First measurement of 30S+α resonant elastic scattering for the 30S(α,p) reaction rate D. Kahl,1,2,∗ H. Yamaguchi (山口 英斉),1 S. Kubono(久保野 茂),1,3,4 A. A. Chen,5 A. Parikh,6 D. N. Binh,1,† J. Chen(陈俊),5,‡ S. Cherubini,7,8 N. N. Duy,9,10 T. Hashimoto(橋本 尚志),1,§ S. Hayakawa (早川 勢也),1 N. Iwasa(岩佐 直仁),11 H. S. Jung(정효순),12 S. Kato(加藤 静吾),13 Y. K. Kwon(권영 관),12,§ S. Nishimura(西村 俊二),3 S. Ota (大田 晋輔),1 K. Setoodehnia,5,¶ T. Teranishi(寺西 高),14 H. Tokieda(時枝 紘史),1 T. Yamada(山田 拓),11,∗∗ C. C. Yun(윤종철),12,§ and L. Y. Zhang(张立勇)4,†† 1Center for Nuclear Study, the University of Tokyo, Wako, Saitama 351-0198, Japan 2School of Physics & Astronomy, the University of Edinburgh, Edinburgh EH9 3JZ, UK 3RIKEN Nishina Center, Wako, Saitama 351-0198, Japan 4Institute of Modern Physics, Chinese Academy of Sciences, Lanzhou 730000, China 5Department of Physics & Astronomy, McMaster University, Hamilton, Ontario L8S 4M1, Canada 7 6Departament de F´ısica, Universitat Polit`ecnica de Catalunya, Barcelona, Spain 1 7Laboratori Nazionali del Sud-INFN, Catania, Italy 0 8Dipartimento di Fisica e Astronomia, Universita` di Catania, Catania, Italy 2 9Department of Physics, Dong Nai University, 4 Le Quy Don, n Tan Hiep Ward, Bien Hoa City, Dong Nai, Vietnam a 10Institute of Physics, Vietnam Academy of Science and Technology, 10 Dao Tan, Ba Dihn, Hanoi, Vietnam J 11Department of Physics, Tohoku University, Sendai, Miyagi 980-8578, Japan 2 12Department of Physics, Chung-Ang University, Korea 1 13Department of Physics, Yamagata University, Japan 14Department of Physics, Kyushu University, Fukuoka 812-8581, Japan ] (Dated: January 13, 2017) x e Background: Type I x-ray burstsare themost frequent thermonuclear explosions in thegalaxy, resulting from - thermonuclear runaway on the surface of an accreting neutron star. The 30S(α,p) reaction plays a critical role l c in burst models, yet insufficient experimental information is available to calculate a reliable, precise rate for this u reaction. n Purpose: Ourmeasurementwasconductedtosearchforstatesin34Aranddeterminetheirquantumproperties. [ In particular, natural-parity states with large α-decay partial widths should dominate the stellar reaction rate. 2 Method: Weperformedthefirstmeasurementof30S+αresonantelasticscatteringuptoacenter-of-massenergy v of5.5MeVusingaradioactiveionbeam. Theexperimentutilizedathickgaseousactivetargetsystemandsilicon 8 detectorarray in inversekinematics. 8 0 Results: We obtained an excitation function for 30S(α,α) near 150◦ in the center-of-mass frame. The experi- 3 mental data were analyzed with an R-Matrix calculation, and we observed three new resonant patterns between 0 11.1 and 12.1 MeV, extracting their properties of resonance energy, widths, spin, and parity. 1. Conclusions: Wecalculated theresonant thermonuclearreaction rateof30S(α,p)based onall available experi- 0 mentaldataof34Arandfound an upperlimit about oneorderof magnitudelarger thanaratedetermined using 7 astatistical model. Theastrophysical impactof thesetworateshasbeeninvestigated throughone-zonepostpro- 1 cessing type I x-ray burst calculations. We find that our new upper limit for the 30S(α,p)33Cl rate significantly : affects thepredicted nuclear energy generation rate duringtheburst. v i X PACSnumbers: 26.30.Ca,25.55.Ci,29.38.-c,29.40.Cs r a I. INTRODUCTION Type I x-raybursters (XRBs) are a classof astronom- icalobjects observedto increase in luminosity by factors ∗ [email protected] oftypicallytenstoseveralhundreds[1]forashortperiod † Present Address: 30 MeV Cyclotron Center, Tran Hung Dao oftime (tens ofseconds)withthe photonfluxpeakingin Hospital,HoanKiemDistrict,Hanoi,Vietnam the x-ray and a total energy output of about 1039–1040 ‡ PresentAddress: NuclearDataCenter, NationalSuperconduct- ergs [2, 3]. The sources of such emission repeat these ing Cyclotron Laboratory, Michigan State University, 640 S. ShawLn,EastLansing,Michigan48824,USA outburststypicallyontimescalesofhoursto days,allow- § Present Address: Institute for Basic Science, Daejeon 305-811, ing for the extensive study of the burst morphology of Korea individualXRBs. Inourgalaxy,over90suchsourcesare ¶ Present Address: Department of Physics, North Carolina State presently known since their initial discovery some forty University,2401StinsonDr,Raleigh,NC27607, USA ∗∗ PresentAddress: YokohamaSemiconductor Co.,Ltd,Japan yearsago. XRBsaremodelledverysuccessfullyasaneu- †† School of Physics & Astronomy, the University of Edinburgh, tron star accreting material rich in hydrogen and/or he- EdinburghEH93JZ,UK lium from a low-mass companion. The accretion mecha- 2 nism causes the formation of an electron-degenerate en- metallicity, as well as the neutron star radius itself [18– velope around the neutron star, where the thin-shell in- 23]. stability triggers a runaway thermonuclear explosion at The (α,p) reactions occurring on lower mass nuclei peak temperatures of 1.3−2.0 GK [4–8], which we ob- such as 14O and 18Ne have been measured directly [24– serve as an x-ray burst. 