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Enhanced radiativestrength inthe quasi-continuum of117Sn U.Agvaanluvsan1,2,A.C.Larsen3 ,R.Chankova4,5,M.Guttormsen3,G.E.Mitchell4,5,A.Schiller6,S.Siem3,andA.Voinov6 ∗ 1Stanford University, Palo Alto, California 94305 USA 2MonAme Scientific Research Center, Ulaanbaatar, Mongolia 3Department of Physics, University of Oslo, N-0316 Oslo, Norway 4Department of Physics, North Carolina State University, Raleigh, NC 27695, USA 5Triangle Universities Nuclear Laboratory, Durham, NC 27708, USA and 9 6Department of Physics, Ohio University, Athens, OH 45701, USA 0 (Dated:January19,2009) 0 2 The radiative strength function of 117Snhas been measured up tothe neutron separation energy using the n (3He,3He′g) reaction. An increase in the slope of the strength function around Eg =4.5 MeV indicates the a onset of a resonance-like structure, giving a significant enhancement of the radiative strength function com- J paredtostandardmodelsintheenergyregion4.5 Eg 8.0MeV.Forthefirsttime,thefunctional formof 9 this resonance-like structure has been measured in≤an od≤d tin nucleus below neutron threshold in the quasi- 1 continuumregion. ] PACSnumbers:25.20.Lj,24.30.Gd,25.55.Hp,27.60.+j x e - Averageelectromagneticpropertiesofatomicnucleicanbe pear above the GEDR tail. Such resonances can be of great l c described by the radiative strength function (RSF). An im- importanceforthenucleosynthesisinsupernovae[6]. u provedknowledgeof the RSF is importantfor many aspects n Recently, a resonance-like structure in the RSF was ob- [ of pure and applied nuclear physics, including calculations servedinthe129 133Snandthe133,134Sbisotopesusingrela- − 3 of nuclear reaction cross sections and nuclear reaction rates tivisticCoulombexcitationmeasurementsininversekinemat- v inextremestellarenvironments. Fortransitionswithelectro- ics[7,8].ThisE1-typepygmyresonancewaslocatedatg -ray 8 magneticcharacterX,multipolarityLandenergyEg,theRSF energies around 8 10 MeV, and was interpreted as excess 4 isdefinedby[1] − neutronsoscillating against the core nucleons. The summed 6 B(E1) strengthofthepygmyresonancewasfoundtobe3.2 .3 fXL(Eg)=hG XifL(Eg)ir (Ei,Jip )/Eg2L+1. (1) and1.9↑e2fm2for130,132Sn,respectively,whichcorrespondto 8 7%and 4%oftheclassicalThomas-Reiche-Kuhn(TRK) 080 Htweereen, htGhXiefLiiniistiathleanmdeafinnavlalsutaeteosf,thaendparrt(iEali,dJeipc)ayiswthidethlebvee-l se≈unmergriuelse.ab≈AosvethtehseenmeuetarsounresempeanratstiaorneerneestrrgiyctSedn,tiotiesxacnitaotpioenn : density for the initial excitation energy Ei and spin/parity question whether additional strength may be found at lower v p i Ji . Forthedominatingdipoleradiation,theRSFisgivenby energies. X f(Eg)= fE1(Eg)+fM1(Eg). In fact, E1 transitions clustered in the 6.0 8.5 MeV re- ar TheRSFrevealsessentialinformationonnuclearstructure. gionof116,124Snhavebeenfoundandstudiedb−ymeansofnu- Inparticular,electrictransitionsbetweenexcitedstatesinthe clearresonancefluorescence(NRF,photonscattering)experi- nucleusare mostly influencedby the proton charge distribu- ments[9].Thestrengthestimatedfromtheg -lineintensitiesin tion,whileformagnetictransitionstheneutronscontributeas theseexperimentswas0.204(25)e2fm2 and0.345(43)e2fm2 wellduetotheirmagneticmoments. Alsotheshapeandsoft- for 