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Low energy measurement of the 7Be(p,γ)8B cross section F. Hammache1,∗), G. Bogaert1,∗∗), P. Aguer2), C. Angulo3), S. Barhoumi5), L. Brillard4), J.F. Chemin2), G. Claverie2), A. Coc1), M. Hussonnois4), M. Jacotin1), J. Kiener1), A. Lefebvre1), C. Le Naour4), S. Ouichaoui5), J.N. Scheurer2), V. Tatischeff1), J.P. Thibaud1), E. Virassamyna¨ıken2) 1) CSNSM, IN2P3-CNRS, 91405 Orsay et Université de Paris-Sud, France 2) CENBG, IN2P3-CNRS, et Université de Bordeaux I, 33175 Gradignan, France 3) Centre de Recherches du Cyclotron, UCL, Chemin du Cyclotron 2, 1348 Louvain la Neuve, Belgium 4) IPN,IN2P3-CNRS et Université de Paris-Sud, 91406 Orsay, France 5) Institut de Physique, USTHB, B.P. 32, El-Alia, Bab Ezzouar, Algiers, Algeria toavoidanycontaminationinbothαandβ+ coincidence Wehavemeasured thecross section of the7Be(p,γ)8Bre- spectra arising from the channel 7Li(p,γ )8Be∗(2α). In 1 1 00 aaspcrteaicodtnrioafaoocrftiβEv+ecma7nB=deα1t8ap5rag.8rettkice(lV1e3s,2f1r3om4mC.7i8)Bk.eaVSnindagn8ldeBe1a∗1n1dd.e7ccaokyien,Vcriedusepsnienccge- t8hBi(sβ+re)a8cBtieo∗n(2αth)eanαdtdheecaβy+odfet8eBcteo∗rciosutldhenostaemffieciaesntilny 2 discriminate β+ particles of interest from electron pairs tively,were measured using a large acceptance spectrometer. produced in the target assembly by γ rays (E =14.8 n The zero energy S factor inferred from these data is 18.5 ± 1 γ1 a 2.4 eV b and a weighted mean value of 18.8±1.7 eV b (theo- MeV). J For the delayed detection purpose, the beam passed retical uncertaintyincluded)isdeducedwhencombiningthis 1 through an electrostatic deflector which was alternately valuewith our previous results at higher energies. 3 switched on and off for time periods of 1.5 s. The PACS numbers : 25.40.LW, 27.20.+n, 26.65.+t prompt events from 9Be(p,α)6Li and 9Be(p,d)8Be were 1 alsorecordedandusedlaterforenergycalibrationofthe v α detectors and normalization purpose (see below). 4 Recent experimental results on solar νe and atmo- The target was located near the solenoid center, per- 1 spheric ν neutrinos support neutrino oscillation scenar- µ 0 ios, in which the oscillation probability depends on the pendicular to the symmetry axis of the field. The target 1 backing of 0.1 mm ultra pure platinum and its holder neutrinomixinganglesandsquaredmassdifferences. For 0 allowed both efficient water cooling and large transmis- ν -ν oscillation, the determination of these fundamen- 1 e x sion for β+ particles. The beam spot at the target posi- tal quantities needs accurate solar modeling and nuclear 0 tionwasmadevisiblebyusinganalumina(Al O )target / cross sections for the reactions operating in the solar 2 3 x which could be moved to the exact position of the tar- core [1–3]. In this respect, the most important nuclear e physicsparameteristhe Sfactorofthe7Be(p,γ)8Breac- get. An optical system provided a magnified image of - l tion which gives rise to the crucial 8B neutrinos [4]. In the beam spot to measure its position and size on the uc a previous work [5], we have measured the 7Be(p,γ)8B target. They weresystematicallydetermined(size about 10 mm2) before and after each run. n reaction cross section for Ec.m. = 0.35 - 1.4 MeV us- : ing radioactive 7Be targets. In this Letter, we report on In order to prevent carbon buildup on the target, a v copperplatecooledwithliquidnitrogenwasplacedinthe new direct measurements of this cross section at center i X of mass energies below 200 keV, where extrapolation to target vicinity. In addition, cryogenic, turbomolecular and ionic pumps were used to keep the vacuum below 5 r solar energies (E = 18 keV) is expected to be almost a cm × 10−7 mbar during the whole experiment. free of theoreticaluncertainties [6], which is not the case Typical beam currents of 10-40µA on the target were for measurements at higher energies. used. To suppress secondary electron escape, the tar- The electrostatic accelerator PAPAP at Orsay sup- get was biased at a positive 300 V. As a consistency plied intense proton beams of well calibrated energies [7]. We useda highlyradioactive7Betarget(131.7mCi) check,currentswerealsomeasuredintheinsulatedcham- ber where the beam was