Precision study of ground state capture in the 14N(p,gamma)15O reaction
M. Marta, A. Formicola, Gy. Gyurky, D. Bemmerer, C. Broggini, A. Caciolli, P. Corvisiero, H. Costantini, Z. Elekes, Zs. Fulop, G. Gervino, A. Guglielmetti, C. Gustavino, G. Imbriani, M. Junker, R. Kunz, A. Lemut, B. Limata, C. Mazzocchi, R. Menegazzo, P. Prati, V. Roca, C. Rolfs, M. Romano, C. Rossi Alvarez, E. Somorjai, O. Straniero, F. Strieder, F. Terrasi, H.P. Trautvetter, A. Vomiero
aa r X i v : . [ nu c l - e x ] J u l as accepted by Phys Rev C rapid communication Precision study of ground state capture in the N(p, γ ) O reaction
M. Marta, A. Formicola, Gy. Gy¨urky, D. Bemmerer, C. Broggini, A. Caciolli,
4, 5
P. Corvisiero, H. Costantini, Z. Elekes, Zs. F¨ul¨op, G. Gervino, A. Guglielmetti, C. Gustavino, G. Imbriani, M. Junker, R. Kunz, A. Lemut, B. Limata, C. Mazzocchi, R. Menegazzo, P. Prati, V. Roca, C. Rolfs, M. Romano, C. RossiAlvarez, E. Somorjai, O. Straniero, F. Strieder, F. Terrasi, H.P. Trautvetter, and A. Vomiero (The LUNA Collaboration) Forschungszentrum Dresden-Rossendorf, Bautzner Landstr. 128, 01328 Dresden, Germany INFN, Laboratori Nazionali del Gran Sasso (LNGS), Assergi (AQ), Italy Institute of Nuclear Research (ATOMKI), Debrecen, Hungary Istituto Nazionale di Fisica Nucleare (INFN), Sezione di Padova, via Marzolo 8, 35131 Padova, Italy Dipartimento di Fisica, Universit`a di Padova, Italy Universit`a di Genova and INFN Sezione di Genova, Genova, Italy Dipartimento di Fisica Sperimentale, Universit`a di Torino and INFN Sezione di Torino, Torino, Italy Istituto di Fisica Generale Applicata, Universit`a di Milano and INFN Sezione di Milano, Italy Dipartimento di Scienze Fisiche, Universit`a di Napoli ”Federico II”, and INFN Sezione di Napoli, Napoli, Italy Institut f¨ur Experimentalphysik III, Ruhr-Universit¨at Bochum, Bochum, Germany Osservatorio Astronomico di Collurania, Teramo, and INFN Sezione di Napoli, Napoli, Italy Seconda Universit`a di Napoli, Caserta, and INFN Sezione di Napoli, Napoli, Italy INFN, Laboratori Nazionali di Legnaro, Legnaro, Italy (Dated: October 8, 2018)The rate of the hydrogen-burning carbon-nitrogen-oxygen (CNO) cycle is controlled by the slowestprocess, N(p, γ ) O, which proceeds by capture to the ground and several excited states in O.Previous extrapolations for the ground state contribution disagreed by a factor 2, corresponding to15% uncertainty in the total astrophysical S-factor. At the Laboratory for Underground NuclearAstrophysics (LUNA) 400 kV accelerator placed deep underground in the Gran Sasso facility in Italy,a new experiment on ground state capture has been carried out at 317.8, 334.4, and 353.3 keV center-of-mass energy. Systematic corrections have been reduced considerably with respect to previousstudies by using a Clover detector and by adopting a relative analysis. The previous discrepancyhas been resolved, and ground state capture no longer dominates the uncertainty of the total S-factor.
