Resonance strengths in the 14N(p,gamma)15O astrophysical key reaction measured with activation
Gy. Gyürky, Z. Halász, G.G. Kiss, T. Szücs, A. Csík, Zs. Török, R. Huszánk, M.G. Kohan, L. Wagner, Zs. Fülöp
aa r X i v : . [ nu c l - e x ] J u l Resonance strengths in the N(p, γ ) O astrophysical key reaction measured withactivation
Gy. Gy¨urky, ∗ Z. Hal´asz, G.G. Kiss, T. Sz¨ucs, A. Cs´ık, Zs. T¨or¨ok, R. Husz´ank, M.G. Kohan, L. Wagner,
3, 4, † and Zs. F¨ul¨op Institute for Nuclear Research (Atomki), H-4001 Debrecen, Hungary Department of Engineering Sciences and Mathematics,Lule˚a University of Technology, 97187 Lule˚a, Sweden Helmholtz-Zentrum Dresden-Rossendorf, Germany Technische Universit¨at Dresden, Germany (Dated: July 18, 2019)
Background
The N(p, γ ) O reaction plays a vital role in various astrophysical scenarios. Its reaction rate must be accuratelyknown in the present era of high precision astrophysics. The cross section of the reaction is often measured relative to alow energy resonance, the strength of which must therefore be determined precisely.
Purpose
The activation method, based on the measurement of O decay, has not been used in modern measurements of the N(p, γ ) O reaction. The aim of the present work is to provide strength data for two resonances in the N(p, γ ) Oreaction using the activation method. The obtained values are largely independent from previous data measured byin-beam gamma-spectroscopy and are free from some of their systematic uncertainties.
Method
Solid state TiN targets were irradiated with a proton beam provided by the Tandetron accelerator of Atomki using acyclic activation. The decay of the produced O isotopes was measured by detecting the 511 keV positron annihilation γ -rays. Results
The strength of the E p = 278 keV resonance was measured to be ωγ = (13.4 ± p = 1058 keVresonance ωγ = (442 ±
27) meV.
Conclusions
The obtained E p = 278 keV resonance strength is in fair agreement with the values recommended by two recentworks. On the other hand, the E p = 1058 keV resonance strength is about 20 % higher than the previous value. Thediscrepancy may be caused in part by a previously neglected finite target thickness correction. As only the low energyresonance is used as a normalization point for cross section measurements, the calculated astrophysical reaction rate ofthe N(p, γ ) O reaction and therefore the astrophysical consequences are not changed by the present results.
PACS numbers: 26.20.Cd,25.40.Lw
I. INTRODUCTION
Catalytic cycles of hydrogen burning represent an al-ternative way to the pp-chains for converting four pro-tons into one alpha particle in stellar interiors and forproviding thus the energy source of stars. The simplestcycle is the first CNO or Bethe-Weizs¨acker cycle [1] wherecarbon, nitrogen and oxygen isotopes are involved. TheCNO cycle is the dominant energy source of main se-quence stars more massive than about 1.3 solar massesbut it also plays an important role in various astrophys-ical scenarios including quiescent and explosive burningprocesses [2, 3, e.g.].In the 21 th century, astronomical observations as wellas astrophysical models are becoming more and more pre-cise. The insufficient knowledge of nuclear reaction ratesoften represent the largest uncertainty of stellar models.Increasing the precision of experimental nuclear cross sec-tions is thus needed in order to provide accurate reactionrates for the models. For solar models, for example, a ∗ Electronic address: [email protected] † Present address: National Superconducting Cyclotron Labora-tory, Michigan State University, East Lansing, USA precision well below 5 % is required for the N(p, γ ) Oreaction discussed in the present work [4].The slowest reaction of the CNO cycle is the radia-tive proton capture of N and therefore the rate of this N(p, γ ) O reaction determines the rate of the cycle andhence its efficiency and its contribution to the stellar en-ergy generation. Realizing its importance, many experi-ments have been devoted to the measurement of its crosssection (the full list of references can be found in [5] andthe three latest sets of results are published in [6–8]).Depending on the astrophysical site, the relevant tem-perature where the CNO cycle is active and important isbetween about 15 and 200 MK. This translates into as-trophysically relevant center-of-mass energy ranges (theGamow-window) of the N(p, γ ) O reaction between 20and 200 keV. Measured cross sections are available onlydown to 70 keV. Consequently, for lower temperature en-vironments (like for example our Sun with its 15.7 MKcore temperature) theoretical cross sections or extrapo-lation of the available data are necessary.At low energies the N(p, γ ) O reaction proceedsmostly through the direct capture mechanism with con-tribution from wide resonances. The total cross section isdominated by the capture to the E x = 6.79 MeV excitedstates in O but the capture to the ground state and tothe E x = 6.17 MeV excited state also contributes