Deformation dependence of the isovector giant dipole resonance : the neodymium isotopic chain revisited

Contents lists available atScienceDirect

Physics

Letters

B

www.elsevier.com/locate/physletb

Deformation

dependence

of

the

isovector

giant

dipole

resonance:

The neodymium

isotopic

chain

revisited

L.M. Donaldson

a

,

b

,

C.A. Bertulani

c

,

J. Carter

a

,

V.O. Nesterenko

d

,

P. von Neumann-Cosel

e

,

∗

,

R. Neveling

b

,

V.Yu. Ponomarev

e

,

P.-G. Reinhard

f

,

I.T. Usman

a

,

P. Adsley

b

,

g

,

J.W. Brummer

g

,

E.Z. Buthelezi

b

,

G.R.J. Cooper

h

,

R.W. Fearick

i

,

S.V. Förtsch

b

,

H. Fujita

j

,

Y. Fujita

j

,

M. Jingo

a

,

W. Kleinig

d

,

C.O. Kureba

a

,

J. Kvasil

k

,

M. Latif

a

,

K.C.W. Li

g

,

J.P. Mira

b

,

F. Nemulodi

b

,

P. Papka

b

,

g

,

L. Pellegri

a

,

b

,

N. Pietralla

e

,

A. Richter

e

,

E. Sideras-Haddad

a

,

F.D. Smit

b

,

G.F. Steyn

b

,

J.A. Swartz

g

,

A. Tamii

j

a_{SchoolofPhysics,UniversityoftheWitwatersrand,Johannesburg2050,SouthAfrica} b_{iThembaLABS,P.O.Box 722,SomersetWest7129,SouthAfrica}

c_{DepartmentofPhysicsandAstronomy,TexasA&MUniversity-Commerce,Commerce,TX 75429,USA}

d_{BogoliubovLaboratoryofTheoreticalPhysics,JointInstituteforNuclearResearch,Dubna,Moscowregion,141980,Russia} e_{InstitutfürKernphysik,TechnischeUniversitätDarmstadt,D-64289Darmstadt,Germany}

f_{InstitutfürTheoretischePhysikII,UniversitätErlangen,D-91058Erlangen,Germany} g_{DepartmentofPhysics,UniversityofStellenbosch,Matieland7602,SouthAfrica} h_{SchoolofGeosciences,UniversityoftheWitwatersrand,Johannesburg2050,SouthAfrica} i_{DepartmentofPhysics,UniversityofCapeTown,Rondebosch7700,SouthAfrica} j_{ResearchCenterforNuclearPhysics,OsakaUniversity,Ibaraki,Osaka567-0047,Japan} k_{InstituteofParticleandNuclearPhysics,CharlesUniversity,CZ-18000,Prague 8,CzechRepublic}

a

r

t

i

c

l

e

i

n

f

o

a

b

s

t

r

a

c

t

Articlehistory:

Received20December2016

Receivedinrevisedform6November2017 Accepted13November2017

Availableonline20November2017 Editor:V.Metag

Keywords:

144,146,148,150_Nd,152_{Sm(p, p}₎

Ep=200 MeV θlab=0◦

RelativisticCoulombexcitationoftheIVGDR Comparisonwithphoto-absorptionresults Transitionfromsphericaltodeformed nuclei

ProtoninelasticscatteringexperimentsatenergyEp=200 MeV andaspectrometerscatteringangleof 0◦ wereperformedon144,146,148,150_Ndand152_{SmexcitingtheIsoVectorGiantDipoleResonance(IVGDR).} Comparisonwithresultsfromphoto-absorptionexperimentsrevealsashiftofresonancemaximatowards higherenergiesforvibrationalandtransitionalnuclei.Theextractedphoto-absorptioncrosssectionsin the mostdeformed nuclei, 150_{Nd and} 152_{Sm,exhibit apronouncedasymmetry rather thanadistinct} double-humpstructureexpectedasasignatureofK -splitting.Thisbehaviourmayberelatedtothe prox-imityofthesenucleitothecriticalpointofthephaseshapetransitionfromvibratorstorotorswithasoft quadrupoledeformationpotential.Self-consistentrandom-phaseapproximation(RPA)calculationsusing the SLy6Skyrmeforceprovidearelevant descriptionofthe IVGDR shapesdeduced fromthe present data.

