Physics Letters B 323 (1994) 113-117 North-Holland PHYSICS LETTERS B Time scale for proton emission from highly excited projectiles R J. Charity a, L.G. Sobotka a, G. Van Buren a,1, F.A. Txbbals a,2, J. Barreto a,4, D.R. Bowman b,5, M. Chartler b,6, J. DlnlUS b, D. Fox c,5, C K. Gelbke b, D.O. Handzy b, W.C. Hsl b, P.F. Hua a, A.S. Klrov a,3, M.A. Lisa b,7, W.G. Lynch b, G.F. Peaslee b,8, L Phair b,7, D.G Sarantites a, C. Schwarz b, R.T. de Souza c, M B. Tsang b and C. Williams b a Department ofChemtstry, Washmgton Untverstty, St Louts, Mtssourt 63130, USA b Nattonal Superconducttng Cyclotron Laboratory, Mtchlgan State Umverstty, East Lansmg, Mtchtgan 48824, USA c Department ofChemtstry, Indlana Umverslty, Bloommgton, Indmna 47405, USA Received 21 October 1993, revised manuscript received 14 December 1993 Editor J P Schiffer Highly fragmented exit channels produced by the decay of excited 24Mg projectiles were detected The longatudmal velocity spectra of protons and alpha particles from such channels are offset This offset is consistent with post-breakup Coulomb accelerations from the 197Au target nuclei implying that the protons were emitted within 3× 10 -22 S after the target-projectile separation At low to m e d i u m excitation energies, the hfetlmes of c o m p o u n d nuclei are much longer than the time scale for their creation and the Bohr hypothesis concernlng the independence of c o m p o u n d nucleus creation and decay is experimentally confirmed However as the excitation energy increases, the lifetime for a c o m p o u n d nucleus decreases and at some point approaches the time scale for its creation. At this point, the Bohr hypothesis is expected to break down As the excitation energy is further increased, novel new decay mechanisms involving volume or surface msta1 Present Address Massachusetts Institute of Technology, Boston, Massachusetts 2 Present Address University of Chicago, Chicago, Illinois 3 On leave from Faculty of Physics, Sofia University, Bulgaria 4 On leave from InstltUtO de Fis]ca da UFRJ-21945 RJ, Brazil s Present Address Chalk River Laboratories, Chalk River, ON, Canada 6 Present Address Institut de Physique Nucl6alre, Orsay, Cedex, France 7 Present Address Lawrence Berkeley Laboratory, Berkeley, Cahfornla 8 Present Address Department of Chemistry, Hope College, Holland, Michigan blhtles [ 1 ] may occur resulting in a rapid or prompt disintegration of the nucleus system as opposed to the slower sequential evaporation or binary fiss]on processes observed at lower energies Experimentally our knowledge of the time scale for the decay of highly excited nuclei is hmlted. Intensity lnterferometry techniques probe the space-time dimensions of a emitting source [2], but it is not always possible to extract both the source size and hfetlme mdependently Fortunately, an alternative method exits for projectile fragmentation. If the projectile disassembles in the VlClmty of the target, the charged projectile fragments will undergo post-colhslon accelerations due to the action of the target's Coulomb field Fragments with the larger Z / A ratios will be accelerated more and, on average, will have larger final velocities than fragments with smaller Z / A values For a prompt decay, the average increase in the energy/nucleon of a fragment relative to that of the center of mass of all the detected fragments is (ignoring target recoil effects) Zte 2 (A(E/A)) = A(Z/A) -- (1) r Here r is the separation between the centers of the target and the projectile when the projectile dlsassem- 0370-2693/94/$ 07 00 (~ 1994-Elsevier Science B V All rights reserved SSDI 0 3 7 0 - 2 6 9 3 ( 9 3 ) E 1585-L 113 Volume 323, number 2 bles, Zte is the target charge and A(Z/A) is the difference o f the fragment's Z/A value from that o f all the detected fragments F o r a sequential decay, the average shift m the E/A o f a fragment should reflect not the Z/A o f the fragment, but the Z/A o f its parent present during the post-collision acceleration phase In the limit that the projectile decays a long distance from the target, (A(E/A)) should be zero for all Z/A values Additional effects result from the gradient of the Coulomb field which causes distortions in the shape of the fragment spectra as a function of the emission direction [3]. These effects are observable only for very small target-proJectile separations as the gradient decreases as r -3 whereas the Coulomb field decreases as r -2. Although there have been studies searching for spectral & s t o m o n s [ 3-5 ] in projectile fragmentation, simple post-breakup acceleration