signifi-cantly. At higher energies, on the other hand, where crosssection data are available, transitions to other states aswell as narrow and wide resonances play important roles. A. The importance of the E p = 278 keV resonance The extrapolation of the cross section to astrophysicalenergies is typically carried out using the R-matrix ap-proach. For a reliable R-matrix extrapolation, high pre-cision experimental data in a wide energy range is neededfor all the relevant transitions and for the resonances aswell as for the direct capture.At E = 259 keV center-of-mass energy the N(p, γ ) Oreaction exhibits a strong narrow resonance. Its energy istoo high for any direct astrophysical relevance, however,it plays an important role in the experiments targetingthe N(p, γ ) O cross section measurement. In directkinematics this resonance is observed at E p = 278 keVproton energy and often serves as a normalization pointfor the measured non-resonant cross section data, i.e.the cross section is measured relative to the strength ofthis resonance. Therefore, the precision of this resonancestrength directly influences the precision of the cross sec-tion data at low energies.The available measured E p = 278 keV resonancestrength values are summarized in Table I. Based onseveral measurements, the recommended value of thestrength has an uncertainty of 4.6 %, as given by the lat-est compilation of solar fusion reactions [5]. In the paperof Daigle et al. [6] published after the above cited com-pilation, a new result was presented and the literaturedata were also critically re-analyzed. Their recommendedvalue is in agreement with that of [5] but its uncertaintyis reduced to 2.4 %. This uncertainty seems surprisinglylow considering on one hand the stopping power uncer-tainty which is common to almost all the experimentsand on the other hand the difficulty in characterizing theimplanted targets used by Daigle et al. [6].In the present work the E p = 278 keV resonancestrength is measured using an independent method, theactivation technique [9]. As an additional result, thestrength of the E p = 1058 keV resonance in N(p, γ ) Oreaction is also measured. This resonance plays no role inastrophysics, but it can also be used as a reference pointfor the N(p, γ ) O non-resonant cross section measure-ments and an R-matrix extrapolation of experimentaldata also requires the knowledge of the parameters ofthis resonance. Although this resonance is stronger thanthe E p = 278 keV one, its strength has been measured infewer experiments (see Table II) and the precision of thestrength recommended by Marta et al. is not better thanabout 5 %. B. The activation method for the study of the N(p, γ ) O reaction
The proton capture of N at the E p = 278 keV and E p = 1058 keV resonances leads to the formation of Oin excited states of E x = 7556 keV and E x = 8284 keV, re-spectively. These excited states decay to the O groundstate by the emission of prompt γ -radiation through sev-eral possible cascades. The detection of this γ -radiationhas been used in almost all the experiments to determinethe resonance strengths (see the entries in tables I andII labeled as ’prompt gamma’). For a precise resonancestrength measurement the γ -detection efficiency (up to8 MeV γ -energy), the angular distribution of the varioustransitions as well as the branching ratio of these transi-tions (including the weak ones) must be known precisely.All these factors introduce systematic uncertainties in theresonance strength determination.Since the reaction product of the N(p, γ ) O reac-tion is radioactive, the resonance strength can also bemeasured by activation. O decays by positron emis-sion to N with a half-life of 122.24 ± γ -radiation,however, the 511 keV γ -ray following the positron an-nihilation provides a possibility for the reaction strengthmeasurement with activation. This method is free fromsome uncertainties encumbering the prompt gamma ex-periments. The decay occurs isotropically, thus no angu-lar distribution needs to be measured. The γ -detectionefficiency must be known only at a single, low energypoint (511 keV) where it is measured more easily thanat several MeV’s. Since by the activation method thenumber of produced isotopes is measured, this techniqueprovides directly the total reaction cross section or res-onance strength (independent from the decay scheme ofthe exited levels) and therefore no uncertainty arises fromweak transitions.The activation method was used only by some veryfirst studies of the N(p, γ ) O reaction about 70 yearsago (see tables I and II) and these measurements did notlead to precise resonance strengths. In the present workthis method is used again to provide precise resonancestrength values which are largely independent from theones measured with prompt gamma detection. The nextsection provides details of the experimental procedurewhile the data analysis is presented in Sec. III. The finalresults, their comparison with available data and conclu-sions are given in Sec. IV.
