Z. Phys. A 357, 283–289 (1997) ZEITSCHRIFTFUR PHYSIK Ac© Springer-Verlag 1997

Cross section and resonance strengths of the19F (p, αγ)16O reactionin the energy range Ep = 0.8− 3.6 MeV

K. Spyrou, C. Chronidou, S. Harissopulos, S. Kossionides, T. Paradellis

N.C.S.R. “Demokritos”, Institute of Nuclear Physics, Laboratory for Material Analysis, Aghia Paraskevi Attikis, GR-153 10 Athens, Greece

Received: 11 October 1996Communicated by D. Schwalm

Abstract. An excitation function of the19F (p, αγ)16O reac-tion has been measured over the proton beam energy rangeEp=0.8-3.6 MeV using a 4π NaI summing spectrometer. Theabsolute efficiency of this spectrometer was determined byMonte Carlo simulations. The results from the efficiency cal-culations have been experimentally confirmed by measuringknown resonances of three nuclear reactions. The propertiesER,ΓR,σR andωγ have been extracted for ten narrow reso-nances (Γ ≤ 20 keV) by analysing the excitation functionand taking into account all the involved effects such as tar-get thickness, beam energy distribution and energy straggling.Total cross section vs. proton energy has been obtained forthe rest of the excitation curve, where the thickness and stoi-chiometry of the targets was determined by using three nuclearanalytical techniques.

PACS: 25.40

1 Introduction

The absolute total cross section of the19F (p, αγ)16O reac-tion is of importance in the field of nuclear astrophysics[1].Complete information concerning the total cross section isthe necessary requirement for the determination of the reac-tion rate vs. temperature. Moreover, the resonance strengths ofthis reaction are of importance for quantitative nuclear analy-sis in material science[2, 3]. Measurements of the excitationcurve (e.g[3− 5]) and strengths or cross sections for indi-vidual resonances[6, 7] of 19F (p, αγ)16O reaction exist inthe literature. Given the importance of this reaction, a con-cise and complete measurement of the relevant quantities wasdeemed necessary. The determination of absolute cross sec-tion or resonance strengths requires an accurate knowledge ofcertain parameters, such as target thickness and stoichiometryand absolute detection efficiency[8]. In cases where chemicalcompounds are involved for the production of targets, largeerrors can be induced by the assumed target stoichiometrywhich may be different from the stoichiometry of the originalmaterial used for the target production.

In the present work, all the above mentioned requirementsfor the absolute measurement of cross section are fulfilled.By using the 4π detection system, direct measurement of thetotal cross section has been achieved. The efficiency of thissystem was determined via Monte-Carlo calculations and theresults have been verified using nuclear reactions[9]. De-tailed analysis of the targets was made using different ana-lytical techniques such as XRF and RBS measurements andusing the known properties of the19F (p, αγ)16O resonance atER = 872 keV.

2 Experimental setup and procedures

The experiment was carried out at the 5.5 MV T11 Van deGraaff Tandem accelerator of the Institute of Nuclear Physicsat N.C.S.R. ‘Demokritos’. The energy of the proton beamvaried fromEp= 800 to 3600 keV with typical currents inthe rangeIp = 10 to 30 nA on the target (limited by deadtime). The accelerator has been energetically calibrated us-ing the well known energy of the19F (p, αγ)16O resonance atER = 872.11± 0.20 keV and the27Al(p, γ)28Si resonanceatER = 991.86± 0.03 keV. The spread of the proton beamenergy was found to be∆b = 1.6± 0.2 keV.

A schematic diagram of the detection system is shown inFig. 1a. The main component is a NaI(Tl) detector. It con-sists of two scintillation crystals of cylindrical shape (diame-ter: 305mm, height:152.5mm). Each crystal is segmented in4 equal parts. The NaI(Tl) detector has an axial throughhole(diameter 35 mm) as well as a radial throughhole (diameter:83mm) where two extra NaI(Tl) detectors have been placed.Hence, the solid angle of approximately 96% of 4π is coveredfor the γ-rays emitted from the target. The signals from thephotomultipliers are summed to obtain the final signal whichgoes to the ADC for data acquisition. The beam collimatingand target system is shown in Fig. 1b. The proton beam passesthrough two apertures (6 mm and 3 mm diameter) and is fo-cused into a spot of about 7 mm diameter on the target. Thetarget is placed at the end of a stainless steel tube at a distanceof 100 cm from the first collimator. The second collimator isplaced 40 cm away from the target. A hard PVC material isplaced at a distance of 5 cm from the end of the tube to isolatethe target holder which can be mechanically mounted on the