28], and the properties of resonances in the compound The sharp rise of the x-ray fluence is understood to nuclei have been the subject of a plethora of indirect be poweredby explosivehelium burning on the neutron- studies (see e.g. Refs. [29, 30] and references therein). deficient side of the Segr`e chart [6, 8–11]. In a mixed In spite of these extensive works, those cross sections hydrogenandhelium shell, the explosivenucleosynthesis still remain quite uncertain. Unfortunately, the situa- initially manifests as a series of (α,p)(p,γ) reactions on tion is much more dire in the case of the (α,p) reactions oxygen seed nuclei near the proton drip line (14,15O), induced on higher mass targets such as 30S. The only called the αp-process [12]. One such sequence in this experimentalinformationon the structure of 34Ar above burning pathway is the α-threshold and the 30S(α,p) stellar reaction rate is limited to a preliminary report on a transfer reaction 3α→ 12C(p,γ)13N(p,γ)14O(α,p)17F(p,γ) study of the compound nucleus 34Ar at high excitation (1) 18Ne(α,p)21Na(p,γ)22Mg(α,p)25Al, energy [31] and a time-reversal study [32]. The present workis the firstexperimental investigationusing the en- which continues as trance channel 30S+α. 25Al(p,γ)26Si(α,p)29P(p,γ)30S(α,p)33Cl(p,γ) (2) 34Ar(α,p)37K(p,γ)38Ca(α,p)41Sc. II. EXPERIMENT In this sequence, the (α,p) reactions proceed through T = N−Z =−1compoundnuclei. Theαp-processgives Weperformedthefirstmeasurementofαresonantelas- wzaytot2herapidproton-captureprocess(rp-process)near tic scattering on a 30S radioactive isotope beam (RIB) the Z ≈20 region owing to the ever increasing Coulomb using a thick target in inverse kinematics [33]. The ex- barrier and decreasing (α,p) Q-values. Aside from the periment was carried out at the CNS Radioactive Ion twoprotonsconsumedinthenucleartrajectoryfrom12C Beamseparator(CRIB)[34,35], ownedandoperatedby to14O,theαp-processisschematicallypureheliumburn- the Center for Nuclear Study (CNS), the University of ing (since the abundance of hydrogen is constant), and Tokyo, and located in the RIKEN Nishina Center. The it does notinclude any β+ decayswhich tend to hamper CRIB facility has been a workhorse for measurements the energy generation rate in explosive nucleosynthesis. of elastic scattering of primarily astrophysical interest Whileaplethoraofnuclearprocessestendtotakeplace [36–49],schematicallyusingsimilartechniquestotheone in a given regime of stellar nucleosynthesis,typically the adopted in the present study. preciseratesofonlyahandfuloftheseprocessesinfluence The 30S RIB was produced inflight using the the predictednature andmagnitude ofactualastrophys- 3He(28Si,30S)ntransferreaction. A28Si9+primarybeam ical observables. It is these specific nuclear quantities was extracted from an ECR ion source and accelerated which should be well constrained by laboratory experi- to 7.3 MeV/u by the RIKEN AVF cyclotron (K ≈ 70) mentation. This general picture is confirmed in XRBs, with atypicalintensity of 80pnA. We impingedthe 28Si where the nuclear reaction network includes hundreds of beam on the production target located at the entrance species and thousands of nuclear transmutations. Stud- focalplanetoCRIB,comprisedofawindowed,cryogenic ies have shown that it is only a small subset of these nu- gas cell [50]. 3He gas at 400 Torr was cooled to an effec- clear transmutations which need to be known precisely, tivetemperature of90KwithLN2; the gaswasconfined as they make a predominant contribution to the nuclear by 2.5 µm Havar windows in a cylindrical chamber with trajectory to higher mass and energy generation [13], at a length of 80 mm and a diameter of 20 mm, yielding least for the examined models. The 30S(α,p) reaction a 3He target thickness of approximately 1.7 mg cm−2. is identified as one such important reaction, contribut- As the fully-stripped species 30S16+ is the easiestto sep- ing more than 5% to the total energy generation [13], arate and distinguish from the primary beam, we used influencing the neutron star crustal composition [6] rele- Be (2.5 µm) and C (300 µg cm−2) stripper foils immedi- vant to compositionalinertia [14], moving materialaway ately afterthe productiontarget;when the Be (C) strip- from the 30S waiting point [15], and possibly accounting per foil was new, the 30S16+ purity was 88% (67%), but for double peaked XRBs [16]. A recent study found the decreased as the beam degraded the foils. The resulting 30S(α,p)reactionsensitivityinXRBsamongthetopfour cocktailbeamwasseparatedbyadoubleachromaticsys- inasinglezonemodel[17],aswellashavingaprominent tem(setto ∆p =1.875%withslitsatthedispersivefocal p (but unquantified) impact on the burst light curve in a plane) and further purified with a Wien (velocity) filter. multizone model. A firmer understanding of the input The30SRIbeamarrivedontargetwithtypicalpurityof nuclear physics for XRB models will allow for more reli- 28%andanintensityof8×103pps,successfullyinjecting able comparison with observations to constrain neutron 1.6×10930Sionsduringthemainmeasurementovertwo starbinarysystemproperties,suchasaccretionrateand days. 3 FIG. 1. (Color online) Schematicof theexperimentalsetup, consisting of two PPACs, theactive target, and silicon telescope arrays. Note that between PPACb and the active target, the beam impinges on an entrance window, which retains the active targetfillgas. Thebeamistrackedinthecentrallow-gain region(“activetargetregion”,20cm),surroundedonthreesidesby high-gain regions and silicon telescopes to measure outgoing light ions (right side telescope not depicted). Beneath each GEM isareadout pattern,separated into4mmthickbackgammon pads. ∆E issimply proportional tothechargecollected byeach pad. ThecoordinatesystemisonewherethebeamaxisdefinespositiveZ,therestfollowingleft-handedconventions. Z andX positions are determined by the pad number and comparing charge collection on either side of the backgammon, respectively. The Y position is determined by theelectron drift time. 196 mm .LG +CO 2 P P 63 mm .GE Hegas P P M A A C C K a b a 30S beam tpioflon (cid:2)E1 (cid:2)E2 θ θ ..HGEG DSS1a M 1 2 (cid:1)2 156 mm (cid:1)1 452 mm 288 mm 368mm 20 mm FIG. 2. Top-down cartoon of selected portions of the experimental setup (not to scale). The differences between a higher energy scattering (denoted ‘α1’) and a lower energy scattering (‘α2’) are shown. The setup at the experimental focal plane, shown in ‘b’, respectively) [51], which served to track the beam Figs.1&2,consistedoftwobeamlinemonitors,anactive