effects have largely been ignored One recent exception is the observation o f a post-breakup Coulomb acceleration in the Coulomb disassociation o f 11L1 fragments [6] In this letter we report the observation o f post-breakup C o u l o m b acceleration effects for highly fragmented and well charactenzed exit channels from the breakup of 24Mg projectiles The 24Mg projectiles o f E/A= 60 MeV, extracted from the N S C L K1200 Cyclotron, were excited through peripheral interactions with 197Au target nucleL The charged projectile fragments were detected in the Washington University M I N I W A L L detector array consisting of 128 plastlc-CsI sclntdlator detectors covering angles from 3 3 ° to 25 5 ° These detectors have isotope resolution for Z ~< 4 Events were selected where the total charge o f the detected fragments was equal to that o f the projectile F o r such events, the projectile velocity in the reaction center o f mass frame Vp was extracted. The projectile fragment velocmes were then determined in the frame o f the projectile using Lorentz transformations and the sum kinetic energy, ~ Ek, o f these fragments in this frame was calculated. In order to look for shifts in the energy spectra from post-breakup accelerations, it is i m p o r t a n t to minimize biases o f the detection apparatus, especially from the low- and high-energy thresholds. F o r low values o f Vp, protons emitted backwards in the projectile frame m a y have energies below the low-energy thresholds o f 114 10 March 1994 PHYSICS LETTERS B Table 1 Projectile exit channels observed in this work, with their breakup Q-values, detected yields and the estimated average projectile excitation energies per nucleon The number of neutrons assumed for each channel in the simulations to estimate E*/A are indicated in the parentheses Channel 5c~ + 3He + (n) 5c~ + 2p + (2n) 4c~ + 3He + 2p + (3n) Q ( MeV ) Detected events (E*/A) -49 1 -56 6 -77 2 1798 3833 914 42 48 62 (MeV) the detectors (10-20 MeV for unambiguous identification) Such events will be missing in the selected ensemble o f events and thus, on average, the detected protons will have velocities larger than Vp and give rise to a nonzero value o f (A(E/A)) Similarly for high values of Vp, protons emitted forward m a y exceed the high-energy threshold (98 MeV) associated with punching through the CsI crystals and this will result in a bias in the opposite direction In order to reduce such biases, two extra selection criteria, namely Ek < 70 MeV and Vp > 0.83 x Vbeamwere used to h m i t the magnitude o f emission velocities and magnitude of the projectile velocity, respectively This letter will also be restricted to exit channels containing p, a, and 3He fragments for which accurate energy calibrations are available Events where two alpha particles simultaneously hit the same detector were well resolved m the experiment and were included in the analysis Most, but not all, of these detected doublea events originate from the decay o f the long hved (~,-.~10 -16 S) ground state of 8Be Three exit channels, 5a + 2p, 5a + 3He and 4a + 3He + 2p, with yields listed in table 1, were found that satisfied the above conditions Fragment velocity spectra (AV~.y,z) were reconstructed in center o f mass frame o f all the detected fragments. The z axis was chosen to be parallel to the Vp vector with the x axis in the reaction plane determ i n e d by Vp and the b e a m axis The y axis is out o f this plane Emission parallel to the b e a m &rectlon corresponds to positive AVz and negative AVx. The proton velocity spectra obtained from the 5c~+2p channel are &splayed m fig 1 The spectra for the x and y velocity components are strongly distorted at Volume 323, number 2 1600 " ' ' PHYSICS LETTERS B ' ' Protons I " ' I . , , 10 March 1994 i . i i i 3 "1~12~ 2"@ 3He 1200 2a 0 -1 Proton -Q •-, , . . . . . . . . . . . . . . . . . . . - Z ' 0~ , 2| al 0-5 -4 -3 -2 -1 AV 1 2 3 4 -1 I , t. •. •. small veloclttes by the M I N I W A L L angular acceptance (fragments with small transverse veloctties generally pass through the hole in the M I N I W A L L array at 0 ° - 3 3 ° and are not detected) These components however are approximately centered around AV = 0 On the other hand, the z or longitudinal c o m p o n e n t which suffers less distortion is not centered at zero, but is shifted up to a higher mean velocity The shift in the proton spectra is with respect to the alpha particles as they essentially define the center of mass o f the detected fragments Therefore the data are consistent with the action o f post-breakup