Relative proton and gamma widths of astrophysically important states in 30S studied in the beta-decay of 31Ar
G. T. Koldste, B. Blank, M. J. G. Borge, J. A. Briz, M. Carmona-Gallardo, L. M. Fraile, H. O. U. Fynbo, J. Giovinazzo, J. G. Johansen, A. Jokinen, B. Jonson, T. Kurturkian-Nieto, J. H. Kusk, T. Nilsson, A. Perea, V. Pesudo, E. Picado, K. Riisager, A. Saastamoinen, O. Tengblad, J.-C. Thomas, J. Van de Walle
aa r X i v : . [ nu c l - e x ] M a y Relative proton and γ widths of astrophysically important states in S studied in the β -decay of Ar.
G. T. Koldste, B. Blank, M. J. G. Borge, J. A. Briz, M. Carmona-Gallardo, L. M. Fraile, H. O. U. Fynbo, J.Giovinazzo, J. G. Johansen, A. Jokinen, B. Jonson, T. Kurturkian-Nieto, J. H. Kusk, T. Nilsson, A. Perea, V. Pesudo, E. Picado, K. Riisager, A. Saastamoinen, ∗ O. Tengblad, J.-C. Thomas, and J. Van de Walle Department of Physics and Astronomy, Aarhus University, DK-8000 Aarhus C, Denmark Centre d’ ´Etudes Nucl´eaire de Bordeaux-Gradignan,CNRS/IN2P3 – Universit´e Bordeaux I, F-33175 Gradignan Cedex, France Instituto de Estructura de la Materia, CSIC, E-28006 Madrid, Spain Grupo de F´ısica Nuclear, Universidad Complutense, E-28040 Madrid, Spain Department of Physics, University of Jyv¨askyl¨a, FIN-40351 Jyv¨askyl¨a, Finland Fundamental Fysik, Chalmers Tekniska H¨ogskola, S-41296 G¨oteborg, Sweden GANIL, CEA/DSM-CNRS/IN2P3, F-14076 Caen Cedex 5, France CERN, CH-1211 Geneva 23, Switzerland (Dated: October 30, 2018)Resonances just above the proton threshold in S affect the P( p, γ ) S reaction under astro-physical conditions. The ( p, γ )-reaction rate is currently determined indirectly and depends on theproperties of the relevant resonances. We present here a method for finding the ratio between theproton and γ partial widths of resonances in S. The widths are determined from the β p - and βpγ -decay of Ar, which is produced at the ISOLDE facility at the European research organizationCERN. Experimental limits on the ratio between the proton and γ partial widths for astrophysicalrelevant levels in S have been found for the first time. A level at 4689 . γ spectrum, and an upper limit on the Γ p / Γ γ ratio of 0 .
26 (95 % C.L.) is found. In the two-protonspectrum two levels at 5227(3) keV and 5847(4) keV are identified. These levels were previously seento γ decay and upper limits on the Γ γ / Γ p ratio of 0 . PACS numbers: 26.30.–k, 23.40.Hc, 27.30.+t
I. INTRODUCTION
Detailed knowledge of the energy levels of exotic nuclei,especially the ones just above the thresholds for particleemission, is important for understanding astrophysicalprocesses such as explosive hydrogen burning. S is sit-uated close to the proton drip line and is produced in the P( p, γ ) S reaction in the r p - and αp -process in type Ix-ray bursts [1, 2]. The relatively long life time of Smakes it a critical waiting-point nucleus for these pro-cesses [3].The P( p, γ ) S reaction is also interesting for thestudy of presolar dust grains. The most extensively stud-ied grains are SiC grains, because they are relativelyabundant. A small fraction of these have been suggestedto originate from classical novae [4]. They are character-ized by low C / C and N / N ratios, high Si / Siratios, and Si / Si ratios close to or lower than terres-trial values. The silicon isotopic abundance can provideinformation on the dominant nuclear synthesis paths fol-lowed by the thermonuclear runaway, which sets in nearthe base of the accreted layers from a main sequence staronto a white dwarf in a binary system [5]. In order tounderstand the origin of the isotopic ratios observed, the ∗ Present address: Cyclotron Institute, Texas A&M University,College Station, TX 77843-3366, USA processes that create and destroy the different silicon iso-topes have to be well understood. One of these is the P( p, γ ) S reaction. If this reaction is faster than the β + decay of P, the amount of Si would increase andthe amount of Si would decrease [6].The Gamow window of the P( p, γ ) S reaction fortemperatures relevant for astrophysics spans 100 keV to1100 keV. This, along with the proton separation energyof S being 4395 . S interesting for astrophysics lie below 6 MeV.Iliadis et al. [8] predicted that the reaction rate of the P( p, γ ) S reaction was dominated by two resonancesin S with spins 3 + and 2 + and excitation energies of4733(40) keV and 4888(40) keV, respectively, which hadnot been observed at that time. The first experimen-tal evidence came through studies of S( p, t ) S by Bar-dayan et al. [9] and Setoodehnia et al. [10]. The