HungPLB 2018

Contents lists available atScienceDirect

Physics

Letters

B

www.elsevier.com/locate/physletb

Study

of

giant

dipole

resonance

in

hot

rotating

light

mass

nucleus

31

P

Debasish Mondal

a

,

∗

,

Deepak Pandit

a

,

S. Mukhopadhyay

a

,

b

,

Surajit Pal

a

,

Srijit Bhattacharya

c

,

A. De

d

,

N. Dinh Dang

e

,

f

,

N. Quang Hung

g

,

Soumik Bhattacharya

a

,

b

,

S. Bhattacharyya

a

,

b

,

Balaram Dey

h

,

Pratap Roy

a

,

K. Banerjee

a

,

b

,

1

,

S.R. Banerjee

i

a_{VariableEnergyCyclotronCentre,1/AF-Bidhannagar,Kolkata700064,India}

b_{HomiBhabhaNationalInstitute,TrainingSchoolComplex,Anushaktinagar,Mumbai400094,India} c_{DepartmentofPhysics,BarasatGovernmentCollege,Kolkata700124,India}

d_{DepartmentofPhysics,RaniganjGirls’College,Raniganj713358,India}

e_{QuantumHadronPhysicsLaboratory,RIKENNishinaCenterforAccelerator-BasedScience,RIKEN,2-1Hirosawa,WakoCity,Saitama351-0198,Japan} f_{InstituteofNuclearScienceandTechnique,Hanoi122100,Vietnam}

g_{InstituteofFundamentalandAppliedSciences,DuyTanUniversity,HoChiMinhCity700000,Vietnam} h_{SahaInstituteofNuclearPhysics,1/AF-Bidhannagar,Kolkata700064,India}

i_{(Ex)VariableEnergyCyclotronCentre,1/AF-Bidhannagar,Kolkata700064,India}

a

r

t

i

c

l

e

i

n

f

o

a

b

s

t

r

a

c

t

Articlehistory:

Received21May2018

Receivedinrevisedform3July2018 Accepted27July2018

Availableonline30July2018 Editor: V.Metag

Keywords:

Isovectorgiantdipoleresonance Statisticaltheoryofnucleus BaF2detectors

An exclusive systematic study of the giant dipole resonance (GDR) parameters has been performed in very light mass nucleus 31_{P in the temperature range of ∼0.8–2.1 MeV and average angular}

momentum of∼11–16 _¯h.The high-energy

γ

rays fromthe decay ofthe GDR, evaporated neutrons and

γ

-raymultiplicitieshavebeenmeasured. Theangulardistributionofhigh-energy

γ

rayshasalso beenmeasuredat Ebeam=42 MeV.TheGDRparameters,nuclearleveldensityparameterandnuclear

temperaturewerepreciselydeterminedbysimultaneousstatisticalmodelanalysisofhigh-energy

γ

ray andevaporatedneutronspectra.Itisobservedthatthemeasuredwidthremainsroughlyconstantupto atemperatureof_∼1.6 MeV.Moreover,thethermalpairingplaysnoroleindescribingtheGDRwidth inthisopen-shelllightnucleusattheabove-mentionedtemperatures andangularmomenta.Thepresent measurementsprovideanexcellentplatformtoextendtheapplicabilityoftheexistingtheoreticalmodels downtotheverylightmassnuclei.

©2018TheAuthors.PublishedbyElsevierB.V.ThisisanopenaccessarticleundertheCCBYlicense (http://creativecommons.org/licenses/by/4.0/).FundedbySCOAP3.

The isovector giant dipole resonance (IVGDR or commonly

knownas GDR)is a memberof abroad familyof collective res-onancesinnucleicalledgiantresonances[1,2].Macroscopically,it isconceivedastheout-of-phaseoscillationofprotonandneutron fluids,whilemicroscopically,itisdescribedasthecoherent excita-tionof1 particle–1 hole(1p–1h) configurationsacrossone major shell. The short lifetime of this resonance makes it an excellent probeto studythe nuclear properties atextremeconditions, e.g. nuclear shapesanddeformations at hightemperature and angu-larmomentum [3–10], fissiontime scale [11–13], isospinmixing [14–20], the ratio of nuclear shear viscosity to entropy volume density[21,22] etc.

