documentni

VOLUME 76, NUMBER 9 P H Y S I C A L R E V I E W L E T T E R S 26 FEBRUARY 1996

If

Missing Isoscalar Monopole Strength in58Ni

D. H. Youngblood, H. L. Clark, and Y.-W. LuiCyclotron Institute, Texas A&M University, College Station, Texas 77843

(Received 18 August 1995)

The giant resonance region in58Ni was studied with inelastic scattering of 240 MeVa particles atsmall angles including 0±. It is shown that the total isoscalar monopole strength in the regionEx 12to 25 MeV is ,50% of the E0 energy-weighted sum rule, and that the centroid of theE0 strengthEGMR . 24.8 MeV in contrast to theEGMR ø 17 MeV expected from systematics of other nuclei.there is similar unobservedE0 strength in other nuclei,EGMR for those nuclei may be significantlydifferent from those used to extract nuclear matter incompressibility.

PACS numbers: 24.30.Cz, 25.55.Ci, 27.40.+z

o

cae

as

e

ena

thtee

Ao

t

e

v

tha

ngyR

tr

edat

a

ssis

ata

en

inedgar

se

r-g

weels

sta-ceis.

e

The isoscalar giant monopole resonance (GMR) isparticular interest because its energy is directly relatedthe compressibility of nuclear mattersKnmd [1]. In orderto account for contributions from finite nuclei and extraKnm, macroscopic analyses [2] of the GMR require ththe energy of the GMR be known in nuclei over a widrange ofA. However, significant monopole strength hbeen located [2] in only a few nuclei withA , 90. Onlysmall amounts ofE0 strength have been located in nuclaroundA 60. Approximately 25% of theE0 energy-weighted sum rule (EWSR) has been located in58Ni[3,4], and 30% in64,66Zn [5] with inelastic scattering of130 MeVa particles. Small amounts ofE0 strength havealso been seen [3] with3He scattering, but the continuumin the 3He spectra is apparently obscuring significantE0strength in many nuclei [6]. However, in all of thesstudies, a large continuum (background?), the constitueof which were not known, was subtracted before the pewas analyzed for monopole strength. The location ofremainder of the monopole strength could not be restricby these experiments. It might be broadly distributover the region of the giant quadrupole resonance (GQand subtracted as part of the continuum, or locatedexcitation energies well above the GQR (or both).the nuclear compressibility is related to the centroidthe monopole strength [EGMR sm3ym1d1y2, wheremk isthe RPA sum rule [1,7]mk

Pn sEn 2 E0djk0jr2jnlj2],

knowledge of the general location of this missing strengcould be important for extractingKnm.

All of the definitive monopole measurements have usinelastic alpha scattering withEa # 130 MeV. Unfor-tunately, thesa, 5Li d and sa, 5Hed reactions with sub-sequent decay of the mass five products into ana

particle and a nucleon produce broad peaks in thea

particle spectrum which, forEa 130 MeV, are in theexcitation region corresponding to22 , Ex , 46 MeVin 58Ni. These peaks would obscure GMR strength aboEx ø 22 MeV.

We have studied58Ni using 240 MeV a particleswhere the “pickup-breakup” peaks appear aboveEx 40 MeV, well outside of the region where GMR strengis expected. We report here results with excellent pe

0031-9007y96y76(9)y1429(4)$06.00

fto

tt

i

tsked

dR)atsf

h

d

e

k-

to-background ratios at small scattering angles includi0±. For the first time, it can be shown that the majoritof the isoscalar monopole strength does not lie in the GregionsEx 12 25 MeVd or lower and hence must be ahigher excitation energy. This results in a lower limit foEGMR well above that expected from extrapolating GMRsystematics from heavier nuclei or energies predictfrom recent RPA calculations using interactions threproduce GMR energies in heavier nuclei.