PACS numbers: 25.40.Ep, 25.40.Lw, 26.20.Cd, 26.65.+t
Recent data on the abundance of the elements carbon,nitrogen, and oxygen (CNO) in the solar atmosphere [1]lead to a contradiction between solar model predictionsand measurements for several helioseismological quanti-ties [2]. In the present precision era, this puzzle repre-sents the foremost problem of the standard solar model[2] since the resolution of the solar neutrino puzzle [3].In order to address this point, it has been suggested todetermine the CNO abundances in the solar center fromneutrino data [4]. Neutrinos emitted in solar CNO cycleburning are expected to lead to about 1000 events/yearboth in the Borexino detector [5] and in the proposedSNO+ detector [6]. A correct interpretation of this ex-pected data, based on the known solar core temperatureand known neutrino properties [4], requires the rate ofthe CNO cycle to be known with systematical uncertaintymatching these statistics.The rate of the CNO cycle is controlled [7] by the N(p, γ ) O reaction. Its cross section σ ( E ), parame- terized as the astrophysical S-factor S ( E ) = σE exp h . / √ E i , (1)has been extensively studied in the past [8, and referencestherein]. Recently, it has been shown that capture to theground state in O (fig. 1), previously [8] believed to ac-count for half of the S-factor extrapolated to zero energy S tot (0), is strongly suppressed [9, 10, 11, 12, 13, 14, 15].This finding is independently supported by a reductionin the γ -width of the subthreshold state at 6792 keV in O seen in Doppler shift attenuation [9] and Coulombexcitation [12] works, and by fits [10, 11, 13, 14, 15] inthe R-matrix framework (table I). The resulting 50% re-duction in the total cross section has subsequently beendirectly observed at an energy as low as E ≈
70 keV [16]. E p denotes the beam energy in the laboratory system, and E the effective energy in the center of mass system in keV. S i (0) denotes the S-factor, extrapolated to zero energy, for cap-ture to the state at i keV in O. S GS (0) and S tot (0) refer toground state capture and to the total S-factor, respectively. TABLE I: Measured quantities used to obtain an extrapolated S GS (0) [keV barn] in recent studies.Group Quantity used [taken from] S GS (0)TUNL [9] γ -width [9] 0.12–0.45Brussels [10] Cross section [8] 0 . +0 . − . Texas A&M [11] ANC [11], cross section [8] 0.15 ± a ± ± a Ref. [8] data have been corrected [13] for summing-in.
For the Gamow peak of the Sun ( E ≈
27 keV), how-ever, extrapolations remain indispensable. For the dom-inant contribution to S tot (0), i.e. capture to the stateat 6792 keV, recent experimental data and R-matrix fitsare consistent [14, 15]. For capture to the ground state,recent experimental data ( E ≈ S GS (0) values [13, 14] disagree sig-nificantly (table I). This discrepancy has 15% impacton S tot (0), limiting its precision. In addition to differ-ently treating previous data [8] in the fit, Refs. [13, 14]had employed large germanium detectors in close geome-try, enhancing the detection efficiency but incurring truecoincidence summing-in corrections of 100-250% for theground state data, which, in turn, lead to considerablesystematic uncertainty.The aim of the present work is to address the conflict-ing extrapolations [13, 14] with a precision cross sectionmeasurement. In order to minimize the uncertainties,the analysis is limited to the ratio of the cross sectionsfor capture to the ground state and to the 6792 keV state.An energy range above the 259 keV resonance, where thefits for ground state capture pass through a sensitive min-imum [10], has been selected [17]. A second sensitive en-ergy region lies below the 259 keV resonance. Since thecross section is a factor 100 lower there, the latter ener-gies were not probed in the present work. The experimentwas performed at the Laboratory for Underground Nu-clear Astrophysics (LUNA) at the Gran Sasso NationalLaboratory (Italy), which has ultra-low