*

Correspondingauthor.

E-mailaddress:[email protected](D. Mondal).

1 _{Presentaddress:DepartmentofNuclearPhysics,ResearchSchoolofPhysicsand}

Engineering,TheAustralianNationalUniversity,ACT0200,Australia.

AfterthefirstobservationoftheGDR builton thenuclear ex-citedstatesinheavy-ion fusionreactionsnearly fourdecadesago [23], a greatwealthofdatahasbeenaccumulatedovertheyears regarding the properties of the GDR parameters [1,24–27]. It is

observed that the GDR energy remains roughly constant at the

ground-state value with increasing nuclear temperature (T) and angular momentum (J), while the width increases with both T

and J. It is worth mentioning, in this context, that in a heavy-ion fusion reaction, the compound nucleus (CN) is populated at high J alongwiththeintrinsicexcitation.Itis,therefore,very dif-ficult to disentangle the effects of T and J on the GDR width. Researchers have also used inelasticscattering to studythe GDR [28–30].Inthiscase,theCNispopulatedatlow angular momen-tumbutwithabroadrangeofexcitationenergy.Anotherexcellent technique to studythe exclusive temperature dependence of the GDR is using the light-ioninduced fusion reaction, in which the CNispopulatedatadefinite initialexcitationenergyandasmall distribution of J as compared to that obtained in the heavy-ion

https://doi.org/10.1016/j.physletb.2018.07.052

GDR lineshape isthe superpositionof thelineshapes ofan en-sembleofnucleihavingdifferentdeformations[35–39].Thismodel predicts the J dependence quite well. However, it deviates from the measured data at low as well as hightemperatures. At low temperatures, it is observed that the GDR width remains at the ground-statevalueup to T

∼

1 MeV and increasesthereafter[33,

34],whereasathightemperatures(T

>

2

.

5 MeV)thewidth satu-rationoftheGDRisstill underdebate[40–44].Inthiscontext,it shouldbehighlightedthat,byincludingthethermalpairinginthe TSFMcalculations,theGDRwidthhasrecentlybeenfairlywell de-scribedatT

<

1

.

5 MeV inopen-shellnuclei[45].Interestingly,the microscopic phonon damping model (PDM) [46,47], which states thattheGDRwidtharisesowingtothecouplingoftheGDRstate tothenon-collective phstates(quantalwidth)aswell aspp and

hhstates(thermalwidth),describesthemeasuredwidthquitewell atbothlowandhighT,whereitpredictsasaturationoftheGDR width.Recently,a phenomenologicalmodel,calledcritical temper-atureincludedfluctuationmodel(CTFM),hasbeenproposed[33]. Accordingtothismodel,theGDRwidthremains constantuptoa criticaltemperature andincreases thereafter.This model also re-producestheGDRwidthatlowaswellashighT and J quitewell [33,34,48,49].

The conclusions drawn so farare mainly based onthe

exper-imental studies in medium andheavy mass nucleiin which the

GDRstrengthiswellconcentrated.However,veryfewexperiments existbelowthemass A

∼

100 [7,34,44,49–54] and,especially be-lowA

∼

50 [55],wheretheGDRischaracterizedbyitsown promi-nent features, e.g. configurational splitting [56], isospin splitting [57,58], etc. In this mass region there are some studies related toisospin mixingathightemperatures [14–20] and Jacobishape transitions[59–64].However,anexclusiveandsystematicstudyof thevariationoftheGDRparameterswithT and J isstillabsent.

InthisLetter, we presentthe firstexclusive studyofthe GDR width in A

∼

30 mass region, utilizing the light-ion beam (

α

).

