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Production of charged pions in intermediate-energy heavy-ion collisions
Nuclear Physics @ North-Holland
A423 (1984) 51 l-524 Publishing Company
PRODUCTION
OF CHARGED
IN INTERMEDIATE-ENERGY V. BERNARD,
J. GIRARD, Centre
A. OSKARSSON,
PIONS
HEAVY-ION
J. JULIEN,
R. LEGRAIN
COLLISIONS and J. POITOU
d' _&des Nucliaires, Saclay, France
L. CARLEN, H-A. GUSTAFSSON*, B. NOREN, I. OTTERLUND
B. JAKOBSSON, and H. RYDE
P. KRISTIANSSON,
Dept. of Physics, University of Lund, Sweden T. JOHANSSON**
and G. TIBELL
The Gustaf Werner Inst., Vppsala, Sweden R. BERTHOLET,
C. GUET,
M. MAUREL,
H. NIFENECKER,
Centre d’l&udes Nu&aires, M. BUENERD,
P. PERRIN
and F. SCHUSSLER
Grenoble, France
D. LEBRUN
and P. MARTIN
Institute des Sciences Nuclhaires, Grenoble, France G. LBVHBIDEN Dept. of Physics, University of Bergen, Norway J. P. BONDORF
and O-B. NIELSEN
The Niels Bohr Institute, Copenhagen, Denmark and A. PALMER1 Inst. Nazionale di Fisica Nucleare, Sezione di Catania, Italy Received 5 April 1983 (Revised 19 August 1983) Abstract: Cross sections for the production of rr+ and x- have been measured over a wide range of angles for “C +‘Li, “C + ‘*C and ‘*C +*‘sPb collisions at 60A, 75A and 85A MeV. Energy distributions are less steep and absolute yields of pions larger than expected from a straightforward Fermi gas nucleon-nucleon scattering prescription. The apparent velocity of the system in which the QT+emission is symmetric, is closer to the nucleus-nucleus c.m. velocity than to the mean speed system. The Coulomb-corrected m-/ rr+ ratio is close to unity for ‘? + ‘*C. The corresponding ratio for ‘*C +*‘*Pb is, however, much larger than expected from the neutron excess in “‘Pb only. E
NUCLEAR
REACTIONS
‘Li, ‘*C, *‘*Pb(‘*C (E,
* Present address: Lawrence Berkeley Laboratory, ** Present address: CERN, Geneva, Switzerland. 511
r*),
6;. USA.
E =60A,
75A, 85A MeV;
measured
512
V. Bernard et al. / Production of charged pions
1. Introduction
It is tempting to believe that the substantial cross section for pion production, which has been found in heavy-ion collisions with bombarding energies far below the free nucleon-nucleon (NN) threshold I*‘), is an indication that more than two nucleons interact cooperatively. The excitation spectra of light nuclei in (p, T) [ref. ‘)I and (3He, n-) [ref. “)I reactions have certainly supported such a view. When discussing heavy-ion collisions, we must bear in mind that the double Fermi momentum boost brings down the threshold of pion production also in a quasi-free NN-scattering picture, to only a few tens of MeVper nucleon ““). So far, all heavy-ion experiments have been performed well above this threshold. Since it is sometimes claimed that pion production, particularly at backward angles, in relativistic heavy-ion reactions can be explained only with a coherent (cumulative) mechanism ‘), it is of great interest to confront data at much lower beam energies both with coherent models and with NN-scattering models. In this paper we report on an experiment, where we have measured T+ and 7~~ cross sections for symmetric (“C +“C) as well as asymmetric (“C +‘Li, ‘*C +*‘*pb) heavy-ion collisions. The data is compared with the results from a Fermi gas NN-scattering calculation where attention is paid to Pauli blocking and absorption. It should be noticed that due to the large angles and high velocities of all registered pions (& > 0.5 compared to p projs 0.4), we should not expect any Coulomb focusing effects of the kind discussed for experiments at much higher beam energies 8*9).
2. Experimental
details
The high intensity ‘*C beam at the CERN synchrocyclotron
has made it possible cross sections at energies far below the free NN-
to measure pion production scattering threshold *). In the present experiment four plastic scintillator range-telescopes, placed outside a vacuum scattering chamber, viewed the target from positions between 20” and 150” (fig. 1). Each telescope consisted of 12 plastic scintillators (S, -S,,) covering a solid angle of 10-20 msr. The first four scintillators were mainly used for discrimination against the intense proton background. Detectors S&S,, are the elements in which stopping pions were detected (27 MeV< E,, < 82 MeV). S,, and S12 (with a Cu absorber in between) enabled counting of the high-energy pions (Em > 82 MeV). Measurements at the same angle with different telescopes, verified their mutual normalisation. The proton background is strongly dependent on the detection angle, due to the stronger forward peaking of fast protons ‘4, compared to pions in nuclear collisions at these energies (up to =104 protons per emitted pion at forward angles). Thus a powerful hardware rejection of protons is needed to reduce the number of stored events. For particles stopping in Si (or Si+j), the maximum signal for pions from
513
V. Bernard et al. / Production of charged pions
FARADAY
St?AK S,,
b
THICKNESS (mm1 AVERAGE ENERGY
5 5 10 15 25
30
30
30
30
30
32
43
52
61
70
78
PION
IO 20 10
(MeVl
Fig. 1. Schematic drawing of the telescope arrangement around the scattering chamber (a) and one of the four {A-D) identical ptastic scintillator range-telescopes (b). The average energies of pions stopping in the scintiltators are presented.
514 Si+z
V. Bernard et al. j Production of charged pions
is always
smaller
than the minimum
set between
these values,
was efficient
enough
removed
to enable
signal
for protons.
99% of the proton
measurements
at angles
A discriminator
background.
level,
The rejection
8 3 27”.
