Physics Letters B 274 ( 1992 ) 260-267 North-Holland
PHYSICS LETTERS B
Hypernuclei formation at CERN and SIS energies J. A i c h e l i n a a n d K. W e r n e r b a Institut de Physique NuclOaire, UniversitO de Nantes, 2, Rue de la Houssinikre, F-44072 Nantes Cedex 03, France b lnstitutJ~r Theoretische Physik, Universitdt Heidelberg, Philosophenweg 19. W-6900 Heidelberg, FRG
Received 18 June 1991; revised manuscript received 29 October 1991
We investigate whether hypernuclei can be produced at CERN (200 GeV/n) or SIS (2 GeV/n) energies. Employing microscopical theories - VENUS for CERN energies and QMD for SIS energies - we calculate the primordial distribution of A's, K-'s and n's. We find that at CERN energies these particles cannot be trapped in the spectator matter, thus hypernuclei formation is unlikely. At SIS energies further collisions can slow down the A's considerably, thus they can be trapped. However, the probability of hypernuclei formation remains low.
I. Introduction Can high-energy heavy-ion experiments be used to study A hypernuclei or even multi A hypernuclei? At first sight relativistic heavy-ion collisions seem to be an ideal tool [ 1 ]. Experiments have shown [2,3] that m a n y strange particles are p r o d u c e d in these reactions and in a d d i t i o n there are energetic non-strange mesons which can p r o d u c e strange particles with an appreciable cross section. The question is, however, whether the p r o d u c e d A ' s or Z's can be t r a p p e d in an already existing cluster or whether they can form, together with other nucleons, a cluster by coalescence [4,5]. At low energy (Ekin/N< 1 G e V ) this process could not be established in Q M D calculations. Also at higher energies the existence o f a coalescence process in not established yet but could be experimentally tested by measuring the p r o d u c t i o n o f anti-alpha's or o f larger clusters o f antimatter. A detailed theoretical investigation of the coalescence process requires not only a detailed knowledge o f the space time evolution o f all particles at high energies (which can be p r o v i d e d by models like V E N U S [6] or R Q M D [ 7 ] ) but also o f the q u a n t u m mechanical description o f how neighboring nucleons coalesce to a This work has been funded in part by the Gesellschafl f'tir Schwerionenforschung (GSI) Darmstadt under the contract number HD HUT. 260
cluster. Since this description is not available yet and because m e d i u m mass nuclei A > 4 are most probably very rarely p r o d u c e d by coalescence we neglect this possible contribution in this letter. Rather we concentrate on the question whether hyperons can be t r a p p e d in spectator matter, i.e. in clusters which survive the reaction. I f hypernuclei should be formed by trapping the A or Y in already existing clusters o f nucleons, the first question is, o f course, whether such clusters exist at all. There is experimental evidence that these clusters exist in a s y m m e t r i c systems up to C E R N energies [8,9 ]. The experiments revealed that b e y o n d an energy o f 1 G e V / n the cross section for radioactive isotopes is constant [9]. This is expected theoretically on the basis o f the phenomenological p a r t i c i p a n t spectator model and has recently been confirmed in microscopical calculations [10]. Both, the microscopic as well as the phenomenological model, predict that it is useful to discriminate between participants, i.e. nucleons in the geometrical overlap o f projectile and target and spectators. The spectator m a t t e r decays into fragments. The participant nucleons interact with each other. At m o d e r a t e energies, Ek~n/n< 2 GeV, they form a fireball [ 11]. At higher energies E k i , / n . ~ 200 GeV it is more appropriate to apply the string model by describing the h a d r o n production via the formation and the subsequent decay o f strings [6,7,12]. At the energy in be-
0370-2693/92/$ 05.00 © 1992 Elsevier Science Publishers B.V. All rights reserved.