ions event-by-event. Each SSD was 0.5 mm thick and target system (see below), and an array of silicon strip had an active area of 91×91 mm2, 8 strips on one side, detectors (SSDs). The beamline monitors were paral- and a single pad on the reverse. A scattering chamber lelplateavalanchecounters(PPACs,enumerated‘a’and filled with about 1 atm 90% He + 10% CO gas mix- 4 2 4 1.6 20 14 350 V) 1.4 Me 18 12 1.2 300 E) ( 16 250 D ( 14 α 10 ∆E (MeV)00..681 125000 osited in SS 11028 68 p 0.4 100 y de 6 4 0.2 50 erg 4 En 2 p d 2 0 0 0 5 10 15 20 25 30 35 40 45 0 50 100 150 200 250 300 Pad No. Energy deposition in active target (∆E) (keV) FIG.3. (Coloronline)CalibratedBraggcurveoftheunscat- FIG. 5. (Color online) ∆E–E plot for light ion particle tered 30S beam over the low-gain region of the active target. identification during the scattering measurement. The long- Each pad is 4 mm in depth. Data from several pads are not dashedblackline, short-dashedgrey line,andsolid (red)line shownforavarietyofreasons;ingeneralitwaseitherbecause show calculations for α-particles, deutrons, and protons, re- the electronics did not record a signal, or the energy deposit spetively,using theexperimental conditions. was arbitrarily lower than expected. beam interaction position rather than extrapolating or 60 interpolatingdataacquiredonlybydetectorsoutsidethe 103 targetregion. The readoutsectionofouractive targetis 50 an etched copper plate placed under the field cage, op- 40 positeto the cathodetopplate,sothatelectronscreated s) inthe electricfield ofthe cageby ionizing radiationdrift n RF ( 30 30S16+ 102 tsoecwtaiorndss:iot.neTfohredreetaecdtoinugt tphaedsbeaarme oserphaeraavtyedreicnotiolsfaonudr 20 three for detecting outgoing light ions. Forty-eight pads comprisethe beam readoutsection,while the regionsfor 10 29P15+ detecting light ions are comprised of eight rectangular pads each. The pads are 3.5 mm in depth, surrounded 0 -20 -15 -10 X-5 Positi0on (mm5) 10 15 20 by 0.25 mm of insulation on all sides (making 0.5 mm of insulation between each pad). Each pad is also bi- FIG. 4. (Color online) RF versus PPACa X position for the sected diagonally into two congruent right triangles, so unscattered beam, showing gates for 30S and 29P. The RF thatthecollectedchargecanbereadoutfromtwooppos- signal isrecorded withPPACaasthestartandthecyclotron ing sides (backgammon pads). The section for detecting radiofrequency signal as the stop, and thus it represents a the beam ions is the largest and located at the center, relative flight time between ions in thecocktail beam. slightly shifted towards the beam upstream direction af- ter installation in the scattering chamber. The regions fordetectinglightionssurroundthe beamsectiononthe turehousedboththeactivetargetsystemandtheSSDs.1 left,right,anddownstreamsides. Gaselectronmultiplier The He + CO gas pressurewas monitoredcontinuously 2 (GEM)foilswereusedtosetdifferenteffectivegainsover throughoutthescatteringmeasurementandmanagedby the beam and light-ion regions. Over the center of the a dedicated system; we set the gas flow controller to cir- downstreamhigh-gainGEMswasabridgetopreventthe culate fresh gas into the chamber at 20 standard liters unscattered beam ions from saturating the light ion sig- per minute with the evacuation rate regulated to keep a nals. constant gas pressure of 194.2±0.5 Torr during the en- We quantified the measurement capabilities of the ac- tire measurement. The gas-filled chamber was sealed off tive target using both online and offline measurements. from the beamline vacuum with a 7.4 µm Kapton foil; Forthe low-gainregion,we comparedthe positionof30S the entrance window was 40 mm in diameter. ions derived from the active target to those determined Anactive targetisa device wherea materialservessi- by extrapolation of the PPAC data. For the high-gain multaneously as a target and part of a detector, in prin- region, we analyzed the aggregate track width of radia- ciple allowing one to perform direct measurements at a tion emitted from a standard α source in a fixed posi- tion as measured by the active target; the tracks were softwaregatedtobe incoincidencewithageometrically- 1 Gasmixturepercentages arequotedbyvolume. centralSSDstrip. AssumingastandardPPACresolution 5 of 0.9 mm and the knownfinite strip size of the SSD, we variedthe active targetresolutionina Monte Carlosim- ulation until the calculations agreed with the data. The performanceoftheactivetargetdependedonthetypeof 102 measurement, quoted below at 1σ. The Y-position, de- terminedbythe electrondrifttime, wasthemostprecise s being0.5mm. TheX-positionresolution,determinedby nt u charge division in the backgammon pads, was 3 mm. Co10 In the present work, the typical 30S scattering labo- ratory angle and change in energy loss was difficult to reliablydistinguishfromthe unscatteredbeamgiventhe 1 above resolution for the active target in X. Considering the close spacing of the high-gain GEM data and their 1500 2000 2C50e0nte3r0-0o0f-m3a50s0s en40e0r0gy 4(5k0e0V)5000 5500 6000 relativelylargedistancefromtypicalscatteringlocations, extrapolatingsuchavectorresultsinalargeuncertainty. FIG. 6. Energy spectrum of scattered α particles gating on Instead, we found that averagingthe pad X and Y data the 30S RIB determined by the kinematic solution. As the overthe center(inZ)ofthe high-gainGEMreducedthe high-gain GEM and SSD must both be hit for an event to uncertainty and was sufficient for our purposes. register, it is only a portion of the total eventswhich are an- The 30S energy on target was measured to be 48.4± alyzed. Hintsof some resonant structure can be seen around 4500 and 5000 keV. The data cut off at low energy as the 2.0MeV.Thestoppingpowerfor30SintheHe+CO gas 2 