Lifetime measurements of excited states in ^{15}O
B. Frentz, A. Aprahamian, A.M. Clark, C. Dulal, J.D. Enright, R.J. deBoer, J. Görres, S.L. Henderson, K.B. Howard, R. Kelmar, K. Lee, L. Morales, S. Moylan, Z. Raman, W. Tan, L. E. Weghorn, M. Wiescher
AAPS/123-QED
Lifetime measurements of excited states in O B. Frentz,
1, 2
A. Aprahamian,
1, 2
A.M. Clark,
1, 2
C. Dulal,
1, 2
J.D. Enright,
1, 2
R.J. deBoer,
1, 2
J. G¨orres,
1, 2
S. L. Henderson,
1, 2
K.B. Howard,
1, 2
R. Kelmar,
1, 2
K. Lee,
1, 2
L. Morales,
1, 2
S. Moylan,
1, 2
Z. Raman,
1, 2
W. Tan,
1, 2
L. E. Weghorn,
1, 2 and M. Wiescher
1, 2 Department of Physics, University of Notre Dame, Notre Dame, Indiana 46556 USA The Joint Institute for Nuclear Astrophysics, University of Notre Dame, Notre Dame, Indiana 46556, USA (Dated: December 25, 2020)The CNO cycle is the main energy source in stars more massive than our sun, it defines the energyproduction and the cycle time that lead to the lifetime of massive stars, and it is an important toolfor the determination of the age of globular clusters. One of the largest uncertainties in the CNOchain of reactions comes from the uncertainty in the N( p, γ ) O reaction rate. This uncertaintyarises predominantly from the uncertainty in the lifetime of the sub-threshold state in O at E x = 6792 keV. Previous measurements of this state’s lifetime are significantly discrepant. Here, wereport on a new lifetime measurement of this state, as well as the excited states in O at E x = 5181keV and E x = 6172 keV, via the N( p, γ ) O reaction at proton energies of E p = 1020 keV and E p = 1570 keV. The lifetimes have been determined with the Doppler-Shift Attenuation Method(DSAM) with three separate, nitrogen-implanted targets with Mo, Ta, and W backing. We obtainedlifetimes from the weighted average of the three measurements, allowing us to account for systematicdifferences between the backing materials. For the 6792 keV state, we obtained a τ = 0 . ± . τ = 7 . ± . τ = 0 . ± . PACS numbers: Valid PACS appear here
I. INTRODUCTION
The measurements of solar neutrinos [1] have con-firmed the prediction of the pp -chains as the dominantenergy source of our sun. Only about 1% of the solarenergy in the sun comes from the CN cycle, C ( p, γ ) N N (cid:0) β + ν (cid:1) C C ( p, γ ) N N ( p, γ ) O O (cid:0) β + ν (cid:1) N N ( p, α ) C , but it quickly becomes the dominate source of energyproduction in stars with masses M (cid:38) M (cid:12) . One of themajor uncertainties in the description of the sun, in theframework of the standard solar model [2, 3], is the metal-licity of the solar core, which is determined by its carbon,nitrogen, and oxygen content [4]. The expected elementabundances, based on the spectroscopic analysis of thesolar atmosphere, disagree with the solar profiles of soundspeed and density as well as the depth of the convectivezone and the helium abundance obtained by helioseis-mology measurements [5]. It has been pointed out that adirect study of the CN neutrinos, coming from the β de-cay of N and O, can provide an independent measureof the solar metallicity [6]. However, the CN neutrinoflux not only depends on the CN abundance in the solarinterior, but also on the associated CN reaction rates,such as C( p, γ ) N and N( p, γ ) O respectively. The BOREXINO collaboration has succeeded in thefirst measurement of the CNO neutrinos associated pri-marily with the O β decay [7]. The abundance of O depends critically on the N( p, γ ) O reaction rate,which is the slowest in the CN cycle, and therefore de-termines the O equilibrium abundance. Extensive ex-perimental efforts have been undertaken to determine areliable reaction rate at the solar energy range.The first comprehensive study of the N( p, γ ) O re-action was performed by Schr¨oder et al. [8], covering theproton energy range from E p = 0.2 to 3.6 MeV. The to-tal S -factor at zero energy, S (0), was determined to be3.20 ± E x = 6.79 MeV excited state in Owere dominant, contributing S g.s. (0) = 1 . ± .