Volume 274, number 3,4
PHYSICS LETTERS B
tween, where the transition between these two approaches takes place the situation is less clear. In agreement with experiments [ 13 ] the microscopic model [ 10 ] predicts that besides a large target remnant whose mass is strongly related with the impact parameter, in asymmetric collisions several intermediate mass fragments (IMF) ( 3 < Z < 30) are formed [14]. Their momentum is slightly larger than the momentum of the target remnant [ 13 ] but still very low (several tens of M eV/n) as compared to the beam momentum. For semicentral symmetric systems it predicts an almost complete disintegration of projectile and target into many small fragments [ 15 ] with momenta close to projectile and target momentum, however there exist no fragmentation data for symmetric systems above Ekin/n ---=200 MeV yet.
2. Hypernucleus formation at CERN energies We start out with the investigation of hypernucleus formation in semiperipheral (b ~ l 0 fm) reactions at 160 G e V / n Pb + Pb. We assume that the hypernuclei are formed by the following mechanism: initially in the geometrical overlap of projectile and target, strings are formed and fragmented employing the VENUS model [6 ] which has been successfully applied to describe the data O + A u and S + A u at 200 GeV/n. This model predicts the triple differential cross section for all particles. The spectator nucleons are assumed to move undisturbed with projectile or target momentum. Particles having a rapidity close to the projectile respectively target rapidity may enter the cold spectator matter and collide with spectator nucleons. If these particles carry strangeness (A, K - ) , they can be trapped in the spectator matter, if not (n), they may create a A in the first collision. After the first collision the probability for hyperon production is low, because the available energy is already low for the first collision and becomes even lower in subsequent collisions. Finally only those A's form a hypernucleus which are trapped in the spectator matter. The number of hypernuclei formed in a collision in this approach is given by
16 January 1992
PM = J gM ( P l , Yproj)gY (P) WM (p±, p, PA, Pr) Xeabs(PA) d2p± d3p d3pf d3pA,
(1)
where gM (P±, Yproj) is the transverse momentum distribution of the mesons of type M produced from string fragmentation at y ~ Yproj.gN (P) is the momentum distribution of the nucleons inside the spectator matter which is taken as a Fermi distribution. WM(Pz, P, PA, Pf) is the probability that a meson with the momentum p± together with a nucleon of momentum p forms a A with momentum PA and a meson with Pr. In the actual calculations f Wd3pfd3pA is taken as a constant above threshold as will be explained later. Pabs(PA) finally is the probability that the hyperon with momentum PA is trapped inside the spectator matter. It is assumed that gN is normalized to 1. Fig. 1 displays the rapidity distribution and fig. 2 the average ( p 2 ) as a function of the rapidity as predicted by the string model VENUS for the reaction 160 G e V / n P b + P b for semicentral collisions. The observables are displayed separately for different species of mesons and baryons. The transverse momentum distribution is assumed to be of the form
g(p±, y) ~ e x p ( --PT/x/ ½(p2(y) ) )f(y) . The average (p~- ( y ) ) depends on the rapidity and is largest at midrapidity. Assuming that only particles with Ybeam-- 0.3 < y < beam+ 0.3 can enter the spectator matter which is expected at Y~Ybeam we see that only K - ' s and n's are possible candidates for hyperon production. Both have very little transverse momentum at beam rapidity. For the calculation we take ( p 2 ( y ) ) =0.1 and 0.04 ( G e V / c ) 2 for K - and n, respectively. We calculate the integral dPM
dp_~d ~
= 2 n J gM(P±, Yproj)gN(P)
Xa3(p~ +p--pA--&)a(E~ +E-EA-EO X d3pfd3p p ± p2A d-QA
with a Monte Carlo procedure. For a given set of initial momenta the final momentum of the A is completely determined. We display dPM/dpz dPA as a scatter plot in figs. 3 and 4. The momenta are displayed in the spectator rest system (Y=Yproj, pz = 0). 261
Volume 274, number 3,4
PHYSICS LETTERS B
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Fig. 3 d i s p l a y s t h e f i n a l m o m e n t u m o f t h e A f o r m e d in t h e r e a c t i o n ~ + N ~ A + K as a f u n c t i o n o f t h e t r a n s v e r s e m o m e n t u m o f t h e p i o n , fig. 4 d i s p l a y s t h e 262
m o m e n t u m d i s t r i b u t i o n o f A ' s f o r m e d in K - + N ~A+n as a f u n c t i o n o f t h e k a o n t r a n s v e r s e momentum.
