Observation of isoscalar multipole strengths in exotic doubly-magic $^{56}$Ni in inelastic α scattering in inverse kinematics

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Observation of isoscalar multipole strengths in exotic

doubly-magic

56

_{Ni in inelastic α scattering in inverse}

kinematics

S. Bagchi, J. Gibelin, M.N. Harakeh, N. Kalantar-Nayestanaki, N.L. Achouri,

H. Akimune, B. Bastin, K. Boretzky, H. Bouzomita, M. Caamano, et al.

To cite this version:

S. Bagchi, J. Gibelin, M.N. Harakeh, N. Kalantar-Nayestanaki, N.L. Achouri, et al.. Observation of

isoscalar multipole strengths in exotic doubly-magic

56

_{Ni in inelastic α scattering in inverse kinematics.}

Contents lists available atScienceDirect

Physics

Letters

B

www.elsevier.com/locate/physletb

Observation

of

isoscalar

multipole

strengths

in

exotic

doubly-magic

56

_Ni

_in

_inelastic

_α

_scattering

_in

_inverse

_kinematics

S. Bagchi

a

,

∗

,

J. Gibelin

b

,

M.N. Harakeh

a

,

N. Kalantar-Nayestanaki

a

,

N.L. Achouri

b

,

H. Akimune

c

,

B. Bastin

d

,

K. Boretzky

e

,

H. Bouzomita

d

,

M. Caamaño

f

,

L. Càceres

d

,

S. Damoy

d

,

F. Delaunay

b

,

B. Fernández-Domínguez

f

,

M. Fujiwara

g

,

U. Garg

h

,

G.F. Grinyer

d

,

O. Kamalou

d

,

E. Khan

i

,

A. Krasznahorkay

j

,

G. Lhoutellier

b

,

J.F. Libin

d

,

S. Lukyanov

k

,

K. Mazurek

l

,

M.A. Najafi

a

,

J. Pancin

d

,

Y. Penionzhkevich

k

,

m

,

L. Perrot

i

,

R. Raabe

n

,

C. Rigollet

a

,

T. Roger

d

,

S. Sambi

n

,

H. Savajols

d

,

M. Senoville

b

,

C. Stodel

d

,

L. Suen

d

,

J.C. Thomas

d

,

M. Vandebrouck

b

,

d

,

i

,

J. Van de Walle

a

a_{KVI-CART,UniversityofGroningen,NL-9747AA,Groningen,TheNetherlands} b_{LPCCaen,ENSICAEN,UniversitédeCaen,CNRS/IN2P3,Caen,France} c_{DepartmentofPhysics,KonanUniversity,Kobe568-8501,Japan}

d_{GrandAccélérateurNationald’IonsLourds(GANIL),CEA/DSM-CNRS/IN2P3,BvdHenriBecquerel,14076Caen,France} e_{GSIHelmholtzzentrumfürSchwerionenforschungGmbH,64291Darmstadt,Germany}

f_{UniversidadedeSantiagodeCompostela,E-15706SantiagodeCompostela,Spain} g_{ResearchCenterforNuclearPhysics,OsakaUniversity,Osaka567-0047,Japan} h_{PhysicsDepartment,UniversityofNotreDame,NotreDame,IN 46556,USA}

i_{InstitutdePhysiqueNucléaire,UniversitéParisSud,IN2P3-CNRS,F-91406OrsayCedex,France} j_{InstituteofNuclearResearch(ATOMKI),Debrecen,P.O.Box51,H-4001,Hungary}

k_{G.N.FlerovLaboratoryofNuclearReactions,JointInstituteforNuclearResearch,Dubna,Moscowoblast,144980,Russia} l_{InstituteofNuclearPhysicsPAN,ul.Radzikowskiego152,31-342Kraków,Poland}

m_{NationalResearchNuclearCenter,MoscowEngineeringPhysicsInstitute,Kashirskoesh.31,Moscow,115409,Russia} n_{InstituutvoorKern- enStralingsfysica,KULeuven,B-3001Leuven,Belgium}

a

r

t

i

c

l

e

i

n

f

o

a

b

s

t

r

a

c

t

Articlehistory:

Received8May2015

Receivedinrevisedform10October2015 Accepted23October2015

Availableonline28October2015 Editor:V.Metag

The Isoscalar Giant Monopole Resonance (ISGMR) and the Isoscalar Giant Dipole Resonance (ISGDR) compressionmodeshavebeenstudiedinthedoubly-magicunstablenucleus56_{Ni.Theyweremeasured}

by inelastic

α

-particle scattering ininverse kinematics at 50 MeV/u with the MAYA active target at theGANILfacility.ThecentroidoftheISGMRhasbeenobtainedatEx=19.1±0.5 MeV.Evidencefor thelow-lying partoftheISGDRhasbeenfoundatEx=17.4±0.7 MeV.The strengthdistributionfor thedipolemodeshowssimilaritywiththepredictionfromtheHartree–Fock(HF)basedrandom-phase approximation(RPA)[1].Thesemeasurementsconfirminelastic

α

-particlescatteringasasuitableprobe forexcitingtheISGMRandtheISGDRmodesinradioactiveisotopesininversekinematics.

©2015TheAuthors.PublishedbyElsevierB.V.ThisisanopenaccessarticleundertheCCBYlicense (http://creativecommons.org/licenses/by/4.0/).FundedbySCOAP3.

Recentdevelopmentsin nuclearphysics involvethe studiesof short-livedexoticnuclei.Newphenomena,suchas,neutronhalos, neutronskins, andmodification ofthe magic numbers, occur for largeneutron-to-proton(N/Z)ratiosfarfromstability.Thestudyof collective modes, the so-called giant resonances, in stablenuclei hasbeenoneoftheimportantphysicsmotivationsthroughoutthe historyofnuclear physics.However, very littleinformation about

*

Correspondingauthor.

E-mailaddress:soumya.bagchi87@gmail.com(S. Bagchi).

thecollectivepropertiesofexoticnucleiisavailable.Amongthese

collective modes, the ISGMR and the ISGDR are of prime

inter-est astheir excitation energies aredirectly relatedto the incom-pressibilityofanucleus,KA[2,3].Theincompressibilityofnuclear matter (K_∞) is defined asthe curvature of the energy per par-ticle atthe saturation density [4], and can be deduced from KA

[4–6].Itisanimportantkeyinputtotheequationofstate(EoS)of nuclearmatterwhich,inturn,isusefulinunderstandingsome as-trophysicalquantities, suchas, radii andmassesofneutron stars,

and also in understanding the mechanism of supernovae

explo-sions.

http://dx.doi.org/10.1016/j.physletb.2015.10.060

372 S. Bagchi et al. / Physics Letters B 751 (2015) 371–375

ThevalueofK_∞ obtainedfromtheISGMRandtheISGDRdata instablenuclei is240

±

10 MeV[4,6–8]. Theoretical calculations witheffective interactions using thisvalue of K_∞ can reproduce wellthecentroidenergiesoftheISGMRfor90_Zr,144_Sm,and208_Pb.

Ontheotherhand,theyoverestimatethecentroidenergiesforthe ISGMRstrengthdistributionsinSn[9,10]andCd[11]isotopes, al-though they can reproduce well the ground-state properties for theseisotopes. Nevertheless,theinvestigationoftheISGMRalong the isotopicchains of Cd [11] and Sn[12] helped determinethe symmetryenergyoftheEoS.Inspiteofsignificanttheoretical ef-fortsto reproducesimultaneouslythe ISGMRcentroidenergiesin

90_Zr,208_{Pb,andinSn/Cdisotopes,theproblemremains astowhy}

theisotopesofSnandCdare soft[9–11].Itshouldbementioned thatarecentattempttofitthecentroidenergiesofsoft120_Snand

stiff 208Pbsimultaneously [13,14] yielded a smaller value of K_∞ withalargeuncertainty,i.e.,230

±

40 MeV.Therefore,itisuseful tostudycompressionmodesforanotherseriesofisotopes to de-termineboth K_∞ andthesymmetryenergyparameteroftheEoS. NiisotopesprovidesuchanisotopicserieswidelyrangingoverN/Z ratios.Therefore,effortshavebeenputtostudyindetailthe com-pressionmodesforseveralstableandunstableisotopesofNifrom the neutron-deficient to the neutron-rich regions of the nuclear chart.