The GDR and nuclear level density (NLD) parameters have been

determined properly by simultaneous statistical model analysis

of the measured high-energy

γ

ray and neutron spectra. The

angular momentum of the CN has been determined by

mea-suring the low-energy

γ

-ray multiplicities. The angular distribu-tionofhigh-energy

γ

rays hasbeen performedtodeterminethe bremsstrahlungcomponent. The presentstudyprovides an excel-lent testing ground for the existing theoretical models in their applicationdowntoverylight-massnuclei.

The experiments were performed at the Variable Energy

Cy-clotron Centre (VECC), Kolkata. A self-supporting 27Al target was bombarded witha pulsed 4He beam ofenergies Ebeam

=

28, 35,

42 MeVfromK-130cyclotron.Theinitialexcitationenergiesofthe CN31P were34.1,40.2,and46.2 MeV,respectively.Itshouldagain beemphasizedthat,duetotheavailabilityof4He beam,31P could bepopulatedbelowthecriticalangularmomentum Jcr

=

19h

¯

[65]

fortheJacobishape transition, alreadyobservedinthe same nu-cleus[64].Inaddition,theCNwaspopulatedjustabovethecritical angular momentum Jc

=

10

.

5 h

¯

[31]. Therefore the effect of J

castle typegeometry.Themultiplicity filterwas alsoemployedas a start trigger for the time of flight (TOF) measurement, which was used toreject theneutronbackground.As the energyofthe GDRisrelativelylargeforlightnuclei,theyieldof

γ

rays issmall in the GDR region. Therefore, special cares were taken to sup-press the background events, especially the cosmic backgrounds. The cyclotronrf timespectrum was recordedwithrespectto the multiplicity filtertominimizetherandomcoincidences.The spec-trometerwas surroundedby a10 cmthick passiveleadshield to block the

γ

-raybackgrounds.Thecosmicmuonswererejectedby usingtheir hit-patterninthe highlygranular LAMBDA array [66]. Inaddition,thedatawererecordedonlywhenatleastone

detec-tor of the LAMBDA array above a threshold of

∼

4 MeV fired in

coincidencewithboththetopandbottommultiplicity filters.This techniquesignificantlyreducesthebackgroundevents.Theangular distributionofhigh-energy

γ

rayswas measuredat

θ

=

55◦,90◦, 125◦forEbeam

=

42 MeV.Intheoff-lineanalysisdifferent

angular-momentum-gated high-energy

γ

spectra were reconstructed by

the cluster summingtechnique [66].The pile-up eventswere re-jected byusingthepulseshapediscrimination(PSD) method per-formedbycollectingthechargeovertwotimegatesof50 ns(short gate)and2 μs(longgate).Theevaporatedneutronenergyspectra were measured, in coincidence with the

γ

-ray multiplicities, by usinga liquid-scintillator-basedneutronTOF detector[68] (5 di-ameter,5length),whichwasplacedatadistanceof150 cmfrom the target position and at an angle of 150◦ withrespect to the beamdirection.ThePSDtechniquecomprisingoftheTOFandzero cross-over time (ZCT) was utilized for the n

−

γ

discrimination.

ThemeasuredTOFspectrawereconvertedto

angular-momentum-gated neutronenergy spectraby takingthe prompt

γ

peak as a time reference.Thespectrawere thenconvertedfromthe labora-tory frameto the center ofmass (CM) frame.The typical energy resolution of the present set-up is of

∼

17% at 1 MeV. The de-tailedenergy-dependentneutrondetectionefficiencycanbefound inRef. [68].

