This paper reports calculations of the influence of a reaction time T>10-21 s in deep-inelastic Xe-Pb collisions on the energy spectrum of &#948; electrons ejected in the same collision. It is shown that the lifetime of the superheavy composite system causes pronounced oscillations of width &#949;=h/T in the electron distribution, which survive the inclusion of multistep excitations and the folding with a lifetime distribution function. This effect may serve as an atomic clock for deep-inelastic collisions

Greiner, Walter

Müller, Berndt

Reinhardt, Joachim

Soff, Gerhard

English

Hochschulschriftenserver - Universität Frankfurt am Main

VOLUME  43, NUMBEK  27  PHYSICAL REVIEW LETTERS  31 DECEMUER  1979 (1968). 5~.  Beck,  H. J. Mang,  and  P. Ring,  2. Phys. 231, 26 (1970). 6~.  R. Hilton,  in Proceedings  of  tke Symposium on Present Status and Novel Deuelopments in the Nuclear Many -Body  Pvoblem, Rome, September 1972, edited by  F. CaIogero and  C.  Ciofi degli Atti (Editrice Com- positori, Bologna,  1973), Vol. 1, p.  669. 'R.  R. Hilton,  in Proceedings of tke Extended Nucle- ar Pkysics Seminar on Heavy-Ion,  HigizSpin States and Nuclear Structure,  Trieste, September 1973 (In- ternational Atomic Energy Agency,  Vienna,  1975), VOI. 11,  P.  227,  IAEA-SMR.  14/23. 'R.  R. Hilton,  in Pvoceedings of  the International Symposium on Higkly Excited States in Nuclei, Jülich, Federal Republic of  Germany, 1975, edited by A.  Faess- ler, C.  Mayer-Böricke,  and  P. ?iUrek (Kernforschung- sanlage Jülich GmbH,  filich, Federal Republic of Germany,  19751, Vol. 1, p. 33. 9~.  Hamamoto,  Nucl.  Phys. &,  15 (1976). 'OE.  R. Marshalek and  A.  L.  Goodman,  Nucl.  Phys. A294,  92  (1978). "F. Grümmer,  K.  W. Schmid,  and A.  Faessler,  Nucl. Phys. a,  77  (1978). "A.  L.  Goodman,  Phys. Rev. Lett. G,  357 (1979). 13~.  J. Mang and R. R. Hilton,  in Proceedings of  the Joint Nuclear Physics Spring Meeting of  Deutsche Physikalische Gesellschaft, Nederlandse Natuurkundige Vereniging, Dansk Fysisk Selskab, and Belgische Na- tuurliundige ~ereni~ing-~oci6t6  Belge de Physique, Gent,  Belgium,  March 1979 (unpublished). I4s.  Cohen,  F. Plasil,  and W. J. Swiatecki,  Ann. Phys. (N.Y.) 82, 557 (1974). 15~.  BOhr  and  B.  Mottelson,  Phys.  Scr, z,  13 (1974). Delta-Electron Emission in Deep-Inelastic Heavy-Ion Gollisions Gerhard Soff Gesellschaft für Schwerionenforsckung, 6100 Darnzstadt,  Germany and Joachim Reinhardt,  Berndt Müller,  and Walter Greiner Institutfir Theoretische Physik der Jolmnn Wolfgang Goethe -Universität,  6000 Frankfurt am Main,  Germany (Received 21 September 1979) This paper repozts calculations of  the influence of  a reaction time T >10-2i s in deep- inelastic Xe-Pb collisions on the energy spectrum of  6 electrons ejected in the same collision.  It is shown that the lifetime of the superheavy composite  system causes pronounced oscillations of width t = /%/T  in the electron distribution,  which survive the inclusion of  multistep excitations and the folding with a lifetime distribution function. This effect may serve as an atomic clock for deep-inelastic  collisions. Deep-inelastic  heavy-ion scatteringl has be- come one of  the best-studied phenomena in nu- clear heavy-ion physics.  To explain a wide range of  observations two kinds of  models have been proposed:  microscopic models (shell-model frag- mentation the~ry,~  time-dependent Hartree-Fock: etc.) and statistical models (diffusion the~ry,~ etc.).  In the diffusion model,  the experimentally observed widths of  the fragment mass,  charge, angular momentum,  and energy distributions are in first approximation proportional to the avail- able reaction time T.  The magnitude of  this time, however,  must usually be determined by  semi- empirical procedure~,l*~~~  which yield times in the range  s c  T 5 10-'O  s.  