Measurementsof giantresonances in unstable nucleiare

par-ticularly challenging. Up to now such measurements have been

mainly performed to study the isovector giant dipole resonance in neutron-rich radioactive oxygen [15], neon [16], and tin [17]

isotopes, and in 68Ni [18]. These studies have been performed throughCoulombexcitationbyscatteringfromaPbtargetat rela-tivistic energies. Onthe other hand, thebest probe to studythe isoscalar modes in a nucleus is either inelastic

α

-particle scat-teringorinelastic deuteronscatteringasboth the

α

particle and deuteronhavezeroisospin. Theisoscalarresponses havebeenso farmeasuredfortheunstabledoubly-magic56Ninucleusby inelas-ticdeuteronscattering[19]andfortheunstableneutron-rich68Ni nucleusby inelastic

α

-particleanddeuteronscattering[20,21].In our experiment, we focused on the study of isoscalar responses in 56Ni via inelastic

α

-particle scattering. The choice was made because ofthe fact that, the56_Ni(

_α

_,

_α

₎56_{Ni* reaction has higher}

crosssection thanthe 56_Ni(d

_,

_d₎56_{Ni* reactionandtheunwanted}

backgrounddueto deuteronbreakupcanbe avoided.Another in-terestingreasontostudythecollectivemodesin56_{Niisbecauseof}

theimportantrole56_{Niplaysintheastrophysicalscenarios.}56_Ni,a

doubly-magicclosed-shellnucleus,isoneofthewaitingpoint nu-cleiinthestellarnucleosynthesisanditwasfoundintheejectaof supernova1987A[22].

TheISGMRcrosssectionispeakedat0◦ inthecenter-of-mass (CM)frame,whichcorrespondstothedetectionofverylow-energy recoil

α

particles in the laboratory frame. To measure the exci-tationenergy rangingfrom0 MeV (elastic scattering) to35 MeV ininversekinematics,itis necessarytodetectthe recoil

α

parti-cleshavingenergies upto 4.5 MeV,which correspondsto 8◦ CM angle. Detection of such low-energy recoil

α

particles (including sub-MeV)witha particletelescopewouldnecessitate avery thin target (

∼

30 μg/cm2_{) toallow the}

_α

_{particles toemerge fromthe}

targetandtominimizethestraggling.Thiswouldconsequently re-quirethe radioactiveion beamto have an intensityof the order of5

×

106 particles/sorabove inordertohavereasonable yields (

≥

1000countsforthe ISGMR at5.5◦ CM angle fora beamtime runof 5days).Althoughthisisfeasible withastorage-ring facil-ity, such as the Experimental Storage Ring (ESR) at GSI [23–25], anotheralternativeistouseanactive-targetdetector.Anexample ofsuch detectoris IKAR[26],developed atGSI, which was used tostudytheelasticscatteringofexoticbeamsatrelativistic ener-gies. Anotherexampleis MSTPC[27],builtin Japan,for studying

fusion reactions and reactions of nuclear-astrophysics interest at low energies.In ourexperiment, weused theMAYAactive-target detector [28]. Itis a gas target wherethe target gasacts alsoas a detector.Inan active targetsuch asMAYA,the targetthickness can be increased withoutsevere loss of energyresolution by in-creasing the gas pressure. In this Letter, we present the results of thefirst measurementof theisoscalargiant resonancesin the doubly-magic56Niinvestigatedwithinelastic

α

-particlescattering ininversekinematicsusingtheMAYAactive-targetdetector.