mostrecent studies of S can be found in Refs. [10–14], whilethe results from previous experiments are combined inRef. [15].The reaction rate is calculated using the energy, spin,and the proton and γ partial width of the relevantresonances. The improvements on the energies of the3 + and 2 + levels have reduced the uncertainties of the P( p, γ ) S reaction rate significantly for the relevanttemperatures. The calculations made by Setoodehnia etal. [12] shows that the uncertainties are now so small thatthey no longer significantly influence the silicon abun- Ar Cl S + p P + 2p pp p β + γ I γ γ γ γγ II 2 1 4 3 β + p IAS p AB C p FIG. 1. (Color online) The β decay of Ar. Different protondecays are drawn as an illustration. The marked proton lev-els in S correspond to Fig. 3 and the marked γ transitionscorrespond to Fig. 4. dances. These calculations, however, use proton and γ partial widths, which are calculated based on the shellmodel and comparisons with the mirror nucleus. Exper-imental values for these would clearly be preferred. Wepresent here a method for finding the ratio between theproton and γ partial widths for the resonances of astro-physical interest using the decay of Ar. Until now thepreferred method for studying these resonances has beenby the use of reaction experiments. The results presentedhere open up a new approach. Further results from ourexperiment will be published separately.The experiment is described in Sec. II. Sec. III presentsthe results of the analysis of the low-lying states of Sand compares then with results in recent papers. It in-cludes the method for finding the ratio between the pro-ton and γ partial widths. Finally, Sec. IV summarizesthe main results. II. THE EXPERIMENT
In this experiment, the resonances in S are studiedvia the β -delayed proton- γ decay and the β -delayed two-proton decay of Ar. The β -delayed two-proton decayis known to be mainly sequential [16]. A partial decayscheme of Ar is shown in Fig. 1. The experiment was
12 6 3 54
FIG. 2. (Color online) The experimental setup used for theexperiment. The beam enters between DSSSD 5 and 6 andis stopped in a foil mounted on a small metal holder enteringbetween DSSSD 3 and 5. Two clustered germanium detectorssituated outside the cube behind DSSSD 3 and 4 are shownon the upper drawing. The top of the cube with three of theDSSSDs is lifted, following the dotted black line, for bettervisualization on the bottom drawing. optimized for detection of the delayed two-proton decaythrough a compact setup including detectors capable ofstopping high-energy protons. This gave substantial β background at low energy, which along with electronicnoise made it challenging to identify low-energy protons.The radioactive 60-keV Ar beam used in the exper-iment was produced at the ISOLDE facility at the Eu-ropean research organization CERN using a CaO targetand a versatile arc discharge plasma ion source [17] cou-pled to the General Purpose Separator (GPS) [18]. Thebeam is produced by irradiating the target with shorthigh-intensity proton pulses at low repetition rate [18].An average Ar yield of about 1 per second was obtainedfor a runtime of about 7 days.The 60-keV beam was collected in a 50- µ g / cm car-bon foil situated in the middle of the detector setupconsisting of the silicon cube detector [19], containingsix double sided silicon strip detectors (DSSSDs): one69 µ m (1), one 494 µ m (5), and four close to 300 µ m (2–4, 6). The setup can be seen in Fig. 2. The DSSSDsare segmented into 16 strips in the front and in the backside, each 3 mm wide and 0 . µ m DSSSDs (2,3, 6) 50 mm ×
50 mm unsegmented silicon pad detectors(thickness close to 1500 µ m) were placed, which enablesparticle identification. In some part of the analysis onlythe four DSSSDs backed by a pad detector are used. Fordetection of γ rays, two cluster detectors, each consistingof three germanium crystals, from MINIBALL [20] wereplaced outside the chamber containing the silicon cube.The energy and geometry calibration of the DSSSDsare made with Ar produced from the same target-ionsource unit as Ar. A number of runs were made with Ar during the experiment to monitor if the energiesdrifted. Ar decays by β -delayed proton emission withwell-known proton energies. For calibration of DSSSD 3–6 three known levels of Cl were used: 3971 . . . . . . Clresonances used could not be identified here. Instead,two higher-lying proton peaks are used. Their energieswere found in the calibrated proton spectra of DSSSD3 and 6, which had a better energy resolution, givingproton energies of 2479 . . .