scattered αparticles donot haveenough energy to reach the mixturewasdeterminedbybothadirectmeasurementof SSDand are instead stopped in thegas. thebeamenergyatfivetargetpressuresandbyacompar- ison of the shape of the Bragg curve and stopping posi- tionofthe unscatteredionsintheactivetargetasshown energy E for elastic scattering, defined as c.m. in Fig. 3; excellent agreement was found between the measurementsandthepredictionusingZiegler’smethod. M +m E = E , (3) The energy loss and the Bragg curve of the contaminant c.m. 4Mcos2ϑ α lab 29P were also reproduced using an identical approach, where M and m are the masses of 30S and 4He, respec- giving us confidence in our treatment of the energy loss tively, ϑ is the laboratory scattering angle, and E is in the PPACs, entrance window, and He+CO gas mix- lab α 2 the laboratory energy of the scattered α particle. Us- ture. The event-by-event particle identification of the ing the experimentally verified stopping power of the cocktail beam is shown in Fig. 4. He+CO gas for 30S ions and α particles, we numeri- We confirmed the energy loss of α particles using a 2 cally solvedthe kinematic equation event-by-eventusing standardtripleαsourceandanαbeamcreatedbyCRIB, test points along the extrapolated 30S ion trajectory in checking that both their Bragg curves and residual en- 1mmsteps untilthe calculatedandmeasuredresidualα ergies agreed with the calculations. A ∆E–E spectrum particle energy disagreed by at most 100 keV; the scat- from the scattering measurement is shown in Fig. 5; the tering depth fixed the allowed values of ϑ and E by figure shows clearly that the measured locus is consis- lab α successive energy loss of the heavy ion. The α spectrum tent with the theoretical trend for α-particles. The dy- is shown in Fig. 6. namic range of the high-gain GEMs was optimized to Thedifferentialcrosssectionwasthencalculatedusing be 10–100 keV corresponding to the energy deposit of α particles, which would always be stopped in the first dσ Y S(E ) m α b = , (4) SSD layer unlike high energy protons. As protons with dΩ I n∆E∆Ω M +m b c.m. enoughenergytoreachanSSDdeposit<5keVperpad, they could not be detected by the active target system. where Yα is the yield of α particles at each energy bin, S(E )is the stopping powerof30S inHe+CO , I is the b 2 b number of 30S beam ions injected into the target, n is the number density of 4He atoms, ∆E is the energy bin III. ANALYSIS size (100 keV), and ∆Ωc.m. is the center-of-mass solid angle at each energy bin. The number of beam ions in- jected into the target I was defined as the coincidence b A. Determination of cross section between the two PPACs, recorded as a scaler during the run,multipliedbytheaverage30Spurity. Sincethescat- We measured the residual energy of α particles with tering could take place overa range of targetdepths, we an SSD as well as the beam trajectory recorded by the calculatedthesolidangleΩ fromthevantagepointof c.m. two PPACs and the recoiling α particle position deter- eachactualscatteringeventandfitthetrendwithanem- mined by the high-gainportionofthe activetarget. The pirical function. The yield of α particles Y was scaled α information is sufficient to determine the center-of-mass universally by a factor of 2.0 to match the calculated 6 magnitude of Rutherford scattering at lower energies; a similar deficiency was observed in the number of α par- 1000 ticles (producedinthe cocktailbeambyCRIB)detected 900 140 bythehigh-gainGEMcomparedtotheSSDinatestrun. ns) 800 120 The resulting excitation function is shown in Fig. 9(a). ht ( 700 g 100 Fli 600 of- α background 80 e- 500 B. Sources of background m Ti 400 60 m Detected α particles might originate from a source yste 230000 40 S other than elastic scattering of 30S with the helium nu- 100 20 clei in the target gas. We applied software gates to the 0 0 0 500 1000 1500 2000 2500 3000 PPAC data event-by-event to ensure the incident beam SSD Residual Energy (ch) ionswereconsistentwith the propertiesof30S,whichre- movedcontributionstothe αspectruminducedbyother FIG.7. (Coloronline)Residuallightionenergyasmeasured heavy ion species within the cocktail beam. bytheSSDinchannelsontheabscissaagainstthesystemToF One mightimagine variousreactions with the PPACs, in nanoseconds on the ordinate. Significant α background is Kapton window (stoichiometry C H N O ), or the seenaroundchannel1000intheSSDenergy. Thelocusoftrue 22 10 2 5 elasticscatteringeventsselectedbythekinematicsolutionfall CO used as a quenching gas in the active target. The 2 withinthedepictedgate;however,itcanbeobservedthatone standardPPACsusedatCRIBareeachfilledwith9Torr locus of the beamlike α particles overlaps with the region of C F over a length of ≈ 35 mm (≈ 0.3 mg cm−2) con- 3 8 thetrueevents. See thetext. fined with 2 µm aluminized Mylar windows (H C O ) 8 10 4 and interspaced with a further three 1.5 µm similar foils (8.5 µm in total). monotonic cross sections for 12C and 16O with 30Si, the The30SbeamprofileonPPACadoesnothavealineof mirrornucleusof30S.Suchbehaviorimpliesthataback- sighttothehigh-gainGEM,althoughtheedgeofthe30S groudsourceofαparticlesinthepresentworkinducedby profile on PPACb does have such a line of sight. Thus, CNO-groupelements shouldhavea relativelyflatenergy we can geometrically rule out PPACa (but not PPACb) distribution. Figure 9(a) shows that our observed res- as a source of background α particles. onant structure is manifested as destructive interference Although the CNO-group elements require some con- withpureRutherfordscattering. Itmeansthatanyunac- sideration, we can immediately rule out hydrogen as a countedforbackgroundofαparticlesarisingfromthe30S background source of α particles, because the 30S(p,α) beam interacting with CNO-group elements