Coulomb and nuclear excitations of narrow resonances in ^{17}Ne

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Physics Letters B

www.elsevier.com/locate/physletb

Coulomb and nuclear excitations of narrow resonances in ¹⁷ Ne

J. Marganiec

^a^,^b^,^c

, F. Wamers

^a^,^b^,^c^,^d

, F. Aksouh

^b

, Yu. Aksyutina

^b

, H. Álvarez-Pol

^e

,

T. Aumann

^a^,^b

, S. Beceiro-Novo

^e

, C.A. Bertulani

^f

, K. Boretzky

^b

, M.J.G. Borge

^g

, M. Chartier

^h

, A. Chatillon

^b

, L.V. Chulkov

ⁱ^,^b

, D. Cortina-Gil

^e

, H. Emling

^b

, O. Ershova

^b^,^j

, L.M. Fraile

^k

, H.O.U. Fynbo

^l

, D. Galaviz

^g

, H. Geissel

^b

, M. Heil

^b

, D.H.H. Hoffmann

^a

, J. Hoffmann

^b

, H.T. Johansson

^m

, B. Jonson

^m^,∗

, C. Karagiannis

^b

, O.A. Kiselev

^b

, J.V. Kratz

ⁿ

, R. Kulessa

^o

, N. Kurz

^b

, C. Langer

^b^,^j

, M. Lantz

^p

, T. Le Bleis

^b^,^q

, R. Lemmon

^r

, Yu.A. Litvinov

^b

,

K. Mahata

^b^,^s

, C. Müntz

^b

, T. Nilsson

^m

, C. Nociforo

^b

, G. Nyman

^m

, W. Ott

^b

, V. Panin

^a^,^b

, S. Paschalis

^b^,^h

, A. Perea

^g

, R. Plag

^b^,^j

, R. Reifarth

^b^,^j

, A. Richter

^a

, C. Rodriguez-Tajes

^e

, D. Rossi

^b^,^u

, K. Riisager

^l

, D. Savran

^c^,^d

, G. Schrieder

^a

, H. Simon

^b

, J. Stroth

^j

, K. Sümmerer

^b

, O. Tengblad

^g

, S. Typel

^b

, H. Weick

^b

, M. Wiescher

^t

, C. Wimmer

^b^,^j

aInstitutfürKernphysik,TechnischeUniversitätDarmstadt,DE-64289Darmstadt,Germany bGSIHelmholtzzentrumfürSchwerionenforschungGmbH,DE-64291Darmstadt,Germany cExtreMeMatterInstituteEMMIandResearchDivisionGSI,DE-64291Darmstadt,Germany dFrankfurtInstituteforAdvancedStudiesFIAS,DE-60438FrankfurtamMain,Germany

eDepartamentodeFísicadePartículas,UniversidadedeSantiagodeCompostela,ES-15782SantiagodeCompostela,Spain fDepartmentofPhysicsandAstronomy,TexasA&MUniversity-Commerce,TX75429,USA

gInstitutodeEstructuradelaMateria,CSIC,ES-28006Madrid,Spain

hDepartmentofPhysics,UniversityofLiverpool,Liverpool, L693BX,UnitedKingdom iNRCKurchatovInstitute,RU-123182Moscow,Russia

jInstitutfürAngewandtePhysik,GoetheUniversität,DE-60438FrankfurtamMain,Germany

kDepartmentofAtomic,MolecularandNuclearPhysics,UniversidadComplutensedeMadrid,ES-28040Marid,Spain lDepartmentofPhysicsandAstronomy,UniversityofAarhus,DK-8000Aarhus,Denmark

mFysik,ChalmersTekniskaHögskola,SE-41296Göteborg,Sweden

nInstitutfürKernchemie, JohannesGutenberg-UniversitätMainz,DE-55122Mainz,Germany oInstytutFizyki,UniwersytetJagello´nski,PL-30-059Krakóv,Poland

pInstitutionenförFysikochAstronomi,UppsalaUniversitet,SE-75120Uppsala,Sweden qPhysik-DepartmentE12,TechnischeUniversitätMünchen,DE-85748Garching,Germany rNuclearPhysicsGroup,STFCDaresburyLab,Warrington, WA44AD,Cheshire,UK sNuclearPhysicsDivision,BhabhaAtomicResearchCentre,Trombay,Mumbai,400085,India tJINA,UniversityofNotreDame,NotreDame,USA

uNationalSuperconductingCyclotronLaboratory,MSU,EastLansing,MI 48824,USA

a r t i c l e i n f o a b s t ra c t

Articlehistory:

