Sensitivities of the relative velocity between fragments on the decay mechanism

Volume 232, number 1

PHYSICS LETTERS B

23 November 1989

SENSITIVITIES OF THE RELAI'IVE VEI,OCITY BETWEEN FRAGMENTS O N T H E DECAY M E C H A N I S M J. P O C H O D Z A L L A Institut fiir Kernphysik, Universitgitl"rankfi~rt, D-6000 l"rankfurt, I"RG W. T R A U T M A N N and U. LYNEN GesellschaftJ~r Sch werionenforschung, D-61 O0 Darmstadt, FRG Received 7 July 1989

Relative velocity spectra of two intermediate mass fragments (IMF) emitted in tsO induced reactions on 197Auat E/A = 84 MeV were investigated. The average relative velocity measured at small and also large relative angles is satisfactorily reproduced by calculations that model the sequential emission of IMF's and light particles on the basis of statistical model calculations. A similar agreement is found for the average relative velocity measured in ct+ 19ZAureactions at E/A = 800 MeV. Thus, no conclusive evidence for a transition from a conventional multi-sequential decay to a true multifragmentation process can be found at an excitation energy between 3 and 4 MeV per nucleon.

Relative velocities between fragments are one of the rare fingerprints o f the disintegration process o f nuclear systems [ 1-3 ]. Relative velocity distributions measured at small relative angles are controlled by the interaction between the coincident detected fragments. Since the interaction is d o m i n a t e d by the mutual C o u l o m b repulsion, the shape o f the relative velocity distribution is a measure o f the distance between the fragments and thus a measure o f the time scale governing the multifragment decay [ 1 ]. On the other hand, thc relative velocity between nuclear fragments emitted in opposite hemispheres [1,4] probes the mutual interaction between all fragments prescnt in the disintegration region and thus is sensitive to the breakup configuration: F o r a conventional multi-sequential emission o f two intermediate mass fragments (IM F's) their relative velocity should correspond to a p p r o x i m a t e l y twice the value o f the individual emissions from the heavy recoil nucleus. The C o u l o m b energy may be reduced if the breakup occurs out o f an e x p a n d e d state, as expected in the case o f multifragmentation, leading to a reduced relative velocity. A m e a s u r e m e n t o f the two-fragment velocity correlation function at small relative angles for the reaction ~80+ 19YAH at E / A = 8 4 MeV indi-

cared a rather long emission time for I M F ' s o f about 1000 f m / c (ref. [ 1 ] ). This time scale c o m b i n e d with the average excitation energy E x ~ 600 MeV deposited in the compositc system [5] was found to be consistent with a multi-sequential decay [6]. Furthermore, the associated I M F multiplicity [ 5 ] is significantly lower than predicted by statistical multifragmentation models [ 7 ]. Recently, Klotz-Engmann and co-workers analysed relative velocity distributions o f I M F ' s at large relative angles measured in the reaction ct+ 197Au at E / A = 800 MeV and interpreted them as a clear signal for multifragmentation [ 3,4 ]. They explicitly exclude a sequential evaporation-type emission. Since the excitation energy is only slightly higher in this system (E~ = 800 MeV, rcf. [ 8 ] ), these results would suggest a rather sharp transition from multi-sequential decay to multifragmcntation between E x / A = 3 MeV and 4 MeV as predicted e.g. by Gross and coworkers [ 9 ]. In view of the far reaching implications o f such a result a further critical investigation o f the information contents o f relative velocity distributions measured at large relative angles seems justified. Fig. 1 shows distributions o f I M F - I M F coincidences as a function o f their relative velocity for the

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41

Volume 232, number 1

PHYSICS LETTERS B

180 + m;'Au 20

-~

I

10

I

E / A = 84 MeV ,

:--

I

~

I

"-"

(a)

23 November 1989

cess o f independent decays which are, however, constrained by conservation laws. Due to recoil effects, the average relative velocity between two I M F ' s and the average relative velocity for the individual emission process, v0, are related according to: < vrcl > ~ Vo

o -+-4

,~ ,,h

o o

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0

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4

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12

Vrel" ( c m / n s )