The angular momentum of the CN was determined from the

measured fold distribution (number ofmultiplicity detectorfired in each event) by using the geant simulations. A detailed

simu-lation was necessary to account forthe data recordingcondition (top–bottom coincidence), whichselects aslightly higherangular momentumspace. A triangulardistributionof

γ

-raymultiplicities

was thrown with an adjustable peak and a width, which were

determined by comparing the measured and simulated fold

dis-tributions. TheseareshowninFig.1along withtheincidentand different fold-gatedangular momentum distributions. The details ofthistechniquearedescribedinRef. [67].Thesimulatedangular momentum distributionswere thenincorporatedinthestatistical model code cascade [69]. As the isospin splitting is crucial for

GDR in light nuclei, thestatistical modelanalysiswas performed

by using a version of the cascade _{code, which was modified to}

us-Fig. 1.(a) Experimental(greensymbols)andsimulated(redline)folddistributions for31_{P populatedatinitialexcitationenergyof46.2 MeV.(b) Incidentanddifferent} fold-gatedangularmomentumdistributions.(Forinterpretationofthecolorsinthe figure(s),thereaderisreferredtothewebversionofthisarticle.)

Fig. 2.Variationofa1(Eγ)withtheγ rayenergy.Thegreensolidcirclesare ex-perimentally determined,whilethe redsolid lineis theoretically calculatedfor

E0=5.3 MeV.

ingthereciprocityrelationassumingaLorentzianphotoabsorption crosssectionintheinversechannelgivenby

σ

abs

(

Eγ

)

=

4

π

e2_h

_¯

mpc

N Z A SG

GEγ2

(

E2

γ

−

E2G

)

2

+

2GE2γ

,

(1)

where N and Z are the neutronand protonnumbers and mp is

theprotonmass.SG, EG,and

G aretheGDRfractionoftotal

en-ergyweighteddipolesumrule,theenergyandthewidth, respec-tively.The variation of EG along thedecay cascadewas properly

takencare of.The GDR parameters were extractedby comparing themeasured high-energy

γ

rays withthe statistical model cal-culationsalongwithabremsstrahlungcomponentparametrizedas

σ

=

σ

0exp

(

−

Eγ

/

E0

)

andfoldedwiththeresponsefunctionofthe

LAMBDA array. At Ebeam

=

42 MeV the slope parameter E0 was

determined fromthe measured angular distribution ofthe high-energy

γ

rays,whichisslightlyforwardpeakedintheCM frame because of the non-statistical bremsstrahlung component. In the CMframethe

γ

rayangulardistributionwasassumedtohavethe formW

(

Eγ

,

θ )

=

W0

(

Eγ

)

[

1

+

a1

(

Eγ

)

P1

(

cos

θ )

+

a2

(

Eγ

)

P2

(

cos

θ )

]

.

Inthenucleon–nucleonframeofreferencethebremsstrahlungwas assumedto be isotropic and the slope parameter E0 was

deter-minedbycomparingthemeasuredandcalculateda1

(

Eγ

)

(Fig.2).

Theextractedslope parameters were roughlyconsistent withthe systematics E0

=

1

.

1

[

(

Ebeam

−

Vc

)/

Ap

]

0.72,with Vc and Ap being

theCoulombbarrierandprojectilemass,respectively[70].Atother beam energies, E0 was guided by this prescription and the

vi-sualinspectionofmeasured

γ

raysabove Eγ

∼

25 MeV.Itshould

beemphasized herethat themainingredient ofstatisticalmodel calculations is the NLD, which was properly determined in the

Fig. 3.Differentfold-gated high-energyγ rayspectra(left panel)and the evap-oratedneutronenergyspectra(rightpanel)for31_{P.Thegreensolidsymbolsare} experimentallymeasuredspectra,whiletheredsolidlinesarethecorresponding resultsofthestatisticalmodelcalculations.

present study. In the cascade _{code, the level density was taken}

basedonFermigasmodelgivenas

ρ

(

E∗

,

J

)

=

2J

+

1 12 3/2

√

aexp

(

2

√

aU

)

U2

,

(2)

where

=

(

1

+

δ

1J2

+

δ

2J4

)

is the deformable liquid drop

moment of inertia;

=

2Ir

/

h

¯

2, Ir

=

2

/

5M R2 is the rigid body

moment of inertia and

δ

1,

δ

2 are the deformability coefficients.