periodically deflected, at the prepared as in ref. [8,9] additionally containing approx- imately 3.1016 atoms of 9Be. β+ and α particles from SOLENOentrancecollimatorandattheαdetectortube 8B(β+)8Be∗(2α) decays were detected at forward and (see below) where negligible currents were observed. All the currents were integrated, digitized, recorded cycle- backwardanglesrespectively. Weusedthesolenoidalsu- by-cycleandanalyzedoff-line. Verygoodagreementwas perconductingmagnetSOLENO[10](3.2Tatthecenter, foundbetweenintegratedchargesforbeamontargetand 1.22mlong,32cmofinternaldiameter)inordertodetect bothαandβ+ particleswithhighefficiency (11.5%and beamofftarget,andtheoveralluncertaintyonthetarget integrated charge was 2 %. 25% respectively) due to the focusing power of the field. Both singles and coincidence events between α and β+ β+particles(Emax=14MeV)weredetectedinasetof 6 successive cylindrical plastic scintillators (diameter 20 particles were recorded, the latter providing spectra free mmandthickness3,3,8,8,8and10mm)centeredonthe of backgroundevents even at low bombarding energies. Offbeamdetection(8Bperiod=0.77s)wasnecessary field axis and 22 cm away from the target. The number 1 and thickness of the plastic scintillators were optimized wasmadetoensurethatanullextrabackground(within from GEANT simulations [11] to discriminate MeV β+ statistical uncertainties) was introduced when the beam particles from the huge number of γ rays and photoelec- hit a pure platinum target. Backgroundsubtraction was tronsproducedinthetargetbackingbytheE =478keV performedbysimplynormalizingthecorrespondingspec- γ radiation from 7Be decay while still measuring β+ ener- trum to counting time. For comparison, the coincidence gieswithareasonableprecision. Thisdiscriminationwas delayedαparticlespectrummeasuredinthesamerunsis effective when at least two β detectors were required to showninfigure1.b. Itcanbeseeninfigure1thatthelow fire. energy (< 1 MeV) component in the singles spectrum, α particles (from 8Be∗ decay) with energies below 3.5 correspondingtopileupeventsduetophotoelectronscre- MeV andemissionangles betweenapproximately95 and ated by the 478 keV γ rays, has completely vanished in 150 degrees with respect to the beam direction were de- the coincidence spectrum. The solid curve in figure 1.b flectedtowardsthesolenoidaxisanddetectedinanarray is obtained from a least squares fit to this background of 6 × 4 Si detectors (22 mm × 45 mm × 0.1 mm). The free coincidence spectrum. We see in figure 1.a that the detectorsweremountedincylindricalgeometry(internal same curve also provides a reasonable fit to singles data diameter of 4 cm) aligned on the solenoid axis. Depend- (after normalization to counting), as expected from an ing on energy and emission angle, α particles were de- unbiased backgroundsubtraction process. tected at distances ranging from 18 to 36.5 cm from the The α detection efficiency in the 1.00-3.36 MeV en- target. Backscattered protons were deflected along dif- ergyrangewasdeterminedwiththesamedetectionsetup ferent paths and were not able to reach the α detectors. fromananalysisofthereaction7Li(p,γ )8Be∗ performed 1 The data were recorded event by event. They in- with an enriched 7Li target at E = 160 keV. As ex- p cluded the measurements of α and β+ energies, num- plained above, the 14.8 MeV γ rays create e+-e− pairs 1 ber and identification of detectors fired and the time of in the target backing which were detected in the plastic flight difference between α and β+ particles for coinci- scintillator counter, while 8Be∗ decay into two α parti- dence events. In the data analysis, events where more cles detected in the silicon array (the same α’s as in the than one α detector or less than two β+ detectors fired channel 8B(β+)8Be∗). The α detection efficiency was were rejected. A pulse generator was used for dead time deducedfromthe number ofcountsinthe plastic scintil- measurements. lator taken in singles and in coincidence with the silicon detector. The singles γ ray yield was taken to be 0.680 1 Counts 678000 a single s pEepc=tr2u1m7 keV a) Counts 111468 a coincidenc Ee ps=pe2c1t7r ukmeV b) ±suclain0t.ti0oil4nla3st[oc1ro2nf]rfitorimmmeebsdottthhheaγtt0otpaaanlidrcoγdu1entctehscataniorninseilnse.gffiGicniEetnAhcNeieTpslawssiemtrice- 50 12 the same, within less than 1%, for γ0 and γ1. The angu- 40 10 lar correlation between e+-e− pairs and α particles was 8 30 alsocalculatedandfoundnegligibleforthes-waveproton 6 20 4 capture at this low bombarding energy. 