Fig. I. (a) Distribution of the relative velocity v~ between two IMF's cmined approximately back-to-back. (b) The same distribution tbr events where more than two IMF's were observed. reaction 180 + 197Au at E/A = 84 MeV. Due to the detection properties o f the e m p l o y e d parallel plate detectors [1, I0] the selected fragments arc d o m i n a t e d by the range o f a t o m i c numbers 8 ~100 ° and 150 ° < k O < 2 1 0 ~. Here 0, and 02 denote the emission angles with respect to the beam axis and AO=OI--~2 is the difference o f the corresponding azimuthal angles. F o r these events the relative velocities peak at a value ( v ~ t > = 4 . 7 _ ~ 0 . 2 c m / n s . A selection o f high fragment multiplicities, i.e. at least 3 I M F ' s observed, does not seem to result in a different distribution o f relative velocities ( =4.6--+0.5 c m / n s , see fig. lb). Thc obscrvation o f identical velocity distributions for '¢/~MF= 2 and /> 3 events supports the interpretation o f multi-fragment emission as a sequcntial pro42

x

Here, A 2 denotes the average mass o f the second 1MF emitted and Aris the mass o f the residual nucleus immediately after the emission o f the second IMF. A0 is the angle between the two I M F velocity vectors in the CM frame. The average values expected according to eq. ( 1 ) are shown by the line in fig. 2 together with a scatter plot o f the measured correlation between the relative velocity and 0s,m. For Vo we a d o p t e d the experimental average velocity between an I M F and a targctlike recoil [ 10] o f 2.7 c m / n s . The average mass /12=23 was d e t e r m i n e d by folding the inclusive I M F distribution with the detection efficiency function [ 10]. Furthermore, the effects o f s u m m i n g over a finite range o f A¢ and o f the center-of-mass velocity o f 0.5 c m / n s are taken into account in the calculations• Note only the absolute values o f the average relative velocities but also the observed variation o f the relative velocity as a function o f the s u m m e d emission

180 + m;'Au 250 ,

i

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F / A = 84 MeV

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0

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Z~ 6 8 Vre[ (cm/ns)

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Fig. 2. Scatter plot of two-fragment coincidences from reactions 180+ 197Au at E/A =84 McV as a function of summed laboratory angles, 0s,m, and of their relative velocity, vr,t. The line is explained in the text.

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PHYSICS LETTERS B

angles 0sum are in reasonable agreement with the prediction of eq. (1) assuming a mass of Af= 1 5 6 2A2 = 110 for the residual nucleus. The reduced mass of the emitting system results from the emission of light particles prior to the IMF's. In order to obtain a realistic estimate of the mass loss due to non-IMF particles we performed calculations with the statistical model code GEMINI [11]. A compound nucleus with mass Ao= 190 and charge Zo= 75 was assumed to be representative for the reaction 180+ m7Au(rcf. [5] ). The calculations were performed with initial angular momenta J = 0 and 50 at various excitation energies E~. Only those Monte Carlo events, in which two fragments within the relevant charge range have been produced, were selected for the analysis (approximately 8 ~
200

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,--,., :

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seq. emLss.

100 ,, ,ii, i i l f f , , , , l , , , , l 200 600 1000 z+ 5 Ex(MeV) (cm/ns ) Fig. 3. Left park Predictions of the GEMINI calculations for the difference Ar=Ao-AA between the initial mass Ao and the s u m m e d mass AA of all particles (not including the first IMF), which are emitted prior to the second IMF. The solid and dotdashed lines correspond to Ao= 190 and 184, respectively. Right part: The predicted average relative velocity, (v,c~>, of two I M F s emitted back-to-back as a function of the effective mass Ae~rof the emitting system.