As the basic as- sumptions of  the various models are  not acessible to direct experimental verification,  it is extreme- ly difficult to discriminate between the various proposed models.  It would,  therefore, be of great interest to have an independent clock for the time scale in deep-inelastic nuclear reactions. In the following,  we propose a measurement of T by  means of  the kinetic energy distribution of ejected  6  electrons.  Recent experiments6-B  have confirmed earlier predictionsg  that inner-shell ionization is highly sensitive to the short-time structure of  the electric field generated by the two nuclei during a heavy-ion collision. Accordingly,  the 6-electron distribution may be employed1° for the analysis of  electronic binding energies and the high momentum components of bound-state wave functions in the transient united atom."  The spectrum has an  exponential shape, the steepness being a function of  the combined nuclear charge Z = Z, + 2,  and the minimal dis- tance of  approach of  the two nuclei.  For a typical center-of-mass energy of  3 MeV/u,  a minimal distance of  15 fm corresponds to a time scale of O 1979 The American Physical Society  1981 VOLUME  43, NUMBER  27  PHYSICAL REVIEW LETTERS  31 DECEMBER  1979 the order of  10-*l s.  Any modification of  this time structure due to nuclear reactions will pro- duce observable changes in the ionization proc- ess. The simplest possible modification is a nuclear sticking time T that separates the incoming and outgoing Coulomb trajectory.  It is easy to see that this corresponds to a phase shift between the ionization amplitudes from the two parts of  the Coulomb orbit, the magnitude of  which depends on the energy transferred to the electron. The utilization of  atomic ionization measure  - ments for the determination of  nuclear reaction times was first suggested by Ciocchetti,  Molinari, and Malvano.12  Blair et aL.13  recently succeeded in measuring the ionization amplitude for the half trajectory by investigating a proton resonance in j8~i.  The influence of  a time delay on the brems- strahlung spectrum was discussed by Eisberg, Yennie,  and Wilkinson,14 the influence on quasi- molecular spectra and K X  rays by ~rornleyl" and two of  the authors and recently by Anholt,'" Röhl,  Hoppenau,  and Dost and Chemin et al.17 Rafelski,  Müller,  and Greiner18 proposed that a nuclear delay time could increase spontaneous positron production in heavy-ion collisions.  In this Letter we show that there is a pronounced effect on the electron spectrum. We now  turn to the theoretical concepts for inner-shell ionization.  We have to solve the time- dependent Schrödinger equation it7  aYi/at  = H(R(~))$,, with the relativistic Dirac Hamiltonian H.  Since binding energies and wave functions change strong- ly as  function of  the internuclear separation R, the total wave  function pi is expanded in terms of  the adiabatic basis states <pj(R(t))  which are solutions of  the stationary two-center  Dirac equa- tion Hpj  = E,  (R)  qj. We then obtain a set of  coup- led differential equations for the occupation am- plitudes aij  of  state cp,  by electron number i: The adiabatic electron energy enters via the phase The mechanism by which a nuclear time delay in- fluences the excitation amplitude becomes most transparent in first-order perturbation theory, where Eq. (1) is solved explicitly by a,,(t) =- Jt  -  W dtticii, l(a/atr)  V,) xexp((i/E)[ xJ  (t') -  xi(tt)1}.  (3) This perturbative treatment correctly describeslg the ionization probability except for an overall normalization factor. If  we denote the ionization amplitude at the end of  the incoming Coulomb orbit by aij  '=aiJ(t  = O), we find that the probability of  ionizing an electron from state i into the continuum state j  for a fixed delay time T is given by dpi  (AE, T)/~E, =4~aiJ'/2sin2[(~/2)~~i3+arg(ai,')].  (4) Here AEij=  E, -  E, is the energy difference be- tween states i and j  in the nuclear compound con- figuration.  