Beams of 240 MeV a particles from the TexasA&M K500 superconducting cyclotron bombardedself-supporting 12.4 mgycm2 foil enriched to greaterthan 98% in58Ni mounted in the target chamber of themultipole-dipole-multipole spectrometer [8]. Beam wadelivered to the spectrometer through a beam analysystem having two bends of 88± and 87± [9]. Thehorizontal acceptance of the spectrometer was 4±, and raytracing was used to reconstruct the scattering angle. Dwere taken with the spectrometer central anglesuspecdset at 0± and at 4±, covering the scattering angle rangfrom 0± to 6±. The focal plane detector and calibratioprocedures are described in detail in Ref. [10].f is notmeasured, so the average angle for each bin was obtaby integrating over the height of the solid angle defininslit and the width of the angle bin. A spectrum taken ne0± (average angle 1.08±) is shown in Fig. 1. For thesedata, the beam (at 0±) and elastically scattered particlewere stopped just in front of the detector, limiting thobserved excitation energy range to2 , Ex , 30 MeV.Elastic and inelastic scattering data were taken for nomalization with a different magnetic field setting coverin210 , Ex , 18 MeV. We previously reported [11]cross sections for elastic and inelastic scattering to lolying states in58Ni, and absolute cross sections werobtained from these data by normalizing to optical modcalculations with potentials from Ref. [11]. The crossections for a peak atEx 4.54 MeV in 58Ni differed inthe elastic and giant resonance spectra by 5% (2% nettistical error), and cross sections for the giant resonanspectra were renormalized upward 5% to account for th

Distorted-wave Born approximation (DWBA) andoptical-model calculations were carried out with the cod

© 1996 The American Physical Society 1429


va

dm

a

yanen

gs1

s

for

are-

ent

FIG. 1. Spectra obtained for58Nisa, a0d at Ea 240 MeVfor two angles. The lines show the background and the fipeak fits to the data. The dominant multipolarities in the peare indicated.

PTOLEMY [12] using collective form factors describeby Satchler [13] and optical model parameters froClark et al. [11]. Monopole and dipole form factorswere calculated externally and read intoPTOLEMY. TheSatchler version 1 (breathing mode) form factor wused for the monopole. Input parameters forPTOLEMY

were modified [14] to obtain a relativistic kinematicallcorrect calculation. The energy-weighted sum rulesgiven by Satchler for the monopole and quadrupole ahigher multipoles in Ref. [13], for the isovector dipolin Ref. [15], and for the isoscalar dipole by Harakeh aDieperink [16].

The giant resonances were analyzed by subtractinbackground, then doing a five peak fit [4] simultaneouto the spectra. The resulting fits are shown in Fig.

1430

eks

s

red

d

aly.

FIG. 2. Angular distributions of the differential cross sectionfor the broad peaks in the58Ni spectra plotted vs averagecenter of mass angle. The lines are DWBA calculationsthe multipolarities and strengths indicated.

The angular distributions obtained for the broad peaksshown with DWBA calculations in Fig. 2. The parameters obtained, summarized in Table I, are in excellagreement with previous measurements [2,4].

the

5

TABLE I. The % EWSR strengths extracted from DWBA fits to the cross section ofcontinuum for12 # Ex # 25 MeV, the cross section of the continuum only for12 # Ex #25 MeV, and the three broad peaks only.

% EWSR forL valuesFit condition 0 1 sT 1da 1 sT 0da 2 3 4

Peaks and continuum 28 100 30 56 20 212 # Ex # 25 MeV

Continuum only 0 0 30 0 20 2512 # Ex # 25 MeV

Peaks onlyEx 16.08 MeV, G 5.24 MeV 44 6 5Ex 17.42 MeV, G 4.39 MeV 22 6 3 715

23Ex 20.76 MeV, G 5.66 MeV 10 6 2 100 7 6 2aValues were fixed; see text.


e

ith

e

s

Bd

unss

aA

en

sB

areks.tlar

llysut

ent

e

tala

umatep-undoleadsticld

gofar

an0

ged

tnotonumh.

lyser

n.

The angular distribution of the cross section obtainby summing the total yield fromEx 12 to 25 MeV (nobackground subtraction) is shown in Fig. 3(a). Fits wa sum of isoscalar01, 21, 12, 32, and 41, isovector12 resonances, and a linear (withu) background werecarried out. The result is shown by the solid linin Fig. 3(a), and parameters obtained are included

FIG. 3. (a) Angular distribution of the differential crossection for the regionEx 12 to 25 MeV in 58Ni plotted vsaverage center of mass angle. The solid line shows the DWcalculation for the multipolarities listed in Table I. The dotteline shows the calculation with theE0 and E2 componentsremoved. The dashed line shows the linear backgroassumed. (b) Angular distribution of the differential crosection for the regionEx 12 to 25 MeV in 58Ni, aftersubtraction of the contributions of the peaks, plotted vs avercenter of mass angle. The solid line shows the DWBcalculation for the multipolarities and strengths listed in Tabl(0% E0 EWSR). The dotted line shows the DWBA calculatiofor the best fit obtained with 15% of theE0 EWSR included.The dashed line shows the linear background [same aFig. 3(a)]. The dashed–double-dotted line shows a DWcalculation for 68% of theE0 EWSR and 42% of theE2EWSR.