The final off-line separation of charged pions from protons is then straightforward by use of AEi - AEj and CAEi - AEj correlations. Three AE detectors is sufficient to remove the background also at the lowest energies measured. When a K stops, it is captured by a nucleus in the detector material. The extra energy-deposit, by products from the capturing nucleus in the stop detector, can not be resolved from the prompt pion energy-deposit. Thus, in order to lose as few r- as possible, no cuts were made in the stop-energy signal. Two different methods I’) for seljarating n+ from r- were tried, both based on the decay of the T+ into p + + Y with a mean lifetime of r = 26 ns and a monoenergetic muon of 4.2 MeV. (i) The time between the prompt stop signal and the possible delayed (/_L++) signal was measured in a window of 16~ t < 100 ns. The lower limit was set by the fast recovery time of the electronics. An extrapolation of the decay function (-em”+) gave the number of rf at t = 0. The background of accidental stop signals (constant in time) was in all cases negligible. The number of 7~~ was then obtained by subtracting the number of 7rTT+ from the total number of charged pions. (ii) The second method compared two integrations of the energy pulse, one with a prompt time gate (Q,-“the whole pulse”) and the other with the gate delayed by IO-20 ns (Qd - “only the tail”). The QP - Qd correlation was very sensitive to the appearance of the muon signal within the delayed gate I*). The two methods were checked against each other and were found to give consistent results. In this experiment, the efficiency of method (ii) was less accurately known than that for method (i). Thus the results of method (i) were finally used. However,
a recent
test of the telescopes
in 7~+ and K
beams
has shown
that the
Q,- Qd procedure can be made the most efficient one ‘I). Fig. 2 shows a typical example (S, is the first element used as stop detector) of the particle resolution after the restrictions on all AE signals have been applied. The GT+(fig. 2a, c) are isolated
by the requirement
of the delayed
signal.
No remnant
of any proton band could be observed. Only AE signals are used in the 7r- identification. Nevertheless we believe that the background is effectively suppressed for the following reasons which we give for particles stopping in S, (the lowest pion energy). Here we use the information from four independent scintillators +the range measurement, i.e. we have independently recorded five different parameters of each particle in the telescope. First of all it is extremely improbable that anything but a pion, by accident, has acceptable values of all these parameters. Thus the background is very suppressed by the off-line constraints. Furthermore the contribution to the number of 7r- from the particles with larger E signals than those in the pion band (fig. 2b, d) is found to be (30* S)% for all stop detectors, detection angles, targets and beam energies. A background
V. Bernard et al. / Production of charged pions
51
Fig. 2. The AE - E correlations for pions stopping in S, [(a), (c)] and S, [(b), (d)]. The typical examples are taken at 90” from the reaction 12C+12C. The correlations are obtained after restrictions have been applied on all AE signals from the detectors preceding the stop detector. For the separation of ?r+ from 6 the detection of the pL+from the T+ decay is required (method (i) in the text).
of other particles should show a strong variation with these parameters. One also observes that the background at small AE and E values is totally removed by the constraints although no limitations at all have been imposed on the E signal. The number of pions produced in the target is obtained after corrections for losses due to decay in flight and nuclear reactions 13).These corrections are energy dependent and add up to 2040%. The number of secondary reactions in the detector, which increases rapidly with energy, sets the effective upper limit of pion registration (80-90 MeV). One more source of error occurs for T-. When such a pion is captured a secondary particle, which stops in the next scintillator, may be emitted. This results in a false stop signature and the event is therefore lost in the off-line separation. A test of the telescopes in T* beams I’) showed that this loss was about 5%. Absolute cross sections were finally obtained by measurements of the beam current with a Faraday cup lo). The flux was measured with 20% accuracy. The beam flux was continuously checked by a 3-element plastic scintillator monitor. The corrections for dead-time in the data aquisition system were typically a few % at large angles (>60”) and lO-20% at 27”. The uncertainty in the absolute cross sections is estimated to be ~30% for T+ and somewhat higher for T-. This accuracy is supported by the high-energy (EP > 60 MeV) proton spectra, which were registered with all rejecting conditions off, and found to be well in agreement with those obtained in ref. lo). Furthermore the T+ spectra for ‘*C + ‘*C measured in an earlier experiment *) are well within the 30% uncertainty in the absolute yield (fig. 3a).
516
V. Bernard
et al. / Production of charged pions
The intensity of the full energy (85A MeV) beam was 5 x 109-1 x 10” ions/s. Sufficient counting rates could be obtained with thin targets, i.e. 50-100 mg/cm2. The energy loss of the beam in the target is thus <2A MeV. One can also neglect the correction for pions produced in secondary reactions by energetic nucleons from primary collisions. The beam was also degraded to 75A MeV (dp/p at FWHM is -1%) and to 60A MeV with similar intensities as for 85A MeV. In the experiment reported here, we studied n+ and Y emission from 85A MeV ‘*C-induced reactions in ‘Li (27”, 60”, 90”, 120”), i2C (27”, 60”, 90”, 120”, 150’) and 208Pb (27”, 60”, 90”, 120”). 7~+ and rTT-were registered at 27”, 60”, 90 and 120” for ‘*C + ‘*C reactions at 75A MeV and 60A MeV. 3. Experimental
results
In fig. 3 we present the invariant cross sections, (l/p) d*a/da dE, for rrf. The error bars account for the statistical and efficiency errors in each detector. .75AMeV
C+C-rc++..... 85A MeV +
+
b
a.
+ +
t
+ t
t t
t
k
:n 0
I
C
0 t
t
t
This
Johansson
et al
27’
9o”
0 9o”
27=’
n
0.001
work
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.
n
27’
7
60’
0
9o”
a 120°
I
0
/
I
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I
I
60
I
I
80
I
I
I
20
I
I
LO
I
I
60
I
I
80
E,+[MeV)
Fig. 3. Invariant, doubly differential cross sections, (I/p) d*a/dR dE, of P+ emitted in “C +“C at 85 A MeV (a) and at 75A MeV (b). The beam energy for the ‘*C +‘Li (c) and ‘*C +““Pb (d) reactions is 85A MeV. The curves are obtained from an independent, zero-temperature Fermi gas NN-scattering prescription.
V. Bernard et al. / Production of charged pions
1
C+Li--~‘+.....85A
517
C+Pb+rr++.....
MeV
85A
MeV
+,
d.
0 48
+
+
This work n 27’ 0 9o” A120°
0 t 0.001
I
I 20
I
I
I
LO
I 60
C + Pb
Johansson 0 9o”
I’,
I 80 En+(MeVl
et al C+Au
I
I
20
I LO
I
1 60
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I
I
80
Fig. 3 (cont.)