A secondary beam of 56_{Ni at 50 MeV/u was produced at the}

GANIL facility by the In-Flight fragmentation technique. The

pri-mary stablebeamof 58Ni at75 MeV/u impinged on a 525.6 μm

thick9_{BetargetlocatedattheentranceoftheLISE[29]}

spectrom-eter.Twodipolemagnetsanda500 μmachromaticdegraderwere usedtopurifythesecondarybeam.Theaveragebeamintensityof

56_{Niwasoftheorderof2}

_×

₁₀4_{particles/swithapurityofabout}

96%.Aplasticscintillatordetector,followedbytheMAYAdetector, was putatthe endoftheLISEspectrometer.The plastic scintilla-torwasusedtocountthenumberofincomingbeamparticles.The active-targetdetectorMAYA,developedatGANIL,isatime-charge projectionchamberwithanactivevolumeof28

×

25

×

20 cm3.In thepresence ofan electricfield appliedacrossthetarget volume, electrons produced through ionization of thegas by the incident beamorreactionproducts,drifttowardsasetof32amplification wiresthatareparalleltothebeamdirection.Foratwo-body reac-tion, the angle of the reaction plane can be determined by the drift time of the electrons towards the amplification wires. The avalanchesontheamplificationwiresinducesignalsonamatrixof 32

×

32 hexagonalpadsconnectedtoGASSIPLEX[28]chips.MAYA was filledwith95% heliumgasand5% CF4,whichactshereasa

quencher since purehelium cannot beused duetosparking. The pressureofthegas-mixturewasmaintainedat500 mbar.Withthe effectivelengthof20 cm,aluminosityofaround5

×

1024_cm−2_s−1

wasachieved.Anelectrostaticmask[30]wasplacedjustbelowthe beamtrajectoryinMAYA.Thiselectrostaticmaskhelpsinreducing the chargesduetothe highly-ionizingbeamparticles in compar-ison to those induced by the very low-energy recoil

α

particles, thuseffectivelyincreasingthedynamicrangeforcharge-detection. For each event, two observables are measured to reconstruct thereactionkinematics:therangeandthescatteringangleofthe recoil particle. Since MAYA is a time-charge projection chamber, the projected recoil angleis reconstructed using a “globalfitting method”asdescribedinRefs.[20,21,31].Inthismethod,a straight-linetrajectoryisobtainedbyminimizing theorthogonaldistances of the centers of thepads weighted by the chargeson the pads to the fittedtrajectory line. The intersection ofthe fitted trajec-tories of the beam path and the recoil-particle path determines thevertexofinteraction.From thecharge projectionoftherecoil

α

particle,theBraggpeak isdetermined andthe projectedrange of the recoilparticle is measured from the vertexof interaction. Recoilparticlesfromthequenchinggaswererejectedonan event-by-eventbasis usingthe totalcharge integral versusthe rangeof the ionizing particles. The third dimension is obtained from the drift timesof the electrons towards the amplification wires. The scatteringangleisobtainedfromtheprojectedangleonthepads and themeasured drift times. Afterobtaining the rangein three dimensions, the energy ofthe recoil

α

particleis deduced using range-to-energytablesinSRIM[32].Therange,energy,and scatter-ing angleoftherecoilparticleare deducedonan event-by-event basis.Areliabletrajectoryreconstructionhasbeenachievedfor re-coil

α

particleshavingenergieshigherthan600 keV.