10 2 Akinematicscorrectionof9.6%wasappliedtothe ex- 0 0 1 2 3 4 5 0 0 1 2 3 4 5 perimentalefficiency value to take into accountthe 8Be∗ Ea (MeV) Ea (MeV) inflight-decayinthe7Li(p,γ1)8Be∗ reaction. Finally,the FIG. 1. a). Energy spectrum of singles delayed α parti- detection efficiency was ǫ = 0.115 ± 0.008 in the 1.00 - α cles. b). Energy spectrum of delayed α particles detected in 3.36 MeV energy range, in fair agreement with GEANT coincidence with delayed β particles. simulations (12 %). The7Be totalactivityatthe beginningandatthe end of the run at 217 keV, the target area (0.47 ± 0.02 cm2) Cross section measurements were performed at three and the 7Be activity profile were accurately determined protonenergies,217keV, 160keV and130 keV.The ab- with the same instruments and methods used in the ex- solute value of the cross section at the proton energy of perimentdescribedinref.[5]. Afterfittingthe7Bedecay 217 keV was obtained counting singles delayed α parti- function to the measurements, we found an initial total cles in the range from 1 MeV to 3.36 MeV. Figure 1.a. activity of 131.7 ± 2.4 mCi. No loss of activity due to shows the corresponding spectrum, obtained by adding beamimpactwasobservedduringtherun. The7Beareal togetherthe individualαspectrameasuredinthe silicon densityoverthebeamspotwasfinallydeterminedrunby detectors. run(9%uncertainty)byaveragingtheresultsofthe 478 The calibration of the silicon detectors was performed keV γ ray scan over the beam spot dimensions and nor- using the three well defined peaks observed in the sin- malizingthem to the totalactivity per unitsurface area. gles prompt spectra from 9Be(p,d)8Be and 9Be(p,α)6Li A value of σ = 16.7 ± 2.1 nb at the incident pro- reactions. Data shown in figure 1.a were obtained after ton energy of 217 keV was deduced (see the formula 3 subtraction of the background contribution which was in ref. [13]). This value takes into account a 1% correc- determined in a series of measurements of several days tionduetothe8Bbackscatteringonplatinumatomsand withthebeamoffandtheactivetargetinplace. Acheck escape out of the target [14]. This correction was calcu- 2 latedusingaTRIM[15]simulationwithtargetthickness perscripts 7 and 9 label the reactions 7Be(p,γ)8B and and composition determined from consistent RBS, (d,p) 9Be(p,α)6Li, respectively. R(E )7,9 is the coincidence i and PIXE analysis measurements performed during the yield normalized to the α yield from the 9Be(p,α)6Li re- courseofthe experiment. At the beginning of the exper- action,S9istheastrophysicalSfactorofthe9Be(p,α)6Li iment, the targetwas found to contain mainly carbon (9 reaction at the corresponding c.m. effective energy. K µg/cm2), oxygen (7.6 µg/cm2) and less than 4 µg/cm2 is a constant accounting for the changes in dead times, of calcium and other lighter elements, corresponding to in effective time parameters (see parameter β in formula a thickness of 9.6 ± 1.0 keV for protons of 217 keV. 4 of ref. [13]) and in angular distributions of alphas in Thisthicknessleadstoaneffectiveenergyof212.4keV 9Be(p,α)6Li with the bombarding energies. These 3 cor- (E =185.8keV)andanSfactorvalueof17.2±2.1eV rections were found to be very small (less than a few cm b. Thequoteduncertaintyincludesthe6.3%uncertainty percent). The exponential term, in which ∆t is the 1i in the γ branching ratio [12] of 7Li(p,γ)8Be∗. time difference between experimenti and 1, accounts for 1 The cross sections at E = 130 keV and 160 keV were the decrease in the 7Be target activity with time. p determined using α-β coincidence measurements only, IncalculatingR,theαyieldfrom9Be(p,α)6Liresulted because of the decrease of the signal over background from a least-squares analysis of the prompt singles spec- ratioobservedin singlesspectra with loweringbombard- tra where very well defined α peaks show-up. S factors ing energies. The corresponding