All energy distributions fall off exponentially from 40 MeV up to the limit of our measurements. The slope parameter (E,, the apparent temperature) given by the 90” c.m. spectrum is 17 f 2 MeV for “C + “C. This “temperature” is somewhat larger than that for protons ‘4. The slope of the 90” proton c.m. spectrum gives E. = 14 f 2 MeV. At first glance, this result seems to be in conflict with results at higher beam energies, where protons give higher “temperatures” than’pions 14).This latter result has been explained as if pions and protons are probing different regions of a participant gas due to their different mean free paths (A,, < hp). However, for the pion and proton energies measured in our experiments h, = A, and we could thus understand the observed temperatures with the same interpretation as in ref. “). Naturally, this interpretation requires that the thermal description is relevant and some of the results to be discussed in this paper throw some doubt on this. In the picture of a classical Boltzmann gas the highest possible temperature would be T=_l AIA2Einc_mv(Al 3 (A,+&)*
+A*) ’
(1)
518
V. Bernard et al. / Production of charged pions
Ei,, is the beam energy per nucleon, Aiczf stands for the pa~icipating beam (target) mass numbers and rn, is the pion mass. Evaluated for “C + r*C at 85A MeV, the maximum equilibrium temperature would be 10 MeV and both the inclusion of binding energies and relativistic corrections will result in lower temperatures. The high “temperature” measured indicates that pions are emitted in pre-equilib~um processes, before complete thermal equilibrium is reached. For the reaction 12C-t12C the 7~+cross sections is reduced at 75A MeV (fig. 3b) by a factor 3-4 compared to the cross section at 85A MeV and at 60A MeV by a factor 10-20. The K cross sections shown in fig. 4 have larger uncertainties due to the identification procedure. The slopes of the 90”, 7~~ spectra are the same as those for n+ but significant differences in the absolute yields are observed. These differenties could originate from the production rate itself or from Coulomb shifts. For the
0
I
/
,
I
t
I
I
10
20
30
40
50
60
70
E,t
iMeW
Fig. 4. Doubly differential cross sections (d*a/dR dE) for T” and 6 emission at 90” from ‘*C +‘Li “C and “C +“‘Pb interactions at 85A MeV. The curves are introduced to guide the eye.
V. Bernard et al. / Production of charged pions
519
isospin symmetric r2C + 12Csystem the production rate of T+ and r- should be the same. Thus the shift observed (==two times 5 MeV) could be understood only as a Coulomb effect. Since we are discussing pions with large velocities compared to any possible Coulomb source, we can neglect focusing effects. The energy shift corresponds approximately to the compound-nucleus (i.e. 24Mg - no compression) Coulomb potential. For the other two targets a small energy shift is seen in the opposite direction (less mTT+ than rIT- for the same energy). If pions are produced in the bulk of the target nucleus, the isospin weights for the different production channels would imply a T-/T+ ratio of (A-Z)/& i.e. a ratio of 1.33 for the 7Li and 1.54 for the 208Pb target. If, however, compound-nucleus Colomb energy shifts are introduced for the “C + Li reaction the experimentally found T-/ rr+ ratio will be about 2.3, i.e. slightly larger than (A-2)/2. For the 12C+‘O*Pb reaction, the result would be a very large 7~~ excess (about a factor 7). Even if pions are produced far out in the surface region, one could not expect a neutron excess which is large enough to explain this ratio. Neither is it possible to account for large deviations from (A-Z)/2 due to structural effects in the recoil nuclei 15).Thus it seems necessarydo consider a reduced effective Coulomb energy, unless the differences in the T+ and rr- production rates due to the different Fermi energies or the different absorption rates of protons and neutrons could account for such a large P-/T+ ratio in the picture of NN collisions. Without looking into these two last possibilities in detail, it seems likely that the enhanced Pauli blocking with increasing Fermi energy and the principle of detailed balance in production and absorption will counteract a strong T- excess. All curves in figs. 3a-d represent NN-scattering calculations in a straightforward Fermi gas approach. Thus sharp (zero-temperature) internal momentum distributions are introduced: g(p)= -0(P 3
477p:
-Pd
*
(2)
8 is here the theta function and Fermi momenta (pF) are taken from Monitz 16). Binding energies have not been introduced - including them results in somewhat smaller yields and steeper spectra. The number of NN collisions is calculated within the optical limit of Glauber theory. Pauli blocking has been introduced - an effect which reduces the absolute yield by at least one order of magnitude. Finally it should be noticed that the emission cross section should be further reduced by absorption. A Monte Carlo simulation of this effect, assuming a frozen geometry, results in an overall reduction in the yield of about a factor 5 for ‘*C + 12C.However, there is a large uncertainty in this reduction due to the uncertainty in the pion absorption cross section 17)and in the simplified description of the overlap region. It is important to notice that the stong contribution from the NN + drr channels is included in the calculations, and that the deuteron is treated, in the nuclear environment, as two nucleons with the same momentum.
520
V. Bernard et al. / Production of charged pions
The invariant spectra obtained from NN scattering in the zero-temperature Fermi gas description cannot reproduce the experimental data. The absolute yields are in all cases underestimated by at least one order of magnitude and the slopes are everywhere too steep. In order to trace the relevant velocity of the pion production source we show in fig. 5 a contour plot in the plane of &mm, versus the Lorentz-invariant parallel velocity (rapidity) defined as y = 4 In (E +pll)/(E -pII). In the non-relativistic limit Y=PII and PTIm, =& In the plot, points of equal invariant doubly differential cross sections have been connected by contour lines. The reaction displayed is ‘*C + “C at 85A MeV, for which the set of data is most complete. The rapidity of the beam is 0.4 and therefore y = 0.2 represents the rapidity of the NN system and, of course, also the nucleus-nucleus c.m. system. It is clear from fig. 5 that the emission, as expected, is symmetric with respect to the half-beam velocity. In the figure we show a contour (solid curve) for isotropic emission in the half-beam rapidity frame. One notices that the experimental controus are not completely isotropic and the forward-backward peaking seems to be stronger than for highenergy pion emission at higher energies 18,19).However, as was pointed out in ref. I*), at 183A MeV a slight forward-backward peaking appears, for the low-energy pions.
---
NN calculation
-‘-.-
Isotropy
in CM
0.6
0.4
0.2
0
-1.0
- 0.8
-0.6
-0.4
-0.2
0 y+n
0.2 2
0.4
0.6
0.8
1.0
I,
Fig. 5. Contour plot displaying rr+ from the “C + “C reaction in the pr/ m, rapidity plane. connects points of equal invariant cross sections. Neighbouring contour curves differ in by a factor 2. The dot-dashed curve, normalised to the experimental cross section at (y = 0.2, shows isotropic emission in the NN c.m. system while the dashed curve is the result of the calculations.
Each contour cross sections h/m, = 0.86), NN-scattering
V. Bernard
et al. / Production
521
ofchargedpions
The pion production is also forward-backward peaked in the NN calculation, dashed line in fig. 5, as a net result of the input angular distribution in NN scattering, Pauli blocking and reabsorption (included in this calculation). The degree of anisotropy is in fact slightly stronger than that observed in the data. In fig. 6 we show the angular distributions of T+ for all targets at 85A MeV in the laboratory system and the NN c.m. frame. The energy integration is done between 35 and 65 MeV and between 25 and 55 MeV, respectively. It is evident that the laboratory distributions are more forward peaked for smaller target nuclei. In the mean speed system, the symmetry, as observed in the contour plot for ‘*C + ‘*C, is recognised. With a heavy target nucleus, the angular distribution becomes strongly backward peaked, while the opposite is observed for ‘*C +‘Li reactions. This should
I
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I
I
I
v
I
C
.