Received16February2016

Receivedinrevisedform11April2016 Accepted22May2016

Availableonline25May2016 Editor:V.Metag

Newexperimentaldatafordissociationofrelativistic¹⁷Neprojectilesincidentontargetsoflead,carbon, and polyethylenetargetsatGSIare presented.Specialattentionispaidtotheexcitationand decayof narrowresonant statesin¹⁷Ne.Distributionsofinternalenergyinthe¹⁵O+^p+p three-bodysystem havebeendeterminedtogetherwithangularandpartial-energycorrelationsbetweenthedecayproducts in different energyregions. The analysis was done usingexisting experimental data on¹⁷Ne and its mirrornucleus¹⁷N.Theisobaricmultipletmassequationisusedforassignmentofobservedresonances and their spins and parities. A combination of data from the heavy and light targets yielded cross sections and transition probabilities for the Coulombexcitations of the narrow resonant states. The

*

Correspondingauthor.

E-mailaddress:Bjorn.Jonson@chalmers.se(B. Jonson).

http://dx.doi.org/10.1016/j.physletb.2016.05.073

0370-2693/©²⁰¹⁶^TheÂuthors.^Published^byÊlsevier^B.V.^Thisîsânôpenâccessârticleûnder^the^CC^BY^license(http://creativecommons.org/licenses/by/4.0/).Fundedby SCOAP³.

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resulting transition probabilities provide information relevant for a betterunderstanding ofthe ¹⁷Ne structure.

©²⁰¹⁶^TheÂuthors.^Published^byÊlsevier^B.V.^Thisîsânôpenâccessârticleûnder^the^CC^BY^license (http://creativecommons.org/licenses/by/4.0/).FundedbySCOAP³.

The proton dripline nucleus ¹⁷Ne is a candidate for a two- protonBorromeanhalonucleus[1],witha¹⁵Ocoresurroundedby two valenceprotons. The protons are expectedto predominantly possessamixed(1s1/2)²and(0d5/2)²configuration.Thereis,however,norealconsensus abouttherelativestrengthofthes andd configurations,neither experimentallynor theoretically. Estimates basedonexperimentalvaluesforinteractioncross-sectionandmo- mentumdistributions offragmentsinone-protonknockout [2–5], the magnetic dipole moment [6], first-forbidden β⁺-decay [7,8], Coulomb energy difference between the mirror nuclei ¹⁷Ne and 17N[9–13],aswellaspuretheoreticalinvestigations[14–16],pro- videwidelydifferingresults.Differentevaluationsoftheamountof (1s1/2)²inthe¹⁷Neground-statewavefunction,P(s²),range from 15%to100%. Thereare alsostrongcontradictionsbetweendiffer- enttheoreticalmodelsforCoulombdissociationof¹⁷Ne[17–20].

A theoretical study [21] points to the importance of the de- terminationof electric transition strengths to elucidate the two- proton halo properties. The authors emphasise in particular the importance of reduced electric transition probabilities from the 17Negroundstatetolow-lyingstatesasforexampleB(E2,1/2⁻→ 3/2⁻)andB(E2,1/2⁻→⁵/2⁻),thatcouldbedeterminedthrough Coulombexcitation.

This paper presents a new comparative study of nuclear and Coulombexcitationof¹⁷Neatrelativisticenergiesusingpolyethy- lene(CH2),carbon,andleadtargets.

TheexperimentwasperformedattheGSIHelmholzzentrumfür Schwerionenforschung GmbH in Darmstadt, employing the R³B- LANDsetupformeasurementsininverseandfullkinematics.The reactionproducts, from¹⁷Neinteraction, were firstdetected in a pairofsilicon-stripdetectorsandthen separatedinthemagnetic fieldof thelarge dipole magnet(ALADIN).Afterthe magnet, two branchesofdetectorswereused tomeasuretheposition,energy- loss,andtime-of-flight,oneforheavyions(twofibredetectorsand aToF-wall)andanotherforprotons(twodriftchambersPDCand aToF-wall).Thetrajectoriesofchargedparticlesthroughthemag- neticfieldofALADINwerereconstructedforparticleidentification anddeterminationoftheir momentumvectors. The chargeofthe particleswasdirectlymeasuredviatheirenergylossinthesilicon- stripdetectorsandToF-walls,whiletheirmasswasobtainedfrom measurements of B

ρ

using the reconstructed deﬂection anglein the ALADIN magnet. This analysis is based on knowledge of the magneticﬁeld inside andoutside the ALADINmagnet, measured alongall threecoordinateaxesatmanythousandsofgrid points.

The

γ

-raysemittedbythede-excitingfragmentsweredetectedin the4

π

gamma spectrometer, CrystalBall, placed around thetar- get.Asketch ofthepositions ofthecharged-particle detectorsin theexperimentalsetupisshowninFig. 1ofRef.[22].