284

Fig. 1. Schematic diagram of the experimental setupa Detection systembBeam collimating and target sytem

Fig. 2.Output drawing of the simulation programs for the detection system

end of the target tube by tightening a hollow brass cylinder. Alead ring of about 1mm thickness was used as vacuum sealingmaterial between the target holder and the tube while the restof the beam line is sealed with copper gaskets. The beam lineincludes 3 cooling traps and 4 turbo pumps. The last pump islocated at the beginning of the tube before the first collimator,at a distance of about 120 cm from the target position. Withthe setup described above, a vacuum of 3×10−8 torr has beenachieved. The target holder served as the Faraday cup for cur-rent integration. A voltage of -300 V was applied to the otherpart of the beam tube for suppression of secondary electrons.The NaI detector is fixed on an iron frame which can be movedon a railway. Thus, the target holder can be placed at the centerof the detector (see also[10]).

The absolute efficiency of the 4π detection system was de-termined by performing a Monte-Carlo simulation, which wasbased on the GEANT package (version 3.20)[11]. GEANT

Fig. 3. A γ -ray spectrum obtained with the summing detector in the19F (p, αγ)16O reaction

is a system of detector description and simulation tools. Forthe simulation of the detector as well as the target holder, 70different volumes of various shapes describing different ma-terials have been taken into account in order to simulate thephysical processes involved in the detection system. The sim-ulated geometry of the detector is shown in Fig. 2. The outputof the simulation was a histogram, showing the number ofevents vs. the deposited energy in the crystal, which is conse-quently convoluted with a gaussian response function in orderto obtain the final spectrum. The efficiency is calculated by in-tegrating this spectrum for every desired energy window. Thefirst results showed that the absolute efficiency depends on thenumber of cascade photons which are emitted for every event.An example is the case of the simulation of a60Co radioactivesource which decays with the emission of two cascade pho-tons of 1172 and 1332 keV. For a single photon with energy2505 keV, the calculated absolute efficiency of the detectionsystem, integrating the whole spectrum, would be 0.71. How-ever, the fact that we have two photons which sum to an energyof 2505 keV, increases the absolute detection efficiency up to0.95.

Three nuclear reactions were used in order to evalu-ate the results from the Monte-Carlo simulation[9]: the19F (p, αγ)16O resonance atER = 872 keV, the27Al(p, γ)28Siresonance atER = 992 keV and the9Be(p, γ)10B broad res-onance atER = 989 keV.

The resonance strengthωγ was measured for the 872 keVresonance of19F (p, αγ)16O reaction via a thick target meas-urement. Threeγ - rays of energy 6130, 6917 and 7117 keVare expected in this reaction (Fig. 3). The efficiency was cal-culated for these three photons and weighted according totheir branching ratios[12] and it was found to beε = 0.55.This led to a measuredωγcm = 760± 70 eV for the 872 keVresonance, in excellent agreement with the literature value ofωγcm = 780± 60 eV[7]. From this result it is concluded thatthe ratio of the simulated over the experimental efficiency isr1 = εsim/εexp = 1.03.

Deexcitation of the 28Si compound nucleus for27Al(p, γ)28Si reaction atER = 992 keV can proceed viamany cascades[13]. Fifteen different cascades were simulatedto determine the efficiency. The linear combination of all the

285

cascade efficiencies has given a total efficiencyε= 0.70. Usingthis value the resonance strength was found asωγcm = 2.07±0.10 eV. The literature value isωγcm = 2.00± 0.17 eV[13].Thus, the ratio is r2 = εsim/εexp = 0.97.

The excitation function of the9Be(p, γ)10B reaction hasbeen obtained at Ep = 900 - 1065 keV, using a thin berylliumtarget. The maximum of the broad resonance occurs at 989keV. The ground state transition is the dominant deexcitationmode of the compound nucleus (about 93%). Thus, the effi-ciency was found to beε = 0.57 for the integration window3–9 MeV and the cross section was found asσR = 490± 50mb. The adopted literature value isσR = 480± 40 mb[14, 15].Hence the ratio is r3 = εsim/εexp = 0.98.