would tend reaction Q-value is −8.47 MeV, and the 30S+p system todecreaseourobservedresonancedipsandthusourde- Ec.m. <4MeVanywhereafterthedispersivefocalplane. duced partial widths Γi could be modestly smaller than As for the entrance window and quenching gas, the the true values. If we consider the relative differences in Coulomb barriers for 30S+12C, 30S+14N, and 30S+16O the maximum (≈ 60 mb/sr) and minimum (≈ 5 mb/sr) are 24.4, 28.0, and 31.3 MeV, respectively. The 30S differential cross sections around 5 MeV center-of-mass beam energy impinging on the Kapton window is about energy,thenasmoothbackgroundcannotcomprisemore 2.34 MeV/u, yielding Ec.m. = 20.0,22.3,24.3 MeV for than 8% of the measurement in the region of interest. nuclear interactions with 12C, 14N, and 16O, respec- This uncertainty turns out to be smaller than the statis- tively. Asforthe incident30Sbeamenergyimpingingon tical error and as such can be reasonably neglected. the He+CO gas, it is about 1.62 MeV/u, which yields The main sources of energy-dependent background 2 Ec.m. =13.9,16.9MeV for nuclear interactions with 12C couldbeαparticlesoriginatingfromtheRIBproduction and 16O, respectively. Considering that the center-of- targetsatisfyingtheBρselectionaswellascontributions mass energies are always below the respective Coulomb from inelastic scattering. The bumps seen in the excita- barriersforthe entrancewindowandquenchinggas,this tion function around 3.5 MeV in Fig. 9(a) correspond implies that the heavy-ion fusion cross sections should to the region where α particles magnetically selected by bemanyordersofmagnitudelowerthanthatofαelastic CRIB are expected to appear. These background ions scattering. are observedclearly in the spectrum of the SSD residual Although we are not aware of any experimental data energy against the system time of flight (ToF) in Fig. 7. concerning 30S-induced heavy-ion reactions, the fusion TheToFisthetimebetweenPPACaandtheSSD,follow- study with 12C and 16O on the stable isotopes 28,29,30Si ing Ref. [53]. The figure shows all SSD events gated on by Jordan et al. [52] is analogous if we accept isospin incoming 30S ions, about ≈ 80% of which are discarded symmetry. Their center-of-mass energies broadly over- by the requirements of the kinematic solution. The true lap with ours sufficiently to make a germane compari- elastic scattering events fall within a small locus on the son. In that work, the authors see smooth behavior of histogramwithaspecificToF,depictedbyanarrowgate. the excitation functions except in the case of 12C+28Si; Conversely,the beamlike α particlesspanthe entireToF as relevant to the present study, they importantly find rangewithtemporalspacingexactlycorrespondingtothe 7 inverse of the cyclotron radiofrequency signal, because these ions do not deposit enough energy to trigger the 0.12 180 PPAC and merely arrive at the SSD in chance coinci- 175 dence with a 30S ion at the PPAC. Ordinarily, the re- V) 0.1 170s) e Resolution e lcthsoahuofotecrloidrhovceneosefrpocvolkroaeftnnpsattd.uhisslcAehbatsPoreeaadPameAecrsaheCc(slrasiailnesbyteiciegveddFneiacisbflgocle.iaigaln4rohncd)wtdi,edtdbiecin,umnyttccSeheleto.eohctrf.iresAoaIrnIilbseIthlerDaaaaot,dmusioiimgnonihtfoarrdnleomloqdwreouuesisegcttnnhiinocoionnygtf (MResolution in Ec.m.000...000468 Angle 111111445566050505ϑ (degreAverage c.m. individual resonancesin this regionwith widths equalto 0.02 135 the theoretical limit made no discernible change to the 0 130 calculated excitation function given our energy resolu- 1000 2000 3000 4000 5000 6000 E (keV) c.m. tion. Using the Wien filter to steer the beam, we deter- mined that a vast majority of the beamlike α particles FIG. 8. Uncertainty in determination of the center-of-mass are confined to a narrow energy region. energyEc.m. inMeV(solidline)andaveragescatteringangle As for possible contributions from inelastic scatter- ϑc.m. in degrees (dashed line) as functions of the center-of- mass energy in keV. ing, the first excited state of 30S is relatively high at E = 2.21 MeV and with a spin-parity of 2+. The in- 1x creased scattering threshold as well as the requirement center-of-mass energy ∆E can be expressed as for ℓ ≥ 2 from the angular momentum selection rules c.m. indicates that the widths, which decrease with increas- 2 2 ing ℓ as shown in Table III, suggesting a significantly ∆E ∆E cos(ϑ )−cos(ϑ′ ) lower cross section than elastic scattering. For exam- E c.m. =v E α +4 lcabos(ϑ ) lab , c.m. u α ! lab ! ple, in other studies of α elastic scattering, this contri- u t (5) bution was found to be less than 10% [43, 46], where where∆E istheuncertaintyinthemeasuredα-particle the first excited states are much lower in energy. More- α energy, ϑ is the average measured angle, and the un- over, as the resonances we analyzed were in the region lab certainty in the measured angle is ∆ϑ =|ϑ −ϑ′ |. of 4.0 ≤ Ec.m. ≤ 5.6 MeV, contributions from inelastic lab lab lab Inthefollowingillustrativecalculations,E wasvaried scatteringwouldshow upnear 1.8≤E ≤3.4MeV in c.m. c.m. in 1 MeV increments over the range of 2–6 MeV. the elastic spectrum, where resonances were neither re- solved nor analyzed in our data. Therefore, it is reason- Under the experimental conditions, the energy resolu- able to neglect any possible contribution from inelastic tionofthe SSDfor4.78,5.48,and5.795MeVαparticles scattering in the present analysis, as its most important from a standard source was 103, 98, and 87 keV, respec- consequence is on the deduced proton widths Γ , since tively. For higher energy α particles, we assumed the p we assumed any width which was not from the elastic resolution of 15% as measured for the 5.795 MeV α’s, channel would be from the proton channel by neglecting which should be an