γ -ray laboratorybackground [18]. A Clover detector was used, reducingthe summing-in correction by a factor 30 (table II).The H + beam of E p = 359, 380, and 399 keV and 0.25-0.45 mA intensity from the LUNA2 400 kV accelerator[19] impinged on a sputtered TiN target, with 55 keVthickness measured on the E = 259 keV resonance. The γ -rays from the reaction to be studied were detected ina Eurisys Clover-BGO detection system [20]. The frontend of the Clover crystals was positioned at 9.5 cm dis-tance from the target, at an angle of 55 ◦ with respect tothe beam axis. The output signal from each of the fourClover segments was split into two branches; of these + + - + + + +
0 1/2 -14
N + p 7297
FIG. 1: Energy levels of O, in keV [15, 21]. branches, one branch was recorded separately, and thefour spectra were summed in the offline analysis (sin-gles mode). The second branches of the four signalswere added online in an analog summing unit (addbackmode). For experiments off the 259 keV resonance, theaddback mode data were recorded in anticoincidence withthe BGO anti-Compton shield.The γ -ray detection efficiency was obtained using Csand Co radioactive sources calibrated to 1.5% and0.75%, respectively. The efficiency curve was extendedto high energy based on spectra recorded at the 259 keVresonance, using the known 1:1 γ -ray cascades for the ex-cited states at 6172 and 6792 keV. The γ -rays from thedecay of this 1/2 + resonance are isotropic, and their an-gular correlations are well known [22]. The calculatedsumming-out correction in addback mode is 2.9%, withan assumed relative uncertainty of 20%, consistent witha GEANT4 [26] simulation showing (4.5 ± ± ± ± ± ± ± γ -ray from the decay of the6792 keV level (fig. 2, middle column) therefore contains13-55% on-resonance capture, and it was rescaled withthe on/off-resonance ratio obtained from the primary γ -rays (fig. 2, left column). Subsequently, the cross sectionratio R GS / ( E ) = σ GS ( E ) σ ( E ) (2) E =353.3 keV E =334.4 keV E =317.8 keV E =259 keVLaboratorybackgroundCapture to the 6792 keV state Decay of the 6792 keV state Capture to the ground state E γ [keV] C oun t s / k e V hou r FIG. 2: (color online) Solid red (dashed green) line: γ -ray spectra for addback (singles) mode. First three rows: off-resonancedata. Fourth row: laboratory background, negligible at high γ -energy. Fifth row: data at the E = 259 keV resonance. with σ GS ( E ) and σ ( E ) the cross sections for cap-ture to the ground state and to the 6792 keV state in O, respectively, was calculated for each bombardingenergy (table II). The addback and singles mode datafor R GS / were found to be in agreement. Because oftheir lower statistical uncertainty, the addback data wereadopted for the further analysis.The systematic uncertainty for R GS / (table II) de-pends on (1) the summing-in correction for the groundstate γ -ray (up to 4.6% and 0.9% effect on R GS / forthe addback and singles mode, respectively, taking intoaccount the calculated [7] angular correlation), and (2)the slope of the detection efficiency curve over the en-ergy range E γ = 6792-7650 keV (known to 0.8%). Forthe cascade 6792 keV γ -ray, (3) the anticoincidence effi-ciency (1.2% effect), and (4) the summing-out correction(0.6% effect) contribute to the systematic uncertainty for R GS / . The effects of e.g. target composition and pro-file, stopping power, beam intensity, and absolute γ -ray TABLE II: Cross section ratio R GS / ( E ) and relative un-certainty. The size of the summing-in correction is also given. E [keV] mode R GS / ( E ) stat. syst. Summing-in[10 − ] uncertainty correction317.8 ± ± ± detection efficiency cancel out in the relative experiment.The effective energy E was determined from the centroidsof the γ -lines for capture to the ground state and to the6792 keV state and leads to 2.4% uncertainty.The absolute cross section for the ground state transi-tion obtained from the present data was determined bythe