The quantity U

=

E∗

−

−

Erot is the intrinsic excitation

en-ergy with

and Erot

=

J

(

J

+

1

)/

being the pairing and

ro-tational energies, respectively. The parameter a is the NLD pa-rameter, which is proportional to the single particle density of states at the Fermi surface. According to the prescription by Ig-natyuk andReisdorf [71,72], the NLD parameter is givenas a

=

˜

a

(

A

)

[

1

+

_US

{

1

−

exp

(

−

γ

U

)

}]

. Following Ref. [55], in which, the authors performed a detailed studyof NLD in light-mass nuclei, theasymptoticNLDparameterwas takenasa

˜

(

A

)

=

0

.

04543r3₀A

+

0

.

1246r2 0A

2

3

+

0

_.

1523r₀A 1

3.Thenumericalco-efficientsforthe

sur-face andcurvature terms are slightly different from those given by Reisdorf [72]. The shell damping factor

γ

is 0

.

054 MeV−1 [73] and the ground-stateshell correction

S is

−

2

.

23 MeV.As

˜

a depends onboth temperature andangular momentum [73,74],

it was determined by varying the r0 parameter to match the

measured neutron spectra.It should be emphasized that a given fold-gated high-energy

γ

andneutron spectra were analyzed

si-multaneously so that theGDR and theNLD parameters could be

determinedin aconsistentway.The best-fitparameterswere ex-tracted by using the

χ

2 _{minimization technique. The measured}

γ

and neutron spectra along with the best-fit statistical model calculationsare shownin Fig.3. In order to emphasizethe GDR region, the linearized spectra are shown in Fig. 4 by using the quantity

σ

_absexp

(

Eγ

)

=

σ

abs

(

Eγ

)

Yexp

(

Eγ

)/

Ycal

(

Eγ

)

, where Yexp

(

Eγ

)

andYcal

₍

_E

γ

)

arethe experimentalandthebest-fitcascade

spec-tra, whereas

σ

abs

(

Eγ

)

is the Lorentzian absorption cross section

Fig. 4.Differentfold-gatedlinearizedγrayspectrafor31_{P.Thegreensolidsymbols} areexperimentallymeasuredσabsexp(Eγ)(seethetext),whiletheredsolidlinesare thecorrespondingLorentzianshavingtheGDRparametersasshowninTable1.

whereU

=

E∗

−

Erot

−

EG

−

.Weremarkherethat,31P beinga

lightnucleus,theGDRdecayispredominantlyfromtheCNandthe averagingover thedecay cascadereducesthetemperatureatthe highestinitialexcitation energyby only 2%,which iswell within theexperimentalerrorsestimatedconsideringtheuncertaintiesin NLDparameter, J,andEG.

ItisinterestingtonotethattheGDRbuiltontheexcitedstates of 31P fully exhausts the dipole strength, i.e. the GDR remains verymuchcollectiveinthislightnucleus.Moreover,theenergyof theGDR, exceptatthelowesttemperature, remains roughly con-stant ataround 17.5 MeV. The slightlyhighervalue of EG atthe

lowest temperature is due to a bit higher value of the NLD pa-rameterrequiredforfittingtheneutronevaporationspectrum.We remarkherethat,themeasured GDRenergies arelower thanthe ground-statevalue of19.3 MeV obtainedby fittingthemeasured photoabsorption cross section with a single Lorentzian [75]. The GDRwidth,ontheotherhand,remainsroughlyconstantataround 7.5 MeVupto T

∼

1

.

6 MeV andgraduallyincreaseswithT there-after.

In Fig. 5 the measured GDR widths are compared with the

results of calculations within different models and plotted as a

function of T. As the measured angular momentum varies from

11

.

0–15

.

9

_¯

h, the calculations have been performed for J

=

11

.

5 and15

.

