RELATIVISTIC HEAVY-ION PHYSICSWITHOUT NUCLEAR CONTACT

The large electromagnetic field generated by a fast heavy nucleusallows investigation of new electromagnetic processes notaccessible with real photons.

Carlos Bertulani and Gerhard Daur

An increasing number of physicists are investigatingnuclear collisions at relativistic energies. (See figure 1.)Accelerators completely devoted to the study of thesecollisions (such as the Relativistic Heavy Ion Collider atBrookhaven National Laboratory) are under construction.So are hadron colliders (such as the Large Hadron Col-lider at CERN), which can also be used to accelerateheavy ions.1 The aim of these projects is to study whathappens to nuclear matter at high pressures and tem-peratures. The expectation is that such experiments willaccess information that can test important predictions ofquantum chromodynamics—for example, a nuclear mat-ter transition from a mixture of quarks and gluons tohadrons, as occurred in the first moments of the universeaccording to the Big Bang theory.2

Relativistic heavy-ion collisions can also be an im-portant tool for traditional nuclear physics research—forexample, for investigating nuclear structure, hadronicstructure, atomic physics and stellar nucleosynthesis.3This has become more evident in the last few years asan increasing number of experiments have been carriedout for such purposes. These experiments are based onwhat happens in distant collisions between relativisticnuclei, without nuclear contact. They are therefore verydifferent on physical grounds from the frontal collisionsreferred to above. Whereas for central collisions thedriving forces are mainly of hadronic origin, distantcollisions without nuclear contact are completely domi-nated by electromagnetic interactions.

The electromagnetic interactions are so important inhigh-energy collisions between heavy ions primarily be-cause of the ions' large charge (which means that thecross sections are enhanced by the large factors of Z2 andZ4 for one- and two-photon processes, respectively) andthe Lorentz contraction. (See figure 2.) Lorentz contrac-tion implies that in a collision with impact parameter bthe field generated by the relativistic nucleus with veloc-ity v is effective during a time interval A£ given approxi-

Carlos Bertulani is a visiting scientist at the Gesellschaft furSchwerionenforschung, in Darmstadt, Germany, and aprofessor of physics at the Federal University of Rio deJaneiro, in Brazil. Gerhard Baur is a member of the scientificstaff at the Forschungszentrum julich, injlil ich, Germany,and a professor of physics at the University of Basel, in Basel,Switzerland.

mately by b/yv and that the electric (or magnetic) fieldduring this time interval is very intense: E — yZe/b2. Thefactor y, which is (1 - i /c2)"1"2, is very large (on the orderof 104-107) in relativistic heavy-ion colliders.

TheoryIn 1924 Enrico Fermi had an idea that led to what isnow known as the Weizsacker-Williams method (due tothe improvements obtained by Carl Friedrich vonWeizsacker and Evan James Williams).4 Fermi calcu-lated the effect of the time-dependent electromagneticfield of a fast charge, replacing it with an equivalentpulse of real photons. One can calculate the pulse ofequivalent photons classically, and this method of usingequivalent photons is described in textbooks of classicalelectrodynamics.5 With the advent of heavy-ion accelera-tors with relativistic energies—for example, the Bevalacat Lawrence Berkeley Laboratory—it became clear thatheavy-ion physics without nuclear contact could be veryuseful in nuclear physics. Because the electromagneticinteraction is well known, the results of the experimentscould be compared with the theoretical calculations andused to test models for photonuclear interaction andphoton-photon interaction.

For a collision without nuclear contact, the electricfield generated by one of the ions is divergence free inthe interior of the other nucleus. One consequence ofthis is that the matrix elements involved in the nuclearexcitation process are the same as those involved inphotonuclear reactions. The cross sections for all suchelectromagnetic processes in heavy-ion collisions can thenbe written in a factorized form as

d w

(1)

Here fiw is the excitation energy, «•£ is the photonuclearcross section for a given multipolarity, and the nx arevirtual photon numbers, or equivalent photon numbers.The total photonuclear cross section is a sum of thecontributions from all the multipolarities: <ry = S<r£. Equa-tion 1 contains the spirit of Fermi's method, but* it enablesone to calculate the equivalent photon numbers moreaccurately and for all multipolarities.36