©2017TheAuthors.PublishedbyElsevierB.V.ThisisanopenaccessarticleundertheCCBYlicense (http://creativecommons.org/licenses/by/4.0/).FundedbySCOAP3_.

1. Introduction

Giant resonances represent a prime example of collective

modesinthenucleus.A smoothmass-numberdependenceofthe

resonance parameters is characteristic of all nuclear giant

reso-*

Correspondingauthor.

E-mailaddresses:lindsay.donaldson18@gmail.com(L.M. Donaldson),

vnc@ikp.tu-darmstadt.de(P. von Neumann-Cosel).

nances and, as such, a study of them yields information about

thenon-equilibriumdynamicsandthebulk propertiesofthe nu-cleus

[1]

.TheoldestandbestknowngiantresonanceistheIVGDR owingto thehighselectivity forisovectorE1excitation in

photo-absorption experiments. The properties of the IVGDR have been

studiedextensivelyusing(

γ

, xn)-typeexperiments,particularlyin the Saclay [2] and Livermore [3] laboratories. These sets of ex-periments are a major source ofinformation withrespect to the

γ

-strengthfunction

[4]

above theneutron threshold– an impor-tant quantity used in statistical reaction calculations relevant to

https://doi.org/10.1016/j.physletb.2017.11.025

0370-2693/©2017TheAuthors.PublishedbyElsevierB.V.ThisisanopenaccessarticleundertheCCBYlicense(http://creativecommons.org/licenses/by/4.0/).Fundedby SCOAP3_.

134 L.M. Donaldson et al. / Physics Letters B 776 (2018) 133–138

applicationslike astrophysical large-scalereaction networks

[5,6]

, reactordesign

[7]

,andevennuclearwastetransmutation

[8]

.

Recently, a new experimental technique for the extraction

of electric dipole-strength distributions in nuclei via relativistic Coulomb excitation has been developed [9,10]. It utilises proton inelasticscatteringwithenergiesofafewhundredMeVat scatter-inganglescloseto0◦.Althoughmanyoftheseexperimentsfocus onestablishingthe strengthbelowandaroundneutronthreshold anditscontributiontothedipolepolarisability

[11–16]

,such data alsoprovideinformationonthephoto-absorptioncrosssectionsin theenergyregionoftheIVGDR.

The chain ofstable even–even neodymiumisotopes isknown

tocompriseatransitionfromsphericaltodeformedgroundstates forheavierisotopes andthusrepresents an excellenttest caseto studytheinfluenceofdeformationonthepropertiesoftheIVGDR. A (

γ

, xn) experiment at Saclay [17] revealed that the width in-creaseswithdeformationevolvingintoapronounceddouble-hump structureinthemostdeformednuclide150Nd,consideredtobea textbook example [18] of K -splitting owing to oscillations along thedifferentaxesofthequadrupole-deformedgroundstate.Here, wereportnewphoto-absorptioncrosssectionsfor144,146,148,150_Nd

extracted from 200 MeV proton scatteringexperiments with re-sultsdifferingsignificantlyfromRef.[17].Inparticular,no double-humpstructureisobservedin themostdeformed150_Ndnucleus.

This finding is confirmedin a further measurement of the

com-parably deformed 152_{Sm nucleus, again in contrast to a (}

_γ

_{, xn)}

measurementatSaclay

[19]

.Thisunexpectedresultmayberelated tothespecialstructureofthesetwonucleiwhicharepredictedto lie near the critical point [20] of a shape phase transition from sphericaltoquadrupole-deformedgroundstates

[21]

.

2. Experimentandanalysis

Theprotoninelasticscatteringexperimentswereperformedat the iThemba Laboratory for Accelerator Based Sciences (iThemba LABS)inSouthAfrica.TheK600magneticspectrometer,positioned at0◦ withtheacceptancedefinedbya circularcollimatorhaving an opening angle

θ

lab

= ±

1

.