Volume 274, number 3,4
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We start with the discussion of the reaction rt + N--, A + K. Due to the threshold of ~ = 1.61 GeV a large transverse m o m e n t u m of the pion is necessary
that a hyperon can be formed• Only one out of a thousand pions has sufficient m o m e n t u m to form a hyperon with a spectator nucleon. A large transverse 263
Volume 274, number 3,4 1.0
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PHYSICS LETTERS B
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Fig. 4. Momentum of the A in the spectator rest system produced in the reaction K- + N ~ A + n as a function of the transverse momentum of the kaon. The kaons have an exponential transverse momentum distribution and the nucleonsare distributed according to the Fermi distribution. m o m e n t u m means an appreciable velocity of the n N rest systems with respect to the spectator matter and hence the produced A's have an appreciable m o m e n tum in the spectator rest system. The single particle potential of the A's is much weaker than that for neutrons [ 16 ] and even in the heaviest nuclei it does not exceed - 3 0 MeV [5]. As a rough estimate we assume that only those A's are trapped in the spectator 264
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matter whose m o m e n t u m in the spectator matter rest system is less than Pmax= 260 MeV/c. Thus, we assume t°abs(PA)=O(Pmax--PA). Only about 10 -2 of the produced A's fulfill this requirement. As can be seen from the figure, the result is not very sensitive on the cutoffPmax: changing it to 350 M e V / c would only give a factor of two more hypernuclei. We still have to determine ff'(p M, p) = f W(p M, p, PA, Pf) d3pfd3pA. As most A's are produced close to the threshold we can replace the m o m e n t u m dependence of if" by CO(x/ss-x~o), where so is the threshold energy. C is given by the ratio a(rt + n - ~ A ) / ( y l o , ( r t + n ) ~ 0 . 0 2 for n + N , the value at Plab=l.0 G e V / c [ 5,17 ]. This is of course a rough estimate. Collecting now all the terms we obtain a probability of about 10 -v that a A is produced in a n - n u c l e o n reaction and trapped in the spectator matter. One may think also in A production in secondary processes where the n creates first a p or an q. Due to the low average transverse m o m e n t u m of the pion these meson production processes are not only very rate but also the following A production cross section is presumably small as compared to the total cross section. Therefore they will not play a significant role. The K - ' s are much less copiously produced in the target rapidity regime (on the average 5X 10 -3 per collision) as compared to the pions. However, they have no threshold for A production. This has two consequences; first, the production probability is quite large ffr=a(K-p->A+X)/a,o,(K p ) = 0 . 1 3 . For the reaction K-- + n ~ A + X we assume the same cross section. Secondly, the average m o m e n t u m of the A in the spectator matter is much lower and hence more A's (20%) are trapped• Altogether we obtain a probability for hypernucleus production with a K particle of P ( K - ) = 10 -4 with large uncertainties due to the little knowledge of K - production rates close to target respectively beam rapidity. Thus K ' s although less copiously produced create more A's than the pions. The rate, however, is quite low especially if one aims at the production o f m u l t i - A hypernuclei. The double strangeness exchange reaction ( K - K + ) suffers from a threshold and is very unlikely in view of the low transverse m o m e n t u m of the K - . Hence the production of multi-A hypernuclei [18] is proportional to the power of the production of A hypernuclei.