.
.
.
Cl
Li ?\/;
Fig. 6. Angular distributions of ?r+ in the laboratory system (35 S E,, s 65 MeV) and in the NN cm. system (25 s E,, s 55 MeV). The curves are obtained from the NN-scattering calculations (normalized in the 0 = 90” point).
522
V. Bernard et al. / ~oduction
ofchargedpions
imply that the average system, in which the emission is symmetric, is slower than the NN cm. system in the former case and faster in the latter. However, it is not obvious that the observed asymmetry should be interpreted as an effect of the velocity of the source. The pion reabsorption in the shadowing parts of the nuclei, and also Pauli blocking, could cause asymmetry in the NN c.m. frame. The NN scattering model (curves in fig. 6b) gives at least qualitatively the same tendency as seen in the data, although the strong suppression of backward emission in “6 +‘Li is not reproduced. One should bear in mind that the available phase space for the nucleons in pion-producing NN scattering is confined to the end caps of the internal momentum spheres. Therefore also small changes in the Fermi momenta of one nucleus in an asymmetric reaction may affflect the angular distributions drastically. This might be one reason for the drop of the cross section at backward angles for the 7Li target. It should also be noticed that the choice of the volume, from which the pions are assumed to start their penetration through the nuclei, is very critical for the forward-backward asymmetry. The strong suppression of the forward emission in 12C+ “‘Pb collisions can, of course, only occur if central collisions are dominating the scenario. The total 7rt production cross section is difIicult to deduce from the limited ranges of energies and angles measured. Assuming a power law dependence of the cross section on AT (At), one finds 4 s (Y< f when comparing “C and *08Pbat all measured angles. Such values of ty again imply that the cross section is dominated by central collisions. Peripheral collisions would give a: -5 (possible below f due to pion reabsorption). A much stronger A-dependence (o > 1) is observed when comparing ‘Li and ‘*C. Such a strong A, dependence could be attributed not only to different sizes of the nuclei, but could again be a drastic effect of the smaller Fermi momentum of the 7Li nucleus. In the recent experiment of Grosse et al. 20), where the total 7~’ cross sections have been measured, it is suggested that c- A,Aq3 -tATAi’3, i.e. the complete participant part of the A, + A, volume should be involved. Because of the low-energy cut-off at 27 MeV in our experiment we cannot properly test this suggestion which would favour a collective production process. 4. Conclusions
The ari and n- yields decrease with beam energy in the region 60A-85A MeV as expected from the combination of available phase-space and pion-production cross sections for free NN scattering. However, the experimentally observed diff erential cross sections fall off in energy less steeply than an NN-scattering (zerotemperature Fermi gas) process. The absolute yield of pions is also much larger than expected from the NN-scattering description. Furthermore the apparent velocity of the pion emitting source seems to be closer to the nucleus-nucleus cm. system than to the mean speed system. In order to
V. Bernard et al. / Production of charged pions
523
reproduce the spectral shapes of the emitted pions in the NN-scattering description one needs to introduce high internal momentum components “). A first attempt to avoid such classically forbidden momentum components of nucleons in a soft sphere model by placing nucleons in their proper shells has been made by Shyam and Knoll 22). They claim that this approach fails to explain the data. They suggest instead a multi-nucleon cooperative process including the formation of composite particles as an alternative explanation. Another collective process which seems to be able to explain the TO spectra from “C + 12Cat 84A MeV [ref. “‘)I (and therefore probably also our data which is generally in good agreement with the rr” data) is a classical coherent bremsstrahlung process 23). If strong Coulomb effects (the compound nucieus Coulomb energy) are taken into account, the T-/T+ ratio for the light systems (12C+“C and ‘%‘Z+‘Li) could be qualitatively understood if the neutron excess in ‘Li is considered. For the 208Pb target, however, a large n- excess is observed. If we want to keep the strong Coulomb source, which is typical for a pion-producing process in the early stage of the reaction, it seems necessary to consider the different rTf and T- production rates due to differences in the Fermi momenta for protons and neutrons. The strong AT dependence in the cross section indicates that central collisions are dominating among the pion-producing events. Experiments with neutron-rich and neutron-deficient isotopes, especially for lowenergy pions, are necessary to achieve a better unde~tanding of the T-/T+ ratios. This work was made possible because of financial support from the CEN Saclay and the Natural Science Research councils of Denmark and Sweden. The support and interest from the SC machine group at CERN were outstanding. Several enlightning discussions with Dr. M. Prakash are acknowledged. References 1) 2) 3) 4)
W. Benenson ef al., Phys. Rev. Lett. 43 (1979) 683 T. Johansson ei at, Phys. Rev. Lett. 48 (1982) 732 B. Hoistad, Adv. Nucl. Phys. 11 (1979) 135 Y. le Bornec, L. Bimbot, N. Koori, F. Reide, A. ZWiBis, N. Willis and C. Wilkin, Phys. Rev. Lett. 47 (1981) 1870 5) G.F. Bertsch, Phys. Rev. Cl5 (1977) 713 6) B. Jakobsson, Proc. Nordic Meeting on nuclear physics, Fugelso, Denmark (1982) 7) Meng-taXhung and E. Moeller, Phys. Rev. Lett. 41 (1978) 1352 8) J.P. Sullivan er al., Lawrence Berkeley Lab. report, LBL 11971 (1981) 9) K.G. Libbrecht and SE. Koonin, Phys. Rev. Lett. 4 (1979) 1581 10) B. Jakobsson et aL Phys. Lett. 1OZB(1981) 121; A. Oskarsson, dissertation, University of Lund, (1983) 11) J. Julien et aL, to be published 12) J. Julien, Proc. 3rd Int. Conf. on nuclear reaction mechanisms, Varenna 1983 13) J. Chiba, thesis, University of Tokyo report no. UTPN-130 (1979) 14) S. Nagamiya, M.-C. Lemaire, E. Moeller, S. Schnetzer, G. Shapiro, H. Steiner and I. Tanihata, Phys. Rev. C24 (1981) 971 15) D.C. Peaslee, Phys. Rev. 95 (1954) 1580