50 MeV were not stopped inside the detector.For calibration of this detector the Cl resonances at3971 . . . . π , or, if thetwo detectors without backing are disregarded, 27 % of4 π . Protons with energies below 500 keV can be stoppedinside the collection foil depending on their emitted an-gle. The low-energy protons, which are interesting forthis work, have an energy around 280 keV. The angularcoverage of these protons is 20 % of 4 π , when the twodetectors without backing are disregarded.The half-life of Ar is just 14 . Ar was therefore only open for 100 ms aftera proton pulse has hit the target. In addition to this asoftware time window from 5 ms to 100 ms after protonimpact was used.The pad detectors are calibrated with a
Gd sourceand a triple α source consisting of Am,
Pu, and
Cm.The Ge detectors were calibrated using first a
Csand a Co source and then improved using a
Eusource, and lines from the decays of
Ar and
Nwere recorded online. The absolute γ efficiency was foundusing a relative efficiency curve determined in a slightlydifferent detector configuration (using four different γ sources: Eu, Co,
Bi and Be) and an absolutemeasurement with an
Eu source. The result, using
Excitation energy in S (MeV) C oun t s / k e V A B C FIG. 3. (Color online) The excitation energy of S calculatedfrom the energies of the two protons from the sequential two-proton decay as described in Ref. [16]. The energies of themarked peaks can be found in Table I. E γ (MeV) C oun t s / k e V FIG. 4. (Color online) The summed γ spectrum over all crys-tals gated on protons from the decay of Ar. The numberscorrespond to transitions in S and the Roman numbers cor-respond to transitions in P. The energies of the markedpeaks and their relative intensities can be found in Table II. the formula in Ref. [22], is ε γ ( E ) =0 .
21 exp − . − .
457 log (cid:18) E MeV (cid:19) − . (cid:20) log (cid:18) E MeV (cid:19)(cid:21) ! , (1)with an estimated uncertainty of 10 %. III. RESULTS AND DISCUSSION
Table I summarizes the latest published results on thelow-lying levels of S. Included are also the energiesmeasured in this experiment. Fig. 3 shows the levelsabove 5 MeV found, in the present work, using the en-
TABLE I. Energy and spin of the S levels below 6 MeV for the present work and recent previous work. The proton separationenergy of S is 4395 . Setoodehnia et al . [12] Lotay et al . [13] Almaraz-Calderon et al . [14] Present work Si( He , nγ ) S S( p, t ) S Si( He , nγ ) S S( p, t ) S Si( He , n ) S Ar( β + )( p ) S E x (keV) E x (keV) J π E x (keV) J π E x (keV) E x (keV) J π E x (keV)g.s. 0 + g.s. 0 + g.s. g.s. g.s.2210.6(3) 2208(3) 2 + + + + + + + + + + + + + ) 5132.1(1) 4 + + )5225(2) (0 + ) 5218.8(3) 3 + + ) 5227(3)5315(2) (3 − ) (3 − ) 5312.1(20) (3 − )5393(2) 3 + (2 + ) 5382.0(7) 5400(43) (2 + ) 5392(4)5849(2) (2 + ) 5848.0(4) 4 + + ) 5847(4)5947(3) (4 + ) TABLE II. The energies and relative intensities of the γ linesin Fig. 4 normalized to the transition from the first excitedstate to the ground state of S. Peak Energy (keV) Intensity1 1194 . . . . β particles and elec-tronic noise, the levels below 5 MeV cannot be identifiedin the two-proton decay. These levels are known to de-cay mainly by γ emission and are thus identified from theproton-gated γ spectrum presented in Fig. 4. The rela-tive intensities of the γ lines are given in Table II. Onlythe 1194 .
2- and the 2210 . Ar [23]. The 1194 .