d

in

A

d

ge

I

inA

Table I. The monopole and quadrupole strengthsconsistent with those found in analysis of the peaThe isovector12 strength was not varied in the fits buwas fixed at 100%. Strengths obtained for the isosca12, 32, 41 components were not unique, and equagood fits could be obtained with differing combinationof these components. Variations of more than abo20% (0.2 times the strength) of the monopole componproduced significantly worse fits.

The angular distribution of the cross section for thcontinuum fromEx 12 to 25 MeV, obtained by sub-tracting the cross sections of the peaks from the tocross section, is shown in Fig. 3(b). Also shown iscurve representing DWBA predictions for theE0 andE2strength not found in the peaks (42%E2 EWSR1 68%E0 EWSR). This missing strength exceeds the continucross section at the smallest angles. In order to estimthe likely E0 strength in the continuum, several assumtions were made. We used the ansatz of a backgrolinear in angle to model all processes other than multipexcitation in the target nucleus. This may not be a bassumption for statistical processes, however, quasielascattering (knockout) should also contribute and woulikely be strongly forward peaked. Thus ignorinknockout in the fits may result in an overestimatethe E0 strength present. First, fits including isoscal01, 21, 32, and 41 strength, in addition to a linearbackground, were made with no constraints other thlimiting the strength for each component to betweenand 100% of the EWSR. The best fit was with 0%01,while x2 doubled if 10% of theE0 EWSR were includedand quadrupled if 15% ofE0 EWSR were included.E2strength between 0 and 10% of theE2 EWSR was alsoindicated. Differing 32 and 41 strengths were offsetby different linear background parameters. The larsensitivity to01 strength is due to the strongly forwarpeaked nature of the01 angular distribution, which is notpresent in the data.

Multipoles higher than 4 result in essentially flaangular distributions over this angle range and couldmask the monopole. However, the angular distributifor an isoscalar dipole has a peak near the first minimin the 01 and could partly mask monopole strengtThe centroid energy of the isoscalar12 mode shouldbe about 1.5 times the GMR energy [17], or roughEx 30 MeV for mass 60, however, RPA calculation[18] suggest the strength will be widespread in lightnuclei. For40Ca about 16% of the isoscalar12 EWSRis predicted belowEx 25 MeV, while for 90Zr about46% is predicted belowEx 25 MeV. For this analysis30% of the isoscalar12 EWSR was assumed to lie belowEx 25 MeV in 58Ni. Then a good fit could be obtainedif 5% of the E0 EWSR is present in this region (inaddition to that found in the peaks), however,x2 doubledif 15% of theE0 EWSR was assumed to be in this regioIf we use a doubling ofx2 as a reasonable limit, thenthe regionEx 12 to 25 MeV contains less than 15%

1431


e

Ah

lle

ced

innh

id

ohe

ye

erf

pm

uho

nvh--

ty

lid

les

rt-3

,

.

e8

of the E0 EWSR in addition to that already seen in thpeaks. Thus less than 50% of theE0 EWSR is belowEx 25 MeV in 58Ni. DWBA calculations for best fitsassuming 0%E0 and 15%E0 are also shown in Fig. 3(b).

It is possible that the GMR in58Ni is not described wellby a breathing mode form factor, and hence that DWBcalculations are giving too large a cross section. If tGMR in 58Ni (and maybe other nuclei withA , 90) isstructurally different than in heavier nuclei, possibly aof the GMR strength has been located in lighter nuclThe only detailed guidance is from Chomazet al. [19]who compared DWBA calculations for 152 MeV inelastia scattering using microscopic form factors generatfrom Hartree-Fock RPA calculations with results obtaineusing collective form factors, and concluded that60Ni the use of a collective form factor resulted in aunderprediction of the cross section by (10–30)% for tmonopole in inelastica scattering.