524 16) 17) 18) 19) 20)
V. Bernard et al. / Production of charged pions
E.J. Moniz et al., Phys. Rev. Lett. 26 (1971) 445 P. Hecking, Phys. Lett. 103B (1981) S. Nagamiya et al.Lawrence Berkeley Lab. report, LBL 14033 (1982) W. Benenson, Report given at a seminar in State University of New York, Stony Brook 1982 E. Grosse, Reports given at the Niels Bohr Institute, Copenhagen and at the University of Lund 1982; C. Michel, Report at the XXI Meeting on nuclear physics, Bormio 1983 21) R.C. Hatch and SE. Koonin, Phys. Lett. 818 (1979) 1 22) R. Shyam and J. Knoll, Contribution to the 6th Int. Balaton Topical Conf. on high energy nuclear physics, Balatonfiired, Hungary, June 5-l 1, 1983 23) D. Vasak et al., Phys. Scripta 22 (1980) 25; Phys. Lett. 93B (1980) 243
A423 (1984) 51 l-524 Publishing Company
PRODUCTION
OF CHARGED
IN INTERMEDIATE-ENERGY V. BERNARD,
J. GIRARD, Centre
A. OSKARSSON,
PIONS
HEAVY-ION
J. JULIEN,
R. LEGRAIN
COLLISIONS and J. POITOU
d' _&des Nucliaires, Saclay, France
L. CARLEN, H-A. GUSTAFSSON*, B. NOREN, I. OTTERLUND
B. JAKOBSSON, and H. RYDE
P. KRISTIANSSON,
Dept. of Physics, University of Lund, Sweden T. JOHANSSON**
and G. TIBELL
The Gustaf Werner Inst., Vppsala, Sweden R. BERTHOLET,
C. GUET,
M. MAUREL,
H. NIFENECKER,
Centre d’l&udes Nu&aires, M. BUENERD,
P. PERRIN
and F. SCHUSSLER
Grenoble, France
D. LEBRUN
and P. MARTIN
Institute des Sciences Nuclhaires, Grenoble, France G. LBVHBIDEN Dept. of Physics, University of Bergen, Norway J. P. BONDORF
and O-B. NIELSEN
The Niels Bohr Institute, Copenhagen, Denmark and A. PALMER1 Inst. Nazionale di Fisica Nucleare, Sezione di Catania, Italy Received 5 April 1983 (Revised 19 August 1983) Abstract: Cross sections for the production of rr+ and x- have been measured over a wide range of angles for “C +‘Li, “C + ‘*C and ‘*C +*‘sPb collisions at 60A, 75A and 85A MeV. Energy distributions are less steep and absolute yields of pions larger than expected from a straightforward Fermi gas nucleon-nucleon scattering prescription. The apparent velocity of the system in which the QT+emission is symmetric, is closer to the nucleus-nucleus c.m. velocity than to the mean speed system. The Coulomb-corrected m-/ rr+ ratio is close to unity for ‘? + ‘*C. The corresponding ratio for ‘*C +*‘*Pb is, however, much larger than expected from the neutron excess in “‘Pb only. E
NUCLEAR
REACTIONS
‘Li, ‘*C, *‘*Pb(‘*C (E,
* Present address: Lawrence Berkeley Laboratory, ** Present address: CERN, Geneva, Switzerland. 511
r*),
6;. USA.
E =60A,
75A, 85A MeV;
measured
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1. Introduction
It is tempting to believe that the substantial cross section for pion production, which has been found in heavy-ion collisions with bombarding energies far below the free nucleon-nucleon (NN) threshold I*‘), is an indication that more than two nucleons interact cooperatively. The excitation spectra of light nuclei in (p, T) [ref. ‘)I and (3He, n-) [ref. “)I reactions have certainly supported such a view. When discussing heavy-ion collisions, we must bear in mind that the double Fermi momentum boost brings down the threshold of pion production also in a quasi-free NN-scattering picture, to only a few tens of MeVper nucleon ““). So far, all heavy-ion experiments have been performed well above this threshold. Since it is sometimes claimed that pion production, particularly at backward angles, in relativistic heavy-ion reactions can be explained only with a coherent (cumulative) mechanism ‘), it is of great interest to confront data at much lower beam energies both with coherent models and with NN-scattering models. In this paper we report on an experiment, where we have measured T+ and 7~~ cross sections for symmetric (“C +“C) as well as asymmetric (“C +‘Li, ‘*C +*‘*pb) heavy-ion collisions. The data is compared with the results from a Fermi gas NN-scattering calculation where attention is paid to Pauli blocking and absorption. It should be noticed that due to the large angles and high velocities of all registered pions (& > 0.5 compared to p projs 0.4), we should not expect any Coulomb focusing effects of the kind discussed for experiments at much higher beam energies 8*9).
2. Experimental
details
The high intensity ‘*C beam at the CERN synchrocyclotron
has made it possible cross sections at energies far below the free NN-
to measure pion production scattering threshold *). In the present experiment four plastic scintillator range-telescopes, placed outside a vacuum scattering chamber, viewed the target from positions between 20” and 150” (fig. 1). Each telescope consisted of 12 plastic scintillators (S, -S,,) covering a solid angle of 10-20 msr. The first four scintillators were mainly used for discrimination against the intense proton background. Detectors S&S,, are the elements in which stopping pions were detected (27 MeV< E,, < 82 MeV). S,, and S12 (with a Cu absorber in between) enabled counting of the high-energy pions (Em > 82 MeV). Measurements at the same angle with different telescopes, verified their mutual normalisation. The proton background is strongly dependent on the detection angle, due to the stronger forward peaking of fast protons ‘4, compared to pions in nuclear collisions at these energies (up to =104 protons per emitted pion at forward angles). Thus a powerful hardware rejection of protons is needed to reduce the number of stored events. For particles stopping in Si (or Si+j), the maximum signal for pions from
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FARADAY
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b
THICKNESS (mm1 AVERAGE ENERGY
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Fig. 1. Schematic drawing of the telescope arrangement around the scattering chamber (a) and one of the four {A-D) identical ptastic scintillator range-telescopes (b). The average energies of pions stopping in the scintiltators are presented.
514 Si+z
V. Bernard et al. j Production of charged pions
is always
smaller
than the minimum
set between
these values,
was efficient
enough
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to enable
signal
for protons.
99% of the proton
measurements
at angles
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level,
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8 3 27”.