The average ratio from the three reactions isr = εsim/εexp = 1.00± 0.03. Thus, the Monte Carlo simulation resultsfor the absolute efficiency were found to be reliable (εexp =εsim) and were used in this work with an assigned error of±6%, twice the mean value error of the measurements.

Two different runs have been carried out in the experiment.The first run was performed in the proton beam energy rangeEp = 800–1680 keV while the backing material of the fluo-rine target was Cu. In the second run the beam energy variedin the range range Ep = 1680–3600 keV with W as backingmaterial of the target in order to reduce the background fromthe backing. To test possible deterioration of the targets due tobombardment, the 872 keV resonance was frequently scannedand the yield at the maximum was tested for target loss. Onlyafter bombardment at the highest energies a 3% reduction inyield was observed which is within the experimental errors. Atypical spectrum of the reaction is shown in Fig. 3.

3 Analysis and results

3.1 Method of analysis

The reduced reaction yield per incident proton is defined by :

y = C/(ε ·Np ·N∗) = σ · dxF , N∗ = NA/A (1)

where C is the integrated number of counts observed for all thethree transitions (γ1, γ2, γ3), Np the number of incident pro-tons,ε the absolute detection efficiency for the three photons,NA the Avogadro number, A the atomic weight of fluorine,σ the cross section of the reaction in mb anddxF is the in-finitesimal fluorine thickness of the target inµg/cm2. Thus,the reduced yieldy is in µg.

If the target has a finite total thicknessx, the correspondingenergy loss for proton energyEp is ∆lab(Ep) = T (Ep) · x,whereT (Ep) is the stopping power of protons for the targetmaterials. In this case the reduced reaction yield becomes anintegral over the target thickness :

y(Ep) = pF ·∫ x

0σ(E) · dx = pF ·

∫ Ep

Ep−∆lab

σ(E)T (E)

dE (2)

wherepF is the fluorine weight proportion in the target.The cross section of an isolated resonance is given by the

Breit-Wigner formula:

σ(E) = σR ·ERE· Γ 2

R

4 · (E − ER)2 + Γ 2R

(3)

with the assumption that the resonance width is sufficientlysmall so that the partial width ratio is unity and the total widthΓ (E) is equal toΓR. These assumptions do not hold far awayfrom ER and penetration coefficients have to be included inthe calculations.

Two phenomena influence the reaction yield and they havebeen taken into account, that is the beam energy distributionand the energy straggling of protons inside the target. The firstphenomenon has been described with a gaussian distributionof beam energyg(E,Ep) around a mean valueEp.This gaus-sian function modifies the cross sectionσ(E). The second phe-nomenon, the spreading of beam energy which accompaniesthe slowing down of protons inside the target, has also beendescribed with a gaussian distribution around a mean valueEp − ∆lab at a depthx inside the target. The standard de-viation of this straggling distribution is described sufficientlywell by Bohr’s formula [16].

ΩB =

(0.156· z2 · Z

A· x)1/2

(keV ) (4)

x in µg/cm2, Z,A the average atomic number and weightin case of a multielement target andz the atomic numberof the projectile. The total spreading width is the result ofcontributions from straggling and from the intrinsic energyspread of the beam∆b. Both effects have been included in asingle gaussian function[17] in order to avoid a triple integraland to simplify the calculations, namely

g(Ep, E′, x) = B · exp

[−(Ep − E′ − T (Ep) · x

)2

0.36 · Γt

](5)

where B is the normalization constant andΓt is the totalFWHM of the energy spreading:

Γt =

(∆2b + 0.86 · z2 · Z

A· x)1/2

(6)

Consequently, the reduced reaction yield is given by the doubleintegral :

y(Ep) = σR · pF ·∫ x

0

∫ ∞0

ERE′· Γ 2

R

4 · (E′ − ER)2 + Γ 2R

· g(Ep, E′, x) · dE′ · dx (7)

or y(Ep) = σR · pF · xeff (Ep;ΓR, ER, x).The expected experimental resonant yield can be calcu-

lated using formula (7) if the propertiesER, ΓR, σR of a res-onance, target thicknessx and composition are known. More-over, the experimental resonance yield can be fitted using theabove expression for the determination of some of the vari-ables. This procedure has been used in the following manner:the experimental yield of the 872 keV resonance has been fit-ted using expression (7) to determine the target parametersxandpF and the resonance energyER. Subsequently, the ex-perimental yield of all the resonances withΓR ≤ 20 keV hasbeen fitted to determine their properties.