2- and the3407-keV lines both correspond to decays of the secondexcited state in S. Their relative intensity is 0 . σ with the value of 0 . γ andproton decay widths of the 4689 . γ / Γ p ratioscan be found in Table III. The - keV level The level at 4689 . Ar. It is identified in the γ spec-trum (Fig. 4) as peak 3, which corresponds to the decayof the level to the first excited state. It is predicted to de-cay by proton emission as well, but due to contaminationfrom β particles and electronic noise it is not possible toidentify it in Fig. 3. β particles mainly deposit a smallamount of energy in the DSSSD and give a larger sig-nal in the pad detector. Since this source of backgroundcannot be identified in the DSSSDs without backing, theyare omitted in the following analysis.The large background below 5 MeV in Fig. 3 consists ofmultiplicity two events where one of the signals is causedby a β or electronic noise typically in coincidence with aproton from a strong one-proton peak, e.g., a proton from Cl to the ground state in S (see Fig. 1). The back-ground can thus be reduced by including only multiplicitytwo events with a proton that is known to feed the levelconsidered. The protons feeding the 4689-keV level arefound by gating on the 2478 . γ . The protons arefound to have energies in the intervals [1580 , , p / Γ γ ratio can be found. The backgroundcan be estimated by gating on protons in the interval[2040 , Cl to the ground stateof S [16]. The background spectrum then has to bescaled by a factor f = 0 . TABLE III. Ratios between calculated proton and γ partial widths from previous work compared with the 95 % confidencelimits extracted from the present work. Setoodehnia et al . [10] Almaraz-Calderon et al . [14] Present work E x (keV) J π Γ γ / Γ p E x (keV) J π Γ γ / Γ p E x (keV) Γ γ / Γ p +
210 4689.2(24) > . + . +
480 5130 4 + + ≥ . × − + . × − < . − . × − − . + . × − + . × − + . < S energy in a 40-keV interval around 4689 keV,is found to be (26 − f γ rays, corresponding to the decay of the4689-keV level to the first excited state in S, is foundto be (13 − f n i from a proba-bility function P ( n i | n i ), where n i are the four numbersfound from the spectra ( n = 26, n = 33, n = 13, n = 11). This probability function is derived as fol-lows: n i is a number from a Poisson distribution withmean value λ i and the n i ’s needed to create the ensembleare random numbers drawn from a Poisson distributionwith this mean value λ i . The problem arises because λ i is unknown. Therefore, one has to integrate over all thepossible values of λ i weighted with the probability of this λ i given n i : P ( n i | n i ) = R ∞ dλ i P ( n i | λ i ) P ( λ i | n i ) R ∞ dλ i P ( λ i | n i )= Z ∞ dλ i P ( n i | λ i ) P ( n i | λ i ) (2)= ( n i + n i )! n i ! n i ! 12 n i + n i +1 , where the second equality comes from Bayes’s theo-rem that employing a uniform prior distribution gives P ( λ i | n i ) = P ( n i | λ i ) and from the Poisson distributionbeing normalized in λ i .The Γ p / Γ γ ratio can then be found from these fourrandom numbers n i drawn from the four distributionsby correcting for efficiencies:Γ p Γ γ = ( n − f n ) /ǫ p ( n − f n ) /ǫ γ , (3)where the γ efficiency ǫ γ includes the γ intensities mea-sured by Lotay et al . [13]. From the ensemble of 10 Γ p / Γ γ values found in this way, we find a 95 % confi-dence upper limit of 0 .
26 on the Γ p / Γ γ ratio.This limit can be compared to calculations made by Setoodehnia et al . [10] for a 3 + resonance at 4699 keV.They find: Γ p / Γ γ = 0 . × − . Recent developmentswith nano structured CaO targets have increased theyield of Ar up to an order of magnitude [25]. Hence,using this type of target and a setup optimized for low-energy protons, it should be possible to identify the pro-ton decay of the 4689-keV level using the gating tech-nique presented here and thereby deduce an experimentalvalue for the Γ p / Γ γ ratio. The - keV level A level at 5218 . γ decayto the first excited state of S by a 3008 . γ andto the second excited state by a 1814 . γ withrelative branching ratios of 0 . . γ spectrum.Assuming this is the same level as we have identified inthe two-proton spectrum at 5227(3) keV, an upper limiton the Γ γ / Γ p ratio can be found by gating on the pro-tons feeding the level. These protons are found by gatingon the 5227-keV peak in the two-proton spectrum andchoosing the proton with the highest energy as this ismost likely to be the first emitted proton. The two de-tectors without backing are again excluded. The protonsfeeding the level are found to have energies in the inter-vals [1000 , , S with proton energies in the interval[1380 , S peakat 5227 keV is 226 ±
15. The are no γ rays in a 50-keVinterval around 3008 keV, corresponding to the γ decayto the first excited state in S. This gives a 95 % uppervalue for the number of γ rays of 2 . γ intensities from Ref. [13], this gives a 95 % confidenceupper limit of the Γ γ / Γ p ratio of 0 . et al . [10] andAlmaraz-Calderon et al . [14] estimated for a 0 + levelat 5217 . γ / Γ p ≥ . × − and Γ γ / Γ p =0 . × − , respectively. Almaraz-Calderon et al . [14]found a proton branching ratio of 1 . et al . [13] observed γ decaysof a level at 5218 . et al . andAlmaraz-Calderon et al . are made for a 0 + state, but itis not clear whether the level observed around 5220 keVis 0 + or 3 + , or if there are in fact two levels in this energyregion. The - keV level The level at 5847(4) keV has been observed to γ decayto the first excited state of S by a 3637 . γ ray[13]. There is no clear evidence of such a line in the γ spectrum and an upper limit on the Γ γ / Γ p ratio can thusbe found as described for the 5227-keV level. The two de-tectors without backing are again excluded. The protonsfeeding the level are found to have energies in the inter-vals [2220 , , S peak at 5847 keV is 24 ±
5. Thenumber of γ rays in a 50-keV interval around 3638 keVis (2 − f f = 0 . γ rays of 2 . γ / Γ p ratio of 9.Almaraz-Calderon et al . [14] do not observe any signifi-cant proton branch from this level in their Si( He , n ) Sexperiment. This does not agree with our result of a pro-ton branching ratio of at least 0 . + state and estimate that: Γ γ / Γ p = 15 .