overestimate. In an offline test, the inelastic scattering. SSD resolution for the 5.48 MeV line was as good as 29 keV under vacuum which broadened to 70 keV when the chamber was filled with He+CO gas; by folding an 2 assumed 64 keV of broadening from energy straggling with the intrinsic SSD resolution, we were able to repro- duce the measured width. Considering the position of the α source was nearly 40 cm from the SSD in offline C. Experimental error tests and α particles scattered at an initial laboratory energy of 5.5 MeV would be nearly twice as close to the SSD,64keVcanbeconsideredthemaximumuncertainty A number of different factors can influence the deter- for straggling, with higher energy α particles straggling mination of the center-of-mass energy E for a given much less as well as originating much closer to the de- c.m. event: the spread in the beam energy from the momen- tectors. We finally adopted values for ∆Eα by adding tumselectionaswellasstraggling,theSSDresolutionfor the above SSD resolution and the assumed straggling measurementofthe αparticleresidualenergy,the strag- in quadrature, except for the highest energy α particles gling of the α particle, and the position determinations where we simply adopted an uncertainty of 15% since of both the recoiling α and beam ion. However,since we summing the overestimated uncertainties from both res- use the geometric measurements to determine ϑ and olution and straggling effects is unreasonable. lab the residual energy of the outgoing α particle to deduce In order to estimate the uncertainty in ϑ arising lab E , these have the most profound effect on the determi- from the experimental determination of the scattering α nation of E . Based on Eq. 3, the uncertainty in the position, we need to first estimate the average ϑ as c.m. lab 8 a function of E . We plotted both the laboratory scattering anglecϑ.m. and the center-of-mass angle ϑ TABLE I. Coupling schemes for states in 34Ar for Jπ ≤ 4+ event-by-eventinolarbdertodeterminetheiraveragevalcu.mes. for the 33Cl+p channel. The lowest ℓp is assumed, and not all possible linear combinations are denoted. Seethe text. as functions of the center-of-mass energy; the average ϑc.m. is shown in Fig. 8. While the precision of each Jπ ℓp s s1⊕s2 s⊕ℓ PPACto determine a beamparticle’spositionis 0.9mm 0+ 1 1 ↑↓ ↑↓ in both X and Y, the position resolutionbecomes 4 mm 1− 0 1 ↑↓ — in both dimensions when extrapolated to a typical scat- 2+ 0 2 ↑↑ — teringdepth. Theresolutionachievedfortheαparticle’s 3− 1 2 ↑↑ ↑↑ positionwiththe backgammonpadswas3mminX and 0.5mminY. Alltheseuncertaintieswereaddedtogether 4+ 2 2 ↑↑ ↑↑ in quadrature to yield a final uncertainty of 6.4 mm in the determination of ϑ . A new angle ϑ′ was calcu- lab lab lated by shifting the position of the α particle by the ton andα partialwidths, as both channels areopen; the above 6.4 mm, assuming a standard scattering depth Z gamma partial widths Γ are negligibly small for these γ representativeofeachof the five center-of-massenergies. highly excited, particle-unbound states. For the case of The resulting range of ∆ϑlab was found to be 1.3–2.1◦, 30S+α elastic scattering, the situation is simplified for increasing with decreasing Ec.m.. the entrance channel, as both the nuclei have a ground- Finally,weobtainedanestimatefortheuncertaintyof state spin-parity Jπ =0+, and so the quantum selection the center-of-massenergyof about 60–100keVas shown rules dictate a unique resonance Jπ for each ℓ value— α in Fig. 8; the intrinsic resolution of the SSD had the namely that J = ℓ and the parity is always natural for α predominant effect, which was more pronounced at the populated states in 34Ar. higher energies. Thus, it can be seen that the energy The calculated excitation function was broadened binningchoiceof100keVisconsistentwithourachieved based on the experimental energy resolution and per- resolution. formed at an average angle of ϑ = 150◦ as evaluated c.m. We confirmedwith a simple calcuation that the above above in Sec. IIIC. We quantified the quality of a fit by geometricuncertaintiesdominateovertheuncertaintyin the reducedchi-squareχ2, which is the chi-squareχ2 di- ν the beam energy. Suppose we have two identical mea- videdbythenumberofdegreesoffreedomν. Fittingthe surements, but we know that the incident energy differs datawithpureCoulombscatteringresultedinχ2 =4.17 ν between the two beam ions. The result of the kinematic with 35 degrees of freedom, indicating the possibility for solution is that the optimized scattering depth will be significant improvement could be expected by including larger for the higher energy beam ion and vice versa for the interference effect of resonances in an R-Matrix fit. the low energy beam ion, because it is the scattering As there are no known levels in 34Ar with E >8 MeV, ex depth combined with the incident beam energy together wehadtocarefullyintroducenewresonancesuntiltheex- that finally determines E . Assuming a nominal scat- perimental data were reasonably reproduced. The max- c.m. tering energy of E = 4.0 MeV, changing the trans- imum width of a resonance can be estimated with the c.m. versescatteringpositionbythe6.4mmuncertaintymen- Wigner limit [56] as tionedaboveisequivalentto: ∆ϑ =1.7◦,changingthe lab scattering depth ∆Z by 27 mm, or changing the beam 2h¯2 W = P , (6) energyby5.6MeV.Thus,theuncertaintiesofthesemea- Γi µ R2 ℓi i i surementsdominateovertheintrinsicspreadinthebeam energy of 2.0 MeV. whereµisthechannelreducedmass,Risthechannelra- dius,andP isthechannelpenetrability,respectively,for ℓ channeli. WecalculatethepenetrabilityasP = ρ , ℓ Fℓ2+G2ℓ D. R-Matrix analysis where ρ = kR includes the phase space factor k, and F h¯ ℓ and G are the regularand irregularCoulombfunctions, ℓ To