The¹⁷Nebeamwas directedtowards asecondary199mg/cm lead target, used to induce electromagnetic excitation of ¹⁷Ne.

Theexperimentalsotook datawitha 370mg/cm² carbontarget aswell as a 213 mg/cm² polyethylene target, to study nuclear- inducedbreakup.Thebackgroundwasdeterminedinrunswithan emptytarget.

Triple coincidences between ¹⁵O and two protons were se- lected.Theintrinsictwo-protondetectioneﬃciencywas57.8(3.1)%.

Thedetectioneﬃciencywasdeterminedfromlossesoftwo-proton eventsduetotoosmallenergydepositedinthePDCs,lossesdur- ingthereconstruction ofprotontrajectoriesinthemagnetic ﬁeld ofALADIN, andlosses dueto the spatial resolution inthe PDCs.

ThelossesduetoPDCresolutionareincreasing withthedecreas- ing internal energy in the three-body system. However even at theenergyofthe¹⁷Ne(5/2⁻) resonancethechangeinthedetec- tion eﬃciencywas found to be smallerthan its uncertainty. The magneticspectrometer provided largedifference inprotontrajec- tories.Quadruplecoincidences, including

γ

-raydetectors,showed thatcontributionsfromexcitedstatesin¹⁵Oarenegligible.

The momentumvectorsofthe protonsandthe ¹⁵Ofragments wereobtainedintherestframeofthebeam.AsinRef.[22]andits Eq.(1),JacobicoordinatesintheY-systemwereusedintheanaly- sis.Theinternalkineticenergy,E_{f pp},inthethree-body¹⁵O+^p+^p system, aswell asthe fractional energies

f p=Êf p/E_{f pp} in the fragment-proton subsystem and the angle θf p between the two vectorspf p andpp−^{f p},was determinedforeach event.The analysis was done in two consecutive loops through each event, by selectingonedetectedprotonasthefirstoneinthefirstloopand thenchanging totheoppositeorderinthesecond loop.The data were corrected for acceptance. The overall acceptance, including momentumcutsduetothefinitesizeofdetectorsanddeadwires intheprotondriftchambers,wascalculatedinaMonte-Carlosim- ulation under the assumption of isotopic three-body decay. The acceptance function on Ef pp isshown in Fig. 3of Ref. [22].The experimental energyresolutionwas found to becloseto a Gaus- sianshapewithadispersion

σ

=¹.83E⁰_{f pp}^.⁵⁶⁸ MeV.

The correlation functions, for the fractional-energy distribu- tions W(

f p)aswellasfortheangulardistributions W(θf p),normalised to unity (1

0 W(

)d

₌1 and 1

−¹W(θ )dcosθ=¹⁾ ^were thenconstructedandanalysed.

The experimental excitation energy spectra, E^∗ = ^Ef pp + S_2p(¹⁷Ne), shown in Fig. 1,are well described asresulting from the contribution of several excited states in ¹⁷Ne, superimposed onasmoothbackground,shownasdashedlines.Thisbackground corresponds to non-resonant dissociation and may also contain contributionsfromunresolvedresonances.Based onexperimental results[25],thewidthsoftheresonancestructureswereassumed as determined entirely by the experimental resolution. A least- squaresﬁt was performedusingthe functional minimisationand erroranalysis codeMINUIT [24]. The smooth background,shown asdashedlinesinFig. 1,correspondstonon-resonantdissociation and may also contain contributions from unresolved resonances.

Extrapolation of thissmooth backgroundinto theregion ofreso- nanceswas donebyusinginformationfromtheW(

f p)distributions(seeFig. 5).

Five resonance-like structures corresponding to excitations of narrowresonantstatesin¹⁷Neareobservedinthedatafromthe CH2 andCtargets,whileonlythreeareidentifiedinthedatafrom thePbtarget (seeFig. 1andTable 1). Thelevelstructureof¹⁷Ne hasbeenstudiedearlierusingthe three-neutrontransfer reaction 20Ne(³He,⁶He)[25].Theseresultswereusedasafirstguidancein ourinterpretation together withtheavailable experimental infor- mationaboutthestructureofexcitedstatesinthemirrornucleus 17N[26].Atomicmassesandenergylevelsofthe A=^17,^T=³/2 isobaric multiplets taken from Refs. [27,28] were also used together withthe isobaricmultipletmassequation (IMME)andthe Thomas–Ehrmanshifts(TESs) fortheclassificationofthestates.

