PHYSICAL REVIEW C 89, 014601 (2014)

Cross section measurements of the 10B( p,γ )11C reaction between 2.0 and 6.0 MeV

A. Kafkarkou,1,2,* M. W. Ahmed,1,2,3 D. P. Kendellen,1,2 I. Mazumdar,2,† J. M. Mueller,1,2 L. S. Myers,1,2,‡ M. H. Sikora,2,4

H. R. Weller,1,2 and W. R. Zimmerman2,5

1Physics Department, Duke University, Durham, North Carolina 27708, USA2Triangle Universities Nuclear Laboratory, Durham, North Carolina 27708, USA

3Department of Mathematics and Physics, North Carolina Central University, Durham, North Carolina 27707, USA4Department of Physics, George Washington University, Washington, District of Columbia 20052, USA

5Department of Physics, University of Connecticut, Storrs, Connecticut 06269, USA(Received 21 October 2013; revised manuscript received 19 November 2013; published 2 January 2014)

The total cross section of the 10B(p,γ )11C reaction has been measured for bombarding proton energies between2.0 and 6.0 MeV in 500 keV steps for the first time. This reaction is important for potential next-generationboron fueled nuclear reactors. The total cross section was measured by activating a 10B target with protons and,after stopping the beam, detecting the 511 keV γ rays emitted from the β+ decay of 11C, using two LaBr3:Cedetectors. In addition to the total cross sections, astrophysical S factors were also calculated at each energy.

DOI: 10.1103/PhysRevC.89.014601 PACS number(s): 25.40.Lw, 25.60.Dz, 21.10.Jx, 28.52.Cx

I. INTRODUCTION

The 11B(p,α)αα reaction is a candidate for aneutronicenergy production. It has been proposed as the prime candidatefor next-generation colliding beam fusion reactors [1] and wasrecently studied at Triangle Universities Nuclear Laboratory(TUNL) [2,3]. Natural boron consists of 80.1% 11B and 19.9%10B [4]; therefore, nuclear reactions involving 10B may alsooccur in the nuclear fuel. Some of these reactions lead to theproduction of radioactive nuclei which may pose problems inthe use of boron as a nuclear fuel. Thus, an accurate study ofthese reactions is needed for the determination of the requiredenrichment level of the nuclear fuel. Two possible reactionsthat can produce radioactive nuclei are the 10B(p,α)7Bereaction, recently studied at TUNL [5], and the 10B(p,γ )11Creaction. The 10B(p,γ )11C reaction leads to the production of11C, which is a β-unstable nucleus with a half-life of ∼20.4 minthat decays to 11B (the main nuclear fuel) with the emissionof a positron. For laboratory proton energies between 2.0 and6.0 MeV the 11C compound nucleus is produced at highlyexcited states between 10.5 and 14.2 MeV, which are α-and p-unbound. For this reason, one would expect that the11C production cross section via the 10B(p,γ )11C reaction ismuch smaller than the cross sections of other 10B(p, particles)reactions [6]. Consequently, compared with radioactive nucleiproduced in other decay channels, for example, in the (p,α)channel, the production of 11C is expected to be a minorissue for the proposed reactors mentioned above. Nevertheless,experimental proof of the above argument is needed andtherefore the cross section measurement of the 10B(p,γ )11Creaction is of importance.

Very few measurements of the 10B(p,γ )11C reactionhave been performed. In fact in the energy region stud-ied by the present experiment there is only one previous

*adamos.kafkarkou@duke.edu†Currently at Tata Institute of Fundamental Research, Colaba,

Mumbai, 400 005, India.‡Currently at Jefferson Lab, Newport News, VA 23606, USA.

measurement [7]. However, in Ref. [7] only the capture tothe ground state of 11C is measured [10B(p,γ0)11C] so thatno conclusions for the total 11C production cross section canbe drawn. Data also exist covering the bombarding protonenergies between 0.07 and 2.20 MeV [8]. In Ref. [8], the11C production cross section was measured not only forcapture to the ground state but also for capture to the mostprobable excited states [10B(p,γ2)11C∗ and 10B(p,γ5)11C∗] andto some other highly excited states. The total 11C productioncross section at energies between 0.07 and 2.20 MeV can bedetermined by summing together the partial cross sectionsmeasured in Ref. [8]. In Ref. [9] the data from Refs. [7,8]are presented in the form of S factors. Note that Refs. [7,8]measured the cross sections of various decays by directlyobserving the 11C∗ γ -ray decays. In the present experimenta different method is used.