Obviously,  Pij  exhibits regular oscil- lations in the 6-electron energy E, of  width €(T) = h/T.  The minima go through Zero in this ap- FIG. 1.  Differential emission probabilitg with re- spect to kinetic  6-electron energy.  A coincidence with created 1s~  formation is required.  The nuclear delay times T = 0,  3x  10-''  S,  and  10-20  s are considered. The dash-dotted  line represents the total 6-electron spectrum (T = 10-20  S)  stemming from lso, 2su,  and 3su ionization. VOLUME  43, NUMBER  27  PHYSICAL REVIEW LETTERS  31 DECEMBER  1777 proximation.  These oscillations became slightly damped if  higher-order and many-electron ef- fects are included in the calculation.  To show that much of  the effect still survives we have solved Eq.  (1) by coupled-channels  calc~lations~~ for the system Xe-Pb (or ~i).  This system is ideal both from the nuclear and the atomic physics sides (it is asymmetric enough to allow for a separation of  the yuasimolecular 1s  o and 2p,/,0 states) and has been widely studied experimental- Assuming 7-~e~/ii  bombarding energy,  grazing impact parameter b = 6.4 fm, and fully occupied K,  L,  and M shells, we find the electron spectra shown in Fig.  1.  Without nuclear reaction time the spectrum is a smoothly falling function (solid line, T = O),  while a sticking time T = 10-20  s pro- duces oscillations with a period of  400 keV and a maximum-to-minimum  ratio of  Ca.  3.5: 1.  This ratio is considerably increased (to 15: 1) if one observes the lead K vacancy in coincidence.  In this way,  one obtains a suppression of  the con- tributions from all electrons except those origina- ting form the lso  level,  i.e.,  the most deeply bound electronic state that is also most sensitive to nuclear details. The range of  nuclear delay times that lead to observable effects is limited below by the require- ment that at least one oscillation must be ob- served. The upper limit for T is given by the experi- mental energy resolution and the variation of  the electronic transition energy aEi, during the nu- clear reaction.  If  we take E = 10 keV as the small- est detectable period, we obtain a time range 10-21  s < T < 4 X 10-l9 s that is accessible to obser- vation. In the following we discuss the effects that could conceivably destroy the oscillatory pattern as Seen in Fig.  1:  (1) It is impossible to select a unique impact parameter b  in deep-inelastic collisions.  The main effect of  variation of  b is a change in the phase of  ai,'  in Eq.  (4) and hence of  the position of  the minima in d~/dE.  Figure 2(a) shows that the oscillations still prevail, even if  we integrate over all impact parameters that lead to a nuclear reaction.  The ~~~/?~~ratio  is virtually unaltered;  only the FIG.  2.  (a) Notation as in Fig. 1.  Integration over all impact parameters b  bgmZing that lead to a nuclear re- action.  (b) The Same as in Fig. 1  for t~ = 3 fm.  In addition,  the dash-dotted  line represents the 6-electron distri- bution under the assumption of  a relative laboratory energy loss of  10%  on the outgoing path of the trajectory. 1983 VOLUME  43, NUMBER  27  PHYSICAL REVIEW LETTERS  31 DECEMBER  1979 positions are slightly shifted.  (2) Energy dissipa- tion destroys the symmetry between the incom- ing and outgoing branches of  the Coulomb trajec- tory.  We show the effect of  this modification in Fig.  2(b), where was assumed a relative labora- tory energy loss of  10%, corresponding to 100 MeV.  We find that the spectrum as  a whole is lowered,  but the oscillations remain qualitatively unchanged.  We have also calculated the influence of  these effects on the total spectrum and find the Same results.  (3) Dissipation of  angular momen- , For increasing electron energy,  the oscillations become more and more damped.  Remembering that the nth oscillation occurs at AE  iJ  = 2;irz/~~, the number of  observable oscillations is limited to n < T0/nr.  