34 keVb and S . (0) = 1 . ± .
02 keV b, respectively. Fig. 1depicts the level structure of the O compound nucleus.However, an R -matrix analysis by Angulo and Descou-vemont [9] drastically changed the extrapolated S -factorfor both transitions to S g.s. (0) = 0 . +0 . − . keV b and S . (0) = 1 . ± .
17 keV b. Overall, this reduced thetotal S -factor by a factor of 1.7. A number of more re-cent measurements at the LUNA underground accelera-tor [10–13] expanded the reaction data to lower energies,suggesting an even lower S -factor, while an independentstudy by Runkle et al. [14] indicated a higher value for theground state transition. An independent R -matrix anal-ysis of the various reaction channels over a wide range ofenergies by Azuma et al. [15] and Li et al. [16] failed toconfirm the LUNA collaboration measurements and sug-gest a higher low energy S -factor, in particular for thetransition to the ground state. This discrepancy trans- a r X i v : . [ nu c l - e x ] D ec � / � - � ���� / � + ���� ���� / � + ���� ���� / � - ���� ���� / � + ���� ���� / � + ���� ���� / � + ���� ���� / � + ���� ���� / � + ���� ������� - ��� ������ ������� ��� �� � �� � + � FIG. 1: Level scheme of the O compound nucleus. Thebeam (laboratory frame) and resonance (center of massframe) energies and corresponding excitation energies of theimportant states are given. In this work, the lifetimes of thestates at 6792 keV, 6172 keV, and 5181 keV are reported.These states all decay with 100% branching to the groundstate. lates into a substantial uncertainty in the prediction ofthe reaction rate and the associated neutrino flux fromthe decay of O. The very low energy contributions inthe N( p, γ ) O reaction rate come from the tail contri-bution of the subthreshold state at E x = 6.79 MeV in O, which is determined by its radiative width, Γ γ .The 6.79 MeV excited state decays with 100% proba-bility to the ground state by γ -ray emission. Therefore,the total width of the state results solely from the radia-tive width, Γ = Γ γ . The width can be determined bymeasuring the level lifetime, τ , where Γ = (cid:126) /τ . The firstprecision measurement of this lifetime was performed byBertone et al. [17], using the Doppler Shift AttenuationMethod (DSAM) in forward kinematics with targets of Nimplanted into Ta. They populated the state through res-onant capture of protons to the E p = 278 keV resonanceof the N( p, γ ) O reaction and observed the decaying γ -rays at three different angles. The measured lifetime forthe 6.79 MeV state was determined to be τ = 1 . +0 . − . fs,corresponding to a width of Γ = 0 . +0 . − . eV, where thereported uncertainties correspond to a 90% confidencelimit. The authors also noted that their reported valuewould have increased by 100%, to τ = 3 . ± . O nucleiwas performed by fragmentation of an O beam inci-dent on a Be target and then inelastically scattered offof a thick lead target. The de-excitation γ -rays weredetected with an array of NaI (Tl doped) scintillationdetectors. In order to disentangle the 6.79 MeV peak ofinterest from the 6.86 MeV peak in their spectrum, theauthors compared the experimentally obtained spectrumwith the results of a Monte Carlo simulation [18]. Due tothe poor energy resolution of the detector system, the au-thors ultimately had difficulty separating the peaks andwere unable to observe isolated γ -rays from the 6.79 MeVstate. The authors only reported an upper bound on thewidth, Γ = 0 . +0 . − . eV.Sch¨urmann et al. [19] published a new measurement ofthe lifetime of the same state, using the DSAM techniqueand an improved experimental setup. This measurementused a single high-purity germanium (HPGe) detector ona rotating track and measured the angular distributionof the depopulating γ -ray at several angles ranging from40 − ◦ , allowing for a check of asymmetries around the90 ◦ point and reducing systematic uncertainties from theuse of different detectors. Similar to the measurement ofBertone et al. [17], the authors also used implanted TaNtargets and populated the state of interest via the res-onance at E p = 278 keV in the N( p, γ ) O reaction.They obtained an upper limit of τ < .
