NASA NASA-TP-2600 19860021013 _i

Technical t

_Paper _2600

August 1986Cross Section Calculationsfor Subthreshold PionProduction in PeripheralHeavy-Ion Collisions

John W. Norbury,Francis A. Cucinotta,Philip A, Deutchman,and Lawrence W. Townsend

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NASATechnicalPaper2600

1986

Cross Section Calculationsfor Subthreshold PionProduction in PeripheralHeavy-Ion Collisions

John W. Norbury andFrancis A. Cucinotta

Old Dominion UniversityNorfolk, Virginia

Philip A. DeutchmanUniversity of IdahoMoscow, Idaho

Lawrence W. TownsendLangley Research CenterHampton, Virginia

National Aeronauticsand Space Administration

Scienlific and TechnicalIntormalion Branch

Introduction fragmentation (ref. 29) and has since been extendedand utilized to describe pion production by Hiller

In individual nucleon-nucleon collisions, pion pro- and Pirner (refs. 18 and 19) and by Brown, Deutch-duction at energies lower than 290 MeV is forbidden man, Townsend, Madigan, Norbury, and Cucinottaby energy conservation. However, in nucleus-nucleus (refs. 20-27). In its latest formulation (refs. 26 andcollisions, pions have been produced at energies as 27) (described in the next section), which forms thelow as 25 MeV/nucleon (refs. 1 and 2), far below the basis of the calculations in the present paper, it willnucleon-nucleon threshold. Such subthreshold meson be referred to as the "particle-hole model."production is one of the most fascinating phenom-

ena to be observed in heavy-ion collisions in recent Description and History of Particle-Holeyears. One of the original suggestions that such pi- Modelons might be observed dates back to McMillan andTeller (ref. 3), who hypothesized that nucleons could We begin by briefly describing the "particle-holebe boosted to energies above threshold by their Fermi model" as used in the present calculations. Modifi-motions within the nucleus. The first theoretical cations to the previous formulation (ref. 26) and amodel of this type, developed by Bertsch (ref. 4), brief account of its historical development are alsohas been applied to various sets of experimental data presented. Then, total cross sections, angular dis-(refs. 5 and 6). Since the pions in this model are pro- tributions, spectral distributions, doubly differen-duced by a nucleon-nucleon single collision (NNSC) tial cross sections, and Lorentz-invariant differentialprocess whose probability decreases with increasing cross sections for neutral and charged pions producedboosts, it is insufficient to adequately explain all the in carbon-carbon collisions in the energy range of 35data (refs. 6 and 7). However, the possibility that to 86 MeV/N are calculated and compared with re-some of the inclusive pion data are the result of this cent heavy-ion pion data. Finally, the effects on theprocess is not ruled out, since it is likely that several cross sections of including Pauli blocking and pioncompeting processes may contribute, especially for absorption are investigated.incident energies well above the absolute threshold. Pions can be produced by means of intermediate

Since NNSC models are unable to explain all the isobar A(3,3) formation in both 7rN ---*A ---, 7rNdata, statistical and thermal models have been pro- and NN ---*NA ---, NNTc processes. In the formerposed (refs. 6 and 8-10). In these models, the pions process, a real pion interacts with a nucleon toare produced by statistical processes, and the associ- form an isobar which subsequently decays back toated production cross sections are determined from a pion and nucleon. The latter process is similar tothe phase space available to them. The two major the former except that the real incident pions arevariations in this approach involve either (1) corn- replaced by virtual incident pions with the incidentpound nucleus decay (ref. 9) in which pions and nu- nucleon acting as the source for the virtual pions.cleons boil off after statistical equilibrium is achieved Hence, the second reaction proceeds in the sameamong the nucleons in the entire nucleus or (2) statis- manner as the first, except that the incident pionstical equilibrium and subsequent evaporation within are virtual rather than real.subgroups of nucleons (ref. 10) (i.e., "hot spots") It is important to realize that the virtual pionor composite fragments (refs. 6 and 8). At the ab- cloud surrounding a nucleus can be quite differentsolute nucleus-nucleus threshold, pionie fusion, also from the virtual pion cloud surrounding a nucleontermed doubly coherent production, may be the only (refs. 18-20). This difference is essential to thepossible mechanism for pion production. In this present description (refs. 20-27) of subthreshold pionprocess, the colliding nuclei fuse to form a com- production. It is the nucleus as a whole whichpound system and an emitted pion (refs. 11-13). determines the properties of the virtual pion cloud (inExamples of this mechanism inciude the reactions particular, its energy spectrum). In this description,3He(6Li, _-)9C and 3He(3He, 7r+)6Li discussed in these nuclear virtual pions impinge on the nucleons inreferences 11 and 12, respectively, the other nucleus to form isobars which subsequently