Coulomb accelerations as the protons, on average, have larger longitudinal velocities than the alpha particles Shifts in the average energy/nucleon were estimated from the centroids of the AV~ distributions as (2) where mp and mt are the relativistic masses o f the target and projectile in the reaction center o f mass reference frame and the quantities m and A are the relativistic mass and the nucleon n u m b e r o f the fragment type of Interest. The above formula is strictly valid in the h m l t that the change in m o m e n t a induced by Coulom b accelerations are small compared to the total m o m e n t a o f the fragments. The factor (rap +mt ) ~mr is a correction for the fraction o f Coulomb energy which goes into the target's motion. Average energy i i ' P ~ , Slmulatmn i , I , i b) . i 3 Fig 1 The longitudinal (z) and the two transverse (x,y) velocity spectra of protons detected in the 5a + 2p exit channel The experimental data are indicated by the symbols, while the solid and dashed curves show the predictions of the slmulatmns for r = oo and 18 fm respectively (zX(E/A)) = (zXVz) (V,) ~,(mVmt + mt ) m A' I i ' ~ ' i 5 (cm/ns) a) Experiment 1 i r = oo , i , i , , < ~ 0 ~ -1 -0 1 ............... i i 0 0 c) Slmulatmn , , 0Jl r = 1 8 fm , 012 , 013 , 014 0 5 &(Z/A) Fig 2 Average shifts in energy/nucleon derived from the centrolds of the velocity &stnbutlons of protons, 3He, a and double-a (2a) fragments in the experiment and m the two s~mulatmns The square, circular and triangular symbols indicate the 5a+3He, 5a+2p and 4ct+3He+2p exit channels, respectively The points for a and double-a part~cles from the same exit channel have the same value of A(Z/A), but can be dlstlngmshed as the double-a point is always the h~gher of the two The small error bars on the data pomts indicate the statistical error, while the larger error bars without data points show the systemaUc errors associated with the energy cahbratlons of protons and 3He fragments relative to that for alpha particles The prediction for a 18 fm breakup separatmn from eq (1) is indicated by the line shifts were obtained for each o f the three exit channels from the centroids of the velocity spectra for protons, 3He, a and double-c~ fragments. These are plotted as a function of A(Z/A) in fig 2a. The error bars on the experimental data points and the larger error bars without data points are estimations o f the the statistical and the systematic uncertainties respecttvely Detector biases were investigated using Monte Carlo simulations Initially, the simulation was performed for r -- oc where no post-breakup accelerations are present Projectile fragmentation events were generated with a modified version o f the mi115 Volume 323, number 2 PHYSICS LETTERS B crocanomcal algorithm o f ref. [7]. The p r i m a r y projectlle velocity, angle and excitation energy d l s t n b u tlons and correlatmns between these quantities were estimated from the measured q u a n t m e s using an iteratlve process s l m d a r to that d~scussed in ref [3] to remove the detector bins The average projectile exc~tatmn energies are listed in table 1 They are very large corresponding to temperatures o f 6 - 7 MeV. Also, a 40% probabihty that an event initially cont a m e d a SBe fragment was assumed so as to reproduce the observed yield o f double-a events The proton velocity distributions predicted for the 5 a + 2 p channel (solid curves) are c o m p a r e d to the experimental data in fig. 1. The predictions for the transverse components reproduce the experimental data quite well generating the rather complex shapes, thus verifying that these shapes are associated with the detector bias. The predicted z c o m p o n e n t does not show the shift which is seen in the experimental spectrum. Hence, the e x p e n m e n t a l biases cannot account for the measured proton AVz shifts. The values o f (A(E/A)) obtained in this simulation are plotted in fig. 2b. They are generally small indicating that the detector bias is minimal. The 3He points are an exception Their larger values are a consequence o f a high low-energy threshold (~25 M e V / A ) for resolving 3He fragments from alpha particles Detector bmses were also investigated when postbreakup acceleratmns are present. The projectile and target were followed along peripheral colhslon trajectories until a separation o f r = 18 fm was reached At this point the trajectones o f the projectile fragments under the influence o f the target's Coulomb field were followed The resulting d i s t n b u t l o n s show shifts in the longitudinal velocity