The interpretation of equation 1 is that the time-dependent field of a relativistic heavy ion has thesame effect on a target nucleus as would a pulse of real

22 PHYSICS TODAY MARCH 1994 1994 American Insrlrure of Physics

•v--\

m

Experimental setup at the heavy-ion synchrotron at GSI, in Darmstadt, Germany, for observation of thetwo-gamma decay of the double giant dipole resonance in 208Pb. James Ritman of the State University of NewYork, Stony Brook, and GSI monitors the apparatus. Photons are detected with a two-arm photon spectrometer,which is a modular system of BaF2 detectors (at left in the photograph). Peripheral Coulomb-like interactionsare selected using the forward plastic wall of the 4ir spectrometer (right) as a veto detector. The data obtainedwith this setup were published in reference 15. Figure 1

photons. The number of photons for a given electric ormagnetic component A of the field is given by ny Mul-tiplying the number of these "quasireal" photons per unitenergy, nA(ai)/a>, by the photoinduced cross section andintegrating over the photon energy gives the total crosssection for inelastic processes generated by the relativisticheavy ion.

The virtual photon numbers nk are decreasing func-tions of 10. Above a certain cutoff energy they decreaseexponentially with increasing w, meaning that processesthat require energies higher than the cutoff energy arevery unlikely.3 Because the interaction time At in aCoulomb collision (the time during which the field isstrongest) is about b/yv, the cutoff energy £™ax is ap-proximately hi At ^ yhc/b. The value of £™ax defines thekind of photonuclear physics that can be studied bymeans of this mechanism. Table 1 shows the values ofthe cutoff energy in the frame of reference of one of theions for several existing or planned heavy-ion accelera-tors. We use b = 10 fm, which is typical for a grazingcollision. For the planned colliders LHC and RHIC, weused the relation between the Lorentz factors y in thelaboratory and in the frame of reference of one of theions: y = 2yj*ab - 1.

The success of an experiment involving any of themany applications of electromagnetic interactions be-tween heavy ions depends on how accurately one canseparate the hadronic and electromagnetic contributionsto the process. An important quantity that enters equa-tion 1 is the minimum impact parameter for which apure electromagnetic collision is defined. This can betaken as the sum of the projectile and target matter

distribution radii, which are reasonably well known. Forcollisions at smaller impact parameters, the strong inter-action dominates the process.

We will now give examples of various kinds of elec-tromagnetic processes that one can study in heavy-ionaccelerators with increasing energy. We begin with mod-erately low energies of about 100 MeV/nucleon, which arenowadays available in many laboratories.

Nucleosynthesis in the starsThe study of radiative capture reactions is relevant toastrophysics.7 For example, the first two of the followingthree reactions are important for the Big Bang scenario,while the last one determines the carbon/oxygen ratio inthe universe:

• d -> 6 L i +y

a + t ->7Li + y

a + 12C -> 16O + y

The cross sections for such reactions at typical stellartemperatures are sometimes controversial, from thestandpoint of both theory and experiment. The basicreason is the extremely low relative energies of motionat which these reactions should be measured.7 Due tothe Coulomb repulsion the cross sections are very smalland decrease steeply with the relative energy.

An alternative, less direct way to determine theradiative capture cross sections is by measuring thebreakup of a fast-moving projectile in the Coulomb fieldof the target.8 For example, according to equation 1, thecross sections for the reactions 6Li + Pb -> a + d + Pb and

PHYSICS TODAY MARCH 1994 2 3

Reaction product

Reaction product

Enhanced interaction. The Lorentzcontraction (a) of the intense fields generatedby relativistic heavy ions can lead to verylarge cross sections for photonuclearprocesses (b) and for two-photon collisionprocesses (c). Figure 2

y + 6Li -> a + d, at a fixed energy w, are proportional. Thecross section for the latter reaction, in turn, is propor-tional to that of the radiative capture reaction in accordwith the detailed balance theorem. Phase-space consid-erations favor the Coulomb (or electromagnetic) dissocia-tion method over direct measurements.8

