assumed that both laser beams have the intensity I and  come  from  nearly  opposite  directions. Therefore, using a strongly focused high-intensity laser, the EI-M1 transition could be used to measure the energy difference between  the 23~o  and 2 'so  level.  This is  a very interesting quantity in itself  because  it  furnishes a stringent  test  of  relativistic  few-body  theory.  Precise knowledge of this splitting is also essential for the calcu- lation of all parity violating effects in u90+. However, we are forced to conclude that the proposed experiment  to  measure  parity  violation  in  heliumlike uranium is not feasible with  present technology, even if no technical difficulties other than the principal ones dis- cussed here arise. Even so, it may be worthwhile to emphasize some in- teresting details. (i)  While the usual atomic P violation exveriments have enormous difficulties in avoiding fake effects due to stray electric  fields,  this  would  Pose  no  problem  for  our scheme.  The  parity  mixing  induced  by  a  background E.B  field is of the order With  E <<103  V/m  and  B <<10-~ T,  we  find 7'-  IO-'~/AE(~V)  <<T.  Thus background  fields are not a source of problems for this experiment. (ii) The ions have to be  fast to allow their  extraction within the lifetime of  the 3~0  state.  Furthermore, they have to be focused strongly as the large laser intensities are only obtained in a very small region of space, and one would like to bunch the ions in coincidence with the laser pulses.  All of these measures lead to uncertainties in the Doppler effect.  The counting rates decrease if the uncer- tainty  Ay.w  becomes  larger  than  the  transition  width r=5  X 10-~  eV.  For  w=0.5  eV,  this  is  the  case  for Ay > 0.01. We conclude that the measurement of parity violation in  the L  shell of  the u90'  ion by  means of  two-photon spectroscopy is not feasible with presently available tech- nology.  On the other hand, this  technique may  offer  a practical way to determine the energy difference between the 2 3~0  and 2 'so  states  in  heliumlike  uranium  with very high precision. We thank W. R. Johnson, J. P. Desclaux, and J. R. Reinhardt  for helpful  discussions.  Laboratoire de Phy- sique Atomique et Nucleaire is unite associee au Centre National de la Recherche Scientifique No. 771. '~resent  address:  Max-Planck-Institut  für  Kernphysik,  Post- fach 10 39 80, 6900 Heidelberg 1, West Germany. 'M.  L.  Noecker, B.  P.  Masterson, and  C. E. Wieman,  Phys. Rev. Lett. 61, 310 (1988). 2W. R. Johnson, S. A. Blundell, 2. W. Liu, and J. Sapirstein, Phys. Rev. A 37,  1395 (1988). 3W. J. Marciano and A. Sirlin, Phys. Rev. D 27, 552 (1983). 4~.  Gould, Nucl.  Instrum.  Methods  B  9,  658  (1985); Ch. T. Munger and H. Gould, Phys. Rev. Lett. 57, 2927 (1986). S~.  Schäfer, B.  Müller, W.  Greiner, and  G. Soff, Gesellschaft !E  BRIEF REPORTS  7365 für Schwerionenforschung,  Scientific Report No. 85-1, 1984, P.  224. 6J. P. Desclaux, Comput. Phys. Commun. 9, 31 (1975). '0.  Gorceix, P. Indelicato, and J. P. Desclaux, J. Phys. B 20, 639 (1987);  P. Indelicato, D. Gorceix, and J. P. Desclaux, ibid. 20, 651 (1987). 8~.  Indelicato, Nucl. Instrum. Methods B 31, 14 (1988). 9G. W. F. Drake, Can. J. Phys. 66, 586 (1988). 1°W.  R. Johnson and G. Soff, At. Data Nucl. Data Tables 33, 405 (1985). "H. de Vries, C. W. de Jager, and C. de Vries, At. Data Nucl. Data Tables 36, 495 (1987). '*G. Plunien, B. Müller, W. Greiner, and G. Soff, Phys. Rev. A 39, 5428 (1989). 13~.  Achieser and W. Berestezki, Quantenelektrodynamik WEB Deutscher Verlag den Wissenschaften, Leipzig, 1962). 

Prospects for an atomic parity-violation experiment in U90+

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