Apart from NNSC and statistical or thermal rood- decay into real pions.els, the third grouping into which the theoretical This model was first proposed by Brown andmodels may be classified (ref. 14) is the collective Deutchman (ref. 20), who were interested not onlymodels. The two main categories here are pionic in subthreshold pion production but also in a cor-bremsstrahlung (refs. 15-17) and models based on responding signature unique to the above reactionthe WeizsScker-Williams method (refs. 18-27) orig- mechanism, since it was realized that neither thisinally used in electrodynamics (ref. 28). This lat- mechanism (nor perhaps any other) would explainter method was originally used to describe nuclear all the inclusive cross section data. Implicit in the

above description is the notion of a grazing or pe- in the Breit-Wigner term by the explicit dependenceripheral (as opposed to central) collision. If the iso- on the nucleon kinetic energy TN.bar forms in the projectile nucleus, then the target In previous work (refs. 20-26), the A(3,3) for-will go to an excited state because of conservation of mation in the projectile with M1 formation in thespin and isospin. Various states are possible, but the target was considered. In the present work, we haveones concentrated on are the isovector triplet includ- also summed contributions from the process in whiching the magnetic dipole (M1) giant resonance in 12C, the A(3, 3) forms in the target with M1 formation insince it decays by emission of a 15.11-MeV photon the projectile. Summing these contributions is im-in coincidence with the escaping pion, which comes portant, as there is no way for experimentalists tofrom the decay of an isobar in an 160 projectile nu- distinguish between the pions from the projectile orcleus and thus gives a unique signature to the above the target. In the present work, we have also per-reaction mechanism, formed extensive numerical integrations, so that an-

The above ideas were the basis for a first- gular (da/dgt), spectral (da/dE), and total crosssec-quantized formalism (refs. 21-25). Later, however, tions can be calculated in various reference frames.the whole theory was reformulated in second quanti- Furthermore, the presentation of cross sections for azation in which the simultaneous excitation of an M1 much larger range of projectile subthreshold energiesgiant resonance and a A(3,3) giant resonance was de- and pion angles allows a much wider comparison withscribed in a particle-hole model (refs. 26 and 27). experimental data. The effects of Pauli blocking and

pion absorption are studied by varying the width FAPresent Developments of the isobar resonance (refs. 18 and 30) according to

The main purpose of a previous paper by Nor- the prescription of Hiller and Pirner (ref. 18) wherebury, Deutchman, and Townsend (ref. 26) was topresent the basic particle-hole model. In it, Lorentz- FA = )_Ffree + Fab s (2)invariant and doubly differential cross sections formO incident upon 12C at 2.1 GeV/N and 85 MeV/N with Ffree representing the free width of the iso-

bar (115 MeV). The fraction A accounts for Pauliat single fixed angles were presented. In the presentwork, we have evaluated cross sections for 12C in- blocking as the free width is reduced as a result ofcident upon 12C because of the greater availability the closed decay channels when the A is a nuclearof experimental data for this reaction. Consequently medium. The term Fabs accounts for pion absorp-

the lPl/2 shell is no longer filled with nucleons, so tion effects.The final improvement is that we now distin-tile particle-hole coefficients Xph(P) describing tile guish between charged and neutral pions from con-probability for excitation of a particular nucleon to siderations of pions produced in elementary nucleon-an isobar are different from previous work, as are nucleon collisions by means of isobar formationthe sums over various j values. The net result is (refs. 31 and 32). Here one simply calculates thethat the Lorentz-invariant differential cross section

probabilities (i.e., isotopic spin Clebsch-Gordon coef-for pion production in a 12C projectile with M1 gi- ficients) of pion production through the various pos-ant resonance formation in a 12C target now becomes sible channels and then deduces the relative contribu-

(ref. 26) tions of the proton-proton (pp), proton-neutron (pn),

d3a (rr/) or neutron-neutron (nn) cross sections for producinga particular pion species. The contribution (refs. 31c3 d3pTr/E:r and 32) for 7r° production is

13 25 r u \3] \ m:rc2 ] 1/3app T 2/3apn,_AT(_A)x

(T N q- TTr + mrrc 2 q- my c2 -- mAc2) 2 + (FA/2) 2 and the contribution for r + or rr- production is

×r2(kz.)/2(kz.) (:)5/6app + 1/6apn

where aAT(WA), the isobar formation cross section,is given by equation (64) in reference 26, and tile with the assumption thatform factors F 2 (k_=) and f2 (k/3,_) are given byequations (39) and (48) in that same work. The Opp = ann (3)unrationalized coupling constant, f2 = 0.08, andthe other symbols, if not obvious, are described in Note that the cross section for 7r+ and 7r- productionreference 26. Note that nucleon recoil is now included is the same in the above simple picture.

Results Although not plotted, the 7r° total production crosssection at 25 MeV/N for 160 + 27A1is estimated to

Neutral Pion Production be 5.0 nb by using the "scaling" formula (ref. 33)

Since the results displayed in this work representthe sum of cross sections for pions being produced /'27 ×16_ 2/3

either in the projectile or in the target (unless oth- a(O-A1) = _,]2x --_12] a(C-C) (4)erwise indicated), it is instructive to decompose the