23 November 1989

( 1)Due to the lower initial mass for the Ao= 184 case (dotdashed curve), Ar is lower by about 6 mass units compared to Ao= 190 (solid curve). (The different N/Z ratios of the initial nuclei have only a minor effect. ) (2) Because of the higher threshold in the TOF arm used in the a + 197AHexperiment (see fig. I in ref. [3 ] ), the average IMF mass is slightly larger than in the 180+ 197Au c a s e . As a consequence the mass loss via non-IMF's, AA is typically 10% higher in the e t + 197AH reactions. (3) Based upon the observed momentum transfer, one expects for the reaction (l+197Au at E/A=800 MeV only a small angular momentum (.I~ 10) in the initial system, For simplicity we, therefore, assumed J = 0 to be representative for this system. Similarly, the momentum transfer measured [ 1 ] in the reaction '80 + 197Au at E/A = 84 MeV indicates average angular momenta of the decaying system of J ~ 50. At this high angular momentum, AA is larger by typically 5 nucleon masses compared to the case J = 0 . The differences due to effect (2) and (3) approximately cancel each other. At Fx=800 MeV [9] a mass 184 nucleus emits on the average zXA=52 nucleons via non-IMF decay prior to the second IMF according to the sequential code GEMINI (see point on the dotdashed curve in fig. 3 ). On the other hand, the mass ofa Ao = 190 nucleus with E~---580 MeV and J = 50 will have been reduced by only 34 nucleons at the time of the second IMF emission (see point on the solid line in fig. 3). In either case, approximately 40% of the mass loss zXA is due to neutron evaporation. It is further interesting to note, that at initial excitation energies between 500 and 800 MeV the dominant fraction of the mass loss (typically 70%) happens even before the first IMF's is emitted. On the average, a mass of only 10-15 nucleons is lost between the emission of the two IMF's and typically 15 mass units are emitted after the second IMF decay. The existence of a window for IMF decay at relatively low temperature, i.e. latc times, in statistical decay sequences was also observed by Friedman and Lynch [ 12 ]. Motivated by the prediction that only a few light particles are emitted between the two IMF's we have performed Monte Carlo calculations, simulating the successive emission of two IMF's as described in ref. [1 ]. In these simulations two- and three-body 43

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Coulomb trajectories were calculated following the (surface) emission of the first and second IMF, respectively. (Since according to the G E M I N I calculations only very few charged particles are emitted between the two IMF's, we do not expect a significant influence to the Coulomb trajectories of the IMF's due to the presence of other charged particles.) Consistent with the small-angle correlations a half-live of 1000 fm/c was used in these calculations [ 1 ]. The decay configurations were chosen as described in ref. [ 1 ]. Detector acceptances as given above or in refs. [3,4] were applied. In order to model the mass loss due to non-lMF decays we reduced the initial mass of the emitting system to a value Act~. between the two IMF's for back-to-back emission. In accordance with the mass dependence of the recoil effect (cf. eq. 1 ), (v~¢1) is significantly lower for smaller values of A~fr. The solid and the dotdashed curves reflect the different experimental conditions for the ~80+ ~7Au and ct+ ~97Au reaction, respectively. Obviously, these calculations are not very sensitive to the details of the detector geomet~,. Thc assumed neutron-to-proton ratio of the IMF's, however, has a perccptiblc influence. In the present calculations the most probable mass, as predicted by the G E M I N I calculations, has been used for a given Z value, which corresponds to an average neutron-to-proton ratio of about 1.2. If one assumes N/Z= 1.5 (ratio equal to No/Zo of the initial nuclei) (vr~j) is rcduced by 0.2 cm/ns. A reduction o f t h e half-live to 500 fm/c shifts - for the mass range from A~fr= 130 to 160 - the cu~'es in fig. 3b by approximately 0.2 c m / n s towards larger relative velocities, whereas an increase of the half-live by a factor of two reduces (V~l) by less than 0.1 cm/ns. Because of the relative small mass loss between the IMF emissions, we can approximate the cffective mass used in the trajectory calculations by the mass A~ predicted by the GEM1NI simulations, i.e. A~cf~A~. (Note that in eq. ( 1 ) ( u ~ ) depends only on A2 and Af,~A~--2A2.) From fig. 3a one finds for Ao= 190 at E ~ = 5 8 0 MeV and Ao= 184 at E x = 8 0 0 MeV values for A~n-of 156 and 132, respcctively. For these effective masses the trajecto~ calculations then predict average rclativc velocities (v~,~)=4.3_+_0.3 c m / n s 44