77 fs for the life-time with 68.3% confidence. In contrast with the resultof Bertone et al. [17], however, the authors note only a2% change in the reported lifetime by changing the targetdensity to TaN in their analysis.Galinski et al. [20] performed another DSAM measure-ment at the TRIUMF facility. The major difference be-tween past measurements was that the reaction was per-formed in inverse kinematics, emulating a measurementfrom over 50 years ago [21]. The O in this experi-ment was produced via the He( O , α ) O reaction witha He-implanted gold-foil. The de-excitation γ -rays weredetected with a clover HPGe detector and filtered in co-incidence with the reaction α -particles. The authors per-formed a Bayesian line-shape analysis of the spectra and,using the maximum likelihood method, recommended anupper limit of τ < . d ( N , O) n reaction. The γ -rays from this measurement were de-tected with the state-of-the-art AGATA Demonstratorarray using γ -ray tracking for precision angular data. Aline shape analysis of the data was performed by com-paring with the results of a Monte Carlo simulation, alsoobtaining an upper-bound on the lifetime, τ < . N ), but calculated the lifetimes assumingtarget densities and stopping powers equal to those ofpure tantalum, calculated in SRIM [23]. However, theauthors note that accurate densities would have changedthe inferred lifetimes of their works by 100% [17] and 2%[19], respectively.This work reports on a new measurement of the thelifetime of the 6.79 MeV excited state in O by popu-lating it with the same N( p, γ ) O reaction in forwardkinematics at proton energies ranging from E p = 1 . − . O, which are in the fsrange and thus used to validate the results for the stateat 6.79 MeV.In this work, the experimental details are first dis-cussed in Sec. II, covering the target implantation andlifetime measurements. In Sec. III, a Monte Carlo sim-ulation is described followed by the calculation of thelifetime via the observed Doppler shifts. In order todemonstrate the effect of the lifetime measurement andits uncertainty on the N( p, γ ) O reaction, preliminary R -matrix calculations are described in Sec. IV. Summaryand conclusions are presented in Sec. V. II. EXPERIMENTA. Implanted targets
Isotopically pure targets were made by implantationusing the 5 MV Sta. Ana accelerator at the Universityof Notre Dame’s Nuclear Science Laboratory (NSL). 350keV N ions were implanted into Ta, W, and Mo back-ings of 0.5 mm thickness. A similar implantation tech-nique was used in another study [24] that showed a deeperdistribution of nitrogen in the target. The Ta was cho-sen to compare with the earlier measurements of [17, 19],which used Ta N , while the W and Mo were used toidentify and highlight any systematic differences arisingfrom the choice of backing material. This also provided a method of disentangling the effects of the high beam cur-rents used in the measurement. Before the implantation,the target backings were cut and cleaned using ethanol,acetone, and with an oxygen plasma. Throughout the im-plantation, the beam was rastered over the backing sur-face in order to produce a uniform implantation. Addi-tionally, in order to reduce the carbon buildup on the tar-get face during the implantation, a liquid-nitrogen cooledcopper cold trap was employed. Due to the beam inten-sities used, the target backings were water cooled.The nitrogen content in the targets was assessed byscanning the 1057 keV resonance in the N( p, γ ) O re-action and comparing the yield with that of a target pre-viously used by Li et al. [16]. The Ta, Mo, and W targetswere found to have nitrogen contents of 21.3 ± ± ± × atoms / cm . Earlier targetswere produced to saturation of the nitrogen in interstitiallattice sites, resulting in targets of 60% nitrogen. Thesetargets, however, were produced to 36, 26, and 22 per-cent, respectively for the Ta, Mo, and W targets. Asthe backing materials saturate with nitrogen to differentcompounds, a lower nitrogen content was used to allowfor improved consistency between the different targets. B. Lifetime Measurement Method