smnmed Lorentz-invariant differential cross section This calculated value compares very well with the re-into the projectile and target contributions. This cently measured value (ref. 2) of 5.8 nb. (Note thatis done in figure 1 for neutral pions produced at 0° one must be very careful in using eq. (4) for inci-in the laboratory by 75 MeV/N carbon-carbon col- dent energies close to absolute threshold.) However,lisions. As expected, in the laboratory frame low- because the theoretical value quoted above does notenergy pions are produced mainly from the target, include threshold effects, the above scaling formulawhereas the higher energy pions come from the pro- should be approximately valid.jectile. The dip in the projectile cross section curve at For the sake of further qualitative comparisonsabout 10 MeV is caused by the fact that the cross sec- of the shape of the spectral and angular distribu-tion is zero for pions of zero energy in the rest frame tions, the inclusive data of Braun-Munzinger et al.of the nucleus emitting them. The net effect of sum- (ref. 1) are presented for the reaction AI(14N, 7r°) inming projectile and target cross sections is a broader figures 6 and 7. Also shown are calculated valuesenergy distribution than that obtained from consid- for the carbon-carbon system. Although the nucleieration of pions produced only from the projectile are different and only rough qualitative agreement isnucleus (ref. 26). In figure 2, the Lorentz-invariant sought, one can see that the magnitudes and shapesneutral pion production cross sections for 75 MeV/N are reasonably well predicted by our theory. Againcarbon-carbon scattering are presented as a function measurements for the carbon-carbon system wouldof laboratory pion kinetic energy and angle. As ex- be helpful to validate the theory.pected, the cross section decreases at higher pion en- In summary, the agreement between theory andergies as the laboratory angle increases. Similar be- experiment is quantitatively excellent for the produc-havior is displayed in figure 3 for the noninvariant tion of neutral pions especially in view of the lack ofdoubly differential cross section at 85 MeV/N. any arbitrarily adjusted parameters in the theoretical

As mentioned previously, the present work studies formalism.pion production in the carbon-carbon collision sys-

tem, rather than the oxygen-carbon system of refer- Charged Pion Productionence 26, so that more definitive comparisons with re-cent experimental data are made. Figure 4 presents The Lorentz-invariant differential cross sectionsspectral distributions for various subthreshold pro- for _r+ production at 85 and 75 MeV/N are shown injectile energies. Also plotted are the experimental figures 8 and 9 together with the data of Bernard etmeasurements of Noll et al. (ref. 7). Since we have no al. (ref. 34), and Johansson et al. (ref. 5). Noninvari-arbitrarily adjusted parameters or scale factors in our ant doubly differential cross sections at 85 MeV/Ntheory, the quantitative agreement between theory are shown in figure 10 with the data of Johansson etand experiment is excellent. Discrepancies between al. (ref. 5) and Jakobsson (ref. 35). For the highertheory and experiment are largely the result of the in- pion energies, the qualitative behavior of the theo-clusive nature of the experimental data, whereas the retical predictions follows the data in that there is atheory represents an exclusive process. One would decrease in the cross sections as the pion energy istherefore expect that the agreement between the in- increased and also as the angle increases. However,clusive data and the exclusive theory should improve the quantitative agreement between theory and ex-as the projectile energy is lowered (ref. 24), and this is periment for the charged pions is not as good as theclearly true for these spectral distributions. This im- agreement for neutral pions.proving agreement is also obvious in the total cross By comparing our theoretical predictions for 7r+sections displayed in figure 5. Agreement with the production in figures 9 and 10 with those for 7r° pro-total cross section at 35 MeV/N is within the quoted duction in figures 2 and 3, one can see that the crosserror. Thus one would expect that the prediction sections are quite similar. As noted before, com-of the spectral distribution at 35 MeV/N (in fig. 4) parison between theory and experiment for 7r° pro-would reproduce the full inclusive spectrum at this duction is very good. Thus we attribute the poorerenergy. We encourage experimentalists to undertake agreement for 7r+ production to the fact that we havesuch measurements in order to test this prediction, not included Coulomb distortion effects (refs. 36-38).

It is well known, for instance, that the 7r+/Tr- ratio have made use of a free isobar width of 115 MeV.varies significantly (refs. 36-38), yet at present, this If a nucleon is excited to an isobar in a certain shellratio is always unity in theory. Work on Coulomb ef- model state, then it becomes possible for a nucleon infects is currently underway and is considered to be of a higher state to fill the nucleon hole that was createdcrucial importance in applying our theory to charged below it before the isobar decays. Therefore when thepion data. isobar does eventually decay into a nucleon and pion,

The curves for O_r = 90° in figure 10 are shown there is now no vacant hole for the nucleon to fallagain in figure 11, but this time a decomposition of into. Thus the decay of the isobar is inhibited, whichthe summed cross section is shown for charged pions means that the half-life of an isobar in a nuclearcoming from the projectile and target at 90°. At this medium will be longer than its free half-life. Con-angle, the behavior is reversed from that in figure 1. sequently, the decay width of an isobar in a nuclearAt 90°, the higher energy pions observed in the lab- medium is smaller than that of a free isobar. This ef-oratory come mainly from the target, whereas lower feet is represented by the AFfree term in equation (2),energy pions come from the projectile. Continuing where A is a fraction less than unity, and AFfree repre-with comparison to the charged pion data, figure 12 sents the nuclear decay width due to Pauli blocking.shows noninvariant cross section data of Chiavassa et There is, however, another effect that tends to in-

al. (ref. 39) for both 7_+ and 7r- at 0°. Clearly the crease the width. Not only can the isobar have inter-_r+/_r- ratio varies significantly. Shown also are our actions within the nuclear medium (refs. 40 and 41),calculated values for charged pions, but after the isobar decays, the emitted pions can be