116,124Sn, respectively, corresponding to 0.4% and ness of the nuclear surface are important factors for the nu- 0.6% of the TRK sum rule. Preliminary resu≈lts on 112,124S≈n clearresponsetoelectromagneticradiation. from the HIg S facility at TUNL [10] are consistent with the The most dominant feature of the RSF is the giant elec- resultsof[9]. Inaddition,variousrandom-phaseapproxima- tricdipoleresonance(GEDR),whichiscenteredaroundEg = tion calculationspredictE1 strengthin thismass and energy 15MeV.Inamacroscopicpicture,theGEDRisduetothenu- region[11,12]. Thecalculationsindicatethatastrongerfrag- clearcharge,theprotons,oscillatingagainsttheneutroncloud. mentation of the dipole strength is expected in exotic nuclei Other resonancessuch as the magnetic dipole spin-flip reso- with a large mass-to-chargeratio comparedto stable tin iso- nance and the electric quadrupole resonance have also been topes,andthishassofarbeensupportedby[7,8,9,10].New discovered,butareingeneralsignificantlysmallerinmagni- 117Sn(g ,n) cross-section data [13] together with 116Sn(n,g ) tudethanthe GEDRandhaveless influenceonthe RSF [2]. cross-sectionmeasurementsandcalculations[14]givefurther However,therearecollectivemodessuchastheso-calledM1 supporttothepresenceofapygmyresonanceaboveneutron scissorsmode[3,4]andtheE1skinoscillationmode[5]that thresholdalsoin117Sn. aresmallcomparedtotheGEDR,butstilllargeenoughtoap- For tin isotopes, one might also expect the appearance of enhanced M1 strength since the proton Fermi surface is lo- catedrightinbetweentheg andg orbitals,whileforthe 7/2 9/2 ∗Electronicaddress:[email protected] neutrons the h11/2 and h9/2 orbitals come into play. Thus, 2 the g g (protons) and h h (neutrons) 7/2 ↔ 9/2 11/2 ↔ 9/2 magnetic spin-flip transitions may show up as concentrated strengthintheRSF.Inprotoninelasticscatteringexperiments 106 on120,124SnwithEp=200MeVatveryforwardangles[15], Oslo data 117Sn an M1 resonance centered at an excitation energy E 8.5 Known levels MeVisobserved.Recent(g ,n)experimentson91,92,94Z≈r[16] 105 r from neutron res. data 1) have revealed an enhancedM1 resonanceat 9 MeV in these -V e nteumclaetii,csw.ith about75%morestrengththanpredictedby sys- E) (M104 InthisLetter,wepresentcomplementarymeasurementsto ( the above-mentioned experiments for the tin isotope 117Sn. rsity 103 The Oslo method permits the simultaneousdeterminationof n e theleveldensityandtheradiativestrengthfunction[17]. For el d102 bothofthesequantitiestheexperimentalresultscoveranen- v e ergyregionwherethereislittleinformationavailableanddata L are difficult to obtain. The Oslo method, which is sensitive 10 to radiative strength for Eg < Sn, reveals the total intensity andthefunctionalformofthe∼RSFforg -raytransitionsinthe quasi-continuum. 0 1 2 3 4 5 6 7 Excitation energy E (MeV) TheexperimentwascarriedoutattheOsloCyclotronLab- oratory using a 38-MeV 3He beam with an average beam currentof 1.5 nA impingingon a 117Sn targetwith thick- FIG.1:Normalizedleveldensityof117Sn. ness of 1.9≈mg/cm2. Particle-g coincidence events were de- tected using the CACTUS multidetector array. The reaction channel117Sn(3He,3Heg )117Snwasselectedusingeightparti- Thea parameterisdeterminedfromtheslopeofthelevel ′ cletelescopesplacedat45 withrespecttothebeamdirection. density based on known low-lying