The excited 5.18 MeV, 6.17 MeV, and 6.79 MeV ex-cited states in O were populated with the N( p, γ ) Oreaction, where protons of E p = 1020 keV and E p =1570 keV were delivered to the targets. At both ener-gies, the reaction proceeds primarily through the direct-capture mechanism and these energies were chosen toprovide the best signal-to-background discrimination forthe states of interest. The energy spread of the beam wasapproximately 1 keV and the current on target through-out the experiment ranged from 20 - 50 µ A, dependenton accelerator stability. Targets were mounted on a 45 ◦ target holder, relative to the beam axis, and due to thehigh beam currents, the backings were constantly cooledwith recirculating de-ionized water. A copper cold fin-ger, biased to −
400 V and cooled with a liquid nitrogenreservoir, was utilized to limit carbon build-up and sup-press secondary electrons throughout the measurements.To keep the beam focused and centered through the runs,some of which lasted several hours, pairs of upstream slitswere utilized. These prevented the beam from drifting tothe edges of the implanted area on the targets where thenitrogen content was lower.The de-exciting γ rays were observed with one of theGEORGINA detectors, a coaxial n-type HPGe detector,of 109% relative efficiency. 1.5 mm lead shielding wasplaced in front of the crystal’s face to attenuate the low-energy x rays entering the detector, reducing the countrate from the low energy background. The lifetimes weremeasured by the DSAM method. A single detector wasused to measure the depopulating γ -rays at different an-gles of 0 ◦ , ◦ , ◦ , ◦ , ◦ , ◦ , ◦ , and − ◦ relative FIG. 2: Schematic of the experimental setup. It is importantto note that the same HPGe detector was set on a rotatingtable and set to each of the angles, not seven different detec-tors. hist_Ta30_90deg
Entries 3257743Mean 6789Std Dev 24.936740 6760 6780 6800 6820 6840Energy (keV)20406080100120140160180 C oun t s hist_Ta30_90deg Entries 3257743Mean 6789Std Dev 24.93 o Positional check: Gamma Energy Shift at +/- 90 o Detector at 90 o Detector at -90
FIG. 3: Measured energy spectrum of the 6.79 MeV transitionat ± ◦ . At these two angles, the energy of the γ ray is notDoppler shifted. Therefore, by comparing the position of thepeaks at these angles, we confirm accurate position of thedetector relative to the target and centering of the beam ontarget. to the beam direction. The detector was placed 25.4cm away from the target on a rotating table with an-gular precision such that the detector’s center could beplaced within ± ◦ of the intended angle. Fig. 2 showsa schematic of the experimental setup. Data at − ◦ were taken and compared to those at 90 ◦ to prove thatthe beam was centered on target, since γ rays detectedat these corresponding angles are unshifted. These twospectra are included in Fig. 3. Additionally, the data at90 ◦ were used to calibrate the spectra in the detector.In order to prevent any peak shifting from smearingthe peaks at a given angle, the data were saved hourlyto track the stability of the detector. This allowed the FIG. 4: An example of the Monte Carlo method for a simu-lated decay curve. For 100,000 decays with λ = 50 (chosensimply for demonstration), the normalized decay curve agreeswith the exponential decay law. monitoring of the detector for gain shifts throughout theexperiment. Additionally, a CeBr detector was fixed ata backward angle of − ◦ in order to provide a con-sistency check throughout the experiment and monitorfor any drifting. By monitoring background lines, wefound no signs of instability of the detector or electron-ics. The data from both detectors were collected witha Mesytec MDPP-16 module, which amplified and digi-tized the data. III. ANALYSIS AND RESULTSA. Monte Carlo simulation