II. EXPERIMENT

The experiment was conducted at Triangle UniversitiesNuclear Laboratory at Duke University. Figure 1 shows adiagram of the experimental setup used for this experiment.The protons were accelerated to 2.0–6.0 MeV by a 10 MVFN Tandem accelerator and were directed to the center of asmall vacuum chamber. The beam energy uncertainty from theaccelerator was ±10 keV. A 10B target was placed in the centerof the chamber. The target consisted of a thin 10B layer, 98%isotopically enriched and ∼400 μg/cm2 nominal thickness,deposited on a piece of tantalum that was thick enough to stopall of the protons. The total energy loss in the target rangedbetween 50 and 20 keV depending on the incident energy. Theenergy spread in the target was ∼13 keV for the lower incidentenergies. The integrated beam current was measured from thetarget using a beam current integrator (BCI). A potential issuewith this technique is the loss of secondary electrons generatedby the protons. To stop secondary electrons from leaving thetarget and altering the measured current, the target was biasedto +300 V. A 3.5% systematic uncertainty was estimated forthe integrated beam current. The beam current was kept at

0556-2813/2014/89(1)/014601(5) 014601-1 ©2014 American Physical Society

A. KAFKARKOU et al. PHYSICAL REVIEW C 89, 014601 (2014)

FIG. 1. (Color online) Experimental setup used for this experi-ment. The two LaBr3:Ce detectors used for the experiment are shownalong with the 5 mm diameter collimator and the liquid nitrogen trap.Two lead shields were used as shown to shield the detectors fromupstream backgrounds.

∼200 nA for all the runs. A small 5 mm diameter collimatorwas placed in the beam line, ∼10 cm from the target, to ensurea well defined beam spot on the target. The vacuum in thechamber was kept at ∼10−6 torr, and a liquid nitrogen trapwas located just upstream of the chamber in order to minimizethe carbon buildup on the target.

The cross section was measured by first activating the targetthen interrupting the beam and counting the subsequent β+decays of the produced 11C nuclei. The method used forthis measurement takes advantage of the fact that the 11Cnuclei produced via proton capture will either be producedin the ground state or if they are produced in an excited statethey will quickly γ decay to the ground state of 11C. 11Cdecays from its ground state to 11B with the emission of a β+particle with a half-life of ∼20.4 min. The emitted β+ particlethermalizes, interacts with an atomic electron from the targetand annihilates, giving two 511 keV γ rays emitted at an angleof 180◦ with respect to each other. Consequently, detectingthese two γ rays in coincidence can determine the number of11C decays and therefore the number of 11C nuclei produced.

To produce the 11C, the target was normally irradiated for1 h (∼3 11C half-lives) at each of the proton energies mentionedabove. After each irradiation the beam was interrupted and thetwo coincident 511 keV γ rays emitted by the activated targetwere measured for another hour. The measurement wouldusually start ∼120 s after the end of the irradiation. The511 keV γ rays were deemed coincident if they arrived within10 ns of each other. In this way a decay curve was recorded.These data were then used to determine the total number ofobserved decays. From the observed decays, the total numberof 11C nuclei produced during the irradiation was extractedand the total cross section was calculated.

Two identical, large volume LaBr3:Ce scintillation detec-tors (see Fig. 1), manufactured by Saint Gobain Inc., wereused to measure the emitted 511 keV γ rays. The newlyinvented and marketed LaBr3:Ce are the finest scintillators interms of energy resolution with very fast timing, comparableto BaF2 crystals [10,11]. Each of the two detectors used in

[keV]DetE400 450 500 550 600 650

[ke

V]

Det

E

350

400

450

500

550

600

650

0

200

400

600

800

1000

1200

FIG. 2. (Color online) Two-dimensional plot of the energy sig-nals from the two detectors for 4.0 MeV incident protons. To eliminateaccidental coincidences, only the events included between the twohorizontal and the two vertical dashed lines were used (511 keVevents).

the present measurement was comprised of two cerium dopedLaBr3 crystal bars (4 in. long and with a 2 × 2 in.2 crosssectional area), optically coupled to make a 2 × 2 × 8 in.3 bar.Each detector was enclosed in an aluminum casing with aglass window at one of the two ends, and was viewed by a 2in. diameter ET-9266B photomultiplier tube. The detectorswere operated at a voltage of −800 volts and the energysignals were drawn from the sixth dynode of the eight-stagedynode chain. This was done to improve the linearity of theresponse of the detectors. The timing signals were drawn fromthe anode. The dynamic range of the detectors was kept at∼2.0 MeV. The performance of the detectors (energy andtiming resolutions, linearity, and uniformity of response) wasthoroughly documented up to 6.0 MeV prior to the presentmeasurements.