II. EXPERIMENTAL PROCEDUREA. Target preparation and characterization
In many of the past experiments solid state titanium-nitride (TiN) targets proved to be an excellent choice tocarry out ion-beam induced reaction studies on nitrogenisotopes [7, 8, 19, 21, e.g.]. TiN can be produced at
TABLE I: Available E p = 278 keV resonance strength data in the literatureReference Year Method Resonance strength ωγ /meVE.J. Woodbury et al. [10] 1949 activation 10D.B. Duncan, J.E. Perry [11] 1951 activation 20S. Bashkin et al. [12] 1955 prompt gamma 13 ± et al. [13] 1963 prompt gamma 14 ± et al. [14] 1982 prompt gamma 14 ± et al. [15] 2005 prompt gamma 13.5 ± et al. [16] 2005 prompt gamma 12.9 ± et al. [17] 2006 prompt gamma 12.8 ± et al. [6] 2016 prompt gamma 12.6 ± et al. [5] 2011 13.1 ± et al. [6] 2016 12.6 ± E p = 1058 keV resonance strength data in the literatureReference Year Method Resonance strength ωγ /meVD.B. Duncan, J.E. Perry [11] 1951 activation 630D.F. Hebbard et al. [13] 1963 prompt gamma 394U. Schr¨oder et al. [18] 1987 prompt gamma 310 ± et al. [19] 2010 prompt gamma 364 ± et al. [19] 2010 353 ± the required thickness and purity and these targets canwithstand intense beam bombardment. The Ti:N atomicratios are typically found to be very close to 1:1 in suchtargets.Considering the advantages, solid state TiN targetswere used also in the present work. They were pre-pared by reactive sputtering of TiN onto 0.5 mm thick Tabackings at the Helmholtz-Zentrum Dresden-Rossendorf,Germany. The nominal thicknesses of the TiN layerswere between 100 and 300 nm, but for the purpose of theresonance strength measurements presented here, only300 nm thick targets were used. This corresponds toroughly 1.5 × N atoms/cm .For the resonance strength determination, the totalthickness of the targets does not play a role (as longas the thick target assumption holds, see Sec. III). Thestoichiometry, i.e. the Ti:N ratio, on the other hand,is a crucial parameter as discussed in Sec. III. The Ti:Nratio and the amount of impurities were therefore mea-sured with three independent methods: SNMS, RBS andPIXE, as described below. For these measurements, TiNlayers sputtered onto Si wafers were used. These sampleshad been prepared together with the actual targets on Tabackings in the same sputtering geometry and thereforethe layer compositions are the same.Secondary Neutral Mass Spectrometry (SNMS) tech-nique was used to measure the target composition as afunction of the depth of the layer. The measurementwas done with the INA-X type (SPECS GmbH, Berlin)SNMS facility of Atomki [22, 23]. Figure 1 shows a typ-ical SNMS profile of a 300 nm target. Besides the small (cid:19) (cid:24)(cid:19) (cid:20)(cid:19)(cid:19) (cid:20)(cid:24)(cid:19) (cid:21)(cid:19)(cid:19) (cid:21)(cid:24)(cid:19) (cid:22)(cid:19)(cid:19) (cid:22)(cid:24)(cid:19)(cid:19)(cid:20)(cid:19)(cid:21)(cid:19)(cid:22)(cid:19)(cid:23)(cid:19)(cid:24)(cid:19)(cid:25)(cid:19)(cid:26)(cid:19)(cid:27)(cid:19)(cid:28)(cid:19)(cid:20)(cid:19)(cid:19) (cid:70) (cid:82)(cid:81) (cid:70) (cid:72)(cid:81) (cid:87) (cid:85) (cid:68) (cid:87) (cid:76) (cid:82)(cid:81) (cid:3)(cid:62) (cid:68) (cid:87) (cid:82) (cid:80) (cid:76) (cid:70) (cid:3) (cid:8) (cid:64) (cid:71)(cid:72)(cid:83)(cid:87)(cid:75)(cid:3)(cid:62)(cid:81)(cid:80)(cid:64) (cid:3)(cid:49)(cid:3)(cid:55)(cid:76)(cid:3)(cid:50)(cid:3)(cid:54)(cid:76) FIG. 1: Concentration of the various elements in the targetas a function of depth measured with the SNMS technique. amount of oxygen contamination on the surface, no ele-ments other than nitrogen and titanium were observed.The Ti:N ratio was found to be uniform along the thick-ness of the target within the statistical fluctuation of thedata and the average ratio is 1.015 ± (cid:20)(cid:19)(cid:19) (cid:21)(cid:19)(cid:19) (cid:22)(cid:19)(cid:19) (cid:23)(cid:19)(cid:19)(cid:19)(cid:24)(cid:19)(cid:19)(cid:20)(cid:19)(cid:19)(cid:19)(cid:20)(cid:24)(cid:19)(cid:19)(cid:21)(cid:19)(cid:19)(cid:19) (cid:70) (cid:82)(cid:88)(cid:81) (cid:87) (cid:86) (cid:18) (cid:70) (cid:75)(cid:68)(cid:81)(cid:81)(cid:72) (cid:79) (cid:70)(cid:75)(cid:68)(cid:81)(cid:81)(cid:72)(cid:79)(cid:3)(cid:80)(cid:72)(cid:68)(cid:86)(cid:88)(cid:85)(cid:72)(cid:71)(cid:3)(cid:87)(cid:82)(cid:87)(cid:68)(cid:79)(cid:3)(cid:86)(cid:76)(cid:80)(cid:88)(cid:79)(cid:68)(cid:87)(cid:72)(cid:71)(cid:3)(cid:49)(cid:3)(cid:54)(cid:76)(cid:3)(cid:55)(cid:76) FIG. 2: A typical measured and simulated RBS spectrum.TABLE III: Measured Ti:N ratios of the used targets. Theadopted ratio is the weighted average of the results of thethree methods.Method Ti:N atomic ratioSNMS 1.015 ± ± ± ± α -beam provided by the 5 MV Van de Graaff acceleratorof Atomki was focused onto the targets in an Oxford typemicrobeam setup [24]. The scattered α -particles were de-tected by two ion-implanted Si detectors positioned at135 and 165 degrees with respect to the incoming beamdirection. Figure 2 shows a typical RBS spectrum. Basedon the evaluation of the RBS spectra with the SIMNRAcode [25], a Ti:N ratio of 0.976 ± ± ± (cid:19) (cid:20) (cid:21) (cid:22) (cid:23) (cid:24) (cid:25) (cid:26) (cid:27)(cid:20)(cid:20)(cid:19)(cid:20)(cid:19)(cid:19)(cid:20)(cid:19)(cid:19)(cid:19)(cid:20)(cid:19)(cid:19)(cid:19)(cid:19)(cid:20)(cid:19)(cid:19)(cid:19)(cid:19)(cid:19) (cid:3)(cid:80)(cid:72)(cid:68)(cid:86)(cid:88)(cid:85)(cid:72)(cid:71)(cid:3)(cid:71)(cid:68)(cid:87)(cid:68)(cid:3)(cid:73)(cid:76)(cid:87) (cid:70) (cid:82)(cid:88)(cid:81) (cid:87) (cid:86) (cid:18) (cid:70) (cid:75)(cid:68)(cid:81)(cid:81)(cid:72) (cid:79) (cid:40) (cid:91)(cid:16)(cid:85)(cid:68)(cid:92) (cid:18)(cid:78)(cid:72)(cid:57) (cid:55)(cid:76)(cid:54)(cid:76)(cid:49) FIG. 3: PIXE spectrum of a TiN target. Major elementsincluded in the fit are labeled.