For this analysis, a DSAM program was written to sim-ulate the expected Doppler shift. The approach utilizedMonte Carlo sampling to simulate the radioactive decayof a nucleus with a given lifetime according to the normalexponential decay law: P ( t ) = e − t/τ . (1)The generator function for exponential decay, takes therandom number, r , within the range [0, 1], and propa-gates it to the simulated decay time through t = 1 λ ln (cid:18) − r (cid:19) , (2)where λ = 1 /τ is the width of the state. To demonstratethis, Fig. 4 provides an example of the simulated decayprobability as a function of time for radioactive nucleifollowing the decay law of Eq. (1).These simulated lifetimes (with the target backingsetc.) were used in conjunction with the output from theSRIM stopping power software [23]. Targets were gener-ated in the software and then used to simulate ion recoiltracks within the target after the reaction. The initialenergy of the recoil was randomly assigned to a reason-able range based on the energy loss in the target and allrecoils were assumed to have an initial velocity parallelto the incident beam axis. For 10,000 different ions, theentire travel path of the recoil through the target wassimulated and saved. The energy of the recoiling nuclei,in the case of this experiment, was not high enough towarrant relativistic corrections, like the method of [20],so the SRIM output was sufficient.Based on the SRIM simulation, further informationabout each individual ion’s travel was calculated. Utiliz-ing the position of each interaction, the particle’s trajec-tory was calculated between each position. The recordedenergy at each interaction was used to calculate the ion’sspeed in the step. Finally, these data allow for the time ofthe interaction to be calculated (in femtoseconds). Thisprovided a complete picture of any single recoiling ion’smotion in the target. Additionally, in Ziegler et al. [23],the SRIM software quotes stopping power uncertaintiesof 5%. The code took this uncertainty into account andpropagated it through to an uncertainty in the initialenergy of the recoil ion.Next, the program used Eq. (2) to randomly simulatea decay time to the decaying nucleus (for a specified life-time) and randomly assigned this decay time to one ofthe SRIM tracks. Then, the code interpolated betweeninteraction points to find the position and velocity of thedecaying nucleus at the generated instant of decay. Withthis information, the Doppler shifted de-exciting γ en-ergy, E γ was calculated by E γ = E oγ (1 + RβF ( τ ) cos( θ )) , (3)where E oγ was the unshifted γ ray energy, R represents acorrection to account for the detector size and resolution(obtained from experimental spectra), β = v/c was therecoil’s velocity relative to the speed of light, F ( τ ) wasthe attenuation factor (encapsulating the relationship be-tween the lifetime of the decaying state and the mediumthrough which the nucleus moves), and θ was the angleat which the γ was observed. This process was repeated50,000 times for each combination of detection angle, life-time, and target backing material in order to build up acomplete Monte Carlo simulation of the experiment.An example of a complete simulation for the 6.79 MeVstate de-excitation at all angles, τ = 0 . F ( τ ), was determined as a functionof the nuclear lifetime, τ , for each individual target. Thisrelationship is plotted in Fig. 6. This was ultimately usedto determine the experimental lifetime by comparing the FIG. 5: Simulated energy deposition histogram for the 6.79MeV state de-excitation, at all detection angles, τ = 0 . γ -rays’ energy with angle,the relationship upon which the entire DSAM was predicated.FIG. 6: The simulated attenuation factors, F ( τ ), for the var-ious experimental backings, as a function of the state’s life-time, τ . This was used to calculate the measured lifetimefrom the experimental attenuation factors. The simulationswere also carried out to lifetimes well beyond what was ex-pected from literature values to ensure that the relationshipwas robust around the lifetimes of interest. measured attenuation factors to those of the simulatedcurves to extract the corresponding lifetime and uncer-tainty.A significant difference between this procedure andother, previous