extract the resonance parameters of interest, we respectively. Such a physical constraint is particularly performed a multilevel, multichannel R-Matrix calcula- relevant when introducing new resonances to help limit tion [54] with the sammy8 code [55]. Succinctly, the R- the parameter space. We adopted the channel radius Matrix method calculates the interference between the given by R = 1.45(A1/3 +A1/3) fm, where A and A i 1 2 1 2 regular and irregular Coulomb functions with physical are the mass numbers of the two species in channel i; resonances. The resonances are parameterized by their an identical parameterization was used in the studies of energy E (the same as E from elastic scattering as 21Na+α [57] and 26Si+p [44], which are two of the most r c.m. Q=0),channel ipartialwidths Γ ,andthe angularmo- similarexperimentstothepresentwork. Forconsistency, i mentatransferℓ . Theresonanceshapeisdeterminedby thesameα-channelradiuswasalsousedintheR-Matrix i the entrance channel ℓ , the resonance height from the calculation. α entrance channel Γ , and the resonance width depends At the outset, we began with a single channel (Γ = α on total width Γ. The total width is a sum of the pro- Γ ),singlelevelmanualanalysisstartingwiththelowest- α 9 450 160 sr)334050000 (a) 4P4..u33r55e 24C++o;; u44l..o77m88 b22 ++;; ; χ 552../33n44d f22=++4;; . χ1χ272//nnddff==00..7840 sr)111024000 (b) EEEEEEErrrrrrr ======= 4444444.......77777778888888 MMMMMMMeeeeeeeVVVVVVV,,,,,,, fsipdgh---w----wwwwwwaaaaaaavvvvvvveeeeeee;;; ;;;;χ χ χχχχχ222/2222/n/n////nnnnndddddddff=f=ffff=====1211022..8.9....777931817404 mb/250 mb/ Ω (200 Ω ( 80 d d σ/ σ/ 60 d150 d 40 100 50 20 0 0 2 2.5 3 3.5 4 4.5 5 5.5 4 4.2 4.4 4.6 4.8 5 5.2 5.4 E (MeV) E (MeV) cm cm FIG.9. (Coloronline) 30S+αelastic scatteringexcitation functionincludingfits. (a) Theenergyrangedisplayedistheentire setof continuousdataintherawexcitation function,exceptat thelowerenergysidewheretheplot isterminatedatthepoint where all the α particles can no longer reach the detector from stopping in the fill gas. The bumps observed around 3.5 MeV correspond toaregion oflarge αbackground,asdepictedinFig. 7. Threeresonance-likestructuresareseen between4.0 MeV < Ec.m. < 5.5 MeV. The data are fit with a multichannel (α and p), multilevel R-Matrix formalism, and the results for a selected combination of ℓα transfers are shown (though all combinations up to ℓα ≤ 4 were tested, and ℓα = 5,6 never gave goodfits). TheadoptedparametersofthesethreenewlydiscoveredresonancesareshowninTableII.(b)Allphysicallyallowed ℓα valuesfor theEr =4.78 MeV resonance, showing the unambiguousassignment of ℓ=2. See thetext. TABLEII.Bestfitlevelparametersof34Ardeterminedbythepresentwork. Alllevelsarenewlyproposed. Thetableisarranged such that the corresponding physical property of each state in 34Ar precedes the corresponding R-Matrix fit parameter. As we could not uniquely constrain the spin-parity of the 11.09 MeV level, two possible assignments are given, as well as the corresponding widths. The12.08 MeV level isshown in italic letters as thereis a large systematic uncertaintyassociated with it. Seethe text. Eex (MeV) Er (MeV) Jπ ℓα Γα (keV) θα2 (%) Γp (keV) ξ (%) 11.092(85) 4.353(85) (2+,4+) 2, (4) 20+60, (0.5) 40+120, (8) 25+500, (0.3) 2, (1) −18 −36 −20 11.518(89) 4.779(89) 2+ 2 100+120 90+110 210+600 7 −60 −55 −170 12.079(95) 5.340(95) (2+) 2 260+400 100+150 340+550 9 −120 −45 −200 energy features and slowly moving to higher exctiation actions always appear as peaks in the differential cross energies in discrete steps of 100 keV. The width was set section, in the case of elastic scattering the interference to the Wignerlimit (Γ =W ) to determine whichfea- pattern caused by a resonance can be observedas a dip- α Γα tures could be resolved by assuming the existance of a like structure rather than as a peak, particularly below physical resonance. At this time we also checked pos- the Coulomb barrier. sible values of the angular momentum transfer ℓ ; al- α For the proton channel, we assumed the lowest ℓ al- p thoughtheexperimentalsetupallowedforvaluesofupto lowed would have the predominant contribution. The ℓα =6,ℓα ≥5nevergavegoodfits,sinceresonanceswith spinoftheprotons = 1 andthespinofthe33Clground these higher transfer are essentially not visible within state s = 3, which1 can2 align (↑↑) or anti-align (↑↓) to the present resolution. Only under this condition where 2 2 give the total spin s = s ⊕s , and the same is true for 1 2 Γ = 0 and Γ was at the Wigner limit was it possi- p α the resulting spin s coupling with ℓ to sum J =ℓ ⊕s. p p ble to observe a change of any kind in the calculation Anexample ofthe lowest-ℓ coupling schemesareshown p for E ≤ 3.8 MeV, and even so the calculated de- c.m. in Table I for up to 4+ natural-parity states in 34Ar. viation from pure Coulomb scattering was of a smaller For convenience, we introduced the dimensionless re- magnitudethanthe experimentaldata,particularlynear duced partial width θ2 = Γ /W , in order to easily en- 3.5 MeV. The calculations were consistent with our in- i i Γi sure that, regardless of ℓ, θ2 ≤ 1. Resonant elastic scat- terpretationthatthefluctuationsbelow3.8MeVaresta- i tering is often analyzed by a single-channel formalism tistical or background induced. The subsequent multi- because the resonance shape and height are not affected level, multichannelanalysis thus focuses onthe regionof by the other channels; thus at the outset we simplified 3.9–5.6 MeV and assumes ℓ ≤ 4; three resonance-like α our model by controlling the proton width via a uni- structures couldbe resolvednear E ≈4.35,4.78,and c.m. versal ratio of the dimensionless reduced partial widths 5.34 MeV. Although resonances observed by transfer re- ξ ≡ θ2/θ2, which was found