(1) The ﬁrstpeak inthe spectrumisdueto an unresolved doublet consisting of two narrow states at 1.764(12) MeV (Iπ= 5/2⁻) and at 1.908(15) MeV (1/2⁺) [25]. The relative contribu-

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Fig. 1. Excitationspectraof¹⁷Neafterbreakupof¹⁷Ne500MeV/u beamto¹⁵O+ p+^{p in}polyethylene,carbonandleadtargets.Thenumbersinparentheses referto theresonancespresentedinTable 1.

tions of these two states were obtainedfrom an analysisof the three-body correlationsin theenergyregion 0<E_{f pp}<1.4 MeV (seebelow).

(2) The second peak at E^∗=².652 MeV (see Table 1) is close in energy to the observed excited state at 2.651(12) MeV [25]. This state was interpreted to be an Iπ =⁵/2⁺ state. How- ever,a5/2⁺state isunlikelytobefedinaPbtarget byCoulomb excitation due to the small strength of the required E3 or M2 transitions. Hence, the possibility that the observed peak is due to an unresolved doublet cannot be excluded. Overlapping states withthespin-parity,5/2⁺₁ and5/2⁻₂,wereproposed(seeRef.[25]

andreferences therein).However, in thiscasean unusuallylarge

Table 2

Isobaric multiplet mass equation coeﬃcients and Thomas–Ehrman shifts (keV), (TES),forA=17,T=3/2 states.Seeexplanationsinthetext.

I^π a b c χ² TES

3/2⁻₁ 13025(1.2) −²⁸⁴⁴.8(1.3) 219.8(3.6) 0.39 −⁴⁷⁽¹⁴⁾ 5/2⁻₁ 1349(2.5) −²⁸²⁵.0(3.5) 210.10(4.9) 0.61 20(16) 1/2⁺ 13523(3.8) −²⁸⁹⁶.4(4.7) 240.28(5.5) 0.00 −^190(19) Assuming 5/2⁺₁ and 3/2⁻₂ both at E^∗=².651 MeV.

5/2⁺₁ 14219(2.9) −²⁹¹⁰.5(3.8) 247.9(4.9) 2.4 3/2⁻₂ 14729(3.2) −2699.4(4.5) 169.4(5.0) 2.4 Fit to only¹⁷F,¹⁷O and¹⁷N isobars.

5/2⁺₁ 14220(3.0) −2906.2(4.7) 237.8(8.1) – −220(23) 3/2⁻₂ 14730(3.2) −2706.2(6.3) 179.5(8.4) – 380(16)

negative cubic-term coefficient is required (d= −²⁵ ^keV) ⁱⁿ ^the isobaricmultiplet massequation(IMME)forthe5/2⁻₂ iso-quartet and furthermore the Thomas–Ehrmanshift for the 5/2⁻₂ state is surprisinglylargeinthiscase(≈^{1 MeV).}¹Ânalternativehypothe- sisisanunresolveddoubletof5/2⁺₁ and3/2⁻₂ states.Theparabolic IMME wasused intheanalysis(see Table 2). The positionofthe T=³/2, Iπ =³/2⁻₂ state in¹⁷Ois not known,but the assump- tionofadoubletrequiresthatthepositionsofthe5/2⁺₁ and3/2⁻₂ statesin¹⁷Nearecloseinenergy,whichonlyleavesonepossibil- ityforthisstate –anarrowstate at14.230(2)MeV. Thefitusing only three states from ¹⁷N, ¹⁷O and ¹⁷F allows then to make a predictionforthepositionsofstates:5/2⁺₁ at2.614(20)MeVand 3/2⁻₂ at 2.692(21) MeV, respectively. The resulting TES(3/2⁻₂)= 380(16)keV,is muchlarger than TES(3/2⁻₁)= −⁴⁷(14)keV. The structureoftheanalogstatesinthemirrornucleus¹⁷Nhasshown that the 3/2⁻₁ and3/2⁻₂ states have wave functions [26] with a 14%configurationwithonevalenceprotoninthes-shellfor3/2⁻₁ and86%for3/2⁻₂ [26].Asimilarstructureisexpectedfortheana- logstatesin¹⁷Ne.ThusasmallvalueforTES(3/2⁻₁)andalargefor TES(3/2⁻₂) can beexplained asa largeasymmetry inthe weights of theconfiguration withone valencenucleon inthe s-shell and thelargespatialextensionofthes-waveprotonwavefunction.²

(3) The excitation energy of the third peak, at E^∗ = 3.415(38) MeV, is close to the observed position of the 9/2⁻ state at E^∗=³.548(20)MeV [25], butthe energydifference and the factthat thereis nosignofa 7/2⁻ state,which should have similar structureasthe9/2⁻ state[26],excludessuchan assign-

1 TheThomas–Ehrmanshift,TES(I^π),wasdeﬁnedasthedifferencebetweenthe distancesfrom7/2⁻toI^πstatesinthemirrornuclei¹⁷Neand¹⁷N.The7/2⁻states werechosenasreferencesincetheCoulomb-energyshiftsforthesestates,having three-bodystructurewithtwovalencenucleonsinthed-shell,areexpectedtobe small.