The final off-line separation of charged pions from protons is then straightforward by use of AEi - AEj and CAEi - AEj correlations. Three AE detectors is sufficient to remove the background also at the lowest energies measured. When a K stops, it is captured by a nucleus in the detector material. The extra energy-deposit, by products from the capturing nucleus in the stop detector, can not be resolved from the prompt pion energy-deposit. Thus, in order to lose as few r- as possible, no cuts were made in the stop-energy signal. Two different methods I’) for seljarating n+ from r- were tried, both based on the decay of the T+ into p + + Y with a mean lifetime of r = 26 ns and a monoenergetic muon of 4.2 MeV. (i) The time between the prompt stop signal and the possible delayed (/_L++) signal was measured in a window of 16~ t < 100 ns. The lower limit was set by the fast recovery time of the electronics. An extrapolation of the decay function (-em”+) gave the number of rf at t = 0. The background of accidental stop signals (constant in time) was in all cases negligible. The number of 7~~ was then obtained by subtracting the number of 7rTT+ from the total number of charged pions. (ii) The second method compared two integrations of the energy pulse, one with a prompt time gate (Q,-“the whole pulse”) and the other with the gate delayed by IO-20 ns (Qd - “only the tail”). The QP - Qd correlation was very sensitive to the appearance of the muon signal within the delayed gate I*). The two methods were checked against each other and were found to give consistent results. In this experiment, the efficiency of method (ii) was less accurately known than that for method (i). Thus the results of method (i) were finally used. However,
a recent
test of the telescopes
in 7~+ and K
beams
has shown
that the
Q,- Qd procedure can be made the most efficient one ‘I). Fig. 2 shows a typical example (S, is the first element used as stop detector) of the particle resolution after the restrictions on all AE signals have been applied. The GT+(fig. 2a, c) are isolated
by the requirement
of the delayed
signal.
No remnant
of any proton band could be observed. Only AE signals are used in the 7r- identification. Nevertheless we believe that the background is effectively suppressed for the following reasons which we give for particles stopping in S, (the lowest pion energy). Here we use the information from four independent scintillators +the range measurement, i.e. we have independently recorded five different parameters of each particle in the telescope. First of all it is extremely improbable that anything but a pion, by accident, has acceptable values of all these parameters. Thus the background is very suppressed by the off-line constraints. Furthermore the contribution to the number of 7r- from the particles with larger E signals than those in the pion band (fig. 2b, d) is found to be (30* S)% for all stop detectors, detection angles, targets and beam energies. A background
V. Bernard et al. / Production of charged pions
51
Fig. 2. The AE - E correlations for pions stopping in S, [(a), (c)] and S, [(b), (d)]. The typical examples are taken at 90” from the reaction 12C+12C. The correlations are obtained after restrictions have been applied on all AE signals from the detectors preceding the stop detector. For the separation of ?r+ from 6 the detection of the pL+from the T+ decay is required (method (i) in the text).
of other particles should show a strong variation with these parameters. One also observes that the background at small AE and E values is totally removed by the constraints although no limitations at all have been imposed on the E signal. The number of pions produced in the target is obtained after corrections for losses due to decay in flight and nuclear reactions 13).These corrections are energy dependent and add up to 2040%. The number of secondary reactions in the detector, which increases rapidly with energy, sets the effective upper limit of pion registration (80-90 MeV). One more source of error occurs for T-. When such a pion is captured a secondary particle, which stops in the next scintillator, may be emitted. This results in a false stop signature and the event is therefore lost in the off-line separation. A test of the telescopes in T* beams I’) showed that this loss was about 5%. Absolute cross sections were finally obtained by measurements of the beam current with a Faraday cup lo). The flux was measured with 20% accuracy. The beam flux was continuously checked by a 3-element plastic scintillator monitor. The corrections for dead-time in the data aquisition system were typically a few % at large angles (>60”) and lO-20% at 27”. The uncertainty in the absolute cross sections is estimated to be ~30% for T+ and somewhat higher for T-. This accuracy is supported by the high-energy (EP > 60 MeV) proton spectra, which were registered with all rejecting conditions off, and found to be well in agreement with those obtained in ref. lo). Furthermore the T+ spectra for ‘*C + ‘*C measured in an earlier experiment *) are well within the 30% uncertainty in the absolute yield (fig. 3a).
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The intensity of the full energy (85A MeV) beam was 5 x 109-1 x 10” ions/s. Sufficient counting rates could be obtained with thin targets, i.e. 50-100 mg/cm2. The energy loss of the beam in the target is thus <2A MeV. One can also neglect the correction for pions produced in secondary reactions by energetic nucleons from primary collisions. The beam was also degraded to 75A MeV (dp/p at FWHM is -1%) and to 60A MeV with similar intensities as for 85A MeV. In the experiment reported here, we studied n+ and Y emission from 85A MeV ‘*C-induced reactions in ‘Li (27”, 60”, 90”, 120”), i2C (27”, 60”, 90”, 120”, 150’) and 208Pb (27”, 60”, 90”, 120”). 7~+ and rTT-were registered at 27”, 60”, 90 and 120” for ‘*C + ‘*C reactions at 75A MeV and 60A MeV. 3. Experimental
results
In fig. 3 we present the invariant cross sections, (l/p) d*a/da dE, for rrf. The error bars account for the statistical and efficiency errors in each detector. .75AMeV
C+C-rc++..... 85A MeV +
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Fig. 3. Invariant, doubly differential cross sections, (I/p) d*a/dR dE, of P+ emitted in “C +“C at 85 A MeV (a) and at 75A MeV (b). The beam energy for the ‘*C +‘Li (c) and ‘*C +““Pb (d) reactions is 85A MeV. The curves are obtained from an independent, zero-temperature Fermi gas NN-scattering prescription.
V. Bernard et al. / Production of charged pions
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Fig. 3 (cont.)
All energy distributions fall off exponentially from 40 MeV up to the limit of our measurements. The slope parameter (E,, the apparent temperature) given by the 90” c.m. spectrum is 17 f 2 MeV for “C + “C. This “temperature” is somewhat larger than that for protons ‘4. The slope of the 90” proton c.m. spectrum gives E. = 14 f 2 MeV. At first glance, this result seems to be in conflict with results at higher beam energies, where protons give higher “temperatures” than’pions 14).This latter result has been explained as if pions and protons are probing different regions of a participant gas due to their different mean free paths (A,, < hp). However, for the pion and proton energies measured in our experiments h, = A, and we could thus understand the observed temperatures with the same interpretation as in ref. “). Naturally, this interpretation requires that the thermal description is relevant and some of the results to be discussed in this paper throw some doubt on this. In the picture of a classical Boltzmann gas the highest possible temperature would be T=_l AIA2Einc_mv(Al 3 (A,+&)*
+A*) ’
(1)
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V. Bernard et al. / Production of charged pions
Ei,, is the beam energy per nucleon, Aiczf stands for the pa~icipating beam (target) mass numbers and rn, is the pion mass. Evaluated for “C + r*C at 85A MeV, the maximum equilibrium temperature would be 10 MeV and both the inclusion of binding energies and relativistic corrections will result in lower temperatures. The high “temperature” measured indicates that pions are emitted in pre-equilib~um processes, before complete thermal equilibrium is reached. For the reaction 12C-t12C the 7~+cross sections is reduced at 75A MeV (fig. 3b) by a factor 3-4 compared to the cross section at 85A MeV and at 60A MeV by a factor 10-20. The K cross sections shown in fig. 4 have larger uncertainties due to the identification procedure. The slopes of the 90”, 7~~ spectra are the same as those for n+ but significant differences in the absolute yields are observed. These differenties could originate from the production rate itself or from Coulomb shifts. For the
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40
50
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Fig. 4. Doubly differential cross sections (d*a/dR dE) for T” and 6 emission at 90” from ‘*C +‘Li “C and “C +“‘Pb interactions at 85A MeV. The curves are introduced to guide the eye.