Figures 13 and 14 show angular distributions in absorbed in the nuclear medium (refs. 42-44). Thiswhich the exclusive theoretical results are below the effect is known to be dependent on the pion energyinclusive data at 85 MeV/N. These results are con- (refs. 42-44). These subsequent interactions of thesistent with the results from the spectral and total pions lead to an effective increase of the isobar decaycross sections for 7r° production (figs. 4 and 5) at width (ref. 14).84 MeV/N. Since the calculation is exclusive, ex- We follow the work of Hiller and Pirner (ref. 18)act agreement is not expected at energies as high as and take the width due to Pauli blocking to be about85 McV/N. (Recall that the agreement for 7r° pro- 80 MeV (with A _ 0.7) and the pion absorptionduction improved substantially for lower projectile width to be 120 MeV. Thus the width with bothenergies.) These angular distribution results are also Pauli blocking and pion absorption is about 200 MeVconsistent with tile kinetic energy distribution com- (ref. 18). In figures 15 through 19, graphs for an iso-parisons of figures 8-12. There the experimental data bar width of 115 MeV (from figs. 4, 6, 7, 8, and 12)were generally well above the theoretical predictions are presented with graphs for isobar widths of 80 and(again at the higher projectile energies). The angular 200 MeV. In figures 16 through 19, as the width in-distributions involve an integration over pion kinetic creases, the cross section decreases as expected, sinceenergy, and thus if the kinetic energy distributions larger widths effectively correspond to greater pionare mostly below the data, one would expect the absorption and thus reduce the pion production crosssame to be true of the angular distributions. Note section. It is noted, however, that the cross sectionsin figure 14 that even though the calculated values are not drastically modified by Pauli blocking andare well below the experimental data, the qualita- pion absorption effects but vary at most by an ap-tive behavior observed experimentally of cross sec- proximate factor of 2 when changing the width fromtions falling as the pion energy increases is predicted 80 to 200 MeV. Again, this approach represents onlytheoretically as well. a preliminary study of these effects. In a more so-

SumInarizing the results for charged pion produc- phisticated treatment, the pion absorption should re-tion, we see in general that the theoretically pre- ally be made dependent on the pion energy and thedieted values are lower than the experimentally oh- charge species, and these effects may introduce someserved data at 75 to 86 MeV/N, a result consistent anisotropy into the angular correlations.with the neutral pion results. Further work on in-cluding Coulomb distortion effects is clearly impor- Conc|uding Remarkstant and needed for definitive comparisons with the A particle-hole calculation for subthreshold piondata. production by means of intermediate isobar and mag-

netic dipole (M1) giant resonance formation has beenPauli Blocking and Pion Absorption extended to a study of the carbon-carbon system.In this section we make a very preliminary investi- The modifications and improvements to the theory

gation of Pauli blocking and pion absorption effects include a 12C projectile (rather than 160), nucleonby noting that all the calculations presented so far recoil, summation of pions from both projectile and

target (rather than projectile only), calculations of and Puddu, G.: Doubly Coherent Production of lr- byspectral, angular, and total cross sections in vari- 3He Ions of 910 MeV. Phys. Rev. Lett., vol. 43, no. 20,

ous reference frames (by numerical integrations), an Nov. 12, 1979i pp. 1466-1470.increased range of subthreshold projectile energies, 12. Germond, Jean-Franqois; and Wilkin, Colin: Coherentconsiderations of Pauli blocking and pion absorp- Pion Production in 3He-3He Collisions. Phys. Lett.,

vol. 106B, no. 6, Nov. 26, 1981, pp. 449-452.tion, and the distinction between neutral and charged 13. Le Bornec, Y.; Bimbot, L.; Koori, N.; Reide, F.; Willis,pion species. Extensive comparisons with experimen- A.; Willis, N.; and Wilkin, C.: Coherent Pion Produc-tal data have been made, and excellent agreement tion Near Threshold With a 3He Projectile. Phys. Rev.has been achieved for neutral pions. Disparities for Lctt., vol. 47, no. 26, Dec. 28, 1981, pp. 1870-1874.charged pions illustrate the need to include Coulomb 14. Guet, C.; and Prakash, M.: Knock Out for Subthresholddistortion. Pion Production. Nucl. Phys., vol. A428, Oct. 22, 1984,

pp. 119c-135c.

NASA Langley Research Center 15. Vasak, David; St5cker, Horst; Mfiller, Berndt; andGreiner, Walter: Pion Bremsstrahlung and Critical Phe-Hampton, VA 23665-5225 nomena in Relativistic Nuclear Collisions. Phys. Lett.,June 2, 1986 vol. 93B, no. 3, June 16, 1980, pp. 243-246.

16. Vasak, D.; Miiller, B.; and Greiner, W.: Pion Radia-tion From Fast Heavy Ions. Phys. Scr., vol. 22, 1980,

References pp. 25-35.I. Braun-Munzinger, P.; Paul, P.; Ricken, L.; Stachel, J.; 17. Vasak, David; Greiner, Walter; Miiller, Berndt; Stahl,

Zhang, P. H.; Young, G. R.; Obenshain, F. E.; and Thomas; and Uhlig, Mark: Pionic Bremsstrahlung inGrosse, E.: Pion Production in Heavy-Ion Collisions Heavy-Ion Collisions. Nucl. Phys., vol. A428, Oct. 22,at Elab/A ----35 MeV. Phys. Roy. Lctt., vol. 52, no. 4, 1984, pp. 291c-303c.Jan. 23, 1984, pp. 255-258. 18. Hiller, Brigitte; and Pirner, Hans J.: Coherent r-