Volume 274, number 3,4 3. A production
at lower
PHYSICS LETTERS B energies
Although at C E R N energies Ekin=200 G e V / n many strange particles are produced, we have seen that only a very small fraction leads to the formation of hypernuclei because most of m o m e n t u m mismatch between the produced mesons and the spectator matter. This m o m e n t u m mismatch is expected to decrease with beam energy because the available rapidity range becomes smaller. Therefore one may conjecture that hypernucleus production is more likely at lower energies although the number of produced mesons decreases as well. In heavy-ion collisions at energies around several GeV the longitudinal m o m e n t u m distributions of A's have been measured [19,20]. This experiment is supplemented by a measurement of the double differential cross section o f K + in the reaction Ne + N a F and N e + P b at 2.1 G e V / n [21 ]. In addition to the heavy-ion experiments there exist also data on the double differential elementary production cross section p + p ~ K + + X [22,23] in the energy domain of interest. The energy distribution of K ÷ (and hence that of A or E as well) is isotropic in the center of mass system. The K + m o m e n t u m is smaller than expected from phase space in the elementary production process due to a strong final state interaction between the baryons. Below Ebeam=2.6 GeV the elementary production cross section is quite well understood [23] and therefore extrapolations to heavy-ion collisions are easily possible. In order to investigate A production at this lower energy we performed calculations for the reaction 2.1 G e V / n N e + A u b = 1 fm employing the Q M D model [ 10,14,15 ]. Since at these low energies the production of A's is a rare process (which occurs only in 1 out of 10 collisions), we have to treat the production in the following way: we parametrize the cross section a A = N + N - ~ A + K + N according to Randrup and Ko [ 24 ] and compare this cross section with the total NN cross section eNN. The ratio
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probability in a nucleus-nucleus collision. For each N N collision with a x/~ larger than the A production threshold (x/s = 2.55 GeV ) we record the N N center o f mass m o m e n t u m with respect to the nucleus-nucleus center of mass as well as v/~. This allows to calculate the A m o m e n t u m if we assume that the final m o m e n t u m distribution of A's is given by the threebody phase space. In the majority of the events the A are produced in the reaction N + A - , A + K + N. Fig. 5a displays these distributions of the newly formed A's in the nucleus-nucleus CM system. The majority of A's has momenta smaller than that of the nucleon-nucleon system (P~NN=I G e V / c ) . However, practically all A's have a m o m e n t u m which is outside the Fermi sphere of the target nucleus (which has an average m o m e n t u m ofp_./n = - 0 . 2 3 G e V / c ) . 2.0
. . . .
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Fig. 5. Scatter plot of the A momenta in the nucleus-nucleus Cu after production (upper panel), and final distribution (lower panel) calculated as explained in the text. The production of A's is calculated with the QMD model [ 10,14,15]. Each point marks a lambda. 265
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Hence it seems that hypernuclei can also not be formed at SIS energies. This is not true, however, because the A's can interact once more with cold target nucleons. Due to our perturbative approach we cannot follow these further collisions of the A's in a microscopical model. In our calculation the A production is a purely imaginary process in the sense that for the further time evolution only non-strange baryons are allowed. In view of the small A production probability this is certainly a good approximation for the true time evolution of the system: We tag, however, those nucleons which were A's in this imaginary process. If we assume that the dynamics of the A's is similar to that of the nucleons, it makes sense to investigate the final momentum distribution of the tagged nucleons. Their momentum distribution is displayed in fig. 5b. We observe a shift of the distribution of Ap-=0.7 GeV/c as compared to the primordial distribution. Now the majority of the "A" 's has less relative momentum to the spectator matter and has therefore a higher change of being trapped. This shift of the A distribution towards the target rest system has also been observed experimentally [19,20]. Fig. 6 shows the momentum distribution of the produced A's as well as that of the final "A'"s. We see clearly the shift in the momentum distribution. As a rough estimate for the production of hyper-
0.20
....
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Fig. 6. M o m e n t u m d i s t r i b u t i o n of the A's in the n u c l e u s - n u c l e u s CM after p r o d u c t i o n (solid line), and final d i s t r i b u t i o n ( d a s h e d line) calculated as e x p l a i n e d in the text. The p r o d u c t i o n of A's is calculated with the Q M D model [ 10,14,15 ].