The most suitable beam energies for performing suchexperiments seem to be around 100 MeV/nucleon. Theseenergies are available at the Grand Accelerateur Nationald'lons Lourds (GANIL), in Caen, France; at the Gesell-schaft fur Schwerionenforschung (GSI, the Institute forHeavy-Ion Research), in Darmstadt, Germany; at Michi-gan State University, in East Lansing; and at the Insti-tute of Physical and Chemical Research (RIKEN), in Wako-shi, Saitama, Japan. The first measurements using thistechnique are encouraging.910 Figure 3 shows data fromtwo of these experiments. The cross sections in figure3a are for the radiative capture reaction 13N(p,y)14O andwere obtained with the Coulomb dissociation methodusing lead targets.9 The experiment obtained the value

ry = 3.1 ± 0.6 MeV for the radiative width of the 1" statein UO at the excitation energy 5.17 MeV. This radiativecapture reaction is of great interest because it determinesconditions for starting the hot CNO cycle rather than theregular CNO cycle.7 Figure 3b shows data from anotherCoulomb dissociation experiment10 (colored points), forthe radiative capture reaction 4He(d,y)6Li. These datawere the first to be obtained in the low-energy region,below the resonance at 0.711 MeV. The other data (blackpoints) were obtained in direct capture measurements.The solid curve is a theoretical calculation.

Radioactive beamsStudies of short-lived nuclei are now possible with heavy-ion accelerators and the development of new detectiontechniques. (See the article by Richard N. Boyd and IsaoTanihata in PHYSICS TODAY, June 1992, page 44.) Theradioactive nuclei are produced in fragmentation reac-tions and further gathered in a secondary beam. Someshort-lived nuclei are so weakly bound that they fragmentwhen they collide with a target nucleus at a very largeimpact parameter. This results in huge cross sectionsfor the electromagnetic dissociation of these nuclei.3Many experiments of this type have been performed atGANIL, GSI, MSU, RIKEN and other accelerators.

An MSU experiment on the electromagnetic dissocia-tion of uLi is a good example.11 The two-neutron sepa-ration energy of this nucleus is 340 ± 50 keV, which isvery small compared with the normal 6-8-MeV bindingenergy of nucleons in nuclei. As a consequence, the lasttwo neutrons in nLi are distributed in a large extensionof radius about 8 femtometers outside a 9Li core. Thestructure and reaction mechanisms for this and otherradioactive nuclei are not very well known. It is notclear, for example, if the excitation and decay of thisnucleus proceeds via an intermediate state or if it is adirect breakup transition. The MSU experiment seemsto indicate that the latter possibility prevails. Figure 4aplots a sample of the data obtained in that experimentin the form of the decay spectrum d<x/d_Ed, which isproportional to the integrand of equation 1 and is directlyrelated to the dipole response function I </l l.vl \i~>\2 ofthe nucleus for a given excitation energy. If the widthof this function is to be associated with the lifetime of aresonant state, the nucleus must decay far away fromthe target. However, a large shift in the energy of the9Li fragments (the Coulomb reacceleration effect) is ob-served, which is inconsistent with the existence of aresonant state. This is shown in figure 4b for the differ-ence in the velocities of the 9Li and neutron fragments.According to the investigators in that experiment thepeak in figure 4a should not be interpreted as the sig-nature of a resonance.11 In fact, it can be explained fromphase-space considerations alone.3

Giant resonancesFrom table 1 we see that the excitation of giant reso-nances in heavy-ion collisions does not require very-high-energy accelerators. In fact heavy-ion excitation of giantresonances is now an important field of research at GANIL,GSI, MSU and RIKEN. A very new topic for nuclearstructure investigation is the electromagnetic excitationof multiphonon resonances—for example, a giant reso-nance excited on top of another one.1213 This kind ofexcitation cannot be achieved in electron scattering orreal photon experiments. But highly energetic heavy ionscan be viewed as intense sources of virtual photons, andthe probability of multiphoton exchange is not small.