HPGe detectorTargetVacuum gaugeport Cabling for collimatorand electron suppressionTarget chamber Pump portAccelerator portCollimator water cooling10 cmLead shielding Beam
FIG. 4: Drawing of the target chamber used for the activa-tions
B. Activations
The proton beams for the excitation of the studiedresonances in the N(p, γ ) O reaction were provided bythe Tandetron accelerator of Atomki. The energy cali-bration of the accelerator has been carried out recently[26] and that was used for setting the energies for the res-onance studies. As the resonances are relatively strong,no high beam intensity was necessary which was usefulto avoid target deterioration. The typical beam intensitywas 5 µ A on target.The applied beam energies for the study of the278 keV and 1058 keV resonances were E p = 300 keV and E p = 1070 keV, respectively. These values correspond tothe middle of the yield curve plateau, where the maxi-mum yield can be reached. See the discussion in Sec. III.The schematic drawing of the target chamber can beseen in Fig. 4. The beam enters the chamber througha water cooled collimator of 5 mm in diameter. Behindthe collimator, an electrode biased at -300 V is placedto suppress secondary electrons emitted from the targetor from the collimator. After the collimator the wholechamber serves as a Faraday-cup to measure the chargecarried by the beam to the target. The measured chargewas used to determine the number of protons impingingon the target. C. Detection of the annihilation radiation
As the half-life of the O reaction product is rathershort (about two minutes), the induced activity was mea-sured without removing the target from the activationchamber. A 100 % relative efficiency HPGe γ -detectorwas therefore placed close behind the target. The dis-tance between the target and the detector end-cap wasabout 1 cm.In order to increase the number of detected decay, thecyclic activation method was applied. The target was ir-radiated for 5 minutes and then the beam was stoppedin the low energy Faraday cup of the accelerator and thedecay was measured for 10 or 20 minutes. This cycle wasrepeated many times (up to 30 cycles in a singe irradia-tion campaign).In order to follow the decay of O, the number ofevents in the region of 511 keV peak (selected by gatingwith a single channel analyzer) was recorded in five sec-ond time intervals using an ADC in multichannel scalingmode. Figure 5 shows typical examples of the recordednumber of counts as a function of time. The upper panelshows a case measured on the E p = 278 keV resonancewith 10 minute counting intervals, while the lower panelrepresents a measurement on the E p = 1058 keV reso-nance with 20 minute counting intervals. During the5 minutes irradiation intervals the events in the detec-tor were disregarded as in these periods the counts weredominated by beam induced background. D. Determination of the detector efficiency
For the absolute measurement of the resonancestrengths the absolute detection efficiency of the HPGedetector must be known in the counting geometry used.In the present case of a positron decaying isotope, thepositron annihilation does not occur in a point-like geom-etry and hence the precise determination of the detectionefficiency is not trivial.The positrons leave the decaying O nucleus with typ-ically several hundreds of keV energy (the positron end-point energy is 1732 keV [20]). The positrons which traveltowards the target backing stop within a few 100 µ m(thus well inside the backing) and annihilate thereforein a quasi point-like geometry. On the other hand, thosepositrons which leave towards the other direction, willmove into the vacuum chamber and travel freely untilthey hit the walls of the chamber. Therefore, their anni-hilation takes place in an extended and not well