The ratio T~/T,  accordingly,  limits the range of  detectable delay times.  It also indi- cates that the reaction time must be fixed in the experiment as  well as  possible.  If  we take f(s) = (l/r)  exp(-T/T),  the shape of  the spectrum is slightly altered but all oscillations vanish,  be- cause T = 0 is the most probable delay time. We  conclude that we have demonstrated the exis- tence of a precise clock which may serve to meas- ure absolute times involved in deeply inelastic en- counters and other processes. This work was supported in part by the Bundes- ministerium für Forschung und Technologie. '~ee  the review by W. U.  Schröder and J. R. Huizenga, Ann. Rev. Nucl.  Sci. E,  465 (1977), and further ref- erences therein. 2J.  A.  Maruhn, J. Hahn,  H. J. Lustig,  K.  H.  Ziegen- hain,  and W.  Greiner,  in Proceedings of the Erice School on  Heavy-Ion  Interactions at High Energy, Erice,  1979,  to be published. 3~.  Y.  Cusson,  R. K.  Smith,  and J. A.  Maruhn,  Phys. Rev.  Lett. 36,  1166 (19761. 4~.  Riedel,  G.  Wolschin,  and W.  NGrenberg,  2.  Phys. A 290, 47 (1979). 'K.  E. Rehm,  H.  Essel, K.  Hartel, P. Kienle,  H. J. Körner, P. Sperr, and W. Wagner,  Phys. Lett. E, 256 (1979). 6~.  S.  Greenberg,  H.  Bokemeyer,  H.  Emling, E. Grosse, D.  Schwalm,  and F.  Bosch,  Phys. Rev. Lett. 39,  1404 (1977). 'R.  Anholt and W. E. Meyerhof,  Phys.  Lett. CA,  381 (1978). turn in tlie nuclear reaction cannot change the spectrum.  This has been confirmed by separate calculations.  (4) For any chosen set of  experi- mental parameters, the nuclear reaction time T may (and will) not be sharp but distributed over a certain range.  The influence of  a distribution function f(~)  * 6(~  -  T,)  can be most illustratively Seen in perturbation theory.  If  we take a Gauss- ian centered at T„ and T 5 2T„  Eq.  (4) is modified to '  8~.  Liesen,  P. Armbruster, H.  H.  Behnke,  and S.  Hagmann,  2.  Phys. A 288,  417 (1978). 'W.  Betz,  G.  Soff,  B.  Müller,  and W. Greiner,  Phys. Rev. Lett. 37,  1046 (1976); G.  Soff,  W. Betz, B.  Müller, W. Greiner, and E. Merzbacher,  Phys. Lett. @, 19 11978). ''G.  Soff,  B.  Müller,  and W.  Greiner, Phys. Rev. Lett. 40,  540 (1978).  - I'c.  Kozhuharov,  P. Kienle,  D. H.  Jakubassa, and M. Kleber, Phys. Rev. Lett. 2,  540 (1977); F.  Bosch, H.  Krimm,  B.  Martin,  B.  Povh,  Th. Walcher,  and K.  Traxel,  Phys. Lett. E,  568 (1978). I2G. Ciocchetti, A.  Molinari,  and R. Malvano,  Nuovo Cimento 29,  1262 (19631;  G.  Ciocchetti and A.  Molinari, Nuovo  Cim. *,  69 (1965). 135. S.  Blair, P. Dyer, K. A. Suover, and T. A.  Train- or, Phys. Rev.  Lett. 4l, 1712 (1978). 14~.  M.  Eisberg, D. R. Yennie,  and D.  H.  Wilkinson, Nucl. Phys. i8,  338 (1960). 15~.  A.  Bromley,  in Pvoceedings of  the International Conference on Reactions between Complex Nuclei, Nashville, 1974, edited by R.  L.  Robinson,  F. K. McGowan,  J. B.  Ball,  and J. H.  Hamilton (North Hol- land, Amsterdam,  1974), p. 603. 16~.  Anholt,  2. Phys. A 292,  123 (1979), to be pub- lished. I'S.  ~Öhl,  S.  Hoppenau,  and M.  Dost,  Phys. Rev. Lett. g,  1300 (1979); J. F.  Chemin,  S.  Andriamonje, J. Rotutier, J. P. Thibaud,  S. Joly,  and J. Uzureau, in Proceedings of the Eleventh International Conference on the Physics of Electronic and Atomic Collisions, Kyoto,  1979, to be published. 185.  Rafelski, B.  Müller, and W.  Greiner,  2. Phys. A 285,  49 (1979). 19~.  Soff,  W.  Greiner, W. Betz, and B. Müller,  Phys. Rev. A 20,  169 (1979). 20~.  Reinhardt,  B. Müller, W. Greiner,  and G.  Soff, Phys. Rev. Lett. 43,  1307 (1979). "W.  U.  Schröder, J. R. Birkelund, J. R. Huizenga, K.  L. Wolf,  J. P. Unik,  and V.  E. Viola,  Phys. Rev. Lett. E,  514 (1976). 

Delta-electron emission in deep-inelastic heavy-ion collisions

Abstract

Similar works

Full text

Available Versions

Hochschulschriftenserver - Universität Frankfurt am Main