V. Bernard et al. / Production of charged pions
519
isospin symmetric r2C + 12Csystem the production rate of T+ and r- should be the same. Thus the shift observed (==two times 5 MeV) could be understood only as a Coulomb effect. Since we are discussing pions with large velocities compared to any possible Coulomb source, we can neglect focusing effects. The energy shift corresponds approximately to the compound-nucleus (i.e. 24Mg - no compression) Coulomb potential. For the other two targets a small energy shift is seen in the opposite direction (less mTT+ than rIT- for the same energy). If pions are produced in the bulk of the target nucleus, the isospin weights for the different production channels would imply a T-/T+ ratio of (A-Z)/& i.e. a ratio of 1.33 for the 7Li and 1.54 for the 208Pb target. If, however, compound-nucleus Colomb energy shifts are introduced for the “C + Li reaction the experimentally found T-/ rr+ ratio will be about 2.3, i.e. slightly larger than (A-2)/2. For the 12C+‘O*Pb reaction, the result would be a very large 7~~ excess (about a factor 7). Even if pions are produced far out in the surface region, one could not expect a neutron excess which is large enough to explain this ratio. Neither is it possible to account for large deviations from (A-Z)/2 due to structural effects in the recoil nuclei 15).Thus it seems necessarydo consider a reduced effective Coulomb energy, unless the differences in the T+ and rr- production rates due to the different Fermi energies or the different absorption rates of protons and neutrons could account for such a large P-/T+ ratio in the picture of NN collisions. Without looking into these two last possibilities in detail, it seems likely that the enhanced Pauli blocking with increasing Fermi energy and the principle of detailed balance in production and absorption will counteract a strong T- excess. All curves in figs. 3a-d represent NN-scattering calculations in a straightforward Fermi gas approach. Thus sharp (zero-temperature) internal momentum distributions are introduced: g(p)= -0(P 3
477p:
-Pd
*
(2)
8 is here the theta function and Fermi momenta (pF) are taken from Monitz 16). Binding energies have not been introduced - including them results in somewhat smaller yields and steeper spectra. The number of NN collisions is calculated within the optical limit of Glauber theory. Pauli blocking has been introduced - an effect which reduces the absolute yield by at least one order of magnitude. Finally it should be noticed that the emission cross section should be further reduced by absorption. A Monte Carlo simulation of this effect, assuming a frozen geometry, results in an overall reduction in the yield of about a factor 5 for ‘*C + 12C.However, there is a large uncertainty in this reduction due to the uncertainty in the pion absorption cross section 17)and in the simplified description of the overlap region. It is important to notice that the stong contribution from the NN + drr channels is included in the calculations, and that the deuteron is treated, in the nuclear environment, as two nucleons with the same momentum.
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The invariant spectra obtained from NN scattering in the zero-temperature Fermi gas description cannot reproduce the experimental data. The absolute yields are in all cases underestimated by at least one order of magnitude and the slopes are everywhere too steep. In order to trace the relevant velocity of the pion production source we show in fig. 5 a contour plot in the plane of &mm, versus the Lorentz-invariant parallel velocity (rapidity) defined as y = 4 In (E +pll)/(E -pII). In the non-relativistic limit Y=PII and PTIm, =& In the plot, points of equal invariant doubly differential cross sections have been connected by contour lines. The reaction displayed is ‘*C + “C at 85A MeV, for which the set of data is most complete. The rapidity of the beam is 0.4 and therefore y = 0.2 represents the rapidity of the NN system and, of course, also the nucleus-nucleus c.m. system. It is clear from fig. 5 that the emission, as expected, is symmetric with respect to the half-beam velocity. In the figure we show a contour (solid curve) for isotropic emission in the half-beam rapidity frame. One notices that the experimental controus are not completely isotropic and the forward-backward peaking seems to be stronger than for highenergy pion emission at higher energies 18,19).However, as was pointed out in ref. I*), at 183A MeV a slight forward-backward peaking appears, for the low-energy pions.
---
NN calculation
-‘-.-
Isotropy
in CM
0.6
0.4
0.2
0
-1.0
- 0.8
-0.6
-0.4
-0.2
0 y+n
0.2 2
0.4
0.6
0.8
1.0
I,
Fig. 5. Contour plot displaying rr+ from the “C + “C reaction in the pr/ m, rapidity plane. connects points of equal invariant cross sections. Neighbouring contour curves differ in by a factor 2. The dot-dashed curve, normalised to the experimental cross section at (y = 0.2, shows isotropic emission in the NN c.m. system while the dashed curve is the result of the calculations.
Each contour cross sections h/m, = 0.86), NN-scattering
V. Bernard
et al. / Production
521
ofchargedpions
The pion production is also forward-backward peaked in the NN calculation, dashed line in fig. 5, as a net result of the input angular distribution in NN scattering, Pauli blocking and reabsorption (included in this calculation). The degree of anisotropy is in fact slightly stronger than that observed in the data. In fig. 6 we show the angular distributions of T+ for all targets at 85A MeV in the laboratory system and the NN c.m. frame. The energy integration is done between 35 and 65 MeV and between 25 and 55 MeV, respectively. It is evident that the laboratory distributions are more forward peaked for smaller target nuclei. In the mean speed system, the symmetry, as observed in the contour plot for ‘*C + ‘*C, is recognised. With a heavy target nucleus, the angular distribution becomes strongly backward peaked, while the opposite is observed for ‘*C +‘Li reactions. This should
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Cl
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Fig. 6. Angular distributions of ?r+ in the laboratory system (35 S E,, s 65 MeV) and in the NN cm. system (25 s E,, s 55 MeV). The curves are obtained from the NN-scattering calculations (normalized in the 0 = 90” point).