The two detectors were placed outside the chamber at ascattering angle of 90◦ on the left and the right side of the beam(Fig. 1). Both detectors were placed at a distance of ∼2.5 cmfrom the target. A 137Cs source and a 60Co source were usedfor energy calibration. During each measurement the timingsignals of the two detectors were used to generate coincidenceevents. The energy signals were used to place software energycuts in order to choose only the 511 keV events and to eliminateaccidental coincidences (see Figs. 2 and 3). Figure 4 shows asample decay curve collected using 4.0 MeV incident protons.In this figure the data points represent the number of 511 keVcoincidence events as a function of time and the solid line theresult of fitting the data (see next section). During the activationand the measurement time the integrated beam current fromthe BCI was also recorded as a function of time to monitorbeam fluctuations during the irradiation.

III. ANALYSIS METHOD

The 11C production cross section is described by thefollowing differential equation:

d(NC(t))dt

= σ

(NB

A

)dQ (t)

dt� (ti − t) − λNC(t), (1)

where NC(t) is the number of 11C nuclei in the sample asa function of time, σ is the 11C production cross section,

014601-2

CROSS SECTION MEASUREMENTS OF THE 10B(p, . . . PHYSICAL REVIEW C 89, 014601 (2014)

[keV]DetE400 420 440 460 480 500 520 540 560 580

Co

un

ts

0

200

400

600

800

1000

1200

1400

FWHM 30keV

FIG. 3. (Color online) Projection of Fig. 2. The full width at halfmaximum (FWHM) is shown. The dashed lines are the energy cutsapplied. Any background that may exist in this energy spectrum issubtracted by including a constant (flat background) in the fit functionwhen fitting the decay curve of 11C (see Sec. III).

NB

Ais the number of 10B nuclei in the sample per unit area

(target thickness), � (ti − t) is the Heaviside function, ti is theirradiation time, and λ is the 11C decay constant. dQ(t)

dtis the

incident proton current with Q (t) being the integrated charge(number of incident protons on the target) at time t . IntegratingEq. (1) from t = 0 to t = ti while keeping NB constant in timegives

σ =Nd exp[λ(ti+�t)]

1−exp(−λtm) − n

χε

[Q (ti) exp (λti) − λ

∫ ti0 Q (t) exp (λt) dt

]

= Y

χε

.

(2)

In Eq. (2), Nd is the number of 11C decays recorded by thedetecting system during the measurement time tm (normally1 h), ti is again the irradiation time (also 1 h), and �t is thetime between the end of the irradiation and the start of themeasurement (∼120 s). n is the number of 11C nuclei thatexisted in the target at the time that the irradiation started; nwas taken to be zero for the very first run and subsequently itcould be calculated based on the decay curve for the previous

FIG. 4. (Color online) The 11C decay curve for 4.0 MeV incidentprotons. The data points represent the number of 511 keV coincidencecounts per 10 s bins as a function of time. The solid line is the resultof fitting these data using the method described in Sec. III.

run. Y is defined as the yield of the reaction: the total numberof the 10B(p,γ )11C reactions detected over the total number ofthe incident protons. Finally, χε is a correction factor in unitsof μb−1 which includes the target thickness NB

Aand the total

efficiency ε of the detection system:

χε = NB

Aε. (3)

The first step in calculating the cross section at each energywas to determine the number of the observed decays Nd ateach beam energy. This was done by fitting the decay curves(see Fig. 4) collected for each energy with exponential decayfunctions. When fitting the decay curves extra care had tobe taken to account for possible backgrounds. A possiblebackground may emerge from traces of 12C that may existin the target (for example, from carbon buildup). These traceswill lead to the creation of 13N which also decays via β+ decaywith a half-life of ∼10 min and gives background 511 keVcoincidence counts. The half-life of 13N is large enough(about one-half of the half-life of 11C) so that 13N nucleiwill survive long enough to cause background coincidences inthe measurement. Other 511 keV backgrounds can be causedby traces of 14N and 16O in the target. Both nuclei produceβ+ emitters (15O and 17F, respectively) when irradiated withprotons. For the case of 14N this is unlikely to be a problemsince 14N is unlikely to be found in the target. 16O is more likelyto be found in the target due to oxidization of 10B. However, inboth cases the produced β+ emitters have very short lifetimes(∼122.2 and ∼64.5 s, respectively) and, given that the countingperiod would start ∼2 min after the end of the irradiation, thesetwo nuclei are unlikely to introduce substantial backgrounds.Finally, a flat background can be expected from accidental511 keV coincidences from other sources in the room.