The rest of the excitation function consists of broader reso-nances and the cross section was extracted from the thin targetrelation

y = pF · x · σ (8)

286

Fig. 4. The RBS spectrum obtained by bombarding the target with 1.2 MeVprotons

using an effective beam energy of

Eeff = Ep −∆lab(Ep)/2 (9)

which accounts for the target thickness.

3.2 Energy range Ep=800-1680 keV

3.2.1 Target analysis.The target used in this run was pro-duced localy by evaporating natural CaF2 powder on a 0.7 mmclean Cu backing. The target was analyzed using three analyt-ical methods: XRF (X-Ray Fluorescence), RBS (RutherfordBackscattering Spectroscopy) and the known propertiesERandΓR [12] of the 872 keV resonance of the19F (p, αγ)16Oreaction.

The XRF method led to the Ca thickness in the target:xCA = 22.5 ± 2.2 µg/cm2 or NCA = 3.4 ± 0.3 × 1017

atoms/cm2. The RBS method, using 1.2 MeV protons, hasrevealed the composition and depth profile of the target. TheRBS spectrum (Fig. 4) showed three peaks which correspondto 12C, 19F and40Ca. The resulting Ca content was found tobe NCa = 3.4± 0.4× 1017 atoms/cm2 in excellent agreementwith the XRF analysis. The results for C and F NC = 1.5×1017

atoms/cm2 and NF = 5.0×1017 atoms/cm2 were used as theinitial values for the third main method of target analysis, thefitting process of the 872 keV resonance.

The thick target measurement of this resonance has givenωγ =760± 70 eV.Using the well known energy and width ofthis resonance[12] the cross section was determined asσR =590± 50 mb, in excellent agreement with the reported value[7] of σR = 600± 40 mb. SinceER, ΓR, σR and the Ca thick-nessxCA are known, the experimental yield of the 872 keVresonance has been fitted using formula (7) and having as freefit parameters the total target thicknessx and the weight pro-portion of fluorinepF . The weight proportion of carbon in thetarget is defined aspC = 1−pF −xCa/x since these three el-ements are the constituents of the target. The results are (table1) : x = 44± 3 µg/cm2, pF = 0.38± 0.03.

It is obvious that large errors can arise if one would assumethat the composition of the target is identical to natural CaF2.

Table 1.Results from target analysis

x(µg/cm2) pi(weight proportion)

F 16.7±1.7 0.38±0.03Ca 22.5±2.2 0.51±0.06C 4.8±2.9 0.11±0.07

total 44±3 1

3.2.2 Results.The excitation function of19F (p, αγ)16O hasbeen obtained at Ep = 800-1680 keV. Many resonances ap-pear in this region. The energy step varied from 1 keV(whenscanning a resonance) to 10 keV (for large gaps between reso-nances). The spectrum integration window was 2.8 MeV to 9MeV. The absolute efficiency for this energy region was com-puted tobeε = 0.55± 0.03. Dead time effects were accountedfor. The accumulated charge at the target varied between 0.5and 10µCb with an estimated error of 3%. The backgroundfrom the Cu backing of the target was measured by bombard-ing a single Cu backing and has been accounted for.

The excitation function is shown in Fig. 5. The target hasan energy thickness∆lab(1 MeV) = 8.1 keV and the energystraggling width is∆s = 4.2 keV. The yield of each one of theobserved resonances has been independently fitted using ex-pression (7). The fit parameters in this case wereER, ΓR, σR,since target thickness and composition have already been de-termined. In the cases of the 832 keV and 898 keV resonancesthere are significant contributions from the two strong adjacentresonances at 872 keV and 934 keV. In these cases calculationof the expected experimental yield of the two strong reso-nances was initially performed, using formula (7) and thensubtracted from the experimental yield of 832 keV and 898keV resonances before the fitting procedure. Subtraction ofa smooth yield background below the resonance points dueto the contribution of other resonances, was also performedwhere necessary. The resonance strength was calculated forevery narrow resonance, using the relation ([1]) :

ωγ = µ · ER · σR · ΓR/(2πhà 2) (10)

In Table 2, the resulting fit parameters for the resonancesare summarized and compared with literature values. The ER

andΓR results are in good agreement with literature. A dis-crepancy inσR of about a factor of two from older valueswas found in two cases, namely, for the 1134.4 and 1343.6keV resonances. The resonance strength for the 1086.4 keVresonance was deduced from a thick target measurememt.