The reconstructedthree-dimensionalscatteringofthe recoil

α

Fig. 1. (Coloronline.)Scatter plotofthe kineticenergyversusthescattering an-gle,reconstructedfor the recoil αparticles,is shown. Thesolidlinesrepresent theLISE++kinematics[33]calculationsobtainedfor Ex=0 MeV (elastic

scatter-ing),2.7 MeV(first-excitedstate),16 MeV,20 MeV,and30 MeVof56_Ni.SeveralCM

anglesaredepictedonthekinematicslines.

linesshow thekinematicscurvesfor Ex

=

0 MeV (elastic scatter-ing),2.7 MeV (first-excited state of56_{Ni),16 MeV, 20 MeV, and}

30 MeVof56Ni.

Data are transformed into the CM frame using two-body rel-ativistic kinematics, and are corrected for geometrical and re-construction efficiencies along with detector acceptances. These

efficiencies are deduced from simulations having inputs from

LISE++ kinematics [33] and SRIM [32] outputs; details are given in Ref. [34]. The peak around Ex

=

0 MeV corresponds to elas-ticscatteringandthefirst-excited state of56Ni. Thefull widthat halfmaximum(FWHM)ofthis“elastic-scattering”peak isaround 4.5 MeV. Thebroadening ofthispeak is dueto trajectory recon-struction of low-energy recoil

α

particles and due to the pres-ence of low-lying states mainly the 2+ state which is situated at Ex

=

2

.

7 MeV [35]. In this context, it is worthwhile to men-tion the detector resolution for different excitation energies, ob-tainedfromsimulations[34].Thedetectorresolutions(FWHM)for Ex

=

0 MeV,10 MeV,20 MeV,30 MeV,and40 MeVareobtainedto be2.24 MeV,2.16 MeV,1.90 MeV,1.38 MeV,and1.23 MeV, respec-tively.Itis,therefore,clearthatastheexcitationenergyincreases, the resolution of the detector improves. This is due to the fact thatwiththe increase ofexcitation energy,theenergy ofthe re-coil

α

particleincreasesforagivenCMangle(ascanbeseenfrom thekinematicslinesinFig. 1)whichleads tobettertrajectory re-constructionoftherecoilproductsinMAYA.Sixexcitation-energy spectra are obtained for the angular bins 3◦–4◦, 4◦–5◦, 5◦–6◦, 6◦–7◦,7◦–8◦,and8◦–9◦.Fig. 2displaystheexcitation-energy spec-trumfor a 1◦ bin centered around 5.5◦ CM angle.The fact that there are several peaks in the excitation-energy range between

5 MeVto 35 MeV points to the presence of severalfragmented

isoscalarmodes.

The data analysis is first performed by fitting the excitation-energyspectraforthedifferentCManglesbelow9◦.Inspectionof thespectrashowedthat atcertainangles somepeaksare promi-nent resulting in a total of nine peaks being prominent at dif-ferent angles for the excitation-energy range 5–35 MeV. There-fore, a 9-peak fit is performed for all excitation-energy spectra usingGaussian functions. This large number of fragmentsof the multipolestrengthhasbeenpreviously observed inthismass re-gion[36,37,39].The backgroundshape is obtainedby firstfitting

the excitation-energy spectra between 5 MeV and 35 MeV with

apolynomialoforder4assumingnogiant-resonancestructuresin thespectra.Concerningthebackgroundshape,wehavedecidedon

Fig. 2. (Coloronline.) Excitation-energyspectrum of56_{Nifor a 1}◦ _bincentered

around5.5◦θCMangleisshown.Thegreendashedlinerepresentsthebackground

fittotheexcitation-energyspectrumassumingnogiant-resonancestructures.The redsolidlineistheresultofthefittothedatawithnineGaussianpeaksanda fittedbackground.Thegreensolidlinerepresentsthefinalbackgroundinthe to-talfit.ThenineGaussianpeaksareshownseparatelywiththebrownsolidline, purpledashedline,purplesolidline,bluesolidline,reddashedline,blackdotted line,blackdashedline,magentadottedline,andmagentadashedline,identifiedas peaks#1,2,3,4,5,6,7,8,and9,respectively.Peak#1showsanL=1 behav-iorwhereas,peaks#2and3showanL=2 behavior.Peaks #4and5showL=1 and L=0 behaviors,respectively.Peaks#6to9include L=1 modeandhigher multipoles.