To account for the two most likely sources of backgrounds(from 13N and the flat background), the decay curves werefit with the sum of two exponential decay functions (onefor the 11C decays and one for the 13N decays) plus aconstant to account for the flat background. The curveswere fit using the “extended unbinned maximum likelihood”method. The decay constants for the 11C and 13N were fixedto the values calculated by the experimentally measuredvalues of the half-lives adopted by the latest nuclear datacompilations [12,13]: t1/2(11C) = 20.364 ± 0.014 min andt1/2(13N) = 9.965 ± 0.004 min. Additionally, after the lastirradiation of the entire experiment, the sample was measuredfor ∼24 h in order to search for additional backgrounds frompossible long-lived nuclei and for better monitoring of the flatbackground. No traces of other long-lived nuclei were found.The constant used to account for the flat background wasconstrained by these measurements, increasing the accuracyof the results. In all cases, no significant amounts of 13N (i.e.,no significant amounts of 12C) were observed.

The second part of the analysis was the determinationof the term in the denominator of Eq. (2) which containsthe integrated charge Q (t). This was done by calculatingnumerically the integral shown in Eq. (2) using the recordedintegrated beam current (BCI vs time).

Using the number of detected decays determined in thefirst step of the analysis and the part of the denominator of

014601-3

A. KAFKARKOU et al. PHYSICAL REVIEW C 89, 014601 (2014)

Eq. (2) determined in the second step, the yield Y definedin Eq. (2) was calculated. Two sources of uncertainties enterthe calculation of the yield Y : a statistical uncertainty fromfitting the decay curves and a systematic uncertainty of 3.5%from the BCI which affects each yield Y individually. Thestatistical uncertainties ranged from 2% for high statistics runs(above 3.0 MeV) to 10% for lower statistics runs (below3.0 MeV). The two types of uncertainties were added inquadrature defining a total uncertainty for each yield. To lowerthe uncertainties several runs were taken for each energy. Foreach of these runs the yields were calculated as described aboveand their weighted average was calculated. The uncertaintiesfor the weighted average yields ranged from 1.8% to 4.5%depending on the energy. The effects of the uncertainties inthe decay constants of 11C and 13N were investigated and werefound to be negligible compared to the other uncertainties.Additionally, for the runs with the highest statistics (Ep =6.0 MeV) the effects of the time-dependent dead time of thedata acquisition system were studied with again negligibleuncertainties compared to the main uncertainties.

Finally, the value of χε is needed to calculate the total crosssection using Eq. (2). A direct independent measurement ofthis term was not possible since it depends on a number offactors that could not easily be determined (target thickness,detectors’ solid angles, and detectors’ intrinsic efficiencies).To extract this term the data collected at 1.8 and 2.0 MeV inthe present experiment were normalized to the cross sectionspublished in Ref. [8]. As explained in the Introduction,the most probable p+10B capture channels were measuredindividually in Ref. [8]. To extract the total cross section atthe two proton energies of interest (1.8 and 2.0 MeV) fromRef. [8], the individual cross sections for capture to the groundstate and the 4.319 and 6.478 MeV states of 11C at theseproton energies were added together. Also, 20% of the crosssection for capture to the α-unbound 8.424 MeV state wereadded since, as shown in Ref. [8], this state decays to theground state of 11C with a 20% probability. Capture channelsto the 8.655 and 8.701 MeV states are neglected since theyhave negligible probability to γ -ray decay to 11C [8]. Usingdata at 1.8 and 2.0 MeV, two χε values could be determinedwhich agreed with each other within their uncertainties. Theweighted average of these values was χε = 0.0182 ± 0.0016.The total cross sections for energies above 2.0 MeV wereextracted using this factor and the yields. The uncertaintiesposted in [8] and the total uncertainties for the yields at 1.8and 2.0 MeV yield the 8.6% uncertainty for the calculatedχε factor. This uncertainty enters the results as an overallsystematic uncertainty in addition to the total uncertaintiesdetermined for each yield individually.