discrete levels [19] and ◦ EachtelescopeconsistsofaSiD EandaSi(Li)Edetectorwith fromtheneutronresonancespacingD atSn (see[17]forde- thicknesses140 m mand3000m m, respectively. Anarrayof tails). We used the s- and p-wave resonance level spacings 28collimated5 5inchesNaIg -raydetectorswithatotalef- D0=(507 60)eVandD1=(155 6)eVtakenfrom[20] ficiencyof 15×%atEg =1.33MeVwasused. Inaddition, to calculate±the totalleveldensityat±Sn=6.94MeV. Adopt- oneGedete≈ctorwasappliedinordertoestimatethespindis- ing the spin cut-off parameter s =4.44 [21] and taking the tribution and determine the selectivity of the reaction. The averageof theresultsobtainedwith D0 andD1, we obtained typicalspinrangeisJ 2 6h¯. r (Sn) = (8.55 1.24) 104 MeV−1. The normalized level The energy of the ∼eject−ile is transformed into excitation densityisshow±ninFig.·1. energy using reaction kinematics. The particle–g -ray coin- The scaling parameter B is determined using information cidence spectra were unfolded with the NaI response func- ontheaveragetotalradiativewidth G g atSn asdescribedin tion usingthe Comptonsubtractionmethod[17]. A subtrac- Ref. [22]. We normalize to G g =h(53i 3) meV measured h i ± tionprocedureisadoptedtoextractthefirst-generationmatrix fors-wave neutronresonances[20]. The normalizedRSF of P(E,Eg) containingtheprimaryg -raysemittedfroma given 117SnisdisplayedintheupperpanelofFig.2. excitationenergyE [17].Thematrixisexpressedastheprod- InordertotesttheassumptionthattheRSFof117Snisnot uctofleveldensity(r )andRSF(f): dependentonexcitationenergy,wehavededucedtheRSFfor twoindependentdatasetsoftheexperimentalPmatrix.Inthe P(E,Eg)(cid:181) r (E Eg)f(Eg)Eg3. (2) lower panelof Fig. 2 the resulting RSFs extracted for initial − excitation energies in the intervals 3.4 E 5.8 MeV and ≤ ≤ Thisfactorizationisjustifiedfornuclearreactionsleadingtoa 5.9 E 8.3MeVareshown. TheRSFsobtainedfromthe ≤ ≤ compound state prior to the subsequent g decay. The RSF twointervalsareverysimilar,whichindicatesthattheBrink- is only dependent on the g energy according to the gener- Axelhypothesisisindeedfulfilledintheexcitation-energyre- alized form of the Brink-Axel hypothesis [18], which states gionunderconsiderationinthiswork. thattheGEDRandanyothercollectiveexcitationmodebuilt WeobservethattheRSFexhibitsanabruptchangeinslope on excited states have the same properties as those built on atEg 4.5MeV.Sincetherearestrongindicationsofapygmy the ground state. The functions r and f are obtained itera- reson≈ance that could be due to skin oscillations in the even- tively by a globalized fitting procedure [17]. In this Letter, even stable Sn isotopes, a similar phenomenon should be weshallonlyfocusontheRSF.Therearetwonormalization presentin an odd-A Sn nucleuswith neutron excess as well. parametersto be determined,namely the scaling (B)and the Toinvestigatethisfurther,wehavecomparedourdatatosome slope correction (a ) of the RSF according to the expression oftheavailablemodelpredictionsoftheRSF.Wehavechosen Bexp(a Eg)f(Eg )[17]. two approaches: onewherethe strongestcomponent,the E1 3 formof a standardLorentzianwith parameterizationaccord- ing to [2]. As can be seen from Fig. 3, the data from the 3) presentwork show an enhancedradiative strength compared -eV 117Sn tothemodelintheregionEg =4.5 8.3MeV.Inordertode- M − ( scribethisenhancement,wehaveempiricallyaddedapygmy on 10-7 resonancewithaGaussianform: ti c un 1 (Eg Epyg)2 th f fpyg=Cpyg·√2ps pygexp"− 2s−p2yg #. (3) g n tre 10-8 Here, Cpyg is a normalization constant, s pyg is the standard s y deviation, and Epyg is the mean value (centroid)of the reso- g-ra nMaenVce−.2W, sitphygth=eG1.L5OMEe1V,starnedngEthpywg=ef8o.u7ndMCepVy.gT=he4.r0es·u1l0t−i8s shown in the upperpanel of Fig. 3, together with (g ,x) pho- -3)V 117Sn, E = 3.4-5.8 MeV tonucleardatafromRefs.[25,26,27]. Itcanbeseenthatthe e 117Sn, E = 5.9-8.3 MeV modeldescriptionofthedataworksratherwell,andthatitis M n ( 10-7 indeednecessarytoincludeextrastrengtharoundSn inorder o togetareasonablefit. ItisalsoseenthattheSLOmodelfits ncti the(g ,x)dataverywell;however,itisnotabletodescribenei- u h f thertheshapenorthemagnitudeofourdatabelowtheneutron gt threshold. n e 10-8 InthesecondapproachwehaveappliedresultsfromQRPA r st calculationsonthe E1strength[24]. Itcan beseenfromthe ay lowerpanelofFig.3thattheQRPAcalculationtendstoover- -r estimate the E1 strengthforg -rayenergiesbelowthe GEDR g peakcomparedtoexperimental(g ,x)data.Itisthereforeprob- 0 1 2 3 4 5 6 7 8 9 g -ray energy E (MeV) ablynotacorrectreferencefortheexpectedE1strength;nev- g ertheless,itgivesalowerlimitonthepygmystrength.Again, FIG. 2: Upper panel: Total radiative strength function of 117Sn. we have added the M1 and the E1 strength together with a Lower panel: radiativestrength function of 117Snmeasured at two Gaussian parameterization of the extra strength around neu- differentexcitation-energyregions. tronthreshold.AsshowninFig.3,thetotalmodeldescription ofourdataisnotsogoodasintheGLOcase,especiallyforthe low-energypart. Using the QRPA E1 strength, we obtained contributionfromtheGEDR,isassumedtofollowageneral- C =1.8 10 8 MeV 2, s =1.3 MeV, and E =8.0 pyg − − pyg pyg · izedLorentzian(GLO)[2,23],andonewheretheE1strength MeVforthepygmyresonance. is taken from microscopic calculations based on the quasi- It is clear from our analysis that extra strength is present particlerandomphaseapproximation(QRPA)[24]. Thestan- below and above the neutron threshold in 117Sn. Our data dard Lorentzian (SLO) model[2], which has been very suc- show the functional form of the pygmy resonance below 8 cessful in describing photonuclear cross-section data in the MeVfromlowtohighg -rayenergiesforthefirsttime. Inad- vicinity of the GEDR peak, has not been applied due to its dition, this resonancehas notbeen experimentallymeasured tendencytooverestimateaverageradiativewidthsandcapture in a stable, odd-A tin isotope before, and this has now been cross sections (see Ref. [2] and references therein). This is successfullydonein117Sn. seentobethecasealsofor117Sn[14],andwethereforedeem Measuring the enhancement of our data in the energy re- that this model is not adequate to describe the experimental gionEg =4.5 8.0MeVrelativetotheGLOmodelplusthe − RSFbelowneutronthreshold. LorentzianM1,weestimateanexcessstrengthof11 1(stat) ± For the GLO approach we used experimental Lorentzian 3(syst) MeVmb. Using the QRPA E1 strength plus the ± · parameterstakenfrom[2]. Inthemodelcalculations,wehave LorentzianM1asareferencefortheexpectedstrengthfunc- treatedthetemperatureofthefinalstatesT asafreeparame- tion in the same energy region, an