7, in contradiction to our upper value of 9 (95 % C.L.).
IV. SUMMARY
The levels below 6 MeV in S have been studied bythe β p - and βpγ -decay of Ar.The γ decay of the second excited state of S to theground state has been observed for the first time in thedecay of Ar. The relative intensities of the γ lines corre-sponding to this decay and the decay to the first excitedstate have been found to be 0 . γ decay of the astrophysically interesting level at4689 . Ar.We present a new analysis method that provides exper-imental limits on the ratio between the proton and γ par-tial widths of resonances in S. The upper limit of theΓ p / Γ γ ratio has been found for the level at 4689 . .
26 (95 % C.L.), and upper limits of the Γ γ / Γ p ra-tio of 0 . V. ACKNOWLEDGEMENT
This work was supported by the European UnionSeventh Framework through ENSAR (Contract No.262010). This work was partly supported by the Span-ish Funding Agency under Projects No. FPA2009-07387,No. FPA2010-17142, and No. AIC-D-2011-0684, by theFrench ANR (Contract No. ANR-06-BLAN-0320), andby R´egion Aquitaine. A.S. acknowledges support fromthe Jenny and Antti Wihuri Foundation. [1] J. Jos´e et al. , Astrophys. J. Suppl. Ser. , 204 (2010).[2] J. L. Fisker et al. ,Astrophys. J. Suppl. Ser. , 261 (2008).[3] J. L. Fisker et al. , Astrophys. J. , L61 (2004).[4] S. Amari et al. , Astrophys. J. , 1065 (2001).[5] J. Jos´e et al. , Astrophys. J. , 414 (2004).[6] C. Iliadis et al. ,Astrophys. J. Suppl. Ser. , 105 (2002).[7] M. Wang et al. , Chinese Phys. C , 1603 (2012).[8] C. Iliadis et al. ,Astrophys. J. Suppl. Ser. , 151 (2001).[9] D. W. Bardayan et al. , Phys. Rev. C , 045803 (2007).[10] K. Setoodehnia et al. , Phys. Rev. C , 022801 (2010).[11] K. Setoodehnia et al. , Phys. Rev. C , 018803 (2011).[12] K. Setoodehnia et al. , arXiv:1210.1194 (2012).[13] G. Lotay et al. , Phys. Rev. C , 042801 (2012).[14] S. Almaraz-Calderon et al. ,Phys. Rev. C , 065805 (2012).[15] M. S. Basunia, Nucl. Data Sheets , 2331 (2010). [16] H. O. U. Fynbo et al. , Nucl. Phys. A , 38 (2000).[17] L. Penescu et al. , Rev. Sci. Instr. , 02A906 (2010).[18] E. Kugler, Hyperfine Interactions , 23 (2000).[19] I. Matea et al. ,Nucl. Instrum. Methods A , 576 (2009).[20] N. Warr et al. , Eur. Phys. J. A , 40 (2013).[21] J. Chen and B. Singh,Nuclear Data Sheets , 1393 (2011).[22] D. C. Radford,Nucl. Instrum. Methods A , 297 (1995).[23] L. Axelsson et al. , Nuclear Physics A , 475 (1998).[24] E. Kuhlmann et al. , Nucl. Phys. A , 82 (1973).[25] J. P. Ramos et al. , “Intense 31-35Ar beams producedwith nano structured CaO target at ISOLDE,”(unpublished).[26] G. J. Feldman and R. D. Cousins,Phys. Rev. D57