methods for calculating the lifetimes wasthat they only used numerical calculations. This methodis only a discrete calculation at values chosen across therelevant lifetime landscape. Therefore, these attenuationfactors require an external fit to provide the final rela-tionship. To minimize any artificial bias from the choiceof simulated lifetimes, they were chosen to range beyondexpected values to ensure that the relationship betweenthe lifetime and attenuation factor is robust in the rele-vant lifetime range. hist_Ta30_0deg Entries 3577818Mean 6807Std Dev 15.86 C oun t s hist_Ta30_0deg Entries 3577818Mean 6807Std Dev 15.86
Doppler Shift Spectra for Ta Target o Detector at 0 o Detector at 45 o Detector at 60 o Detector at 75 o Detector at 90 o Detector at 111 o Detector at 135
FIG. 7: Doppler shifting spectra for the 6.79 MeV secondarytransition with detection angle for the Ta target, with allangles (0 ◦ , ◦ , ◦ , ◦ , ◦ , ◦ and 135 ◦ ) plotted together.FIG. 8: Doppler shifted γ -ray energy plotted against cos( θ )to determine F ( τ ), the attenuation factor. The red line repre-sents the orthogonal distance regression best fit and the bandrepresents a two-sigma uncertainty of the fit, incorporatingthe uncertainty in both the slope and intercept. B. Doppler shifts and lifetimes
In the measurement at each of the seven angles(0 ◦ , ◦ , ◦ , ◦ , ◦ , ◦ and 135 ◦ ), the centroid energyof each of the three secondary transition peaks at 5.18MeV, 6.17 MeV, and 6.79 MeV were determined. Ex-ample spectra of the peak Doppler shifting is shown inFig. 7. From this, the relationship between the cosineof the measurement angle, cos( θ ), and the observed en-ergies, E γ , was determined. With uncertainties in boththe angle and the centroid energy, the data were fit withorthogonal distance regression, instead of the traditionalleast-squares method, because it takes into account theuncertainties in both dependent and independent vari-ables, leading to higher fidelity fits. The relationship be-tween shifted γ -ray energy and cos( θ ) is shown in Fig. 8.These figures are representative of the other two targetsas well. TABLE I: Experimental F ( τ ) and corresponding lifetime val-ues obtained in the present work along with a weighted av-erage of the lifetime for the various targets. Note that sincethe attenuation factor is dependent on the backing material,only the average of the lifetimes may be used.Mo Ta W τ average F ( τ ) . . ± .
013 0 . ± .
016 9 . ± . τ . (fs) 7 . +4 . − . . ± . . ± . . ± . F ( τ ) . . ± .
014 0 . ± .
017 0 . ± . τ . (fs) 0 . +0 . − . . ± . . +0 . − . . ± . F ( τ ) . . ± .
019 0 . ± .
019 0 . ± . τ . (fs) 0 . +0 . − . . +0 . − . . ± . . ± . The experimentally determined attenuation factorsand corresponding lifetimes are shown in Table I. Ad-ditionally, the weighted average of the lifetimes has alsobeen calculated. This analysis leads to lifetimes for eachof the 5.18 MeV, 6.17 MeV, and 6.79 MeV excited statesin O. Table I results show no systematic differenceswith the lifetimes extracted from the various target ma-terials. This allowed the exclusion of backing materialsas sources of uncertainties in comparison to earlier mea-surements.The experimentally determined lifetimes are shown incomparison with previous measurements in Table II. Themean lifetime of the 5.18 MeV state agrees well with pre-vious measurements, but has a much larger uncertainty.This large uncertainty arises in part from the double es-cape peak at E γ = 5150 keV (from the E γ = 6172 keVfull energy peak) that complicates the background de-termination (and therefore the peak centroids for theDoppler Shift). For the lifetime of the 6.17 MeV and6.79 MeV states, we find good agreement with the re-sults reported in Sch¨urmann et al. [19] and Galinski et al.