5h

¯

.Moreover,theresultsofcalculationswithintheCTFM

and PDM have also been shown for J

=

0 h

_¯

to visualize the

Fig. 5.ComparisonofthemeasuredGDRwidthwithpredictionsbydifferentmodels asafunctionofT at J=11.5h¯(blackdot-dashedline)and J=15.5h¯(bluesolid line)(measuredrangeofangularmomentum).Theredlong-dashedlinesinpanels (c)and(d)arethepredictionsat J=0h¯.

explicit T dependence. Within the TSFM (Fig. 5a), the GDR

ap-parent line shape at a given T and J was calculated as the

weighted averageofthevariouslineshapescorrespondingto dif-ferentnucleardeformations;theweightbeingtheBoltzmann fac-torexp

(

−

F

(β,

γ

,

J

)/

T

)

,where

β

,

γ

are thedeformation param-eters. The free energy F was calculatedconsidering only the de-formedliquiddropenergyas31_{P isanopen-shellnucleusandthe}

effect of the shell correction is expected to be negligible above

T

∼

1

.

5 MeV [76]. It is obvious from Fig. 5a that the results of TSFM calculations overpredict the measured widths. As can also beseenfromFig.5b,thephenomenologicalthermalshape fluctu-ation model(pTSFM) [31] failstoreproducethemeasuredwidths even afterassumingtheground-statewidthof

∼

3

.

8 MeV, which wastakenforboth120_{Sn and}208_{Pb todescribethewidthsinthese}

massregionsinRef. [31].Interestingly,theTSFMandpTSFMcould describe themeasuredwidthabove T

∼

1

.

5 MeV inmediumand heavy massnuclei. However, in the light massregion, these two models arenot ableto describethe measuredwidths evenup to

T

∼

2

.

1 MeV.

In Fig. 5c the CTFM calculations are presented. Within this model,theGDRwidthremainsconstantattheground-statevalue uptoacriticaltemperatureTc

=

0

.

7

+

37

.

5

/

A duetotheGDR

in-ducedfluctuationandincreasesthereafter.Inthesecalculationsthe ground-stateGDRwidth(

gs)for31P wastakenas7.5 MeV,which

is abit higherthan thevalue of 6.3 MeVobtainedby fittingthe measured photoabsorption crosssection witha single Lorentzian [75].However,theviscoushydrodynamicmodelofAuerbachet al. [77] yields

gs

=

7

.

5 MeV andthemeasureddatawell belowthe

critical temperature are also around this value. Hence

gs was

takenas7.5 MeV.Interestingly,theCTFMreproducesthetrendof measured GDRwidthsquitewellwith Tc of

∼

1

.

9 MeV predicted

Fig. 6.(a)Protonand(b)neutronpairinggapsasfunctionsoftemperatureat differ-entangularmomentacalculatedwithinBCSandBCS1(seetext).

J increasestheGDRwidthfromtheground-statevaluebeforethe criticaltemperature.

ThemeasuredGDRwidthsarecomparedwiththeresultsofthe microscopicPDMcalculationsperformedasafunctionof T and J

withoutthe inclusion of thermal pairing (Fig. 5d). Regarding the latter,thecalculationswithintheBCStheory aswellastheBCS1 one,whichincludesthequasiparticlenumberfluctuation,atfinite

T and J [78] werecarriedout.Theparameters GZ forprotonand GN forneutron pairing interactions were chosen so thatthe

val-uesofthe correspondingpairing gaps (

Z and

N) atT

=

0 are

2.3 MeVand1.85 MeV,respectively,basedontheodd–evenmass differences.TheresultsofcalculationsshowthatincreasingT and

J breaksthepairssothatnopairinggapsremainatT

>

0

.

25 MeV and J

>

11

.

5h

_¯

(Fig. 6).Thisallows ustocarry out thePDM cal-culationswithoutthermalpairing.The single-particleenergiesfor protonsandneutronswerecalculatedwithinthedeformedWood– Saxonpotentialswith

β

=

0

.