91◦,was used to analyse a scattered

200 MeV dispersion-matched proton beam delivered from the

SeparatedSector Cyclotronof iThemba LABS. The self-supporting

144,146,148,150_Ndand152_{Smtargetswereallisotopicallyenrichedto}

values

>

96% (except148_{Ndenriched to90%)witharealdensities}

rangingfrom1.8to 2

.

6 mg

/

cm2_{.The corresponding ground-state}

deformationparameters

β

2 aregiveninthesecondcolumnof

Ta-ble 1.Thebeampreparationandthedetectorsetup aredescribed inRef. [10].Details regardingthe dataextraction andanalysis of thepresentmeasurementscanbefoundinRef.[22].

Inthechosenkinematicconditions,relativisticCoulomb excita-tionofthetargetnucleiisthedominantreactionmechanism.The resultingdouble-differentialcrosssections(witha systematic un-certainty of

±

7%) obtained following the procedures detailedin Ref.[22] are displayedin Fig. 1for20 keVenergybins.A typical

energyresolution



E

=

45 keV (FWHM)was achieved.The broad

structurevisibleinallspectrabetweenapproximatelyEx

=

12 and

18 MeVcorresponds totheexcitationoftheIVGDR.Statistical er-rors in this region are of the order of 2–4%. From Fig. 1 it is immediatelyevidentthatthewidthoftheIVGDRincreasessteadily fromthenearlyspherical144Ndnucleusthroughthetransition re-giontothemoredeformed150_Ndand152_Smnuclei.

In order to compare to the (

γ

, xn) data of Carlos et al. [17, 19], the (p, p) spectra hadto be converted to equivalent photo-absorption cross sections.By wayof example,Fig. 2 provides an overview of the conversion process for 150Nd. It can be divided into three distinct stages, namely, background subtractionin the region of the IVGDR, calculation of the virtual-photon spectrum

Fig. 1. Experimentaldouble-differentialcrosssectionsforthe144,146,148,150_{Nd(p, p}₎

and152_{Sm(p, p}_{)reactionsatEp=200 MeV andθlab=0}◦_±1.91◦_.

andthedivisionbythisspectrummultipliedthroughbythevirtual

γ

energytoobtainequivalentphoto-absorptioncrosssections.This procedurehasbeentestedforseveralcases(48Ca,120Sn,208Pb)and fair agreement ofthe resulting shape andabsolute valuesof the photo-absorption cross sectionswithexperimentsusingreal pho-tonswasobtained

[11–15]

.

Background fromnuclear processes studied in similar

experi-ments at 300 MeV has been found to be small in heavy nuclei

[11–14]. It was modelled in the present case by three compo-nents. The contributions of the IsoScalar Giant Monopole Reso-nance (ISGMR, green line) and IsoScalarGiant Quadrupole Reso-nance (ISGQR, pink line) to the spectrum of Fig. 2(a) were es-timated in the following way [13,15]: Computed angular

distri-butions of theISGMR and ISGQR crosssections were determined

by distortedwave Bornapproximation calculationswiththecode DWBA07

[23]

usingquasiparticle phononmodel (QPM)transition amplitudesandtheLove–Franeyeffectiveinteraction

[24]

asinput (analogoustoRef.[12]).A representativeexampleofsuch calcula-tionsforNdandSmisotopesisshownin

Fig. 3

.

Afteraveragingovertheexperimentalangularacceptance,these calculations providea relation betweentheoretical cross sections

and transition strengths under the assumption of a dominant

one-step reaction mechanism, which should be well fulfilled at

an incident protonenergy of200 MeV. Utilising this proportion-ality, experimental ISGMR and ISGQR strength distributions can then be convertedto (p, p) crosssectionsin thepresentspectra. For comparison, thepredictedIVGDR crosssection is alsoshown and clearly dominates the spectra. However, the B(E1) transition strengths(andthusthephoto-absorptioncrosssections)cannotbe

Fig. 2. (Colouronline).Overviewoftheconversionprocessfrom150_{Nd(p, p}_{)tophoto-absorptioncrosssections:(a) double-differential(p, p}_{)crosssectionandbackground}

components.ThegreenandpinklinesdescribethecontributionfromtheISGMRandISGQR,respectively,andthebluelinethephenomenologicalcomponentexplainedin thetext;(b) virtualphotonspectrum;(c) equivalentphoto-absorptionspectrumresultingfromEq.(1);(d) equivalentphoto-absorptionspectrumrebinnedto200 keVfor comparisonwiththephoto-absorptiondataofRef.[17].