IV. RESULTS AND DISCUSSION

Figure 5 shows the total 11C production cross section via the10B(p,γ )11C reaction with respect to the center-of-mass (c.m.)energy. The uncertainties from the weighted average yields(coming from fitting and charge uncertainties) are smaller thanthe size of the points. An additional 8.6% overall systematicuncertainty from the determination of the value of χε alsoexists for all the points. The results are presented in Table I.

FIG. 5. Excitation function of the total 11C production crosssection via the 10B(p,γ )11C reaction with respect to the c.m. energy.The uncertainties from the weighted averaged yields and the energyuncertainties are smaller than the size of the points. An additional8.6% overall systematic uncertainty also exists for all the points.

As observed in Fig. 5 and in Table I, the total 11C productioncross section via the 10B(p,γ )11C reaction ranges from a fewμb to a few hundred μb. This is to be compared with thetotal 10B(p,α)7Be reaction cross section reported in Ref. [5].This is the 7Be production cross section, and as can be seenin Ref. [5] it is three orders of magnitude larger than the crosssection reported in the present work. This is expected since thecompound nucleus 11C is produced at energies correspondingto p- and α-unbound states which are more likely to decaywith the emission of particles rather than photons [6]. Giventhis and the fact that 11C has a much smaller half-life than 7Be,this experiment confirms that the production of 11C should be arelatively minor problem for the development of the proposedboron fueled colliding beam reactors.

In addition to the cross sections, the astrophysical Sfactors for the 10B(p,γ )11C reaction were calculated using

TABLE I. Total 11C production cross section via the 10B(p,γ )11Creaction. The energies are given in the c.m. system and theuncertainties in energy were calculated by adding in quadraturethe beam energy uncertainty from the accelerator (±10 keV) andthe energy spread in the target. The cross section uncertainties arefrom the weighted average yields. In addition, all the values havean 8.6% overall systematic uncertainty which is not included in theuncertainties shown in the table.

Ec.m. (MeV) σtot (μb)

1.636 ± 0.015 2.57 ± 0.101.818 ± 0.015 3.56 ± 0.162.273 ± 0.015 8.1 ± 0.22.727 ± 0.015 10.5 ± 0.33.182 ± 0.015 92 ± 23.636 ± 0.015 87 ± 24.091 ± 0.015 64 ± 24.545 ± 0.015 118 ± 35.000 ± 0.015 158 ± 45.455 ± 0.015 256 ± 6

014601-4

CROSS SECTION MEASUREMENTS OF THE 10B(p, . . . PHYSICAL REVIEW C 89, 014601 (2014)

FIG. 6. (Color online) Astrophysical S factors with respect to thec.m. energy for the 10B(p,γ )11C reaction. For the data from thisexperiment, the uncertainties from the weighted averaged yields andthe energy uncertainties are smaller than the size of the points. Anadditional 8.6% overall systematic uncertainty also exists for all thepoints. The cross sections from Wiescher et al. [8] (these are the crosssections used to normalized the present data) were taken from theoriginal paper as described in previous sections and were convertedto S factors. The data from Kuan et al. [7] were taken from [14] ascross sections and were converted to S factors. In both cases onlydata with energies that coincide with the energy region studied in thisexperiment are used.

the following equations [9]:

σ (Ec.m.) = S (Ec.m.) exp (−2πη)1

Ec.m.

, (4)

where

η = 0.1575Z1Z2

(A

Ec.m.

). (5)

In these equations, σ (Ec.m.) is the total cross section, S(Ec.m.)is the astrophysical S factor, Ec.m. is the c.m. energy in MeV,

Z1 and Z2 are the atomic numbers of the proton and 10B,respectively, and A is the reduced mass of the proton and 10Bin amu. The determination of S factors in these energy regionsis important for nuclear astrophysics. This is mainly becausethe S factors can be extrapolated to lower energies (energiesthat can be found in stars) more easily than the total crosssections themselves [6]. The extracted S factors are shown inFig. 6 as a function of the c.m. energy and are compared withresults from other measurements in the same energy region.Note that the results of the present experiment are larger thanthe results reported in Ref. [7] (they differ by a factor of ∼10 forcenter-of-mass energies above 3.0 MeV). This was expectedsince, as discussed in the Introduction, only the 10B(p,γ0)11Creaction was measured in Ref. [7].