2. Obenshain, F. E.; Plasil, F.; Young, G. R.; Braun- Production in He3 + Li6 ---*7r- + X at 303 MeV/N.Munzinger, P.; Freifelder, R.; and Stachel, J.: Mea- Phys. Lett., vol. 109B, no. 5, Mar. 4, 1982, pp. 338-340.surement of Neutral Pion Production Cross Section for 19. Pirner, Hans J.: Quasiparticle Properties of the Pion

160 + 27A1at 25 MeV/Nucleon. Bull. American Phys. and Heavy-Ion Collisions. Phys. Rev. C, Third ser.,Soc., vol. 30, no. 4, Apr. 1985, p. 768. vol. 22, no. 5, Nov. 1980, pp. 1962-1970.

3. McMillan, W. G.; and Teller, E.: On the Production 20. Brown, G. E.; and Deutchman, P. A.: Coherent Pionof Mesotrons by Nuclear Bombardment. Phys. Rev., Production in 100 MeV/A C12-Heavy Target ScatteringSecond ser., vol. 72, no. 1, July 1, 1947, pp. 1-6. With High Resolution. Paper presented at Workshop

4. Bertsch, G. F.: Threshold Pion Production in Heavy- on High Resolution Heavy Ion Physics (Saclay, France),Ion Collisions. Phys. Rev. C., Third ser., vol. 15, no. 2, May 31-June 2, 1978.Feb. 1977, pp. 713-718. 21. Townsend, L. W.; and Deutchman, P. A.: Isobar Giant

5. Johansson, T.; Gustafsson, H.-/_.; et al.: Subthreshold Resonance Formation in Self-Conjugate Nuclei. Nucl.Pion Production in Heavy-Ion Collisions at 85A MeV. Phys., vol. A355, 1981, pp. 505-532.Phys. Rev. Lett., vol. 48, no. 11, Mar. 15, 1982, pp. 732- 22. Deutchman, P. A.; and Townsend, L. W.: Coherent735. Isobar Production in Peripheral Relativistic Heavy-Ion

6. Shyam, R.; and Knoll, J.: Subthreshold Pion Production Collisions. Phys. Rev. Lett., vol. 45, no. 20, Nov. 17,in Nucleus Collisions--A Cooperative Process! Phys. 1980, pp. 1622-1625.Lett., vol. 136B, no. 4, Mar. 8, 1984, pp. 221-225. 23. Deutchman, P. A.; and Townsend, L. W.: Isobars and

7. Noll, H.; Grosse, E.; Brann-Munzinger, P.; Dabrowski, Isobaric Analog States. Phys. Rev., ser. C, vol. 25, no. 2,H.; Heckwolf, H.; Klepper, O.; Michel, C.; Miiller, Feb. 1982, pp. 1105-1107.W. F. J.; Stelzer, H.; Brendel, C.; and RSsch, W.: Co- 24. Townsend, L. W.; Deutchman, P. A.; Madigan, R. L.;operative Effects Observed in the _r° Production From and Norbury, J. W.: Pion Production Via Isobar Gi-Nucleus-Nucleus Collisons. Phys..Rev. Lett., vol. 52, ant Resonance Formation and Decay. Nucl. Phys. A,no. 15, Apr. 9, 1984, pp. 1284-1287. vol. 415, Mar. 19, 1984, pp. 520-529.

8. Shyam, R.; and Knoll, J.: A Cooperative Mechanism of 25. Deutchman, P. A.; Madigan, R. L.; Norbury, J. W.; andSubthreshold Pion Production. Nucl. Phys., vol. A426, Townsend, L. W.: Pion Production Through Coherentno. 3, Sept. 24, 1984, pp. 606-624. Isobar Formation in Heavy-Ion Collisions. Phys. Lett.,

9. Aichelin, J.; and Bertsch, G.: Subthreshold Pions From ser. B, vol. 132, no. 1, 2, 3, Nov. 24, 1983, pp. 44-46.the Compound Nucleus? Phys. Lett., vol. 138B, no. 5, 26. Norbury, J. W.; Deutchman, P. A.; and Townsend,6, Apr. 26, 1984, pp. 350-352. L.W.: A Particle-Hole Calculation for Pion Production

10. Aichelin, J.: New Evidence for "Hot Spots" From Sub- in Relativistic Heavy-Ion Collisions. Nucl. Phys. A,threshold Pions. Phys. Roy. Lett., vol. 52, no. 26, vol. 433, no. 4, Feb. 18, 1985, pp. 691-712.June 25, 1984, pp. 2340-2343. 27. Norbury, J. W.; Cucinotta, F. A.; Deutchman,

11. Aslanides, E.; Fassnacht, P.; Hibou, F.; Chiavassa, E.; P.A.; and Townsend, L. W.: Theoretical SpectralDellacasa, G.; Gallio, M.; Musso, A.; Bressani, T.; Distributions and Total Cross Sections for Neutral

Subthreshold Pion Production in Carbon-Carbon Col- Nucleon. Phys. Rev. Lett., vol. 43, no. 10, Sept. 3, 1979,lisions. Phys. Rev. Lett., vol. 55, no. 7, Aug. 12, 1985, pp. 683-686; Errata, vol. 44, no. 1, Jan. 7, 1980, p. 54.pp. 681-683. 37. Bertsch, G.: Charge Dependence of Pion Production in

28. Jackson, John David: Classical Electrodynamic8, Second Heavy Ion Collisions. Nature, vol. 283, no. 5744, Jan. 17,ed. John Wiley & Sons, Inc., c.1975. 1980, pp. 280-281.