Fig. 3. (Colouronline).ExampleofDWBAcalculationsoftheIVGDR(red),ISGMR (blue) and ISGQR (green) excitation cross sectionsin (p, p)scattering at E0=

200 MeV offNdandSmisotopes.

extractedwiththismethodbecausetheCoulomb-nuclear interfer-encetermbreakstheproportionality.

Itohetal.[25]reportedisoscalargiantresonancestrength dis-tributionsfortheSmisotopechainwhichcouldbedirectlyapplied to 152_{Sm. The results of Ref. [25] were also used for the}

corre-sponding Nd isotones, which show very similar deformation pa-rameters, with a correction for the global mass dependences of

the ISGMR and the ISGQR [1]. The ISGQR contribution was

in-dependently estimated from a recent study of the ISGQR in the Ndisotopechain

[26]

withmethodsanalogoustoRefs.[27–29]in goodcorrespondencewithresultsfromtheaboveprocedure.

A phenomenological background shown as blue line Fig. 2(a) describes the behaviour of the double-differential cross section

at the high excitation energy part of the spectrum where the

Coulombexcitation contributionisnegligible.Thiscomponent

in-corporates all unknown multipolarity contributions as well as

quasi-freescatteringandisapproximatedbyfindingthemaximum ofthecrosssectionbetweenEx

=

20 MeV and23 MeVandusing

awidththat bestdescribesthespectrum inthisregion.A similar descriptionfortheshapeofthiscomponentwas foundinastudy of208_Pb

_[30]

_{whereanexperimentalextractionoftheangular}

dis-tributionofthebackgroundwaspossible.

Thevirtual E1photonspectrum

[31]

foreachisotope was cal-culated using the eikonal approximation [32] and averaged over

the angular acceptance of the detector. The equivalent

photo-absorption spectrum (cf. Fig. 2(c)) was then obtained using the followingequation d2

_σ

d



dEγ

=

1 Eγ dNE1 d



σ

πλ γ

(

Eγ

).

(1)

Finally,

Fig. 2

(d) showstheequivalent photo-absorptionspectrum rebinnedto200 keVfordirectcomparisonwiththe(

γ

, xn)results. The presentsetup at

θ

lab

=

0◦ doesnotallow forthe

determina-tionofaccurate verticalscatteringangles,thus limitingthe angu-lar resolution[10].We therefore refrainfrom extractingabsolute photo-absorptioncrosssections.Theexcitationenergydependence oftheconversion,however,isnotaffected.

3. Comparisonwith(γ, xn)results

Through the simultaneous measurement ofthe partial photo-nuclear cross sections

σ

(

γ

,

n

)

+

σ

(

γ

,

pn

)

and

σ

(

γ

,

2n

)

using a

monochromatic photon beam, total photo-absorption cross

sec-tions have been determined in heavy nuclei. Data obtainedwith

this method for the IVGDR in the stableeven–even neodymium

andsamariumisotopicchainsare giveninRefs.[17] and

[19]

, re-spectively. Fig. 4 displays the rebinned spectra from the present

work normalised to the maximum of the photo-absorption cross

sections[17,19] tofacilitatea comparisonoftheevolutionof the shapeoftheIVGDRwithincreasingdeformation.

Carlosetal.[17,19](greenhistograms)observedaspreadingof the IVGDRasthe nucleibecomesofter followedby a splittingof the IVGDR into two distinct dipole modes for 150_{Nd and} 152_Sm,

which were interpreted as K

=

0 and K

=

1 components. The

equivalent photo-absorptioncrosssectionsfromthe presentwork (redhistograms)displayasimilartrend,i.e.,a generalbroadening oftheIVGDRwithincreasingdeformation.Forthemostdeformed

150_Ndand152_{Sm, theresonance becomes skewedwithincreased}

strength on the low-energy side, but no split into two distinct componentsisobserved.