2 NotealsoalargenegativeTESforpositive-paritystates.Thesestatescannotbe incorporatedinthethree-bodymodelsgenerallyusedforthedescriptionof¹⁷Ne structureandreactionsinvolvingthisnucleus.Anexplanationoftheexperimental parity-dependenceoftheCoulomb-energyshiftsoftheA=17 iso-quartetwassug- gested,e.g.,inRef.[13],usingamodelwithﬁvevalencenucleonsaroundthe¹²C core.

Table 1

Excitationenergies(MeV)andcrosssections(mb)with statisticalerrorbarsforobservedresonancestructuresin¹⁷Neexcitationspectra.ThenumberNreferstothe structuresshowninFig. 1.

N CH2 Carbon Lead

E^∗ σ E^∗ σ E^∗ σ

(1) 1.790(5) 4.89(15) 1.780(8) 3.25(15) 1.813(15) 14.08(93)

(2) 2.652(10) 2.39(14) 2.571(37) 1.17(10) 2.603(45) 7.68(74)

(3) 3.422(44) 1.38(12) 3.393(78) 0.646(87) – –

(4) 5.79(12) 1.13(22) 5.40(20) 0.47(19) 5.210(79) 14.4(1.7)

(5) 10.06(16) 2.10(35) 10.69(59) 0.91(46) – –

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Fig. 2. Narrowresonancestatesinthelow-energyregion,0<E^∗<4MeV excited inthe CH2 target.Thethinsolid linesshow negative-paritystates,dashed lines stemforpositive-paritystatesandthedash-dottedlineisphysicalbackground.For energyregionsI,IIandIIIthefractionalenergyspectraareanalysedasshownin Figs. 3,4 and5,respectively.

Table 3

Excitationenergiesandcrosssections(mb)withstatisticalerrorsforresolvedreso- nancesin¹⁷Ne.

I^π E^∗ CH2 C H Pb

5/2⁻ (i) 1.764(12) 4.04(20) 2.44(18) 0.80(14) 11.6(1.5) 1/2⁺ (i) 1.908(15) 0.85(15) 0.81(15) <0.1 2.5(1.2) 5/2⁺ 2.614(20) 0.97(51) 1.14(10) <0.2 7.68(74) (3/2⁻₂) 2.692(21) 1.40(53) <0.3 0.70(26)

(5/2⁻₂) 3.415(38) 1.37(12) 0.62(10) 0.38(8) – (3/2⁺) 5.210(79) 1.13(22) 0.46(19) 0.33(15) 14.4(1.7) (i)EnergiesanderrorsarefromRef.[25].

ment.The¹⁷Nelevelschemeisratherintricate, whichmakesthe analysis knotty. The three-neutron transfer reaction has a selec- tivity to excitation of states with a deﬁnite structure and some states may therefore be missed. A comparison with the level schemeof mirror nucleus, ¹⁷N,suggests that this state could be the second 5/2⁻ state. The analysis given in Ref. [26] for the 5/2⁻₂ state in¹⁷N,gave aweight of72% foraconﬁgurationwith a single proton in the s-shell, a structure similar to that of the 3/2⁻₂ state. The present value TES(5/2⁻₂)=³⁵⁹(40) keV is close to TES(3/2⁻₂)=³⁸⁰(16) keV and is thus in support ofthe 5/2⁻₂ assignmentforthe E^∗=³.415(38)MeV statein¹⁷Ne.

(4)–(5) Two additional resonances at 5.210(79) MeV and 10.06(16)MeVwereobservedinthepresentexperiment,thelatter onlyforthelighttargets.Acomparisonwiththelevelsinthemir- rornucleus¹⁷Nandthefactthat theresonanceat5.210(79)MeV isstronglyexcitedwiththeleadtarget,pointstoanassignmentof Iπ=³/2⁺.

The analysisof the narrow resonant statesin the low energy region,basedonthediscussionabove,isshowninFig. 2andthe results are given in Table 3. Cross sections for excitation of energy levels in the ¹H(¹⁷Ne(g.s.),¹⁷Ne(Iπ )) reaction were obtained fromthe relation:

σ

(CH2)=

σ

(C)+²

σ

(H).Thedatademonstrate differentselectivity forthe differenttargets. Thus, forthe hydro- gentarget,positive-parity stateshavelowerexcitation probability comparedtothosewithnegative-parity.Thepartialdecayscheme withdominatingdecaybranchesisshowninFig. 6.