29. Feshbach, Herman; and Zabek, Mark: Fragmentation of 38. Gyulassy, M.; and Kauffmann, S. K.: Coulomb Effects inRelativistic Heavy Ions. Ann. Phys., vol. 107, nos. 1-2, Relativistic Nuclear Collisions. Nucl. Phys., vol. A362,Sept. 6, 1977, pp. 110-125. no. 2, June 8, 1981, pp. 503-533.

30. Dillig, M.; and Huber, M. G.: Is There a Giant (3,3) 39. Chiavassa, E.; Costa, S.; et al.: Pion Production in 12C-Resonance in Nuclei? Phys. Lett., vol. 48B, no. 5, Mar. 4, Nucleus Interactions at 86 MeV/Nucleon. Nucl. Phys.,1974, pp. 417-419. vol. A422, no. 3, July 2, 1984, p. 621-634.

31. Lock, W. O.; and Measday, D. F.: Intermediate Energy 40. Ginocchio, J. N.: Deep Inelastic Pion-Induced NuclearNuclear Physics. Methuen 8z Co. Ltd., 1970, p. 220. Reactions in the Isobar Model. Phys. Rev. C, Third ser.,

32. Pilkuhn, Hartmut M.: Relativistic Particle Physics. vol. 17, no. 1, Jan. 1978, pp. 195-214.Springer-Verlag, c.1979, p. 404. 41. Moniz, E. J.: A-Nucleus Interactions. Nucl. Phys.,

33. Stachel, J.: Pion Production in Heavy Ion Collisions vol. A354, nos. 1, 2, Feb. 23, 1981, pp. 535c-553c.Close to Absolute Thresholds. Paper presented at the7th High Energy Heavy Ion Study, GSI, Darmstadt 42. Sparrow, D. A.; Sternheim, Morton M.; and Silbar,(Federal Republic of Germany), Oct. 1984. Richard R.: Semiclassical Model for Pion Production by

34. Bernard, V.; Girard, J.; et al.: Production of Neutrons on Nuclei. Phys. Rev. C., Third ser., vol. 10,Charged Pions in Intermediate-Energy Heavy-Ion Col- no. 6, Dec. 1974, pp. 2215-2220.lisions. Nucl. Phys., vol. A423, no. 3, July 23, 1984, 43. Yoo, K.-B.; and Landau, R. H.: Pion Annihilationpp. 511-524. in Nuclei, Spin, Isospin and Energy Dependence. 5th

35. Jakobsson, B.: Pions Produced in Heavy Reactions Far High Energy Heavy Ion Study--Proceedings, LBL-12652Below the Free Nucleon-Nucleon Scattering Threshold. (UC-34, CONF-8105104) (Contract W-7405-ENG-48),Phys. Scr., vol. T5, 1983, pp. 207-212. 1981, pp. 736-737.

36. Benenson, W.; Bertsch, G.; et al.: Low-Energy Pion 44. Ashery, Daniel: Pion Nucleus Reactions. Nucl. Phys.,Production at 0° With Heavy Ions From 125 to 400 MeV/ vol. A354, nos. 1, 2, Feb. 23, 1981, pp. 555c-576c.

6

Symbols F A isobar resonance width, MeV

c speed of light (3 × 108 m/sec) A isobar

c.m. center of mass O pion angle of detection

E energy A Pauli blocking factor,

ETr pion total energy in projectile dimensionless

reference frame, MeV or GeV _r0 neutral pion

f2 unrationalized coupling con- 7r+ positively charged pionstant (0.08), dimensionless

7r- negatively charged pionf2(k_) form factor (defined in eq. (48)

of ref. 26) a total cross section

F2(k¢_) form factor (defined in eq. (39) ann neutron-neutron total crossof ref. 26) section, mb

m N nucleon rest mass, MeV/c 2 Crpn proton-neutron total cross

mix isobar rest mass, MeV/c 2 section, mbOpp proton-proton total cross

mr pion rest mass, MeV/c 2 section, mb

N nucleon a(X-Y) 7r0 production cross section

p momentum for collision involving nuclearspecies X and Y, mb or nb

p/_ nucleon momentum followingisobar decay, MeV/c aZxT(WZx) isobar formation cross section,

mb or nbP_r pion momentum following

isobar decay, MeV/cd3cy_Ir,rf)['x pion production Lorentz-

TN nucleon kinetic energy, MeV c3 d3p_/Er invariant differential cross

Tr pion kinetic energy, MeV section, mb-GeV -2 ormb-MeV -2

Fabs pion absorption effect width,MeV _-f final angular momentum

Ffree free-state isobar resonance f2 solid anglewidth (115 MeV)

i00 l i , '

10-1 12C (12C, TrO) 75 MeV/N -

O;r=0°d3o

/--Summedd3plE' 10-2mb-c3

10-3

Projectile

10-4 , j l0 20 40 60 80 I00

T_ MeV (lab)

Figure 1. Theoretical Lorentz-invariant cross sections for v0 production at O_ = 0° in carbon-carbon collisionsat 75 MeV/N. Theoretical curves show decomposition of summed cross section in terms of contributions ofpions from projectile and target.