definedgeometry. (cid:19) (cid:20)(cid:19)(cid:19)(cid:19) (cid:21)(cid:19)(cid:19)(cid:19) (cid:22)(cid:19)(cid:19)(cid:19) (cid:20)(cid:19)(cid:19)(cid:19)(cid:19) (cid:20)(cid:21)(cid:19)(cid:19)(cid:19) (cid:20)(cid:23)(cid:19)(cid:19)(cid:19)(cid:19)(cid:20)(cid:19)(cid:21)(cid:19)(cid:22)(cid:19)(cid:23)(cid:19)(cid:24)(cid:19) (cid:70) (cid:21)(cid:85)(cid:72)(cid:71)(cid:17) (cid:32)(cid:20)(cid:17)(cid:21)(cid:22)(cid:20) (cid:3)(cid:80)(cid:72)(cid:68)(cid:86)(cid:88)(cid:85)(cid:72)(cid:71)(cid:3)(cid:3)(cid:3)(cid:3)(cid:3)(cid:3)(cid:3)(cid:3)(cid:3)(cid:71)(cid:68)(cid:87)(cid:68)(cid:3)(cid:73)(cid:76)(cid:87) (cid:70) (cid:82)(cid:88)(cid:81) (cid:87) (cid:86) (cid:3)(cid:18)(cid:3) (cid:24) (cid:3) (cid:86) (cid:72) (cid:70) (cid:87)(cid:76)(cid:80)(cid:72)(cid:3)(cid:62)(cid:86)(cid:72)(cid:70)(cid:64) (cid:19)(cid:21)(cid:24)(cid:24)(cid:19)(cid:26)(cid:24)(cid:20)(cid:19)(cid:19)(cid:20)(cid:21)(cid:24)(cid:20)(cid:24)(cid:19)(cid:20)(cid:26)(cid:24)(cid:21)(cid:19)(cid:19) (cid:3)(cid:80)(cid:72)(cid:68)(cid:86)(cid:88)(cid:85)(cid:72)(cid:71)(cid:3)(cid:71)(cid:68)(cid:87)(cid:68)(cid:3)(cid:73)(cid:76)(cid:87) (cid:70) (cid:82)(cid:88)(cid:81) (cid:87) (cid:86) (cid:3)(cid:18)(cid:3) (cid:24) (cid:3) (cid:86) (cid:72) (cid:70) (cid:70) (cid:21)(cid:85)(cid:72)(cid:71)(cid:17) (cid:32)(cid:20)(cid:17)(cid:19)(cid:28)(cid:25) (cid:19) (cid:20)(cid:19)(cid:19)(cid:19) (cid:21)(cid:19)(cid:19)(cid:19) (cid:22)(cid:19)(cid:19)(cid:19) (cid:23)(cid:19)(cid:19)(cid:19) (cid:24)(cid:19)(cid:19)(cid:19) (cid:25)(cid:19)(cid:19)(cid:19) (cid:26)(cid:19)(cid:19)(cid:19)(cid:16)(cid:21)(cid:19)(cid:16)(cid:20)(cid:19)(cid:19)(cid:20)(cid:19) (cid:85) (cid:72) (cid:86) (cid:76) (cid:71)(cid:88)(cid:68) (cid:79) (cid:87)(cid:76)(cid:80)(cid:72)(cid:3)(cid:62)(cid:86)(cid:72)(cid:70)(cid:64) FIG. 5: Number of events detected by the HPGe detector atthe 511 keV peak region as a function of time using 5 secondtime bins. The fit to the data including a time-independentlaboratory background component and using the known half-life of O is also shown. The upper and lower panels show the E p = 278 keV and E p = 1058 keV measurements, respectively.For the latter case the fit residuals are also plotted in orderto indicate that the decay of O alone fits well the measureddata, no other radioactivity was present in significant amount.This is also confirmed by the reduced χ value of the fit beingvery close to unity. In such a situation the direct efficiency measurementwith calibrated radioactive sources is not possible. In-stead, an indirect method using the following procedurewas applied. As a first step, longer-lived positron emit-ters were produced in the activation chamber. For thispurpose F (t / = 109.77 ± O(p,n) F reaction) and N (t / = 9.965 ± C(p, γ ) N reaction) were chosen. Thedecay of these sources was measured with the HPGe de-tector standing next to the chamber (the one which wasused for the N(p, γ ) O reaction) for typically 1-2 half-lives. This measurement gives information about the ef-ficiency in the non-trivial extended geometry. Then thesources were removed from the chamber, transferred toanother HPGe detector (used in many recent experimentsand characterized precisely, see e.g. [27]) where the decaywas followed for several half-lives. At this detector thesources were placed in a position which guaranteed thepoint-like geometry, i.e. the sources were placed between0.5 mm thick Ta sheets which stopped the positrons com-pletely. The absolute efficiency of this HPGe detectorin the used geometry was measured with calibrated ra-dioactive sources to a precision of 3 %. The measurementwith the second detector provided the absolute activityof the sources and – knowing precisely the half-lives andthe elapsed time between the two countings – the ab-solute efficiency of the first detector could be obtained.The efficiency obtained with F and N sources werein agreement within the statistical uncertainties of 0.7 %and 1.5 %, respectively.In addition to the measurements with F and N,the same procedure was followed also with the actual O isotope produced by the N(p, γ ) O reaction. Herethe short half-life resulted in a higher statistical uncer-tainty of 2.5 %, but the obtained efficiency was in agree-ment with the results from F and N. Based on thesemeasurements the final efficiency is determined with aprecision of 4 %.