266
nuclei we sum up the A production probability of all those nucleons which have finally a relative momentum smaller than 0.2 GeV/c with respect to the spectator rest system. We obtain for this approximation a hypernucleus production probability of 2X10 3 which is considerably larger than that obtained for CERN energies. This rises of course the question whether an intermediate energy, as available at the AGS, would be the optimal choice. This may he true and should be explored. On theoretical grounds, however, the AGS energy domain is very complicated because it marks the transition between hadtonic physics and the string models. Thus calculations are bound to be much more vague as compared to higher or lower energies. However, there may be a hope that RQMD like models [ 7 ] succeed in gaining predictive power for hypernuclei production in the target and projectile rapidity domain. In conclusion we have shown that semiperipheral heavy-ion reactions at 200 GeV/n are probably unsuitable for production of hypernuclei. The x's and K's produced in the string fragmentation cannot enter the spectator matter because they are produced at too low rapidity. This does not include of course a possible formation of hypernuclei by coalescence of participants. The present knowledge of this process is too little to allow an investigation. At lower energies (around 2 GeV/n) the A's, when produced, have also a too large relative velocity with respect to the spectator matter to form a hypernucleus. However, they may scatter with other target nucleons. This experimentally observed process slows down the A's with respect to the target rest system to such a degree that some of them can be trapped.
Acknowledgement
oi0
0.05
16 J a n u a r y 1992
We would like to thank Professor H. Gutbrod and Professor B. Povh for attracting our attention to the production of hypernuclei in relativistic heavy-ion collisions. We also thank Professor U. Lynen and Professor J. Zofka for interesting discussions.
References [ 1 ] A.K. K e r m a n and M.S. Weiss, Phys. Rev. C 8 ( 1 9 7 9 ) 408.
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[ 2 ] A. Bamberger et al., Z. Phys. 43 ( 1989 ) 25; J. Bartke et al., Z. Phys. 48 (1990) 191. [3] C. Brechtmann and W. Heinrich, Z. Phys. A 331 (1988) 463. [4] F. Asai, H. Bando and M. Sano, Phys. Lett. B 145 (1984) 19. [ 5 ] H. Bando et al., Nucl. Phys. A 501 ( 1989 ) 900; H. Bando et al., Intern. J. Mod. Phys. A 5 (1990) 4021. [6] K. Werner and P. Koch, Phys. Lett. B 242 (1990) 251. [7] R. Martiello et al., Nucl. Phys., in press, and references therein. [8] C. Brechtmann and W. Heinrich, Z. Phys. A 331 (1988) 463. [ 9 ] V. Aleklett et al., Phys. Lett. B 197 ( 1987 ) 34. [ 10] J. Jaenicke and J. Aichelin, Phys. Lett. B 256 ( 1991 ) 341.
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[ 11 ] G.D. Westfall et al., Phys. Rev. Lett. 37 (1976) 1202. [ 12] B. Anderson et al., Nucl. Phys. B 281 (1987) 289. [ 13 ] A.I. Warwick et al., Phys. Rev. C 27 ( 1983 ) 1083. [ 14] J. Aichelin et al., Phys. Rep. 202 ( 1991 ) 233. [ 15] G. Peilert et al., Phys. Rev. C 39 (1989) 1402. [ 16] M. Rufa et al., Phys. Rev. C 42 (1990) 2469. [ 17 ] CERN Cross section tables, CERN preprint. [ 18 ] M. Wakai, H. Bando and M. Sano, Phys. Rev. C 38 ( 1988 ) 748. [ 19] V.D. Toneev et al., Soy. J. Part. Nucl. 17 (1986) 521. [20] V.D. Toneev et al., Phys. Rev. Lett. 47 ( 1981 ) 229. [21 ] S. Schnetzer et al., Phys. Rev. C 40 (1989) 640. [22] W.J. Hogan, Phys. Rev. 166 (1968) 166. [23] J.M. Laget, Phys. Lett. B 259 ( 1991 ) 24. [24] J. Randrup and C.M. Ko, N ucl. Phys. A 343 (1980) 519; A 411 (1983) 537.
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