23 November 1989

and 3.9 + 0.3 cm/ns, respectively. In particular, the latter value is significantly lower than the average relative velocity of 4.6 c m / n s obtained by the authors ofref. [ 4 ] for sequential IMF decays without preceding non-IMF emission and, therefore, with a smaller recoil effect (cf. the dotdashed curve in fig. 3b for A,~r~ 184). The given errors arise from the following individual contributions: ( 1 ) A variation of the lower limit for Z~MFby + 1 charge unit modifies the emitted mass AA via nonI M F decays predicted by the G E M I N I code by approximately +_ 10%. Therefore, uncertainties of the detailed shape of the efficiency functions introduce an uncertainty offi (v,.c~) ~ 0 . 2 cm/ns. (2) Uncertainties and fluctuations of the excitation energy and the angular m o m e n t u m contribute with about 0.1 cm/ns. (3)Fluctuations of the N/Z ratio of the fragments and possible correlations are not taken into account. We estimate, that this results in an uncertainty of 6(vr~l) ~ 0.1-0.2 cm/ns. ( 4 ) A n uncertainty of typically 0.1-0.2 c m / n s has to be attributed to variations of the IMF lifetime. (5)Statistical and numerical inaccuracies of our calculations contribute an error of 0.1 cm/ns. Assuming, for simplicity, uncorrelated contributions, we obtain the quoted total error of 0.3 cm/ns. Moreover, our calculations ignore the influence of shape distortions caused, for example, by intrinsic angular m o m e n t u m or flow phenomena. Although these phenomena arc partly taken into account by constraining the initial conditions of the trajectory,' calculations in such a way that the inclusive IMF velocity distribution is reproduced, these aspects may be particularly important for heavy ion induced reactions, whereas e.g. ct induced reactions are expected to be less effected. Considering these uncertainties and potential deficiencies, the agreement between the present calculations of 4.3 and 3.9 c m / ns (see dots in fig. 3b) and the experimental average relative velocities of 4.7 _+.0.2 c m / n s (fig. 1 ) and 3.8 c m / n s [4] is satisfactory. Finally, comparing the present results to the prediction [4] of a multifragmentation model [9] ((Vrc,)~3.5 c m / n s ) and in view of the sensitivity of (vr~) to e.g. the breakup volume in such calculations, we are lead to the conclusion, that relative velocities at large relative angles do not allow an unambiguous distinction between se-

Volume 232, number 1

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quential and simultaneous modes of multifragment p r o d u c t i o n . In particular, we b e l i e v e that the s e q u e n tial m o d e c a n n o t be e x c l u d e d on the basis o f these d a t a alone. O n the o t h e r hand, we h a v e also d e m o n stratcd that v e l o c i t y c o r r e l a t i o n s at large angles are s e n s i t i v e to m a n y details o f the e m i s s i o n process and thus m a y play an i m p o r t a n t role in f u r t h e r efforts to u n r i d d l e the n a t u r e o f m u l t i f r a g m e n t d e c a y m o d e s . Wc w o u l d like to t h a n k H. Oeschler, G. KlotzE n g m a n n and D . H . E . G r o s s for s t i m u l a t i n g discussions.

23 November 1989

References [ 1] R. Trockel et al., Phys. Rev. Lett. 59 (1987) 2844. [2] N. Colonna et al., Phys. Rev. Lett. 62 (1989) 1833. [ 3 ] G. Klotz-Engmann et al., Nucl. Phys. A 499 ( 1989 ) 392. [4] D.H.E. Gross, G. Klotz-Engmann, and H. Oeschlcr, Phys. Lett. B 224 (1989) 29. [ 5 ] R. Trockel et al., Phys. Rev. C 39 ( 1989 ) 729. [6] J. Pochodzzlla et al., to be published. [7] J. Bondorf et al., Nucl. Phys. A 444 (1985) 460. [ 8 ] G. Klotz-Engmann et al., Phys. Lett. B 187 ( 1987 ) 245. [9] D.H.E. Gross et al., Phys. Rev. Lett. 56 (1986) 1544. [ 10] R. Trockel, thesis (1987), report GSI-87-17; J. Pochodzalla, Nucl. Phys. A 488 (1988) 353c. [ I 1 ] R.J. Charity et al., Nucl. Phys. A 483 (1988) 37 I. [ 12] W.A. Friedman and W.G. Lynch, Phys. Rev. C 28 (1983) 16.

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