[20]. For each of the states, our recommended lifetimesare taken to be the weighted average of the measurementstaken from each of the targets. These results are depictedin Figs. 9, 10, and 11. IV. R -MATRIX FIT To examine the impact of these new lifetime measure-ments, the data were incorporated into a set of limited R -Matrix fits using the AZURE2 code [15]. These representfits to a selection of data to study the influence of this life-time measurement in particular; a full R -Matrix fit incor-porating these results and new low-energy cross-sectionresults will be presented in a forthcoming paper. In thefits presented here, shown in Figs. 12 and 13, most of theinformation about the levels was taken from Ajzenberg-Selove [25] or Daigle et al. [26] where updated. The widthof the 6.79 MeV excited state in O, corresponding tovalues within the range of our lifetime measurement, wasfixed at a selection of different values. This collection of
TABLE II: Experimentally determined lifetime values (in fs) obtained in this work (as the weighted average of the differenttargets) and their comparison with literature values. E x (keV) Present Ref. [17] Ref. [19] Ref. [20]5181 7 . ± . +1 . − . ± . ± . +1 . − . < . < . . ± . +0 . − . < . < . O obtained inthis work compared with previous measurements. The mea-surement labelled TUNL corresponds to that of Bertone et al.[17], while Bochum to Sch¨urmann et al. [19].FIG. 10: Lifetimes of the 6.17 MeV state in O obtained inthis work compared with previous measurements. The mea-surement labelled TUNL corresponds to that of Bertone et al.[17], Bochum to Sch¨urmann et al. [19], and TRIUMF to Galin-ski et al. [20]. fits, therefore, serves primarily as an illustration of theways in which these new lifetime measurements impactthe low energy extrapolations of the cross section.A channel radius of 5.5 fm was adopted for this work,which matches the analyses done by [27], [16], and [28].Information about the levels and their parameters as usedin
AZURE2 are contained in Table III.The cross-section data utilized in the fitting routinewere from measurements at LUNA [10, 13, 29, 30], TUNL[14], Bochum [8], and the University of Notre Dame [16].All of these data sets were left without scaling during
FIG. 11: Lifetimes of the 6.79 MeV state in O obtained inthis work compared with previous measurements. The mea-surement labelled TUNL corresponds to that of Bertone et al.[17], Bochum to Sch¨urmann et al. [19], TRIUMF to Galinskiet al. [20] and Michelagnoli to Michelagnoli [22], which hasnot been peer reviewed. the fits. The Bochum data from Schr¨oder et al. [8] werecorrected as detailed in SFII [27]. Additionally, the datafrom Li et al. [16] are a differential cross section taken at45 ◦ and are treated as such in the fits. This dataset wasscaled by a factor of 4 π in the plotting only to compareto the angle integrated data.In examining the capture to the ground state in O,the R -matrix fits show the effect of our lifetime measure-ment. Specifically, in Fig. 12, we present fits showingthe whole range of lifetimes for the 6.79 MeV state of τ = 0 . ± .
4. This shows that despite this measurementproviding the most stringent limit on the lifetime, thisrange still translates to dramatic changes in the low en-ergy behavior of the S -factor. Our fits, however, agreewell with the capture data. One of the best fits using ourlifetimes is shown alongside fits from Refs. [14–16, 27] inFig. 13; the impact of higher energy data on the fit inthe low energy range as presented in Li et al. [16] will beaddressed in a forthcoming paper that presents a broadrange of new low energy cross section measurements. V. SUMMARY AND CONCLUSIONS
The N( p, γ ) O reaction was used to populate ex-cited states at 5.18 MeV, 6.17 MeV, and 6.79 MeV in O. The nitrogen targets were made by implantationon backings of Mo, Ta, and W. The Doppler shift of