excess strength of 8 f ± ter. Thebestresultwasobtainedusingaconstanttemperature 1(stat) 3(syst) MeVmb is estimated. For the total pygmy T =0.40MeV, forwhichwe foundareasonableagreement strength±summed ove·r all g -ray energies, we find 40 15 f ± with our data points in the region 1.5 Eg 4.5 MeV, and MeVmb for the GLO approach, and 17 8 MeVmb using (g ,x)data[25,26,27]aroundtheGED≤Rpea≤k(13 Eg 16 theQ·RPAcalculation. ± · ≤ ≤ MeV). Using a constant temperature is consistent with the If one assumes that all of the excess strength is E1, then Brink-Axel hypothesis and our results (see Fig. 2). For the this yields 0.6(2)%of the TRK sum rule for 4.5 Eg 8.0 ≤ ≤ giantmagnetic M1 spin-flip resonance, we have adoptedthe MeVusingtheGLOapproach. FortheQRPAcalculationwe 4 in117Snutilizingotherexperimentaltechniquessuchas,e.g., (n,2g )experiments. ) 3 -V In conclusion, the total RSF in the quasi-continuum for e M 10-6 S 117Sn up to Eg =8 MeV has been measured with the Oslo n ( n method.Asignificantenhancementinthestrengthisobserved ctio icnomthpeaetnibelregiynrsetgrieonngtEhga=nd4p.5o−sit8io.0nMwietVh.tThehipsyegnmhaynrceesmoneanntcies n GLO E1 + M1 fu 10-7 SLO E1 + M1 observedpreviouslyineven-evenSnnuclei.Forthefirsttime, th Pygmy thepygmyresonancehasbeenmeasuredinanodd,stableSn g n nucleus, and the functional form of this resonance has been re M1 determinedfromlowtohighg -rayenergies. st 10-8 y ThisresearchwassponsoredbytheNationalNuclearSecu- a rityAdministrationundertheStewardshipScienceAcademic r - Alliances program through DOE Research Grant No. DE- g 3) FG52-06NA26194.U.A.andG.E.M.alsoacknowledgesup- -V e port from U.S. Departmentof EnergyGrant No. DE-FG02- M 10-6 S 97-ER41042.FinancialsupportfromtheNorwegianResearch ( n n Council(NFR)isgratefullyacknowledged. o ti c n u 10-7 QRPA E1 + M1 f SLO E1 + M1 h t g Pygmy n [1] G.A.Bartholomew,E.D.Earle,A.J.Ferguson,J.W.Knowles, stre 10-8 M1 andM.A.Lone,Adv.Nucl.Phys.7,229(1973). y [2] T.Belgyaetal.,Handbookforcalculationsofnuclearreaction a data,RIPL-2.IAEA-TECDOC-1506(IAEA,Vienna,2006). r - [3] N.LoIudiceandF.Palumbo,Phys.Rev.Lett.41,1532(1978). g 0 2 4 6 8 10 12 14 16 [4] D.Bohle,A.Richter,W.Steffen,A.E.L.Dieperink,N.LoIu- g -ray energy E (MeV) dice,F.Palumbo,andO.Scholten,Phys.Lett.B137,27(1984). g [5] P. Van Isacker, M. A. Nagarajan, and D. D. Warner, Phys.Rev.C45,R13(1992). FIG.3: [Coloronline] Upperpanel: Radiativestrengthfunctionof 117Sn from the present work (black squares), and from (g,x) pho- [6] S.Goriely,Phys.Lett.B436,10(1998). [7] P.Adrichetal.,Phys.Rev.Lett.95,132501(2005). tonuclearreactions(redopentriangles[25],stars[26],andblueopen [8] A.Klimkiewiczetal.,Phys.Rev.C.76,051603(R)(2007). squares[27]).ThesumoftheGLOE1strengthandtheM1spin-flip [9] K.Govaert,F.Bauwens,J.Bryssinck,D.DeFrenne,E.Jacobs, resonance isshown as asolid line. The GLO E1strength, the M1 W.Mondelaers, L.GovorandV.Yu.Ponomarev, Phys.Rev.C spin-flipresonance(dashed-dottedline),andaGaussianparameteri- 57,2229(1998). zationofthepygmyresonance(dashedline)areaddedtogetabestfit [10] A.Tonchev,privatecommunication. (thick,bluesolidline)tothedata. ThesumoftheSLOE1strength [11] N.Paar,P.Ring,T.Niksˇic´,andD.Vretenar,Phys.Rev.C67, andtheM1strengthisshown forcomparison (dottedline). 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