Experiments aiming at multiphonon excitation haverecently been performed at GSI.1415 The experimenters

24 PHYSICS TODAY MARCH 1994

5b"a

O111cococooa:o

HIenUJ

100 -

0.01 •

0 1 2 3 4 5 6SCATTERING ANGLE (degrees)

1 2 3ENERGY (MeV)

Electromagnetic excitation crosssections, a: Differential crosssections of the 1~ resonant state in14O as a function of thecenter-of-mass scattering angle ofthe 14O--08Pb system. The upperand lower colored curves representthe respective contributions of theCoulomb and nuclear interactionsto the excitation. This experimentyielded, with good accuracy, theradiative width of the state, aquantity of great importance innuclear astrophysics. (Adaptedfrom ref. 9.) b: Radiative capturecross section for the reactiond(a,y)bl_i obtained after atheoretical analysis of resultssimilar to those shown in a. Anexperiment using the Coulombdissociation method gave the datarepresented by the colored points.(Adapted from ref. 10.) Figure 3

identified the giant resonance states by measuring theirgamma or particle decays. Figure 5 shows a sample ofthe data. Usual giant resonances are easily identified inthese data at their expected positions and widths. Abump appearing at about twice the energy of the isovectorgiant dipole resonance was identified as a double-phononstate. More studies of the strengths, widths and otherproperties of multiphonon states using the electromag-netic excitation technique are expected to give importantinformation on novel collective vibrations in nuclei.

With increasing energy of the heavy ions we canobtain even higher excitation energies. At the energiesavailable at the Super Proton Synchrotron at CERN, onewould expect that delta resonances could be excited elec-tromagnetically. The deltas are nucleonic excitations ofabout 300 MeV. The decay of such a state to a nucleonand a pion releases about 300 MeV of energy inside thenucleus. The reabsorption of the pion in the nucleusinitiates a complicated cascading process that is of muchinterest for nuclear physics studies. If one uses vetodetectors, which make it possible to separate out thenuclear contribution to the process, the electromagneticexcitation of multiple deltas in the nuclei also could bemeasured. Other useful cases, such as the electromag-netic production of hypernuclei, can also be studied inrelativistic heavy-ion colliders.

The excitation of a single hadron in the strong elec-tromagnetic field of a heavy nucleus is also a powerfulmethod for deducing important features of these particles.A well-known example is the excitation of a A into a 1°.The electromagnetic cross section for this process hasbeen measured at CERN18 and at Fermilab17 using nickeland uranium targets and relativistic A beams. The 2°is a magnetic dipole excitation of the A, with an 80-MeV

Electromagnetic breakup, a: Cross section for theelectromagnetic breakup of "Li projectiles as a function of thefinal relative kinetic energies of the fragments. The curve is aguide to the eye. (Adapted from ref. 11.) b: Distribution of

differences in velocity between the ''Li fragments and thetwo neutrons after the breakup. The histogram shows

the result that would be expected if Coulombreacceleration were not present. Figure 4

excitation energy. Before the introduction of the quarkmodel, the magnetic dipole moment for this transitionwas calculated using the electromagnetic symmetry prop-erties of the hadronic octuplets. The lifetime of the 2°

0.5 1 1.5DECAY ENERGY Ed (MeV)

-0.04 -0.02 0 0.02VELOCITY DIFFERENCE (Vg - V2n)/c

0.04

PHYSICS TODAY MARCH 1994 2 5

240-

E 160-

OujwU)wOD:o

GDR1 phonon 2 phonon 3 phonon

QQP Isoscalar Isovector

20 30

EXCITATION ENERGY (MeV)

40 50

Giant resonance excitation crosssections. Plotted are cross sections forthe electromagnetic excitation of theisovector giant dipole resonance (GDR)and of the isoscalar and isovector giantquadrupole resonances (GQR) in0.7-GeV 136Xe projectiles incident onlead (black points). Also shown areexcitation cross sections of two- andthree-phonon states. Using carbontargets decreases the cross sections bya factor of 100 (red points). (Adaptedfrom ref. 14.) Figure 5

particle is inversely proportional to the square of themagnetic dipole moment for the transition. Using equa-tion 1 and detailed balance, one can determine the pho-todecay cross section for the 1° particle. Figure 6 showsthe cross sections for the electromagnetic productionof 2° on nickel and uranium targets. The theoreticalfit3 (solid lines) to these data gives a lifetime of(7.4 ±0.7) x 10"20 seconds. This agrees very wellwith the theoretical predictions and is an importantpiece of support for the conclusions drawn from thesymmetry properties of the SU(3) group.