coincidence α energy andangulardistributionsconcerningthe9Be(p,α)6Lire- spectra are shown in figure 2 together with time differ- action were taken from the literature [12]. ence spectra between α and β+ particles. The 3 peaks It must be stressed that the normalization to the α in the time spectra correspond to 3 classes of trajecto- yield from 9Be(p,α)6Li eliminates effects due to target ries where α particles can spiral 1,2 or 3 times in the non uniformity, beam position variation and loss of ac- magnetic field before reaching the detectors. The rare tivity of the target due to beam impact as long as the counts found betweenthe peaks and at∆t = 200 ns (i.e. ratioof atomic densities of9Be to 7Be remains constant. nulltimeofflightdifference)infigure2.barebackground This is expected since 9Be was introducedin the 7Be so- events(mostprobablycosmicrays)eliminatedinthe en- lution before electrodeposition of the final target. It was ergy spectra by gating on the three time peaks. verified experimentally through a comparison of 7Be γ ray scan with a 9Be scan using (d,p) reaction analysis Counts 111468 Ep=160 keV a) Counts 4500 ETOp=F1(6ab0 k1e)Vb) wacittuhaallymoicbrsoebrveeadma.ftAerntohnenruenglsigaitblEepl=os1s6o0fkaecVtivaintydw13a0s 12 30 keV,becauseofasignificantincreaseofsputteringeffects 10 8 with decreasing energy. 20 6 For the calculations of the protonenergy losses at 160 4 10 2 and 130 keV, we took into account the loss of target Counts 105 Ep=130 keV a) Counts 34000 Ep=130 keVb) tmhaete9rBiae(lpb,αy)t6hLei rmeoanctitioonri.nWg oefetshtiem9aBteedctohneteunntctehrtraoiungthy 10 TOF(ab 1) on the effective energy to be 2.5 keV, which induces an 20 uncertainty of 2% on the ratio S9(E9 )/S9(E9 ). cm2,3 cm1 5 10 Taking into account a 1% loss of 8B nuclei due to the 8B backscattering [14] we deduced the astrophysical S 0 0 1 2 3 4 5 0 0 100 200 300 factor values of S(134.7 keV) = 19.5 ± 3.1 eV b and Ea(MeV) D tab (ns) S(111.7 keV) = 15.8 ± 2.7 eV b. Final uncertainties FIG. 2. a). Energy spectra obtained at 160 keV and 130 werecalculatedbyquadraticsummationofallindividual keV for delayed α particles detected in coincidence with de- uncertainties related above. layed β particles. b). Corresponding spectra for time differ- Results for the astrophysicalS factor are shownin fig- ence between α and β+ particles obtained using the first of ure3. Extrapolationtozeroenergyusingthecalculations the six plastic scintillators. A null time of flight difference is of ref. [16] and the present low-energy data gives S(0) = arbitrarily at 200 ns dueto delays in theelectronics. 18.5 ± 2.4 eV b where the error bar is only experimental. A negligible dispersion of S(0) is found (0.2 eV b) when various calculated curves [16,18] of S(E) are fitted SfactorsatE =160keVandE =130keV,relativeto p p to the same data. This reflects the agreement between theonemeasuredatE =217keV,wereobtainedbynor- p models at low energy, since the interaction in that case malization to the α yield from the reaction 9Be(p,α)6Li takes place at very large 7Be-p distances and is mainly through the relation: governedby Coulomb physics. As a consequence the to- S7(Ec7m2,3) =KR(E2,3)7,9S9(Ec9m2,3)e−λ7Be(∆t1i) (1) tal uncertainty (experimental + theoretical) is finally ± S7(E7 ) R(E )7,9 S9(E9 ) 2.4 eV b. cm1 1 cm1 Using the calculation of ref. [16], our previous mea- where the subscripts 1, 2 and 3 label the runs at Ep= surements [5] lead to S(0)=19.1 ± 1.2 eV b [19], where 217 keV, 160 keV and 130 keV, respectively, and the su- 3 the error bar is experimental. As the experiment was [1] J.N. Bahcall et al.,Phys. Rev.D 58,096016-1 (1998). performed at higher energies, sophisticated nuclear cal- [2] A.S. Brun et al.,Astrophys.J. 506, 913 (1998). culations are required in that case to describe the shape [3] P. Morel et al., A.