spectra s~milar to those observed In the expenment. The proton spectra predicted for the 5a + 2p channel are indicated by the dashed curves in fig. 1 The longitudinal component o f the velocity is now reproduced by this simulation However, the spectra for the transverse components are only slightly changed by the inclusion o f the post-breakup accelerations. The associated (A (E/A)) values are plotted in fig 2c and show a strong resemblance to the experimental data in fig. 2a The magnitude o f the detector bias can be gauged by c o m p a n n g the simulated data points to the line m fig 2c which shows the prediction o f e q . (1) for r = 1 8 fm In extracting the breakup separation from the data, 116 10March 1994 it should be stressed that alpha particles and SBe fragments, in which most o f the mass of the exit channels is contained, must have small values of (A(E/A)) Also the 3He shifts were not very sensitive to post-breakup accelerations in the simulations due to the high lowenergy thresholds Hence we will concentrate on the shifts for the protons Within the experimental errors, the range of breakup separations consistent w~th the experimental data obtained from simulations such as in fig. 2c is 13 to 30 fm At the lower h m l t the proJectile and target may still be in contact, as the nuclear force is ignored m the simulations. Thus it is concluded that the protons were emitted while the projectlle was still in contact w~th the target nucleus or before a separation o f 30 fm was reached. The time reqmred for the projectile to move from r = 11.5 fm (touching separation for spheres) to 30 fm gives an upper limit o f ~ 3 × 10 -22 s for the average proton emlssmn time As this time is similar to the targetprojectile interaction time, then there is no clear separation in the time scales for the creation and decay o f the emitting system Thus the proton emission m a y even be considered "prompt". This does not mean that the whole projectile d~sassembly was prompt, the time scale for the emission o f the other fragments is not determined m this work. However, most o f the protons cannot be emitted from long-hved intermediates as the Z/A ratios of such fragments are much less than the proton value and are too low to explain the shift This is confirmed by an analysis o f correlatmns between the protons and the other projectile fragments. Only two resonances, 5LI (4× 10 -22 s) and 9B ( 1 × 10-18 s) were found in the 5a + 2p channel and they account for only ~5% and ~2%, respectively, o f the protons. In sp~te o f the p r o m p t nature o f the proton emission, ~t is not clear that the decay ~s inconsistent w~th comp o u n d nuclear decay. By extrapolating low energy systematlcs for hght nuclei [8,9], one finds hfetlmes o f 3 and 4× 10 -22 s for the average energies (table 1 ) assocmted with the 5a + 2p + 2n and 4 a + 3He + 2p + 3n channels, respectively These t~mes match the expenmental upper limit for proton emission and to be conslstent would require the protons to be emitted first. Most of the other fragments would then the emitted on longer time scales In conclusion we have demonstrated a m e t h o d to measure decay time o f projectiles decaying in the Volume 323, number 2 PHYSICS LETTERS B Coulomb field o f the target nucleus F o r the 5a + 2p, 5 a + 3 H e , and 4 a + 3 H e + 2 p exit channels of highly excited 24Mg pro lectdes the average longitudinal velocity of the protons are shifted to larger values with respect to the center of mass velocity o f the all the fragments in the channel These shifts are consistent with post-breakup accelerations due to the Coulomb field o f the 197Au target nucleus F r o m the magmtude o f these shifts it is deduced that proton emission occurs within 3× 1 0 - 2 2 S This work was supported by the U S D e p a r t m e n t o f Energy under contracts Nos DE-FG02-87-ER40316 and DE-FG02-88-ER40406 and by the National Science F o u n d a t i o n under grant n u m b e r PHY-9214992 JB wishes to acknowledge travel expenses provided by CNPq, Brazil. 10 March 1994 References [ 1] L G Moretto and G J Woznlak, Ann Rev Nucl Part So 43 (1993) 379 [2] D H Boal, C K Gelbke and B K Jennmgs, Rev Mod Phys 62 (1990) 553 [3] R J Chanty et al, Phys Rev C 46 (1992) 1951 [4] M Murphy et al, Phys Rev Lett 53 (1984) 1543 [5] A Badalh et al, Phys Rev C 48 (1993) 633 [ 6 ] K lekl et al, Phys Rev Lett 70 (1993)730, D Sackett et al, Phys Rev C 48 (1993) 118 [7] J Randrup, Comp Phys Comm 59 (1990) 439 [8] T Ericson and T Mayer-Kuckuk, Annu Rev Nucl Scx 16 (1966) 183 [9] D Shaplra et al, Phys Rev C 10 (1974) 1063 117