Production of particlesAs in e+e~ colliders, relativistic heavy ions can be usedto investigate photon—photon collisions. (See figure2c.) In analogy with the one-photon process, describedby equation 1, the photon-photon processes can berelated to the real photon processes byis

Here to2 = AOJ^Z- But unlike equation 1, the aboveformula is only approximate; it is valid for very-high-energy beams and small excitation energy fico, such

that the virtual photons are mostly transverse. Theinterpretation of this formula is that each of the tworelativistic ions generates a pulse of photons, n± and n2,respectively. The cross section for the photon-photoncollisions is given by ayy. Integrating over the photonspectrum of each ion yields the cross section for yycollisions in heavy-ion colliders.

An important two-photon process in relativisticheavy-ion colliders is the production of e+e~ pairs. Be-cause the required energy for the process is rathersmall (about 1 MeV), the cross sections are huge, onthe order of tens of kilobarns for RHIC or hundreds ofkilobarns for the LHC. Multiple production of electronpairs would also be possible. The production of e+e~pairs could be an important tool for monitoring thebeam in the colliders.

Keeping the beam running for a long time couldalso be a problem. The probability that an electron iscreated in a bound orbit in one of the ions is notnegligible.3 This process leads to ion losses from thebeam. (The production of free pairs has practically noeffect on the beam lifetime.) Estimates of this processindicate that for the high beam luminosities plannedfor RHIC or the LHC the beam lifetime could be limited

Table 1. Virtual photon cutoffAccelerator

GANIL (France)MSU(US)RIKEN (Japan)GSI (Germany)AGS at Brookhaven

(US)SPSatCERN

(Switzerland)RHIC (planned at

Brookhaven)LHC (planned at CERN)

Lorentz factor

1-2

2-315

200

2 x 1 0 4

3.6 x 107

The cutoff energies are for heavy-ion collisions.given in the reference frame

2 6 PHYSICS TODAY

: of one of the ions.

MARCH 1994

energiesy Cutoff energy

rtnax

-20 MeV

-50 MeVSome 100

MeVSome GeV

Some 100GeV

Some 100TeV

The values of y are

Table 2. Cross sections forprocesses

Free e+e~ pairsExcitation of giant resonancesBound e+e~ pairsExcitation of nucleon

resonancesExcitation of multiphonon statesTT (two photon)Vf]

VbHiggs boson

A uranium-uranium collision is assumed.

electromagnetic

RHIC80 kb100 b80 b20 b

2b12 mb5 mb2 mb5 ixb50 nb

—

LHC400 kb150 b120 b40 b

3b60 mb55 mb40 mb1 mb1 fib1 nb

to about 10 hours.19

As with the e+e~ colliders, one can study particleproduction through the two-photon mechanism inheavy-ion colliders. For example, the number of77° particles that have been produced up to now at theHadron-Electron Ring Accelerator at DESY could becreated in RHIC in three minutes by the two-photonmechanism. Heavy particles (17, 77', qq pairs and so on)could also be produced in this way.18 For example, theproduction of the standard Higgs boson in relativisticcolliders by means of the two-photon process would be ofthe same order as that induced by gluon-gluon interac-tions. However, the main technique for detecting theHiggs is through its bb decay. Because the direct elec-tromagnetic production of bb pairs is larger than that ofHiggs bosons, the two-photon mechanism might not beuseful in this case.20

Table 2 shows the cross sections for several electro-magnetic processes that could be studied at RHIC or theLHC. We used ylab = 100 at RHIC and ylab = 4000 at theLHC. These numbers would be the maximum values forthe cross sections, because we assumed that the collidersare filled with uranium beams. If other nuclei are used,one can extract the respective cross sections from thesenumbers, remembering that one-photon processes scalewith Z2, while two-photon processes scale with Z4. Also,the possibility of measuring these processes depends onthe luminosity of the beam as well as on the detectiontechnique used to disentangle the electromagnetic contri-bution from that originating in hadronic processes.

Not shown in table 2 are many other cases—forexample, the cross sections for atomic ionization, whichare huge (on the order of kilobarns) and can be veryuseful for atomic physics studies, or the cross sectionsfor low-energy-photon production, which are also verylarge and can be useful for beam monitoring.3

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Phys. 88, 612 (1934). E. J. Williams, Phys. Rev. 45,729(1934).5. J. D. Jackson, Classical Electrodynamics, Wiley, New York

(1975).6. A. Winther, K. Alder, Nucl. Phys. A 319, 518 (1979).7. W. A. Fowler, Rev. Mod. Phys. 56, 149 (1984).8. G. Baur, C. A. Bertulani, H. Rebel, Nucl. Phys. A 458, 188

(1986).9. T. Motobayashi, T. Takei, S. Kox, C. Perrin, F. Merchez, D.