Inorder to extract more information fromthe data, the low- energypartoftheE_{f pp} spectrumwas dividedintothreeseparate regions, asshow in Fig. 2, where thefractional energyspectrum W(

f p)andtheangulardistributionW(θf p)wereconstructedand analysed.Asequentialdecayviaanintermediatenarrowresonance in¹⁶Fat

r=^Er/E_{f pp} appearsinthe W(E_{f p})distributionastwo peaksat

r and1−

r.A²Hedecay,ordiprotonemission,would

Fig. 3. FractionalenergyspectraW(f p)intheY-systemfortheregionof¹⁵O+ p+p internalenergy0≤Ef pp≤1.4 MeV fromtheCH2target(a)andPbtarget(b).

Thedistributionsstem fromtheunresolvedresonances¹⁷Ne(5/2⁻)and¹⁷Ne(1/2⁺) decayingtothe¹⁶Fgroundstate.A ﬁtwithonlyonefreeparametergivestheir relativecontributions.

Fig. 4. FractionalenergyspectraW(f p)intheY-systemfortheregionof¹⁵O+ p+^{p internal}^energy¹.4≤^Ef pp≤².2 MeV fromtheCH2 target(a)andPbtar- get (b).Thinsolidand thickdashed linesshowdecays throughtheintermediate 16F(2⁻)and¹⁶F(3⁻)states,respectively.Thesestateshavethestructureof¹⁵Owith oneprotoninthed-shell.Thedashedlinesrepresentdecaystothe¹⁶F(0⁻)state withthestructure¹⁵Owithoneprotoninthes-shell.

Fig. 5. FractionalenergyspectraintheY-systemW(f p)fortheregionof¹⁵O+ p+^{p internal}^energy².2≤^Ef pp≤³.0 MeV fromtheCH2 target(a)andPbtar- get (b).Thethinsolidlinesshowdecaysto¹⁶F(2⁻and3⁻)statesandthedashed linesrepresentdecaysto¹⁶F(0⁻and1⁻)states.

be characterised by an asymmetric angular W(θf p) distribution, increasing when θf p gets close to 180^◦. In the present analysis W(θf p) was found tobe closeto isotropic, within statisticalun- certainties,whichexcludesasigniﬁcant ²Heemission.Theshapes of the W(

_{f p}) distributions are well described by assuming sequential decays through the ﬁrst four excited states in ¹⁶F. The parameters forthesestatesweretakenfromRef.[23].The partial W(

f p)shapesarestronglyinﬂuencedbytheexperimentalresolu- tionandwerecalculatedinMonte-Carlosimulations. TheMINUIT

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Fig. 6. Narrowresonancestatesabovethetwo-protonseparationenergyin¹⁷Ne.

Thedominantdecaybranchesoftheresonantstatesto¹⁵O+2p,viaintermediate resonantstatesin¹⁶F,areshown.Positive-paritystatesarecolouredinredonline.

ResonancesshownasdashedlinesarefromRef.[25]andarenotpopulatedinthe presentexperiment.

code was used forthe least-square ﬁts to the measured W(

f p) spectra.

The fractional energy spectra for the lowest energy bin, 0≤ E_{f pp}≤¹.4 MeV,areshowninFig. 3.Thepanels(a) and(b) show least-square ﬁts tothe W(

f p) distributions assuming sequential decay from states at excitation energies 1.764 MeV (5/2⁻) and 1.908MeV(1/2⁺)[25]throughtheintermediate¹⁶F(0⁻)state.The distributions W(

_{f p}) are normalised to unity and in the ﬁt the relative intensitywas theonly free parameter used. Forthe CH2 targettheﬁtgivesa17.5(3.2)% contributionfromthe1/2⁺ decay, forC25.0(4.3)%(notshown),andforPb17.6(8.7)%,withstatistical errors.

A doublet with 5/2⁺ and 3/2⁻₂ states was identiﬁed in the energyregion1.4≤^Ef pp≤².2 MeV (regionIIinFig. 2).Thediffer- enceinexcitationenergyofthesetwostatesismuchsmallerthan theexperimentalresolutionandthedifferenceinshapeofW(

f p) forthedecaybranchesismarginal.The penetrabilitythroughthe Coulomb andcentrifugal barriersfor thedecay of5/2⁺ to 3⁻ is about20 times smaller than that forthe decay to the 2⁻ state.