136 L.M. Donaldson et al. / Physics Letters B 776 (2018) 133–138

Table 1

ComparisonofLorentzianparameterisations,Eq.(2),forthepresentphoto-absorptioncrosssectionswiththosefrom Ref. [17]forthe neodymium isotopesand fromRef. [19]for152_{Sm.Thequantity R denotesthe ratioof}

photo-absorptioncrosssectionssummedintheexcitationenergyregions10–14 MeV and14–18 MeV,respectively.

Isotope β2[46] E1(MeV) 1(MeV) E2(MeV) 2(MeV) R Reference

144_{Nd 0.13} 15.05±0.10 5.30±0.25 0.55 [17] 15.64±0.01 4.93±0.03 0.42 Present 146_{Nd 0.15} 14.80±0.10 6.00±0.30 0.66 [17] 15.69±0.02 6.11±0.07 0.47 Present 148_{Nd 0.20} 14.70±0.15 7.20±0.30 0.74 [17] 15.52±0.01 5.84±0.04 0.53 Present 150_{Nd 0.28} 12.30±0.15 3.30±0.10 16.00±0.15 5.20±0.15 0.77 [17] 11.97±0.10 2.91±0.40 15.67±0.04 5.64±0.09 0.60 Present 152_{Sm 0.31} 12.45±0.10 3.20±0.15 15.85±0.10 5.10±0.20 0.87 [19] 12.40±0.20 4.73±0.65 16.36±0.07 6.36±0.14 0.62 Present

Fig. 4. (Colouronline).Photo-absorption crosssectionsfromthepresentdata(red histograms)normalisedtothemaximumofthepre-existing(γ, xn)results(green histograms)[17,19].ThebluelinesshowtheresultsofSSRPAcalculationswiththe SLy6forcedescribedinthetext (solid:full,dashed-dotted: K=0 part, dashed:

K=1 part).

The obvious discrepancies (in both the K

=

0 and K

=

1 re-gions)betweenthephoto-absorptionresultsandthepresentdata are reflected in a change ofparameters when attempting to de-scribethe observedresonances byLorentzians.The present

spec-tra were fitted with a modified Lorentzian of the form used in

Refs.[17,19]

σ

(

E

)

∝

E 2

2 R

(

E2

₋

_E R2

)

2

+

E2

2R

,

(2)

where ER corresponds to the resonance centroid energy and

R

totheresonancehalf-width.Forthemoredeformednuclei,a sum of two modified Lorentzianswas used.The best fitto the

exper-imental data was selected such that the value for the reduced

χ

2 _{wasoptimised. Inthecaseofthe}148_{Ndisotope,itwas found}

that the reduced

χ

2 _{value was not improvedthrough the useof}

atwoLorentzianfitasassumedinareanalysis[33]ofthedataof Ref.[17].Theresultsaresummarisedin

Table 1

.Inordertofurther illustratethesystematicdifferencesbetweenthetwoexperiments,

we also provide the ratio R of summed photo-absorption cross

sections inthe excitation energy regions 10–14 and 14–18 MeV, respectively.

Forspherical andtransitionalnuclei, a shift ofthecentroid to higherenergiesisobservedforthepresentdata.Thenew param-eterisations for thedeformednucleidonot yielda ratioof

≈

0

.

5 for K

=

0 and K

=

1 oscillatorstrengths,respectively,asexpected

for prolate deformed ground states [3]. One should remember,

however, that 150Nd and 152Sm lie just above the shape phase transitionfromvibratorstoaxialrotors

[20,34]

.Althoughtheyare alreadywelldeformed,theirdeformationpotentialissoftinthe

β

degreeoffreedom

[21]

.Thecorrespondingshapefluctuationsthus enhancethewidthoftheresonancepeakswhich,inturn,may hin-deracleardiscriminationoftheK

=

0 and1 branches.