TABLE III: Levels used in the R -matrix fits. Bold values indicate parameters which were allowed to vary during the fit. Thesigns on the partial widths and ANCs indicates the relative interferences. The dividing line demarcates the proton separationenergy at E x = 7.2968(5) MeV [25]. Levels where all parameters are fixed are not shown in this table for brevity but wereincluded in the fits. a) Indicates the partial width of the 6.79 MeV state, measured in this experiment to between Γ = 0.66- 3.29 eV. For each individual fit, this width was fixed. However, between each fit, this width was varied to different valueswithin our range to explore how the uncertainty in this measurement affects the low energy extrapolation. These different fitsare shown in Fig. 12 and are otherwise identical. E x (Ref. [25]) E x (fit) J π Channel l s ANC (fm − / ) / Partial Width (eV)0.0 0.0 1/2 − N+p 1 1/2 0.23 N+p 1 3/2 7.46.7931(17) 6.7931 3/2 + 14
N+p 0 3/2 4.75 O+ γ . E1 1/2 a + 14 N+p 2 1/2 -92.2 N+p 0 3/2 × N+p 2 3/2 -509 O+ γ . E1 1/2 − N+p 1 3/2 -5.872 × O+ γ . E2 1/2 -0.303 O+ γ . E1 3/2 -0.0019.484(8) + 14
N+p 2 1/2 77.69 × N+p 0 3/2 × N+p 2 3/2 -7.822 × O+ γ . E1 1/2 − N+p 3 1/2 0.979 × N+p 1 3/2 -6.576 × N+p 3 3/2 -0.985 × O+ γ . E2 1/2 -0.307 O+ γ . E1 3/2 -0.01239.609(2) 9.6075 3/2 − N+p 1 3/2 -13.821 × O+ γ . M1 1/2 O+ γ . E1 3/2 -0.04415 3/2 + 14
N+p 0 3/2 × O+ γ . E1 1/2 the γ -rays emitted by the decaying recoils were mea-sured using the different targets and at seven differentangles. A Monte Carlo simulation was applied to re-produce the experimental shifts and extract the lifetimesfrom the measured attenuation factors. By using multi-ple implanted targets of different backings, we were ableto take a weighted average of our measurements to re-duce the overall systematic uncertainty. Additionally, theMonte Carlo approach allowed us to recreate the depthprofile of implanted targets with a high degree of accu-racy, making the subsequent analysis based on the targetcomposition more robust. The simulation also propa-gates uncertainties throughout every step, allowing it toreflect the experimental conditions more accurately. Thisis an improvement over previous measurements and theirtreatment of their targets.The results show no evidence of systematic variationswith previous measurements arising from the choice ofbacking materials. This work shows a larger uncer-tainty for the lifetime of the 5.18 MeV state but agreeswithin the uncertainties of the previous measurements.For the other transitions at 6.17 MeV and 6.79 MeV, the present measurement agrees well with the values re-ported by [17, 19, 20]. Our work represents the onlymeasurement of a finite lifetime for the 6.79 MeV stateand provides even more stringent constraints on the levellifetimes. The discrepancies in previous measurementswere resolved in this measurement with three differentbackings. These results, alongside recent measurementsof the low-energy N( p, γ ) O reaction capture cross-section will be used in a forthcoming paper to carry outa full R -Matrix fit over a very broad energy range toextrapolate the S -factor to astrophysical energies. Thiscomplete fit of and extrapolation from the data will allowfor a more confident determination of this reaction’s pa-rameters and, therefore, a more complete understandingof this crucial reaction in the CNO cycle. Acknowledgments
Fig. 1 has been created using the SciDraw scientificfigure preparation system [M. A. Caprio, Comput. Phys.Commun. 171, 107 (2005), http://scidraw.nd.edu]. This
FIG. 12: R -Matrix fits exploring the uncertainty of our life-time measurements to the low energy extrapolation. Thewidth of the 6.79 MeV excited state in O is fixed duringeach fit and changed in each subsequent iteration to anothervalue within our uncertainty range. This clearly shows thateven though our lifetime result provides the most stringentlimitation on the lifetime of this state, it still has an out-sized effect on the low energy behavior of this reaction. TheSchr¨oder data are from [8], while the LUNA data representsthe measurements [10, 13, 29, 30], the Runkle data are from[14], and the Li data are from [16]. Of these, the Li data aredifferential and were treated as such in the fitting but scaledup by 4 π for plotting purposes.FIG. 13: R -Matrix fits comparing our best fit to those per-formed in previous works. Our fit used a lifetime value forthe 6.79 MeV excited state in O within our measured rangerange, Γ = 2 .
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