8

100 , , , i

12c (12C,O) 75MeV/N10-I-

d3o

mb.c3 10-2

GeV2

10.40 _0 _0 6'0 _0 _tTTT,MeV (lab)

Figure 2. Theoretical Lorentz-invariant doubly differential cross sections for _r0 production at 75 MeV/N.Angular values are OTr.

g

10o I I i I

12C(12C,7rO) 85MeV/N-I

-10 -

d2o

dEd-"-'_'10-2-

mbGeV-sr

_ 55°

10-3 90 _

10-4 l i I l0 20 40 60 80 100

T_r,MeV (lab)

Figure 3. Theoretical noninvariant doubly differential cross sections for _0 production at 85 MeV/N. Angularvalues are O_r.

10

0 4 I I !! !

12C (12C,_.0)103 ,_.l__X10

.xI0 I_...,

102

do

n._....Lb1°1MeV

10o

I0-I <

35_eW eV/N '

10-2 , _k_,M , ,0 40 80 120 160 200

Tm MeV (c.m.)

Figure 4. Spectral distributions for _r0 production. Solid curves display theoretical predictions of this study;histograms show experimental data of reference 7.

11

100 , , l i

12C (12C,;T0) •10

O,pb 1

10-1

10-2 I I , I0 20 40 60 80 I00

TTr, MeVIN (lab)

Figure 5. Total _o production cross sections as a function of incident projectile energy. Curve displaystheoretical predictions; circles are experimental data of references 1 and 7.

12

1.5i L , ,i Experiment: AI (I4N, 7rO)

Theory: 12C (12C, 7rO)

1.0da 35 MeV/N_-,nb

MeVO.

I I

0 30 60 90 120

TTr,MeV (lab)

Figure 6. Spectral distributions for _0 production. Solid curve displays theoretical predictions of this studyfor 12C on 12C; histogram and error bars display experimental data of reference 1 for A1 on 14N.

10 I I I

Experiment: AI (14N, 7rO)

7. Theory: 12C(12C,7rO) _

do

nb 5.

2.5-

I I I0 45 90 135 180

eTr, deg (lab)

Figure 7. Angular distributions for 7r° production. Solid curve displays theoretical predictions of this studyfor 12C on 12C; histograms and error bars display experimental data of reference 1 for A1 on 14N.

13

I00 , , I ,

27°_.90° _. -_.. i_.

i0-I_ 120°_ -._"'60° "--.-_. "5

_F.,"

d3o _:,_,,

,omb-c3

GeV2-'_ __12 °°

- 12C (12C, m"+) 85 MeV/N --- _'''_10-3

10-4 I { I0 20 40 60 80 100

T_T,MeV (lab)

Figure 8. Theoretical and experimental (refs. 5 and 34) Lorentz-invariant doubly differential cross sections for7r+ production at 85 MeV/N. Solid lines represent theoretical predictions; dashed lines are drawn throughexperimental data points only to facilitate visual inspection; angular values are OTr.

14

100 I , , '

1o-I- _. _--_.. -

.. __." 60o_''"d3o ".. "E ""I 2?°

d-_p/E' ,,.,,,

mb_c__310-2 _ 120°_,'_,90o -

OeV2 _o'_"-.

-' ,. 2,

10"3 12_o_,,,_12c 112C,_+1

15MeVlN

10-4 I I I I

0 20 40 60 80 100

T , MeV (lab)

Figure 9. Theoretical and experimental (ref. 34) Lorentz-invariant doubly differential cross sections for rr+production at 75 MeV/N. Solid lines represent theoretical predictions; dashed lines are drawn throughexperimental data points only to facilitate visual inspection; angular values are Orr.

15

10-1 I I I I

12C112C,7r+1 85MeV/N

-. %

10-2_ !.... _I "-.., "_----_55 °145_""I """3zd2o .,\

dEd---'_' "",.900

130°_ I',%

mb "__

Ge_-sr 10-3_

0 20 40 60 80 i00

T ,MeV (lab)

Figure 10. Theoretical and experimental (refs. 5 and 35) noninvariant doubly differential cross sections for7r+ production at 85 MeV/N. Solid lines represent theoretical predictions; dashed lines are drawn throughexperimental data points only to facilitate visual inspection; angular values are OTr.

16

-I10 i i i i

12C(12C,7r+) 85MeV/N

Projl

10-4 i i i0 20 40 60 80 100

TTr,MeV (lab)

Figure 11. Theoretical and experimental (refs. 5 and 35) noninvariant doubly differential cross sections for 7r+production at 85 MeV/N for OTr= 90°. Theoretical curves (solid lines) show decomposition of summedcross section in terms of contributions of pions from projectile and target.

17

-210 , , , ,

t 12C(12C,-F) t".__ 86MeVlN

/ \ x0 =0° \ ,,

%

10-3 _T _\\

d2o \

mb tX __XXGeV-sr \ \\

10-4 \ _.

\\\\-V

10-5 - m l i I0 40 80 120 160 200

T , MeV (lab)

Figure 12. Theoretical and experimental (ref. 39) noninvariant doubly differential cross sections for ;r+ and

7r- production at 86 MeV/N. Solid line displays theoretical predictions; dashed lines are drawn throughexperimentaldata points only to facilitate visual inspection.