The presentresults do not provide absolute photo-absorption crosssectionsandthus cannotdistinguishwhetherthe main dis-crepancieslie inthe K

=

0 orK

=

1 region,buttheagreementat highexcitationenergiesin

Fig. 4

and

Table 1

suggesttheformer.In anycase,theyclearlyindicateadifferentratioof K

=

0 andK

=

1 componentscomparedtoRefs.[17,19].Thisfindingisindependent ofthebackgroundin thespectraduetonuclearprocessesshown to be smallin the energyregion of the IVGDR, cf.Fig. 2(a). The largestcomponentstemsfromtheISGMR,whoseangular distribu-tion peaks at 0◦.Even at themaximum of the ISGMR peak, the crosssectioncontributiondoesnotexceed10%.

New photo-absorption data are available from (

γ

, n) experi-ments [35,36] in the excitation-energy region between the neu-tronthresholdandEx

≈

13 MeV.A studyoftheSmisotopechain

finds systematically smaller cross sectionsthan Ref. [19], corrob-orating the present results. A similar investigation of 143–148Nd findsagainsignificantlylower crosssectionsthanRef.[17] forthe lighterisotopesbutfairagreementfor146,148_{Nd.Photo-absorption}

cross sections of 154_{Sm [37] have been deduced in a study of}

theE1strengthwithforwardangleprotonscatteringanalogousto the experiments described inRefs. [11–14]. The results doshow a double-humpstructure butwitha clearreductioninthe K

=

0

region anda slight enhancement in the K

=

1 region compared tothe Saclay data [19], againleading toa reduced K

=

0

/

K

=

1 ratioasinthepresentcase.Thesefindingsarequalitatively consis-tentwithaglobalreanalysisofdatatakenwiththeSaclaymethod

[38],which indicates thatthe (

γ

, n) crosssections are systemati-callytoolargeandthe(

γ

, 2n)crosssectionstoosmall.

One may speculate whether the observed differences are re-lated to the reaction mechanism (real vs. virtual photoexcita-tion).However,photo-absorptioncrosssectionsdeducedfrom sim-ilar (p, p) experiments using the virtual photon method show very good correspondence with (

γ

, xn) data in other cases, cf. Refs.[11,14].

4. Comparisonwithmodelcalculations

In order to investigate the role of K

=

0 and K

=

1

com-ponents further, a comparison with RPA calculationsparticularly suitedformodellingtheIVGDRispresented.The calculationsare

performedwithin the SkyrmeSeparable Random Phase

Approxi-mation(SSRPA)approach

[39]

.Themethodisfullyself-consistent sinceboththemeanfieldandresidualinteractionarederivedfrom thesame Skyrmefunctional. Theresidual interaction includes all the functional contributions as well as the Coulomb direct and exchangeterms.Theself-consistentfactorisationoftheresidual in-teraction cruciallyreduces thecomputational effort fordeformed nucleiandmaintainshighaccuracyofthecalculations

[39–41]

.

Wenotethatvariousmethodscanbeappliedtothedescription ofIVGDRandother collective excitationsindeformednuclei, see e.g.approacheswithfinite-rangeGognyforces

[42,43]

anda rela-tivisticmeanfield

[44]

.Some ofthesemoreelaborate approaches basedon thegenerator coordinatemethodtake into account nu-cleartriaxiality

[43]

orinvestigatethebreakingofaxialsymmetry byusingprojectiontechniques

[44]

.However,eithernotheoretical predictionsfor the presentproblemare available

[43,44]

or they showratherlargedeviationsfromexperiments

[42]

.

Here,theSkyrmeparameterisationSLy6

[45]

isusedwhichwas

shown to provide a good description of the IVGDR in

medium-heavy,deformednuclei

[41]

.Thecodeexploitsthe2Dgridin cylin-dricalcoordinates.Theaxialquadrupoledeformationcharacterised bytheparameter

β

2isdeterminedbyminimisationofthetotal

en-ergy,and

β

2valuesobtainedaretypicallyclosetodata

[41]

when

takingintoaccountthatdata,deducedfromB(E2)values,embrace groundstate deformationplussomequantumfluctuationsnot in-cludedinmeanfieldcalculations. Wethusadopttheexperimental values(cf.

Table 1

)forthequadrupoledeformationin146,148,150Nd and 152_{Sm, respectively. For the nearly spherical} 144_{Nd, a}

negli-gible deformation,

β

2

=

0

.