1 obtainedbyfittingthe photoabsorp-tion cross section using the prescription of Junghans et al. [79]. Thetwoparameters F1 andF2 forthecouplingoftheGDRtothe

non-collectivephandpp(orhh)configurations,respectively,were chosensothatthewidthoftheGDRobtainedatT

=

0 and J

=

0h

¯

is equalto around 6.3 MeV (the experimental ground-state GDR width),whereasitsvalueatT

=

0

.

8 MeV and J

=

11

.

5h

_¯

matches thecorrespondingexperimentaldatapoint.Thevaluesofthese pa-rametersarekept unchangedthroughoutthecalculationsatall T

and J. The GDR energy at J

=

0

_¯

h is set equal to ground-state valueof19.3 MeV,whereasat J

=

0h

¯

itis18.0 MeVcomparable totheexperimentalvalues.Astheagreementbetweentheoryand experimentis fairly good,it could be inferred that, pairing plays noroleinthepresentlightnucleus,leavingonlytheeffectof an-gularmomentumontheGDRwidthinit.Itshouldbehighlighted here,thatbothCTFMandthePDM coulddescribetheGDRwidth asa functionofT and J formediumandheavy massnucleiand presentworkpointstowardstheuniversalityofthesemodels.

Insummary,anexclusive,systematicmeasurementoftheGDR

parameters has been performed using the light-ion

α

beam in

very light-mass nucleus 31P. The angular momentum of the CN

hasbeenpreciselydeterminedbymeasuringthelow-energy

γ

-ray multiplicities.The GDR,nuclear leveldensityparameters and nu-clear temperatures have been accurately determined from a si-multaneousstatisticalmodelanalysisofthemeasuredhigh-energy

γ

spectra andthe neutron spectra.The experimentally extracted widthsremains roughly constantup to 1.6 MeVtemperatureand graduallyincreasesthereafter. Themeasured widthscould be

de-scribed very well within the CTFM and PDM, thereby asserting

their universality in describing GDR widthas a function of

tem-perature andangular momentum. Moreover, the paring gaps are

found tovanish inthe ranges of T and J considered inthis ex-periment, therefore,have no effect on the measured GDR width contrarytothatobservedinmediumandheavyopen-shellnuclei.

Acknowledgements

The authors are thankful to VECC cyclotron staffs for smooth

running of the accelerator during the experiment. The

PDM-related calculations were performed on the RIKEN

HOKUSAI-GreatWave Systemandsupportedby theVietnam National

Foun-dation forScience and Technology Developmentunder the Grant No. 103.04-2017.69.

References

[1]M.N. Harakeh, A. van der Would, Giant Resonances: Fundamental High-FrequencyModeofNuclearExcitation,ClarendonPress,Oxford,2001. [2]P.F.Bortignon,A.Bracco,R.A.Broglia,GiantResonances:NuclearStructureat

FiniteTemperature,HarwoodAcademicPublishers,Amsterdam,1998. [3]J.J.Gaardhøje,etal.,Phys.Rev.Lett.53(1984)148.

[4]C.A.Gossett,etal.,Phys.Rev.Lett.54(1985)1486. [5]D.R.Chakrabarty,etal.,Phys.Rev.Lett.58(1987)1092. [6]A.Stolk,etal.,Phys.Rev.C40(1989)R2454. [7]J.H.Gundlach,etal.,Phys.Rev.Lett.65(1990)2523. [8]R.F.Noorman,etal.,Phys.Lett.B292(1992)257. [9]J.P.S.vanSchagen,etal.,Phys.Lett.B308(1993)231. [10]DeepakPandit,etal.,Phys.Rev.C87(2013)044325. [11]M.Thoennessen,etal.,Phys.Rev.Lett.59(1987)2860. [12]P.Paul,etal.,Annu.Rev.Nucl.Part.Sci.44(1994)65. [13]I.Diószegi,etal.,Phys.Rev.C63(2000)014611. [14]M.N.Harakeh,etal.,Phys.Lett.B176(1986)297. [15]J.A.Behr,etal.,Phys.Rev.Lett.70(1993)3201. [16]M.Kici ´nska-Habior,etal.,Nucl.Phys.A731(2004)138. [17]E.Wójcik,etal.,ActaPhys.Pol.B38(2007)1469. [18]A.Corsi,etal.,Phys.Rev.C84(2011)041304(R). [19]S.Ceruti,etal.,Phys.Rev.Lett.115(2015)222502. [20]DebasishMondal,etal.,Phys.Lett.B763(2016)422. [21]N.D.Dang,Phys.Rev.C84(2011)034309.