If the 15% of E0 EWSR which might be present inthe continuum is distributed uniformly betweenEx 12and 25 MeV and the remaining 50% of theE0 EWSRis centered atEx 30 MeV with a 5 MeV width, thenEGMR . 24.8 MeV in 58Ni. Figure 4 shows a plot ofEGMRA1y3 vs A for all spherical nuclei where 100%of the E0 EWSR has been observed [2]. The centroof the observedstrength in58Ni corresponds toEA1y3 72.1 MeV, in reasonable agreement with the trendother nuclei. However, this represents only 32% of tE0 EWSR. The lower limit forEGMR 24.8 MeV givesEGMRA1y3 96 MeV, which is much higher than for anyof the other nuclei.

The disagreement ofEGMR for 58Ni with systematicsof other nuclei may be due to the existence of an asunidentifiedE0 strength at higher excitation in these othnuclei. For example, theE0 strength in90Zr was found[2] to be s90 6 20d% of theE0 EWSR. Thus as much as30% of theE0 EWSR strength could be located at highexcitation. The experimental errors are similar for all othe nuclei shown in Fig. 4. In a recent microscopic aproach to determine nuclear matter incompressibility froGMR energies, Blaizotet al. [20] explore corrections toGMR energies obtained with Hartree-Fock RPA calclations, and their results are also shown in Fig. 4. Tmass dependence they obtain is somewhat different frthe data. In particular,EGMRA1y3 is slightly higher for90Zr than 118Sn, whereas the experimental values aroumass 90 are lower than at mass 118. If there is unobserE0 strength at higher energies in these heavier nuclei traisesEGMR significantly, then an interaction which reproducesEGMR will show a correspondingly higher compressibility. If EGMRA1y3 for 208Pb were as high as thelower limit we obtain for58Ni (96 MeV), a simple estimateshows that the compressibility required to explain the dawould be 305 MeV, rather than the 215 MeV obtained bBlaizot et al.

1432

e

i.

d

e

f

etr

-

-em

dedat

a

FIG. 4. EGMRA1y3 is plotted vs A for nuclei where 100%of the E0 EWSR has been identified (squares). The sotriangle is the value obtained for58Ni using only the strengthobserved in this work (32%E0 EWSR). The solid circle is thelower limit for EGMRA1y3 in 58Ni for 100% of theE0 EWSR.Hartree-Fock RPA calculations are shown by the open triang(Ref. [19]) and diamonds (Ref. [20]).

This work was supported in part by the U.S. Depament of Energy under Grant No. DE-FG03-93ER4077and by the Robert A. Welch Foundation.

[1] J. P. Blaizot, Phys. Rep.64, 171 (1980).[2] S. Shlomo and D. H. Youngblood, Phys. Rev. C47, 529

(1993).[3] M. Buenerdet al., Phys. Rev. Lett.45, 1667 (1980).[4] D. H. Youngblood and Y.-W. Lui, Phys. Rev. C44, 1878

(1991).[5] D. H. Youngbloodet al., Phys. Rev. C23, 197 (1981).[6] G. Duhamelet al., Phys. Rev. C38, 2509 (1988).[7] J. Treineret al., Nucl. Phys.A371, 253 (1981).[8] D. M. Pringle et al., Nucl. Instrum. Methods Phys. Res.

Sect. A245, 230 (1986).[9] D. H. Youngblood and J. D. Bronson, Nucl. Instrum

Methods Phys. Res., Sect. A361, 37 (1995).[10] D. H. Youngbloodet al., Nucl. Instrum. Methods Phys.

Res., Sect. A361, 539 (1995).[11] H. L. Clark et al., Nucl. Phys.A589, 416 (1995).[12] M. Rhoades-Brownet al., Phys. Rev. C 21, 2417

(1980); M. H. Macfarlane and S. C. Pieper, ArgonnNational Laboratory Report No. ANL-76-11, Rev. 1, 197(unpublished).

[13] G. R. Satchler, Part. Nucl.5, 195 (1973); Nucl. Phys.A195, 1 (1972).

[14] G. R. Satchler, Nucl. Phys.A540, 533 (1992).[15] G. R. Satchler, Nucl. Phys.A47, 215 (1987).[16] M. N. Harakeh and A. E. L. Dieperink, Phys. Rev. C23,

2329 (1981).[17] S. Stringari, Phys. Lett.108B, 232 (1982).[18] Nguyen Van Giai and H. Sagawa, Nucl. Phys.A371, 1

(1981).[19] Ph. Chomazet al., Phys. Lett. B281, 6 (1992).[20] J. P. Blaizotet al., Nucl. Phys.A591, 435 (1995).

documentni

Documents