001, is used, since the value given in

Ref.[46]representsadynamicalratherthanaground-state defor-mation. Nd and Sm isotopes in the transitional region, however, show very soft deformation energy surfaces,which gives a large uncertaintytothetheoreticalground-statedeformations.Wehave checkedtriaxialitywithfull3Dmean-fieldcalculationsanddonot findanyforthenucleiconsideredhere, inagreementwitha sys-tematicstudyofnuclearshapesusingtheSkyrmefunctionalSkM*

[47].

PairingistreatedwithdeltaforcesattheBCSlevel

[48]

.A large two-quasiparticle basis up to

∼

100 MeV is taken into account. TheThomas–Reiche–Kuhnsumrule

[49]

forisovectorE1strength isexhausted by 98–100%.Tofacilitatea comparisonbetweenthe experimental results and the model calculations, the SSRPA

pre-dictionswere smoothedwithawidth

=

2 MeV,whichprovides

agood description ofthe broadstructure ofexperimental IVGDR strengthdistributionsinmanyheavydeformednuclei

[41]

.

The resulting photo-absorption cross sections are shown in

Fig. 4asbluelines.Theyare normalisedto thedataatthe

high-energy flank of the IVGDR, where the results of Carlos et al.

[17,19]andthepresentworkagree reasonablywell.Forthemost

deformed nuclei, 150Nd and 152Sm, the separation into K

=

0

(dashed-dotted) and K

=

1 (dashed) components is additionally

shown.Forthesphericalandtransitional nuclei,144,146,148_Nd,the

calculationsare inbetter agreement withthe presentresults,i.e. favouringsmallercrosssectionsonthelow-energyflank.For150_Nd

and152Sm,theSSRPAresultsdisplayadouble-humpstructure,but againwithalower K

=

0 componentthan observedintheSaclay results and total cross sections closer to the present data.Since thereisacertaindegreeoffreedominthenormalisationonecould bringthetheoreticalresultsinbetteragreementwiththeresultsof Carloset al.atlowerexcitation energies,butatthepriceof over-shootingallavailabledataathigher Ex.

5. Conclusions

A measurement of the (p, p) reaction at Ep

=

200 MeV and

θ

lab

=

0◦favouringrelativisticCoulombexcitationintheenergy

re-gionoftheIVGDRhasbeenpresentedfortheeven–even144–150_Nd

isotopic chain as well as for 152Sm. While the high

energy-resolutiondata show considerablefinestructure (even inthe de-formed isotopes),whichcarriesinformation ontherole of differ-ent decaymechanismsof thegiant resonances [27–30] andlevel densities [16,30,50], the present work focuses on a study of the evolutionoftheIVGDRasafunctionofdeformation.

A general broadeningof the IVGDR is observed with increas-ing deformation andthe mostdeformed150Ndand152Sm nuclei exhibitapronounced asymmetryratherthanadouble-hump struc-tureowingtoK -splitting,incontrasttopreviousphoto-absorption datafromSaclay [17,19].Thisisinterpreted asa signature ofthe peculiar nature of these two nuclei which lie close to the crit-ical point of a shape phase transitionfrom vibrators to rotators characterisedbyasoftpotential inthe

β

degreeoffreedom

[21]

. Self-consistentRPAmodelcalculationswiththeSkyrmeSLy6force, particularlysuitedtodescribetheIVGDR,provideafairdescription of the data consistent with a reduction of cross sectionson the low-energysideoftheresonancewithrespecttotheSaclay data. In view of their general relevance, an independent test of these unexpectedresultswouldbehighlyvaluable.Itshouldbepossible to realisesuch experiments inthe nearfuture atthe low-energy taggersystemNEPTUNattheS-DALINAC

[51]

andatELI-NP[52]. Acknowledgements

We thank J.L. Conradie and the accelerator team at iThemba LABS forproviding excellent beams. We are indebted to M. Itoh for providing us with the numerical results of Ref. [25]. This

work was supported by the South African NRF and by the

Ger-man DFG undercontract No. SFB 1245. C.A.B. acknowledges

sup-port bythe U.S.DOEgrant DE-FG02-08ER41533andtheU.S.NSF GrantNo. 1415656andJ.K. bytheCzechScienceFoundation(Grant No. P203-13-07117S).

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