apolynomial oforder4becauseofthefollowing.Simulations for the elasticscatteringpeak showeda tail thatextended to higher excitation energy, resulting from the misidentification of elastic scatteringevents becauseof their very shorttracks inMAYA. On theotherhand,experimentsonstablenucleishowaphysical back-groundathigherenergiesduemainlytothequasi-elasticknockout reaction,whichstarts attheparticleseparationthresholdand in-creasestoalmost aconstant atvery highexcitationenergies.The

sum ofthese two backgrounds justifies the use ofa background

with a trough shape witha broad minimum around 20 MeV. In

the total fit ofthe excitation-energy spectra for a given CM an-gle,i.e.,nineGaussianfunctionsandthebackground,theobtained

background shape is then kept fixed. An extra additive

parame-ter,usedto determinetheheight ofthebackground,iskeptfree. ThewidthofaGaussianfittinganobservedgiant-resonance struc-tureisvariedinthefitfortheCManglewherethecorresponding structureisthemostprominent.Afterobtainingthewidth param-eter in this manner, it has been kept fixed for other CM angles wherethecorrespondingstructureheightislesspronounced.Data upto35 MeVexcitationenergyhavebeenconsidered,abovewhich dataareneglectedbecausetheysufferfromthelow-acceptanceof thedetector.Duetotheuncertaintyinsubtractingthebackground, possiblecontributionsfromthecontinuum duetoknock-out reac-tionscouldalsobepresentatthesehighenergies.

Comparing angular distributions of peaks obtained with this method with results from the calculations using distorted-wave Bornapproximation(DWBA)(seebelow),peaks#2and3inFig. 2

withcentroidpositionsatEx

=

11

.

0

±

0

.

5 MeV and14

.

4

±

0

.

5 MeV, respectively,were foundtohaveangulardistributions characteris-ticofquadrupole(L

=

2)transitions(seeFig. 3).Thecorresponding FWHMsweremeasuredtobe2

.

0

±

0

.

3 MeV and2

.

2

±

0

.

2 MeV, re-spectively.From thequasi-particle RPAwithaSkyrme interaction (SkM*)[38],itcan be seenthat thereexists alow-lying isoscalar

dipole mode (L

=

1) around 16–17 MeV. Evidence forthis

low-lying dipole mode was found in the present analysis (peak #4

in Fig. 2) with the centroid position at Ex

=

17

.

4

±

0

.

7 MeV.

The monopole mode (peak #5 in Fig. 2) was also identified at

374 S. Bagchi et al. / Physics Letters B 751 (2015) 371–375

Table 1

CentroidsoftheISGMRand thelow-lyingcomponentoftheISGDRin56_Niand 58_{Ni[39]obtainedfrominelasticα-particlescattering.Theresultobtainedforthe}

ISGMRin56_{Niwithinelasticdeuteronscattering[19]isalsoshown.Thecentroid}

valueslistedinthetableareobtainedfromthepeakfittingintheexcitation-energy spectra.

ISGMR

Ex[MeV]

Low-lyingcomponentofISGDR

Ex[MeV] 56_Ni(α ,α) (This work) 19.1±0.5 17.4±0.7 56_Ni(d,d_{)[19] 19.5} 58_Ni(α,α_{)[39] 18.43±0.15 17.42±0.25} Table 2

Optical-modelparametersusedintheDWBAcalculations.

Nucleus Eα [MeV] VReal [MeV] VImag [MeV] rReal [fm] rImag [fm] aReal [fm] aImag [fm] rC [fm] 58_{Ni[41] 240 76.6 24.2 1.242 1.435 0.8 0.8 1.3}

Fig. 3. (Coloronline.)Experimentalangulardistributionsforthepeakslocatedat 11.0 MeV(a),14.4 MeV(b),17.4 MeV(c),and19.1 MeV(d)areshownasblack datapointswitherrorbars.ThereddashedlinesshowtheDWBApredictionsfor isoscalarresonanceswithmultipolesL=2 (a)and(b),L=1 (c)andL=0 (d).

here. This rather small value compared to those of neighboring nuclei[39],isprobablyduetothelowstatisticsandsmall signal-to-noiseratio.Errors on thecentroidpositions andthewidths of differentmodesareobtainedfromthe fittingofthepeaksinthe excitation-energy spectra with Gaussian functions. The centroid

positions of the monopolemode andthe low-lying dipole mode

obtainedfromthisworkarecomparedwithotherworks[19,39]in

Table 1.