Further,thisratioisaround1000forthedecayof3/2⁻₂ state.The maindecaybranchesforbothstatesarethereforeexpectedtopro- ceedviathe¹⁶F(2⁻) state.Theanalysisof W(

_{f p})froma carbon target gave a decay branch of 86(2)% while the rest can be at- tributedtothefeedingofthe¹⁶F(3⁻)state.TheW(

f p)fromCH2 andPbtargetswereﬁttedwithanassumptionthatthe¹⁷Ne(5/2⁺) and¹⁷Ne(3/2⁻₂) statesdecay predominantlythrough ¹⁶F(2⁻) and 16F(0⁻)states.Contributionsfromthe¹⁶F(2⁻)branchwere74(2)%

for CH2 and 41(4)% for Pb targets, see Fig. 4. The rest can be attributedtofeedingmainlyofthe¹⁶F(0⁻)statewithasmallcon- tributionfromthe¹⁶F(3⁻)branch.InthecaseofthePbtarget,the mainpartofthe¹⁶F(0⁻)branchiscomingfromacontinuous E_{f pp} spectrum.

Intheenergyregion2.2≤Êf pp≤³.0 MeV acontributionfrom the ¹⁷Ne(5/2⁻₂) state is expected. The decay branches from this resonance should proceed mainly by emission of =^{0 protons,} feeding dominantly 2⁻ and 3⁻ states in ¹⁶F. The population of 0⁻ and 1⁻ states in the resonance decay requires emission of =^{2 protons} ând îs êxpected ^to ^be ^small ^due ^to penetrability

factors.Stillthereare sizeablecontributionsinthe W(

f p)distri- butionfromfeedingtothesestates,especiallypronouncedforthe Pbtarget,asshowninFig. 5.Thesepartsofthedistributionswere treatedasaphysicalbackground.

Theratiobetweenthefeedings

σ

(2⁻)/

σ

(3⁻)≈^{1 was}^obtained forboththeCH2 andtheC target.ForthePbtarget, keepingthis ratio ﬁxed, the W(

f p) cannot be reproduced,which showsthat these events cannot be considered ashaving their origin in the decay of the 5/2⁻₂ state. Theywere thereforealso considered as coming from a continuous E_{f pp} spectrum. The distribution was well ﬁttedwithonlythreedecaybranchedtothe 0⁻,1⁻ and2⁻ statesin¹⁶F.

ThecrosssectionsforCoulombexcitationofresonantstates,

σ

C, were obtained by subtracting the nuclear contribution from the crosssectionsmeasured withtheleadtarget scaled witha factor 1.84(20).Thescalingfactorwasdeterminedexperimentally.Itwas assumedthatCoulombdissociationto¹⁴Ohasaverysmall,ifnot zero, cross section andthe scaling factor was determined as the ratioof (¹⁷Ne,¹⁴O) crosssectionsobtainedwithPbandCtargets.

Thescalingfactorisclosetotheratiobetweennuclearradiiofpro- jectileandtarget, (A¹_Ne^/³+Â¹_Pb^/³)/(A¹_Ne^/³+Â¹_C^/³),reflectingthat the nucleardisintegrationisofsurfacecharacter.Inthisanalysisitwas assumedthatthe5/2⁺stateisnotCoulombexcited.Excitationof thisstatewithalargecrosssectionbyaM2orE3transitionorin amulti-stepprocessisunlikely.CrosssectionsforCoulombexcita- tion oftheidentifiednarrowresonances aregiveninTable 1.For the state at E^∗=⁵.210(79) MeV anda leadtarget the excitation stemsdominantlyfromCoulombinteraction.

The transition probabilities B(

π

λ) from the groundto an excited state in the projectile, where

π

=^{E or} ^{M stands} ^for ^an electric or magnetic transition with multipolarity λ, were calcu- latedbythevirtual-photonmethodforintermediateenergies [29, 30]. The cross section for Coulomb excitation of a narrow reso- nanceat E^∗ is

σ

_C^π^λ

(

E^∗

) = (

2

π )

³

(λ +

¹

) λ[(

2

λ +

1

)!!]

²

_E∗

¯

hc

2λ−¹N

( π λ)

E^∗ B

( π λ),

(1) where N(

π

λ) is the numberof virtual photons atexcitation en- ergy E^∗.Thisexpressionisusedtocalculatethetransitionproba- bilitybasedonthemeasuredcrosssection

σ

_C^π^λ(E^∗)(infm²).

The formalism described in Refs. [29,30] is used to calculate N(

π

λ).InRef. [30]theeffectofstrongabsorptionisincorporated fromthe outset(see Eqs. (13)–(15)),while aminimal impactpa- rameter Bcut has to be used when the analytical semi-classical method fromRef.[29] (Eqs. (2.5.5)) isapplied. Calculationsusing the semi-classical methodwith Bcut=¹⁰.8 fm givethe samere- sultasEqs. (13)–(15) inRef.[30].TheresultingN(

π

λ)andB(

π

λ) valuesaregiveninTable 4.