Rebreyend, K. Ieki, H. Murakami, Y. Ando, N. M. Iwasa, M.Kurokawa, S. Shirato, J. Ruan (Gen), T. Ichihara, T. Kubo, N.Inabe, A. Goto, S. Kubono, S. Shimoura, M. Ishihara, Phys.Lett. B 264, 259 (1991).

10. J. Kiener, H. J. Gils, H. Rebel, S. Zagromski, G.Gsottschneider, N. Heide, H. Jelitto, J. Wentz, G. Baur, Phys.Rev. C44,2195(1991).

11. K. Ieki, D. Sackett, A. Galonsky, C. A. Bertulani, J. J. Kruse,W. G. Lynch, D. J. Morrisey, N. A. Orr, H. Schulz, B. M.Sherrill, A. Sustich, J. A. Winger, F. Deak, A. Horvath, A. Kiss,Z. Seres, J. J. Kolata, R. E. Warner, D. L. Humphrey, Phys.Rev. Lett. 70, 730(1993).

12. D. Lissauer et al., proposal for BNL-AGS experiment 814(accepted October 1985), available at Brookhaven Nat. Lab.library.

13. G. Baur, C. A. Bertulani, Phys. Lett. B 174, 23 (1986).

12 16

TOTAL A AND y MOMENTUM (GeV/c)

20

12 16TOTAL A AND y MOMENTUM (GeV/c)

20

Coulomb production of 5° particles in thefield of uranium (a) and nickel (b).151' Thecurves are theoretical predictions using thevalue of 7.4 x 10~20 seconds for the lifetime ofthe S° particle. (Adapted from ref. 16.)Figure 6

14. R. Schmidt, Th. Blaich, Th. W. Elze, H. Emling, H. Freiesle-ben, K. Grimm, W. Henning, R. Holzmann, J. G. Keller, H.Klinger, R. Kulessa, J. V. Kratz, D. Lambrecht, J. S. Lange,Y. Leifels, E. Lubkiewicz, E. F. Moore, E. Wajda, W. Prok-opowicz, Ch. Schutter, H. Spies, K. Stelzer, J. Stroth, W.Walus, H. J. Wollersheim, M. Zinser, E. Zude, Phys. Rev. Lett.70, 1767(1993).

15. J. Ritman, F.-D. Berg, W. Kuhn, V. Metag, R. Novotny, N.Notheisen, P. Paul, M. Pfeiffer, O. Schwalb, H. Lohner, L.Venema, A. Gobbi, N. Herrmann, K. D. Hildenbrand, J. Mos-ner, R. S. Simon, K. Teh, J. P. Wessels, T. Wienold, Phys. Rev.Lett. 70, 533(1993).

16. F. Dydak, F. L. Navarria, O. E. Overseth, P. Steffen, J. Stein-berger, H. Wahl, E. G. Williams, F. Eisele. C. Geweniger, K.Kleinknecht, H. Taureg, G. Zech, Nucl. Phys. B 118, 1 (1977).

17. P. C. Petersen, A. Beretvas, T. Devlin, K. B. Luk, G. B. Thom-son, R. Whitman, R. Handler, B. Lundberg, L. Pondrom, M.Sheaff, C. Wilkinson, P. Border, J. Dworkin, O. E. Overseth,R. Rameika, G. Valenti, K. Heller, C. James, Phys. Rev. Lett.57,949(1986).

18. G. Baur, C. A. Bertulani, Z. Phys. A 330, 77 (1988).19. P. Giubelino, in Proc. Conf. Particle Production in Highly

Excited Matter, H. H. Gutbrod, J. Rafelski, eds., Plenum, NewYork (1993), p. 117.

20. K. J. Abraham, M. Drees, R. Laterveer, E. Papageorgiu, A.Schafer, G. Soff, J. Vermaseren, D. Zeppenfeld, in Proc. ECFALHC Workshop, vol. II, G. Jarlskog, D. Rein, eds., publ.RD/806-2500, CERN Service d'Information Scientifique, Ge-neva (February 1991), p. 1224. •

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