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ofchargedpions
imply that the average system, in which the emission is symmetric, is slower than the NN cm. system in the former case and faster in the latter. However, it is not obvious that the observed asymmetry should be interpreted as an effect of the velocity of the source. The pion reabsorption in the shadowing parts of the nuclei, and also Pauli blocking, could cause asymmetry in the NN c.m. frame. The NN scattering model (curves in fig. 6b) gives at least qualitatively the same tendency as seen in the data, although the strong suppression of backward emission in “6 +‘Li is not reproduced. One should bear in mind that the available phase space for the nucleons in pion-producing NN scattering is confined to the end caps of the internal momentum spheres. Therefore also small changes in the Fermi momenta of one nucleus in an asymmetric reaction may affflect the angular distributions drastically. This might be one reason for the drop of the cross section at backward angles for the 7Li target. It should also be noticed that the choice of the volume, from which the pions are assumed to start their penetration through the nuclei, is very critical for the forward-backward asymmetry. The strong suppression of the forward emission in 12C+ “‘Pb collisions can, of course, only occur if central collisions are dominating the scenario. The total 7rt production cross section is difIicult to deduce from the limited ranges of energies and angles measured. Assuming a power law dependence of the cross section on AT (At), one finds 4 s (Y< f when comparing “C and *08Pbat all measured angles. Such values of ty again imply that the cross section is dominated by central collisions. Peripheral collisions would give a: -5 (possible below f due to pion reabsorption). A much stronger A-dependence (o > 1) is observed when comparing ‘Li and ‘*C. Such a strong A, dependence could be attributed not only to different sizes of the nuclei, but could again be a drastic effect of the smaller Fermi momentum of the 7Li nucleus. In the recent experiment of Grosse et al. 20), where the total 7~’ cross sections have been measured, it is suggested that c- A,Aq3 -tATAi’3, i.e. the complete participant part of the A, + A, volume should be involved. Because of the low-energy cut-off at 27 MeV in our experiment we cannot properly test this suggestion which would favour a collective production process. 4. Conclusions
The ari and n- yields decrease with beam energy in the region 60A-85A MeV as expected from the combination of available phase-space and pion-production cross sections for free NN scattering. However, the experimentally observed diff erential cross sections fall off in energy less steeply than an NN-scattering (zerotemperature Fermi gas) process. The absolute yield of pions is also much larger than expected from the NN-scattering description. Furthermore the apparent velocity of the pion emitting source seems to be closer to the nucleus-nucleus cm. system than to the mean speed system. In order to
V. Bernard et al. / Production of charged pions
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reproduce the spectral shapes of the emitted pions in the NN-scattering description one needs to introduce high internal momentum components “). A first attempt to avoid such classically forbidden momentum components of nucleons in a soft sphere model by placing nucleons in their proper shells has been made by Shyam and Knoll 22). They claim that this approach fails to explain the data. They suggest instead a multi-nucleon cooperative process including the formation of composite particles as an alternative explanation. Another collective process which seems to be able to explain the TO spectra from “C + 12Cat 84A MeV [ref. “‘)I (and therefore probably also our data which is generally in good agreement with the rr” data) is a classical coherent bremsstrahlung process 23). If strong Coulomb effects (the compound nucieus Coulomb energy) are taken into account, the T-/T+ ratio for the light systems (12C+“C and ‘%‘Z+‘Li) could be qualitatively understood if the neutron excess in ‘Li is considered. For the 208Pb target, however, a large n- excess is observed. If we want to keep the strong Coulomb source, which is typical for a pion-producing process in the early stage of the reaction, it seems necessary to consider the different rTf and T- production rates due to differences in the Fermi momenta for protons and neutrons. The strong AT dependence in the cross section indicates that central collisions are dominating among the pion-producing events. Experiments with neutron-rich and neutron-deficient isotopes, especially for lowenergy pions, are necessary to achieve a better unde~tanding of the T-/T+ ratios. This work was made possible because of financial support from the CEN Saclay and the Natural Science Research councils of Denmark and Sweden. The support and interest from the SC machine group at CERN were outstanding. Several enlightning discussions with Dr. M. Prakash are acknowledged. References 1) 2) 3) 4)
W. Benenson ef al., Phys. Rev. Lett. 43 (1979) 683 T. Johansson ei at, Phys. Rev. Lett. 48 (1982) 732 B. Hoistad, Adv. Nucl. Phys. 11 (1979) 135 Y. le Bornec, L. Bimbot, N. Koori, F. Reide, A. ZWiBis, N. Willis and C. Wilkin, Phys. Rev. Lett. 47 (1981) 1870 5) G.F. Bertsch, Phys. Rev. Cl5 (1977) 713 6) B. Jakobsson, Proc. Nordic Meeting on nuclear physics, Fugelso, Denmark (1982) 7) Meng-taXhung and E. Moeller, Phys. Rev. Lett. 41 (1978) 1352 8) J.P. Sullivan er al., Lawrence Berkeley Lab. report, LBL 11971 (1981) 9) K.G. Libbrecht and SE. Koonin, Phys. Rev. Lett. 4 (1979) 1581 10) B. Jakobsson et aL Phys. Lett. 1OZB(1981) 121; A. Oskarsson, dissertation, University of Lund, (1983) 11) J. Julien et aL, to be published 12) J. Julien, Proc. 3rd Int. Conf. on nuclear reaction mechanisms, Varenna 1983 13) J. Chiba, thesis, University of Tokyo report no. UTPN-130 (1979) 14) S. Nagamiya, M.-C. Lemaire, E. Moeller, S. Schnetzer, G. Shapiro, H. Steiner and I. Tanihata, Phys. Rev. C24 (1981) 971 15) D.C. Peaslee, Phys. Rev. 95 (1954) 1580
524 16) 17) 18) 19) 20)
V. Bernard et al. / Production of charged pions
E.J. Moniz et al., Phys. Rev. Lett. 26 (1971) 445 P. Hecking, Phys. Lett. 103B (1981) S. Nagamiya et al.Lawrence Berkeley Lab. report, LBL 14033 (1982) W. Benenson, Report given at a seminar in State University of New York, Stony Brook 1982 E. Grosse, Reports given at the Niels Bohr Institute, Copenhagen and at the University of Lund 1982; C. Michel, Report at the XXI Meeting on nuclear physics, Bormio 1983 21) R.C. Hatch and SE. Koonin, Phys. Lett. 818 (1979) 1 22) R. Shyam and J. Knoll, Contribution to the 6th Int. Balaton Topical Conf. on high energy nuclear physics, Balatonfiired, Hungary, June 5-l 1, 1983 23) D. Vasak et al., Phys. Scripta 22 (1980) 25; Phys. Lett. 93B (1980) 243