The Coulomb excitation of the ﬁrst two excited states in 17Ne was studied earlier [31] and the transition probability B(E2,1/2⁻→⁵/2⁻)=²⁴ ^e² ^fm⁴ ^was ^deduced. ^However, ⁱⁿ ^the B(E2) calculations the authors included an extra factor e² in Eq.(1),whichmeans thattheobtained B(E2) valuesare inunits offm⁴ andshouldthus bemultipliedwitha factor1.44.Thecor- rected value for B(E2,1/2⁻→5/2⁻) isgiven in thelast rowin Table 4.

The B(E2) values from Ref. [31] without this correction factor were, however,used inRefs. [21,32] asa conﬁrmation ofthe proposed ¹⁷Newave function.The correctedvalue B(E2,1/2⁻→ 5/2⁻)isabouttwicelargerthan thatobtainedinthepresentex- periment.Thismightbeconnectedwiththeassumption,madein Ref.[31],thatthedetectedeventswerefrompureCoulombexcita- tion.Inthepresentexperimentitisshownthatnuclearexcitation contributestothecrosssectionwithabout50%,seeTables 3 and 4.

(6)

Table 4

Coulombexcitationcrosssections,σC,inmb,fornarrowresonantstatesin¹⁷Ne, virtual-photonnumbersandtransitionprobabilitiesB(πλ)in(e²fm²^λ).Thelowest rowgivesB(E2)for 5/2⁻ resonancecalculatedwithEq.(1)usingσC andN(E2) fromTableIinRef.[31].

I^π E^∗ σC πλ N(πλ) B(πλ)

5/2⁻ 1.764 7.13(1.5) E2 11868 90(18)

1/2⁺ 1.908 <2.4 E1 121.43 <0.007

(3/2⁻₂) 2.692 5.57(76) E2 5180.4 69(10) (3/2⁺) 5.141 13.6(1.7) E1 68.68 0.071(9)

5/2⁻ 1.764 29.9(4.4) E2 24990 179(26)

Fig. 7. TransitionprobabilitiesB(E2,1/2⁻→⁵/2⁻)asafunctionofthes-shelloc- cupation,P(s²),in¹⁷Ne(g.s.).ThesolidlinegivesexperimentalB(E2)valueandthe hatchedzoneshowsthe1σ deviationfromthisvalue.Thedashedlinerepresents calculationsfromRef.[21].

A comparison between the B(E2,1/2⁻→⁵/2⁻) values deduced from the present experiment and theoretical calculations from[21]isshowninFig. 7.Themostprobablevalueforthes²oc- cupancywouldbeeitherP(s²)=^{23% or}^P(s²)=^53%.^The^hatched zonesinFig. 7showthe1

σ

deviationsfromthesevalues.

Inconclusion, new experimental data on dissociation of ¹⁷Ne into ¹⁵O+^{2p studied} ^at ^GSI ^with ^a relativistic ¹⁷Ne beam im- pinging on lead, carbon, and polyethylene targets are presented.

Themain attentionis paidtothe excitationanddecayofnarrow resonantstates in¹⁷Ne, for whichcross sectionswere measured.

Three-bodycorrelationswere usedtodetermine therelativecon- tributions tounresolvedresonances. Thedata obtainedfromlead and carbon targets allowed the determination of cross sections and transition probabilities for Coulomb excitation. The reduced electric quadrupole transition probability B(E2,1/2⁻→⁵/2⁻)= 90(18) e²fm⁴ was derived by using the virtual-photon method.

ThemeasuredB(E2)valuewascomparedtothemodelcalculations.

Finally,theobservationofaresonanceatE^∗=⁵.210(79)MeV ten-

tatively interpreted as 3/2⁺ state, mainly Coulomb excited, is of special interestandshould be a subjectof furtherinvestigations.

The excitation of positive parity states implies that three-body models without inclusion of the core intrinsic structure are not able to fullydescribe the reaction mechanism. Theoretical meth- odsareurgentlyneededtodescribeexcitationspectraandreaction mechanisms,includingtechniquesbeyondthree-bodymodels.

Acknowledgements

Thisproject issupported by NAVI,GSI-TUDarmstadt coopera- tion, HICforFAIR, EMMI andBMBF.C.A.B. acknowledges support fromtheU.S.NSFGrantNo. 1415655,andU.S.DOEgrantNo. DE- FG02-08ER41533. The work was also supported by the Spanish governmentgrantFPA2012-32443andtheSwedishResearchCoun- cil.

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Coulomb and nuclear excitations of narrow resonances in ^{17}Ne

Physics Letters B