PHYSICAL REVIEW C VOLUME 46, NUMBER 6 DECEMBER 1992

Quadrupole contribution to two-neutron removal in heavy ion collisions

C. J. BeneshT 5, M-SB888 Los Alamos National Labotutory, Los Alamos, New Mexico 875/5

(Received 20 August 1992)

In this paper, electric quadrupole corrections to the two-neutron removal cross section measured

in heavy ion collisions are estimated for Au and Co targets. The quadrupole process is assumed

to proceed primarily through excitation of the giant isovector quadrupole resonance, which then

decays by neutron emission. For Co, the contribution from E2 radiation is found to be small,

while for Au we find the quadrupole contribution resolves the discrepancy between experiment

and the simple predictions of the Weissacker-Williams virtual photon method.

PACS number(s): 25.75.+r

The combination of large charges and enhancement ofthe radiation pulse at high energies by Lorentz contrac-tion make electromagnetic dissociation (ED) by heavyions an attractive method for measuring low energy nu-

clear cross sections of astrophysical interest [1]. At thesame time, the very large cross sections, on the order ofbarns, attainable in ED will contribute substantially tothe hadronic background at the Relativistic Heavy IonCollider at Brookhaven National Laboratory [2]. A thor-ough understanding of the ED process is necessary toextract meaningful results from these experiments. Itis not clear, however, that such an understanding ex-

ists at present. Indeed, it has been found in targetfragmentation experiments that the single- and double-neutron removal cross sections do not agree with the sim-

ple Weissacker-Williams (WW) theory of the ED reaction

[2—6]. For the most part, the discrepancies in the singleneutron removal process have been resolved by carefulconsideration of the choice of critical impact parameter

[7], inclusion of quadrupole excitations in the EM crosssection [7], and the efFect of the Rutherford bending ofthe projectile's trajectory [8]. Recently, these consider-ations have begun to be applied to the two-neutron re-moval process as well [9]. In this paper, we examine the

role played by quadrupole excitations, in particular, theisovector giant quadrupole resonance (IVGQR), in thetwo-neutron removal process.

To date, the most thorough study of the systematicsof the two-neutron removal process have been carried outby the Iowa State group [2]. For a variety of projectiles,they have measured the two-neutron removal cross sec-tions on ~s7Au and MCo targets (see Table I). Using fac-torization [10] to estimate the piece of the cross sectiondue to nuclear processes, they extract the electromag-netic contribution and find sizeable discrepancies fromthe predictions of the simple WW calculation for the Autarget.

In Ref. [9], Norbury advances the idea that the discrep-ancies may be understood if one assumes that the uncer-tainties in the experimental measurements have been un-derestimated. As evidence for this, he assumes that theratio of the experimental cross sections for one- and two-neutron removal should be independent of the projectile,and then estimates a revised "experimental" cross sectionfor ~s7Au targets using the ssFe data point, which agreeswith the simple VPiV calculation, to normalize the re-maining data. The revised cross sections agree to withina few millibarns with the naive WW prediction. Under-

TABLE I. Two-neutron removal cross sections for Co and Au targets crEM~' from Ref. [11],and U from Ref. [13]. 5o'@2 is the correction to the naive Weissacker-William cross section due238 WW ~

to the isovector E2 resonance.

Projectile

12C

Ne56Fe139L238U

12C

Ne40Ar56F139'238U

Target

"Co59C"Co"Co"Co197Au197A

'"Au197Au197A197A

Energy(MeV/nucleon)

2.12.11.71.26.962.12.11.81.71.2696

exptEM

(mb)

6+43+51316

32+1680+249+1749+1576+1873+13335+49470+110

WW~EM(mb)1.12.91444655143873

238430

6 WWOZ2

(mb)0.50.10.62425132586173

+EM + 6~&2WW

(mb)1.23.014.646697195198

324603

46 2635 1992 The American Physical Society

2636 BRIEF REPORTS 46

lying this procedure is the assumption that the one- andtwo-neutron removal cross sections are both dominatedby the naive WW cross sections, which do have an ap-proximately constant ratio. For single-neutron removal,this assumption is reasonably valid, as the correctionsdue to quadrupole excitations are on the order of 1070for the projectiles under consideration [7]. This is mostlikely not the case for two-neutron removal. Unlike thesingle-neutron case, the two-neutron threshold (15 MeVfor isr Au) lies above the energy of the giant dipole reso-nance (GDR) (13.8 MeV for is7Au), so that contributionof the GDR is considerably smaller than it is for sin-gle neutron removal. On the other hand, the isovectorgiant quadrupole resonance lies above the two-neutronthreshold (23 MeV for Au) and as a result decays pri-marily into two neutrons. In addition, for the lowestenergy projectiles, where the discrepancy is largest, theWW quadrupole flux will be enhanced relative to thedipole Qux. Thus, a reasonable expectation is that thequadrupole contribution will be a significantly larger per-centage of the two-neutron cross section than for single-neutron removal.

In order to estimate this contribution, one needs amodel to separate the quadrupole part of the photoneu-tron cross section from the dipole piece. The quadrupole

I

cross section is assumed to be dominated by the IVGQR,with a correction factor for the two-neutron threshold,

f~EWSREIVGQR (E —Eth)1+ (E —

E&&GER) /E I' A + (E —E )

where f is the product of the fractional saturation ofthe energy-weighted sum rule and the branching ratiofor two-neutron decay, E1vGqR is the resonance energy,I' is the resonance width, Eth is the two-neutron removalthreshhold, oEwsR is the energy-weighted sum rule [9],and A is a parameter that determines how rapidly thetwo-neutron channel opens. From Ref. [11] and statisti-cal model calculations [12], f - 0.8, E1vGqR = 23 MeV,and I' = 7 MeV for rs"Au. For MCo, there are no dataon the IVGQR available, so the parameters for ssNi areused (f - 0.1, ErvGciR = 29 MeV, I' = 9 MeV) Th.eparameter A is determined from photonuclear data to beroughly 2 MeV for both Co and Au targets.

The ED cross section is determined by folding theequivalent photon fluxes [1] over the cross sections. As-suming that only the first two electric multipoles are im-portant,

&ED—th

th

dE crag(E) n@g(E) + dE o'z2(E) nz2(E)Eth

dE

omah()&o(E)

nz&(E) + dE aEs(E) [nz2(E) —nEy(E)],Etl

(2)

where o~h, t~(E) is the experimental photoneutron crosssection, and nE„ is the appropriate photon Qux for thenth multipole from Ref. [1]. The resulting cross sectionsare shown, along with the experimental results and theE2 correction, in Table I.

For Co, the additional contribution from thequadrupole flux is mitigated by the lack of IVGQRstrength, and the already good agreement between the-ory and experiment remains undisturbed. For the Autarget, the ED cross section is increased by roughly athird for all projectiles and agreement with the experi-mental results is improved for all projectiles except Fe,which, as noted in Ref. [9], lies suspiciously low relative

to the other data. The remaining discrepancies are forcases where the measured ED cross section is small, andconsequently more sensitive to possible systematic errorsin measurement and/or extraction of the nuclear contri-bution. Thus, one may conclude that the discrepanciesobserved in the two-neutron ED cross sections may bewell described by the WW method if the E2 strengthpresent in the IVGQR resonance is properly accountedfor.

This work was supported in part by the U.s. Depart-ment of Energy, Division of High Energy and NuclearPhysics, ER-23.

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