III. DATA ANALYSIS
As it can be seen by the red line in Fig. 5, the 511 keVcount rate can be well fitted with a constant backgroundplus an exponential decay with the O half-life. Withthe known detection efficiency and the decay parametersof O the only free parameter of the fit is the yield ofthe reaction (i.e. the number of reactions per incidentproton) which can be related to the resonance strength.With the thick target assumption (i.e. when the ener-getic thickness of the target ∆ E is much larger than thenatural width Γ of the resonance), the resonance strength ωγ can be related to the yield Y measured on the top ofthe resonance by the following formula: ωγ = 2 ǫ eff Yλ (1)where λ is the de Broglie wavelength at the resonance en-ergy in the center of mass system and ǫ eff is the effectivestopping power. If the thick target condition is not met,the maximum yield Y max measured in the middle of theresonance curve plateau can be related to the ideal thicktarget yield leading to the following correction factor [28]: f ≡ Y max Y = 2 π tan − ∆ E Γ . (2)Based on the target characterizations presented inSec. II A, the energetic thickness of the targets used forthe present experiments at the two studied resonances was ∆ E = 51.9 keV and ∆ E = 24.4 keV, respec-tively with about 5 % uncertainty. The natural widthsof the two resonances (taken from the literature) areΓ = 1.12 ± = 3.8 ± f = 0.986 ± f = 0.902 ± ǫ eff in the case of a targetcomposed of Ti and N can be obtained as ǫ eff = ǫ N + N Ti N N ǫ Ti (3)where ǫ N and ǫ Ti are the stopping powers of N and Ti,respectively, taken at the resonance energy and N Ti /N N is the Ti:N atomic ratio as discussed in Sec. II A.The stopping power was taken from the 2013 versionof the SRIM code [30]. The following values were used: • ǫ N (278 keV) = 10.72 eV/(10 atoms/cm ), • ǫ N (1058 keV) = 4.733 eV/(10 atoms/cm ), • ǫ Ti (278 keV) = 22.81 eV/(10 atoms/cm ), • ǫ Ti (1058 keV) = 10.80 eV/(10 atoms/cm ).As for Ti, the stopping power was measured by N.Sakamoto et al. [31] with very good precision of betterthan 1 %. The measured values are in excellent agree-ment with the SRIM data, never deviating more than2 %, Therefore, an uncertainty of 2 % is assigned to ǫ Ti in the present work. The situation is somewhat worse inthe case of nitrogen. The stopping power measured withgaseous N can be different from the solid form (see e.g.[32] for the stopping power dependence on the chemicalform). Therefore, 4 % uncertainty is assigned to ǫ N asrecommended by SRIM. The uncertainty of the effectivestopping power was calculated taking into account theuncertainty of the measured Ti:N ratio and consideringthe ǫ Ti and ǫ N values uncorrelated. The isotopic abun-dance of N in natural nitrogen (99.6337 %) was takeninto account in the calculation of ǫ eff .For the determination of the resonance strength, thenon-resonant component of the reaction yield must besubtracted from the resonant yield. In the case of the E p = 1058 keV resonance the yields below and above theresonance – at E p = 1000 keV and E p = 1150 keV – weremeasured. Based on these measurements a 2.7 % nonres-onant contribution to the resonant yield was determined.This non-resonant yield was subtracted from the resonantyield and a conservative relative uncertainty of 20 % wasassigned to it, leading to a 0.6 % uncertainty of the de-termined resonance strength. TABLE IV: Components of the resonance strength uncertain-tiesSource 278 keV 1058 keVresonancecounting statistics 1.0 % 0.7 %effective stopping power 2.8 %HPGe detector efficiency 4.0 %current integration 3.0 %finite target thickness correction 0.1 % 1.7 %non-resonant yield subtraction 0.3 % 0.6 %total uncertainty 5.8 % 6.0 %