In Fig. 5, the expected yield due to all the narrow reso-nances is shown (solid line), calculated using the parametersobtained from the fit. In this case, penetration coefficients forentrance and exit channels for each resonance were includedin the calculations, in order to obtain correctly the expectedresonant yield for each one away from the resonance energy.There are regions in the excitation function where the yieldis mainly due to broader resonances and contributions fromtails of broader resonances at higher energy. In order to extractcross section information for these regions, the calculated nar-row resonance yield has been subtracted from the experimentalyield.

287

Fig. 5. Excitation function of19F (p, αγ)16O re-action. Thesolid curveis the sum of all the indi-vidual fits to the narrow resonances

Table 2.Fit parameters for19F(p,αγ )16O resonances

ER(keV) ΓR(keV) σR(mb) ωγ(cm)

Previousa Present Previous Present Previous Present Present

832.1±1.0 832.0±0.7 5.6±0.5b 5.0±1.0 19c 12.5±2.5 17±5872.11±0.20 872.11±0.20a 4.53±0.16a 4.53±0.16a 600±40d 590±60 760±70

540c

898.8±1.0b 897.7±0.7 3.5±0.4b 5.0±1.0 23c 18±3 27±7935.4±1.3 934.0±0.7 8.1±0.5a 7.4±0.7 180c 188±15 430±501087.7±1.0 1086.4±0.7 0.15±0.05a ≤1.4 13c 7.9±1.01135.6±1.0 1134.4±0.7 3.1±0.2b 2.5±0.3 15c 31±3 29±41280.0±1.0 1278.7±0.7 15.6±0.8b 16.2±1.7 29c 29.7±2.3 202±261347.7±1.0 1343.6±0.7 4.9±0.7a 4.0±0.8 89c 160±28 280±701371.0±1.0 1370.4±0.7 12.4±1.0a 11.9±1.2 300c 351±27 1860±2301603.0±2.0 1602.2±0.7 4.5±0.3b 2.7±0.6 31±6 44±12

a Ref. [12]b Ref. [3]c Ref. [6]d The value from [7] for theα2 group,σa2

R = 440±13 mb, normalized by theα2 branching ratio 0.73 from [12].

The remaining yield for these regions varies slowly withenergy compared to the energy thickness of the target. Thus,it is a thin target case and the cross section can be determinedusing the relation :σ(Eeff ) = y(Ep)/pF · x, whereEeff isgiven by expression (9). The cross section for these regionswas calculated using the above relation and is shown in Fig. 6.There are two regions which are not included in the graph.These are the regions with the strong 872 keV and 934 keVresonances and the 1343 keV and 1370 keV resonances, wherethe subtraction of large numbers does not permit the extractionof reliable cross sections.

3.3 Energy range Ep=1680-3600 keV

An excitation function has been obtained atEp =1680 to 3600keV, in energy steps of 20,10 and 5 keV (near the resonances).The target was produced by evaporating natural CaF2 powderon a clean tungsten (W) backing. This target was made in thetarget preperation chamber of the Institute of Material Science

Fig. 6.Cross section vs effective proton energy from 1000 to 1680 keV aftersubtraction of the contribution of the narrow resonances

288

Table 3.Astrophysical S-factor as a function of energy Ecm

Ecm S Ecm S Ecm S Ecm S Ecm S(keV) (MeV·b) (keV) (MeV·b) (keV) (MeV·b) (keV) (MeV·b) (keV) (MeV·b)

956.8 16.3 1247.1 22.5 1737.6 95.1 2203.2 234.7 2830.1 72.3966.4 16.6 1394.5 31.5 1756.6 116.9 2212.7 227.6 2849.1 75.5975.9 16.9 1404.0 32.7 1775.7 127.8 2222.2 217.4 2858.6 78.0985.4 17.2 1413.5 39.2 1785.2 129.2 2241.2 205.0 2868.1 74.0994.9 18.0 1432.5 32.5 1804.2 151.6 2260.2 193.7 2877.6 70.6