18

10-2

12C(12C,7r+) 85MeV/N

• 35_<E_r( 65MeV10-3--

do_'_' •

mid •sr •

i0-4_ • _

10-5 I I ,I I I

0 30 60 90 120 150 180

eTr,deg(lab)

Figure 13. Theoretical and experimental (ref. 34) angular distributions for 7r+ production at 85 MeV/N.Curve displays theoretical predictions; circles are experimental data points.

lg

0 | I | I |

12C (12C,TrO) 60MeV/N

103

102

do

"a_' 101nbMeV

100

10

200FA(MeV) = 80 115

10-2 , l , ' '0 40 80 120 160 200

T_,MeV (c.m.)

Figure 15. Spectral distributions for 7r0 production at 60 MeV/N for isobar widths of 80, 115, and 200 MeV.Curves show theoretical predictions of this study. Histograms show experimental data from reference 7.

21

I.51 l I '

I Experiment: AI (14N,_TO)

i lj__rZ_ Theory: 12C(12C,_.0)

(MeV)1.0

n__bMeV 0.5 { TI\\

0 30 60 90 120

T , MeV (lab)

Figure 16. Spectral distributions for 7r° production at 35 MeV/N for isobar widths of 80, 115, and 200 MeV.12 12

Curves show theoretical predictions of this study for C on C. Histograms and error bars showexperimental data from reference 1 for A1 on 14N.

10

Experiment: AI (14N,7rO)

7. Theory: 12C(12C,TrO)

do 55MeV/Nd'Q' (MeV)5.nbsr

,

I I I

0 45 90 155 180

eTr, deg (tab)

Figure 17. Angular distributions for _r0 production at 35 MeV/N for isobar widths of 80, 115, and 200 MeV.12

Curves show theoretical predictions of this study for C on 12C. Histograms and error bars showexperimental data from reference 1 for A1 on 14N.

22

100 j , i i

12C(12C, ;r+) 8.5MeV/N

"_;-. e '= 90°I0-I- "_.T 7T _

d3o £"i

GeV2

10-3

10-4 i l i i0 20 40 60 80 I00

Tn, MeV (lab)

Figure 18. Theoretical and experimental (refs. 5 and 34) Lorentz-invariant doubly differential cross sectionsfor =+ production at 85 MeV/N at O7r = 90° for isobar widths of 80, 115, and 200 MeV. Solid linesare theoretical predictions; dashed line is drawn through experimental data points only to facilitate visualinspection.

23

10-2 I I I I

];'... # 86MeVZN} 2c1 2c,._,$12C(12C' 11-) // ._]"-,.£_

_9_. = 0 ° I \ \80 \ "10-3 \

d2o \

r A (MeV)mbGeVlsr \\

-4 \

\\\.

t-510 I I I I

0 40 80 120 160 200

T , MeV (lab)11

Figure 19. Theoretical and experimental (ref. 39) noninvariant doubly differential cross sections for _-+ and _-production at 86 MeV/N for isobar widths of 80, 115, and 200 MeV. Solid lines are theoretical predictions;dashed lines are drawn through experimental data points only to facilitate visual inspection.

24

Standard Bibliographic Page

1.NAsARep°rtNO.TP_2600 2. Government Accession No. 3. Recipient's Catalog No.

4. Title and Subtitle 5. Report Date

Cross Section Calculations for Subthreshold Pion August 1986Production in Peripheral Heavy-Ion Collisions

6. Performing Organization Code

7. Author(s) 199-22-76-01

John W. Norbury, Francis A. Cucinotta, 8. PerformingOrganizationReport No.

Philip A. Deutchman, and Lawrence W. Townsend L-16129

9. Performing Organization Name and Address 10. Work Unit No.NASA Langley Research Center

Hampton, VA 23665-5225 11. Contract or Grant No.

12. Sponsoring Agency Name and Address 13. Type of Report and Period Covered

National Aeronautics and Space Administration Technical Paper

Washington, DC 20546-0001 14. Sponsoring Agency Code

15. Supplementary Notes

John W. Norbury and Francis A. Cucinotta: Old Dominion University, Norfolk, Virginia.Philip A. Deutchman: University of Idaho, Moscow, Idaho (supported by NSF grant no. PHY 8411009).Lawrence W. Townsend: Langley Research Center, Hampton, Virginia.

16. Abstract

Total cross sections angular distributions, and spectral distributions for the exclusive production of chargedand neutral subthreshold pious produced in peripheral nucleus-nucleus collisions are calculated by usinga particle-hole formalism. The pious result from the formation and decay of an isobar giant resonancestate formed in a 12C nucleus. From considerations of angular momentum conservation and for the sakeof providing a unique experimental signature, the other nucleus, chosen for this work to be 12C also, isassumed to be excited to one of its isovector (1+) giant resonance states. The effects of nucleon recoil bythe pion emission are included, and Pauli blocking and pion absorption effects are studied by varying theisobar width. Detailed comparisons with experimental subthreshold pion data for incident energies between35 and 86 MeV/nucleon are made.

17. Key Words (Suggested by Authors(s)) 18. Distribution Statement

Subthreshold pious Unclassified--UnlimitedSpectral distributionsAngular distributionsNucleus-nucleus collisions

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