[22]DebasishMondal,etal.,Phys.Rev.Lett.118(2017)192501. [23]J.O.Newton,etal.,Phys.Rev.Lett.46(1981)1383. [24]K.A.Snover,Annu.Rev.Nucl.Part.Sci.36(1986)545. [25]J.J.Gaardhøje,Annu.Rev.Nucl.Part.Sci.42(1992)483. [26]A.Schiller,etal.,At.DataNucl.DataTables93(2007)549. [27]D.R.Chakrabarty,etal.,Eur.Phys.J.A52(2016)143. [28]E.Ramakrishnan,etal.,Phys.Rev.Lett.76(1996)2025. [29]T.Baumann,etal.,Nucl.Phys.A635(1998)428. [30]P.Heckman,etal.,Phys.Lett.B555(2003)43. [31]DimitriKusnezov,etal.,Phys.Rev.Lett.81(1998)542. [32]S.Mukhopadhyay,etal.,Phys.Lett.B709(2012)9. [33]DeepakPandit,etal.,Phys.Lett.B713(2012)434. [34]BalaramDey,etal.,Phys.Lett.B731(2014)92. [35]M.Gallardo,etal.,Phys.Lett.B191(1987)222. [36]J.M.Pacheco,etal.,Phys.Rev.Lett.61(1988)294. [37]Y.Alhassid,etal.,Phys.Rev.Lett.61(1988)1926. [38]O.E.Ormand,etal.,Phys.Rev.Lett.77(1996)607. [39]P.Arumugam,etal.,Phys.Rev.C69(2004)054313. [40]A.Bracco,etal.,Phys.Rev.Lett.62(1989)2080. [41]G.Enders,etal.,Phys.Rev.Lett.69(1992)249. [42]M.P.Kelly,etal.,Phys.Rev.Lett.82(1999)3404. [43]O.Wieland,etal.,Phys.Rev.Lett.97(2006)012501. [44]M.Ciemala,etal.,Phys.Rev.C91(2015)054313. [45]A.K.RhineKumar,etal.,Phys.Rev.C91(2015)044305. [46]N.D.Dang,etal.,Phys.Rev.Lett.80(1998)4145. [47]N.D.Dang,etal.,Nucl.Phys.A636(1998)427. [48]C.Ghosh,etal.,Phys.Rev.C94(2016)014318. [49]S.Ceruti,etal.,Phys.Rev.C95(2017)014312. [50]M.Kici ´nska-Habior,etal.,Phys.Rev.C36(1987)612. [51]G.Viesti,etal.,Phys.Rev.C40(1989)R1570. [52]M.Kici ´nska-Habior,etal.,Phys.Rev.C45(1992)569. [53]Z.M.Drebi,etal.,Phys.Rev.C52(1995)578. [54]S.K.Rathi,etal.,Phys.Rev.C67(2003)024603. [55]M.Kici ´nska-Habior,etal.,Phys.Rev.C41(1990)2075. [56]R.A.Eramzhyan,etal.,Phys.Rep.136(1986)229. [57]S.Fallieros,etal.,Nucl.Phys.A147(1970)593. [58]J.D.Vergados,Nucl.Phys.A239(1975)271.

[59]M.Kici ´nska-Habior,etal.,Phys.Lett.B308(1993)225. [60]A.Maj,etal.,Nucl.Phys.A731(2004)319.