In the case of the E p = 278 keV resonance the off-resonant reaction yield was below the detection limit.Based on some recent experiments, a cross section ofabout 1.5 × − barns can be expected at this energy[7, 8]. Such a cross section leads to a calculated non-resonant yield which is 0.3 % of the resonant yield. Thistiny contribution is subtracted from the yield and - asthis value is not based on our own measurement - a 100 %relative uncertainty is assigned to it.Table IV lists the uncertainties of the final resonancestrength values. As the studied resonances are relativelystrong and the cyclic activations were carried out manytimes, the statistical uncertainty of the γ -counting is verylow compared to the other sources of uncertainty. Thequoted total uncertainty is the quadratic sum of the com-ponents. Other uncertainties (like for example the uncer-tainties of the O decay parameters) are well below 1 %and are therefore neglected.
IV. RESULTS AND CONCLUSIONS
The obtained strengths of the two studied resonancesare the following: • ωγ = (13.4 ± • ωγ = (442 ±
27) meV.If we take into account the total uncertainties, the newresult for the E p = 278 keV resonance strength is in goodagreement with the adopted values recommended by theSolar Fusion II compilation [5] as well as by the morerecent work of S. Daigle et al. [6] (see Table I). We donot quote here a new recommended value, we just notethat considering our new value determined with an in-dependent technique, the strength recommended by the Solar Fusion II compilation [5] and especially its some-what higher uncertainty seems more appropriate than thevalue of S. Daigle et al. [6] with its very small error bar.The results of those experiments where the E p = 278 keVresonance is used as a normalization point, do not changeby the present result. Therefore, the astrophysical con-sequences are also unchanged.The strength of the E p = 1058 keV resonance, on theother hand, was measured to be significantly higher thanthe ones determined in the two most recent works (seeTable II). One reason can be that the finite target thick-ness correction might not have been done in those ex-periments. In the case of U. Schr¨oder et al. [18] thereis no information about this in the paper. In the caseof M. Marta et al. [19] it is confirmed that no such acorrection has been applied [33]. Based on the informa-tion available in [19] and [34], the correction should beabout 7 %. This would lead to a resonance strength of ωγ = (389 ±
22) meV. This value still differs from thepresent one by about two standard deviations [35]. Con-sequently, as opposed to the E p = 278 keV resonance, thisstrength value is rather uncertain and further measure-ments would be required.As a summary, the activation technique was success-fully used in the present work for the N(p, γ ) O reac-tion and precise resonance strength values were derived.This technique can also be applied for the measurementof the non-resonant N(p, γ ) O cross section. Such anexperiment is in progress using the setup introduced here.The results will be presented in a forthcoming publica-tion. As the activation method provides data which arecomplementary to the prompt gamma data, the combina-tion of the results can lead to more precise cross sectionof the N(p, γ ) O astrophysical key reaction.
Acknowledgments
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