& A.350, 275 (1999). of S(E) which leads to a higher theoretical uncertainty [4] H. Schlattl, et al.,Phys. Rev.D 60, 60 (1999) on S(0). An S(0) dispersion of ± 2 eV b was found us- [5] F. Hammacheet al.,Phys.Rev.Lett. 80, 928 (1998) ing the available models [16,17] to fit the data. Adding [6] E. Adelberger et al.,Rev.Mod. Phys.70, 1280(1998). thisdispersion,consideredasareasonableestimateofthe [7] G. Bogaert et al.,Nucl. Instr. Meth. B89, 8 (1994). theoreticaluncertainty,totheexperimentalerrorbarand [8] F. Hammache, Thesis, (1999), http://www-csnsm.in2p3.fr/astronuc/ combiningquadraticallytheobtainedresultforS(0)with [9] M.Hussonois, (2000), that of the present low-energy result, we finally obtain a weighted mean value of S(0)= 18.8 ± 1.7 eV b (taking http://xxx.lpthe.jussieu.fr/abs/nucl-ex/0011014 a more conservative value of ±3 eV b for the theoretical [10] J.P. Shapira et al.,Nucl. Instr.Meth. 224, 337 (1984). uncertainty would lead to a very similar result of 18.7± [11] R. Brun et al. GEANT3.16 Users Guide, CERN Program Library Office (1993) 1.9 eV b.). [12] D. Zahnow et al.,Z. Phys. A351, 229 (1995). D. b)35 Zahnow et al.,Z. Phys.A359, 211 (1997). S (eV-30 PRRreeeff..s [e[55n]]t [[1134]] BL..WW.eFisislmipapnoneet aetl.,aNl.,uPclh.yPs.hyRse.vA. L63et0t,.65708,(411929(81)9.83). 25 Backscattered 8B nucleiwhich decay outside the target are lost for delayeddetection inducingsmaller measured 20 cross sections. For heavy elements target backing, the 15 yield of the8B loss dependsstrongly on thebeam energy and on thetarget composition and thickness. In 10 this experiment at low energy,the target deposit was 5 thick enough to stop most of backscattered 8B nuclei 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 resulting in very small 8B loss. In thecase of the E (MeV) c.m. experiment of ref. [5], thecorrections were determined FIG.3. MeasuredSfactorsfromthepresentworkandfrom in thesame manner, takingadvantage of precise reference [5] after backscattering correction. [5]). Error bars knowledge of target composition dueto careful RBS, representrandomuncertainties. Thecurvethroughthedata, (d,p) and PIXEanalysis measurements performed givenforillustrativepurposes,isafittothethreesetsofdata, during thecourse of theexperiment. Fordetails see ref. assumingindependenterrorsandusingthecalculation ofref. [8]. [16]. [15] J.F. Ziegler, J. P. Biersack U. Littmark et al., The Stopping and Range of Ions in Solids, Vol. 1 (Pergamon Press, New York,1985), and theSRIM96 program. These results are in good agreement with some of the [16] P. Descouvemont and D.Baye, Nucl.Phys. A567, 341 previous direct experiments [13,20,21], (see [22] for a (1994). commentontherecoilnucleiescapeinrefs.[13,20]). Con- [17] F.C. Barker, Nucl.Phys. A588, 693 (1995); A.Csoto, cordant results but with larger uncertainties have also Phys. Lett. B394, 247 (1994); K. Benacceur et al., J. been reported in recent studies of the inverse process Phys. G24, 1631 (1998) [23,24] and of transfer reactions [25]. [18] C.W. Johnson et al., Astrophys.J. 392, 320 (1992); The present result, which includes a total uncertainty F.M. Nuneset al., Nucl.Phys. A634, 527 (1998) significantly lower and better-founded than in higher- [19] S(0) = 19.1 ± 1.2 eV b is obtained when experimental energy measurements should help in clarifying the in- values are corrected for the 8B escape effect [14]. S(0) = terpretation of solar neutrino experiments. 18.5 ± 1.0 eV b was deduced from uncorrected datain J.J. Correia, R. Daniel, D. Linget, N. Karkour are reference [5] gratefullyacknowledgedforexperimentalsupport. Valu- [20] F. J. Vaughnet al.,Phys.Rev. C2, 1657 (1970). [21] M. Hass et al.,Phys. Lett. B 462 237 (1999). able discussions with M. R. Haxtonare greatlyacknowl- [22] In thesemeasurements,escape of recoil nucleiout ofthe edged. This work was supported in part by Region target was not corrected, and cannot be accurately Aquitaine. calculated since the detailed compositions of thetargets was not measured. Howeverthe correction is expected to be small (less than 5%) in view of thequoted target thicknesses and takinginto account of the fact that 8B escape is partly counterbalanced by that of 8Liin these measurements which rely on 7Li(d,p)8Linormalization. [23] T. Kikuchiet al.,European. Phys. J. A3 213 (1998). ∗ Present address : GSI mbH,Planckstr. 1, D-64291 [24] N. Iwasa et al.,Phys. Rev.Lett. 83, 2910 (1999). Darmstadt, Germany [25] A. Azhari et al.,Phys. Rev.Lett. 82, 3960 (1999). ∗∗ Permanent address : LPNHE,Ecole Polytechnique, 91128 Palaiseau, France. 4