ratios given in table II normalized with the weighted S G S ( E ) [ k e V ba r n ] E [keV] FIG. 3: S-factor for capture to the ground state. Full tri-angles: present data. Full squares: Ref. [8]. Line: Presentbest R-matrix fit. Data from [13, 15] (empty circles) and [14](empty squares) are shown for comparison but were not usedin the fit; their error bars have been omitted for clarity. average (uncertainty 7.5%) of the S-factor results for the6792 keV transition given in Refs. [8, 14, 15]. From sucha combined fit an ANC of 4.8 fm − / was obtained for the6792 keV state, in good agreement with Refs. [11, 23] andresulting in γ = 0.4 MeV for the reduced width of thesubthreshold state. For the strength of the 259 keV res-onance, 13.1 meV (weighted average of [14, 15, 16, 21])was adopted, for its proton width 0.99 keV [13], and forthe ground state branching, 1.63% (weighted average of[14, 15] and the present work) was used. For all otherparameters, the previous values were taken without anychange [13]: ANC for ground state capture: 7.3 fm − / . E = 0.987 MeV resonance: Γ γ = 26 meV, Γ p = 3 keV. E = 2.187 MeV resonance: Γ γ = 4.4 eV, Γ p = 0.27 MeV.Background pole at E = 6 MeV, Γ p = 8 MeV. In orderto limit the systematic uncertainty due to summing-in toless than the statistical error, only data with less than50% summing-in correction were used for the R-matrixanalysis: i.e. [8] (corrected [13] for summing-in) andthe present data. The interference pattern around the259 keV resonance is fixed by the results of [13, 14, 15],and the interaction radius was set to 5.5 fm [13]. The bestfit (fig. 3) varying only the γ -widths of the subthresholdstate and of the background pole results in S GS (0) =0.20 keV barn with a γ -width Γ γ = 0.9 ± S GS (0) [13] is adopted here, giving S GS (0) = 0.20 ± S tot (0), instead of the previous15%, based on a data set which is nearly free fromsumming problems. On the basis of the present result, S tot (0) = 1.57 ± S (0) = 0.09 ± S tot (0) precisionwould require a fresh study of this contribution. In themeantime, the present ground state data pave the wayfor a measurement of the solar central metallicity [4].The use of the R-matrix code [10] written by P. De-scouvemont (ULB Brussels) is gratefully acknowledged.One of us (H.P.T.) thanks R.E. Azuma, E. Simpson, andA. Champagne for fruitful discussions. — The presentwork has been supported by INFN and in part by theEU (ILIAS-TA RII3-CT-2004-506222), OTKA (T49245and K68801), and DFG (Ro 429/41). [1] M. Asplund, N. Grevesse, and A. Jacques Sauval,Nucl. Phys. A , 1 (2006).[2] J. N. Bahcall, A. M. Serenelli, and S. Basu, Astro-phys. J. Suppl. Ser. , 400 (2006).[3] Q. R. Ahmad et al., Phys. Rev. Lett. , 011301 (2002).[4] W. Haxton, arXiV:0710.2295 (2007).[5] C. Arpesella et al., Phys. Lett. B , 101 (2008).[6] M. C. Chen, Nucl. Phys. B (Proc. Suppl.) , 65 (2005).[7] C. Iliadis, Nuclear Physics of Stars (Wiley-VCH, 2007).[8] U. Schr¨oder et al., Nucl. Phys. A , 240 (1987).[9] P. Bertone et al., Phys. Rev. Lett. , 152501 (2001).[10] C. Angulo and P. Descouvemont, Nucl. Phys. A , 755(2001).[11] A. Mukhamedzhanov et al., Phys. Rev. C , 065804(2003).[12] K. Yamada et al., Phys. Lett. B , 265 (2004).[13] A. Formicola et al., Phys. Lett. B , 61 (2004).[14] R. C. Runkle et al., Phys. Rev. Lett. , 082503 (2005).[15] G. Imbriani et al., Eur. Phys. J. A , 455 (2005).[16] A. Lemut et al., Phys. Lett. B , 483 (2006).[17] H.-P. Trautvetter et al., J. Phys. G , 014019 (2008).[18] D. Bemmerer et al., Eur. Phys. J. A , 313 (2005).[19] A. Formicola et al., Nucl. Inst. Meth. A , 609 (2003).[20] Z. Elekes et al., Nucl. Inst. Meth. A , 580 (2003).[21] F. Ajzenberg-Selove, Nucl. Phys. A , 1 (1991).[22] B. Povh and D. F. Hebbard, Phys. Rev. , 608 (1959).[23] P. F. Bertone et al., Phys. Rev. C , 055804 (2002).[24] D. Sch¨urmann et al., Phys. Rev. C , 055803(2008).[25] S. O. Nelson et al., Phys. Rev. C , 065804 (2003).[26] S. Agostinelli et al., Nucl. Inst. Meth. A506