V. CONCLUSIONS

The total 11C production cross section via the 10B(p,γ )11Creaction was measured for the first time at laboratory protonenergies between 2.0 and 6.0 MeV. The cross section wasdetermined by measuring, in coincidence, the 511 keV γ raysemitted from the annihilation of the β+ particles from the 11Cdecays. The present data were normalized to previous crosssections from Ref. [8] at low energies. Cross sections andastrophysical S factors are reported. On average, this crosssection is three orders of magnitude smaller than the 7Beproduction cross section via the 10B(p,α)7Be reaction [5]. Thisindicates that the production of the radioactive 11C nucleus inproposed boron-fueled colliding beam reactors will be a minorissue compared with the production of 7Be.

ACKNOWLEDGMENTS

This project was supported by Tri-Alpha Energy, Inc., andU.S. Department of Energy Grants No. DE-FG02-97ER41033and No. DE-FG02-97ER41046.

[1] N. Rostoker, A. Qerushi, and M. Binderbauer, J. Fusion Energ.22, 83 (2003).

[2] S. Stave, M. W. Ahmed, R. H. France III, S. S. Henshaw, B.Muller, B. A. Perdue, R. M. Prior, M. C. Spraker, and H. R.Weller, Phys. Lett. B 696, 26 (2011).

[3] M. C. Spraker, M. W. Ahmed, M. Blackston, N. Brown,R. H. France, S. S. Henshaw, B. A. Perdue, R. M. Prior, P. N.Seo, S. Stave, and H. R. Weller, J. Fusion Energ. 31, 357(2012).

[4] J. K. Bohlke, J. R. de Laeter, P. De Bivre, H. Hidaka, H. S.Peiser, K. J. R. Rosman, and P. D. P. Taylor, J. Phys. Chem. Ref.Data 34, 57 (2005).

[5] A. Kafkarkou, M. W. Ahmed, P. H. Chu, R. H. France, H. J.Karwowski, D. P. Kendellen, G. Laskaris, I. Mazumdar, J. M.Mueller, L. S. Myers, R. M. Prior, M. H. Sikora, M. C. Spraker,H. R. Weller, and W. R. Zimmerman, Nucl. Instrum. MethodsB 316, 48 (2013).

[6] C. A. Bertulani, Nuclear Physics in a Nutshell (PrincetonUniversity, Princeton, NJ, 2007).

[7] H. M. Kuan, M. Hasinoff, W. J. O’Connell, and S. S. Hanna,Nucl. Phys. A 151, 129 (1970).

[8] M. Wiescher, R. N. Boyd, S. L. Blatt, L. J. Rybarcyk, J. A.Spizuoco, R. E. Azuma, E. T. H. Clifford, J. D. King, J. Gorres,C. Rolfs, and A. Vlieks, Phys. Rev. C 28, 1431 (1983).

[9] C. Angulo, M. Arnould, M. Rayet, P. Descouvemont, D. Baye,C. Leclercq-Willain, A. Coc, S. Barhoumi, P. Aguer, C. Rolfs,R. Kunz, J. W. Hammer, A. Mayer, T. Paradellis, S. Kossionides,C. Chronidou, K. Spyrou, S. Degl’Innocenti, G. Fiorentini,B. Ricci, S. Zavatarelli, C. Providencia, H. Wolters, J. Soares,C. Grama, J. Rahighi, A. Shotter, and M. L. Rachti, Nucl. Phys.A 656, 3 (1999).

[10] I. Mazumdar, D. A. Gothe, G. A. Kumar, N. Yadav, P. B. Chavan,and S. M. Patel, Nucl. Instrum. Methods A 705, 85 (2013), andreferences therein.

[11] G. A. Kumar, I. Mazumdar, and D. A. Gothe, Nucl. Instrum.Methods A 610, 522 (2009), and references therein.

[12] J. H. Kelley, E. Kwan, J. E. Purcell, C. G. Sheu, and H. R.Weller, Nucl. Phys. A 880, 88 (2012).

[13] F. Ajzenberg-Selove, Nucl. Phys. A 523, 1 (1991).[14] H. M. Kuan, M. Hasinoff, W. J. O’Connell, and S. S. Hanna,

Nucl. Phys. A 151, 129 (1970), data taken from the EXFORdatabase: http://www-nds.iaea.org/EXFOR/C0634.003.

014601-5