TheangulardistributionsoftheGaussianpeaks#2,3,4,and5 inFig. 2areshowninFig. 3.Errorbarsofthedataarethesquare rootsofthequadraticsumsoferrorsduetostatisticalfluctuations, errorsduetoefficiencycalculations,anderrorsinthebackground heights. These angular distributions are well reproduced by the DWBAcalculationsassumingL

=

2,2,1,and0multipolarities, re-spectively. The theoretical calculationswere performed usingthe codeCHUCK3[40].The optical-potentialparameters(listedin Ta-ble 2) were obtained by fitting the 58Ni(

α

,

α

) elastic scattering data and 58_Ni(

_α

_,

_α

_{) inelastic scattering data of the first-excited}

stateof58Ni at60 MeV/ubeamenergy[41].Transitionpotentials areobtainedfromcollectivetransitiondensitiesfollowingthe pro-ceduresdescribedinRefs.[42,43].

Anotherindependentanalysiswas performedusingthe

multi-pole-decomposition analysis (MDA) method to check the

consis-tencyofthe results.Afterbackgroundsubtractionasdescribed in theGaussianpeak-fittingmethod,thedatawerebinnedin2 MeV to improvethe statistics.Angular distributions were obtained for

Fig. 4. (Coloronline.)MDAfittingsoftheexperimentalcrosssections(blackdata points with errorbars)areshown fortwoexcitation-energy ranges;16 MeVto 18 MeV (leftpanel)and18 MeV to20 MeV(rightpanel).Angulardistributions withtheblacksolidline,theblackdashedline,thegreensolidline,andthegreen dashed lineareobtainedfor L=0, L=1, L=2,and L=3 multipoles, respec-tively,fromDWBAcalculationsusingcollectivetransitionpotentials(seetext)and theoptical-potentialparameterslistedinTable 2.Thecalculationsareperformedat theexcitationenergycorrespondingtothebincenterofagivenbinhavingsizeof 2 MeV.Theredsolidlinesrepresentthefitstothedata.

theexcitationenergiesrangingfrom9 MeVto35 MeVwith2 MeV energybinsandwerefittedusingalinearcombinationof theoret-icalangulardistributionsofmultipolaritiesL

=

0,L

=

1,L

=

2,and L

=

3.Since MAYA is phase-spacelimited because ofthe limita-tionsindetectingtheverylow- andhigh-energyrecoil

α

particles, thenumberofdatapointsintheangulardistributionsisalso lim-itedfrom3◦to8◦CMangle.Hence,themultipoleswhichare rele-vantatagivenexcitation-energyintervalhavebeenconsideredin thefittinginsteadofconsideringthecontributionsofallmultipoles atall excitation-energyintervals. Theoreticalangular distributions wereobtainedfromtheDWBAcalculationsasdescribedbefore us-ingtheoptical-potentialparameterslistedinTable 2.FromMDA,it hasbeenfound thatthemonopolemodehasa significant

contri-bution in the excitation-energy region from 18 MeV to 20 MeV

(see the right panel of Fig. 4) with the centroid value of the strength distribution measured at Ex

=

18

.

4

±

1

.

8 MeV and with a root-mean-square widthof 2

.

0

±

1

.

2 MeV. The position of the

monopole mode obtainedfromthe Gaussian peak-fitting method

(19

.

1

±

0

.

5 MeV) andtheMDAare ingoodagreement witheach other.Furthermore,theexcitationenergyofthemonopolemodein

56_{Niisalsoconsistentwiththevalue E}

x

=

19

.