to be 3% in a similar work p α 10 [57]. Although the value of Γ derived this way may IV. DISCUSSION p have a large uncertainty as well as model dependence, it isphysicallyunrealistictoperformasingle-channelanal- Weobservedthesignatureinterferencepatternsofsev- ysis so far above the proton threshold. eral resonances in 34Ar with large α partial widths Γ α viaαelasticscatteringon30S.Theclusterthresholdrule Starting with the first resonance near 4.35 MeV and predicts the existence of these states, which have a large truncating the excitation function towards higher ener- overlap of the cluster configuration to the nuclear wave- gies, a computer code optimized Er, ℓ, θα2, and ξ, un- functionnearbytherespectivecluster’sseparationenergy til all three resonances were introduced and the fit took [58, 59]. Such α-cluster resonances have typically domi- into accountthe entire energy range of the experimental nated the stellar rate of exothermic (α,n) and (α,p) re- excitation function. Once we had such a reasonable fit actions on T = ±1 nuclei, respectively, when they fall z (ξ ≈ 7%), we then allowed θ2 to vary individually for within the astrophysical Gamow burning window [60], p each resonance and again covaried sets of resonance pa- because it is typically the case that Γ ≪ Γ owing α n,p rameterstosearchforthebestfitfortheentirespectrum. to differences fromthe Coulombbarrier. Alpha resonant Insummary,Erwascovariedover200keVin1keVsteps, elasticscatteringhaslongbeenknownasapowerfultool ℓ was covariedfor values overthe rangeof 0 to 4, θ2 was to selectively observe states with large Γ . The effect is α α covaried in 1% steps up to > 99%, and θ2 was varied in especially pronounced in inverse kinematics, where mea- p small increments up to 10% (past where ξ showed poor surements at large backwardangles are possible and the behavior)inoursearchforthebestfit,showninFig.9(a), nonresonant cross sections are minimized; under these wherethehorizontalerrorsarefromthe100keVbinning conditions, one expects to observe states with Γ com- α andthe verticalerrorsarepurelystatistical. Allpossible parable to the experimental energy resolution [33]. Ac- ℓ values for the 4.78 MeV state are shown in Fig. 9(b) cording to calculations of the Wigner limit (see Eq. 6), for illustrative purposes. the maximum theoretical width shrinks rapidly as the energy is reduced towards the threshold. TheresonanceparametersdeducedfromtheR-Matrix Our observation that all three resonances are consis- analysis are shown in Table II. The uncertainties in the tentwitha2+ assignmentmaymakeonewonderifthere adopted level parameters were calculated in the follow- is a reason for such behavior. We note that all three are ing ways. For the excitation energy E , we used the observedasdiplikestructures,soitmaynotbesurprising ex experimentalenergy resolutionas discussed in Sec. IIIC thatfeatures inthe differentialcrosssectionwith similar and shown in Fig. 8. The error of the remaining level interferencepatternscanresultfromphysicalresonances parameters was evaluated considering the range where with the same Jπ. Such a system of α-cluster doublets an individual parameter is allowed to vary within one was observed in the Tz = +1 nucleus 22Ne [61, 62] with standarddeviation of the best fit χ2. The recommended Jπ correlated with increasing energy, albeit for states ν spin-parity Jπ is given, and any other spin-parity which of negative rather than positive parity. Our 11.51 MeV is possible is listed, as are the associated widths in their state could be regarded as a 2+ doublet paired with ei- respectivecolumnsinparenthesis. TheerrorinΓ isseen ther of our other two states, which both have tentative p to be generally larger than in Γ , because the α elastic assignments. Unfortunately,comparisonwithmodelpre- α scatteringresonantstructureismuchlesssensitivetothe dictions is still a challenge for the 30S mass region. proton channel compared to the α channel. The resonance parameters obtained in the present A. Reaction rate study appear to be reasonable except for the widths for the12.08MeVstate. Inparticular,the12.08MeVstate’s Thepeaktemperatureofx-rayburstsisexpectedtobe structurecannotbeapureαclusterwhichalsohasanon- in the range of 1.3–2 GK corresponding to the Gamow negligible proton decay branch. Our favored interpreta- burning windows of 1.5 <∼ Ec.m. <∼ 5.0 MeV. To make tion is that there are one or more unresolved resonances a meaningful evaluation of the stellar reaction rate in with substantial α-cluster configuration in this region. XRBs, we therefore need to consider not only the res- Moreover, the behavior of the resonance tail is uncon- onances discovered in the present work, but also 34Ar strained by the data, and any interference effects from states at lower E . In fact, before the present work ex unknown physical resonances outside the energy range there has never been an evaluation of the 30S(α,p) cross cannot be accounted for. Thus, there are large system- sectionbasedonexperimentallevelstructureof34Arow- atic uncertainties associated with the resonance param- ing to the paucity of such data and the experimental eters extracted from an R-Matrix fit for states near the challenges of studies in this region of the periodic table. boundary of the experimental energy range. However,it The36Ar(p,t)34ArmeasurementperformedattheRe- cannot be doubted that the data indicate one or more search Center for Nuclear Physics (RCNP), Osaka Uni- very strong α-cluster resonance(s) in this region of ex- versity observed resonances above the α threshold at citation energy, which is a point we emphasize in our a relatively smooth interval—about four resonances per discussion of these results below. MeV—over four MeV in excitation energy [31]. Consid-