3

±

0

.

5 MeV which isobtainedfrominelasticdeuteronscatteringoff56Ni[19].

Below15 MeV,thereisevidencefortheexistenceofbothL

=

1 and L

=

2 modes. Like in the Gaussian peak-fitting method,

evi-dence for the low-lying L

=

1 mode has also been found in the

MDAatanexcitationenergyofaround17 MeV(seetheleftpanel of Fig. 4).According to Refs.[39,44],thereis evidencefora low-lyingdipolemodein58_{Niaround16–17 MeVwhichishigherthan}

the 1h

_¯

ω

componentof theISGDR. Surprisingly, Monrozeau etal.

[19] didnot observe anyisoscalar dipole strength at thisenergy noratanyotherenergyin56Ni.Thisisconsistentwithabi-modal natureoftheISGDRwiththecentroidofthehigh-energy compo-nent appearingaround 30 MeV. Inelasticelectronscatteringfrom

58_{NihasbeenmeasuredbyKleinetal.[45].Unfortunately,in}

elec-tron scatteringitisnotpossibletodisentangleeitherisoscalarE0 andE2, orisoscalar E1andE3. However,the structuresobserved are not in disagreement with results from inelastic

α

scattering dependingonthemultipolarityassumed.

Fig. 5. (Coloronline.)ComparisonoftheexperimentalISGDRstrengthdistributionin

56_{Ni(blackdatapointswitherrorbars),obtainedfromtheMDA,isshowntogether}

withthepredictionofarecentHF-RPAcalculation(redsolidline)[1].

above35 MeV, there areno datapoints shownabove35 MeVin

Fig. 5.Duetonon-negligibleuncertaintiesindeterminingthe back-groundlevel and the poor statistics of the data, there are large uncertainties in obtaining the absolute values of the exhausted

fractions of the energy-weighted sum rules (EWSR) in the MDA

analysis. Both the MDA andthe direct comparison of the cross-section angular distribution withtheory could, in principle, give

usthestrength exhausted by a giant-resonancemode. The

num-berweobtainforL

=

0 is240

±

120%,whichis,withintheerrors,

in agreement with the value 136

±

27% obtained by Monrozeau

et al. [19]. Due to strong uncertainties in the normalization as-sociatedwithmeasurements withavailable active targetssuchas MAYA,asobserved herefortheelasticscatteringdata,we cannot giveatpresenta morereliablenumber. Asmentioned earlier, er-ror bars ofthe data includestatistical fluctuations, errors dueto efficiencycalculations,anderrorsinthebackgroundheights.

Tosummarize, inelastic

α

-particle scattering off the 56Ni

nu-cleus has been measured in inverse kinematics using the MAYA

active-targetdetector with an average beam intensity of the or-derof2

×

104 particles

/

s.ThecentroidpositionoftheISGMRhas beenfoundtobeat Ex

=

19

.

1

±

0

.

5 MeV.Alow-lyingcomponent oftheISGDRhasalsobeenfoundaround17 MeV.Thisisthefirst

measurement of the compression modes in a neutron-deficient

unstable nucleus with inelastic

α

-particle scattering. In spite of thelowstatistics,thedifficultiesinbackgrounddetermination,the limitationsof our studied energy rangeto 35 MeV, and the low energyresolution, the present experimental setup is suitable for measuringthepropertiesofunstableandexoticnucleiavailableat rare-isotopebeamfacilities worldwide. Efforts are on the wayto develop new active-target detectors [46], which will provide ac-cesstosmall-anglemeasurementswithbetterenergyandangular resolution.

Acknowledgements

Thisworkwas supportedby theEuropeanCommission within

the Seventh Framework Programme through IA-ENSAR (contract

No. RII3-CT-2010-262010)andGSIHelmholtzzentrumfür

Schweri-onenforschungGmbH,Darmstadt,Germany, andtheUnitedStates

National Science Foundation (Grants Number PHY-1068192 and

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