1004.4 19.6 1442.0 32.7 1813.7 178.3 2279.2 172.6 2887.1 73.11013.9 21.6 1451.5 34.6 1823.2 204.8 2298.2 169.8 2906.1 76.71018.7 23.0 1461.0 37.1 1832.7 240.2 2317.2 185.6 2925.1 80.81023.5 24.2 1470.6 36.5 1837.4 254.3 2336.2 189.2 2944.1 85.41027.3 25.1 1480.1 36.0 1842.2 260.9 2355.2 190.1 2963.1 95.91034.9 29.2 1489.6 36.9 1846.9 246.4 2364.7 189.8 2982.1 119.61038.7 33.6 1519.0 41.7 1851.7 246.0 2374.2 192.1 3001.1 114.81042.5 39.0 1531.4 45.2 1856.4 238.3 2383.7 192.2 3020.1 108.61047.3 46.7 1537.1 49.0 1861.2 235.1 2393.2 200.3 3029.6 103.61052.0 55.5 1541.9 52.9 1865.9 230.1 2402.7 203.5 3039.1 100.21056.8 63.8 1546.6 56.0 1880.2 256.2 2412.2 208.8 3058.1 91.91061.5 68.1 1556.1 64.6 1889.7 281.9 2431.2 222.5 3077.1 80.31066.3 67.9 1566.1 71.5 1899.2 300.2 2450.2 222.7 3096.1 73.01070.1 66.6 1575.6 80.4 1908.7 306.2 2469.2 216.6 3115.1 65.91074.4 68.5 1585.1 95.5 1918.2 299.9 2488.2 208.9 3134.1 61.71078.2 66.0 1594.6 124.8 1927.7 303.2 2497.7 200.9 3153.1 60.61082.0 65.7 1599.9 138.9 1937.2 295.5 2507.2 192.6 3172.1 57.21086.3 64.7 1604.6 166.2 1946.7 281.3 2526.2 166.6 3191.1 54.61090.1 64.2 1609.4 170.2 1956.2 267.2 2545.2 128.1 3210.1 49.41094.8 67.7 1614.1 140.3 1965.7 255.8 2564.2 103.9 3229.1 50.91099.6 69.5 1618.9 113.6 1975.2 236.8 2583.2 98.5 3248.1 47.51104.4 75.2 1623.6 98.4 1994.2 215.9 2602.2 99.7 3267.1 47.51109.1 77.6 1628.4 90.0 2013.2 208.9 2621.2 106.7 3286.1 54.61118.6 79.4 1633.1 83.9 2032.2 214.5 2640.2 119.0 3295.6 53.91128.1 74.9 1642.6 77.7 2051.2 224.8 2649.7 113.9 3305.1 55.71137.7 68.4 1642.6 75.1 2070.2 221.5 2659.2 110.0 3314.6 53.61147.2 61.2 1652.1 70.4 2089.2 224.0 2668.7 106.5 3324.1 53.01156.7 54.2 1661.6 66.4 2108.2 221.7 2678.2 102.0 3333.6 50.41166.2 55.3 1671.1 66.9 2127.2 227.6 2697.2 90.6 3343.1 50.41175.7 48.7 1680.6 66.6 2146.2 222.1 2716.1 80.1 3362.0 48.11185.2 44.3 1690.1 67.5 2155.7 227.6 2735.1 73.8 3381.0 45.91190.0 42.7 1699.6 70.4 2165.2 228.3 2754.1 64.6 3400.0 44.01232.8 25.2 1709.1 73.7 2174.7 230.7 2773.1 59.6 3419.0 41.71237.6 23.0 1718.6 81.0 2184.2 229.7 2792.1 59.0 3438.0 38.91242.3 22.4 1728.1 86.9 2193.7 233.4 2811.1 61.1

at N.C.S.R. “Democritos”. This unit operates on a carbon freeenviroment.

The target was analysed using XRF, RBS and the 872 keVresonance. The RBS spectra did not show any evidence ofcarbon presence. The 872 keV resonance points have beenfitted using formula (7) and the results for the total targetthickness and the fluorine proportion were found to bex =26.0± 2.4µg/cm2 andpF = 0.42± 0.03.

Due to the thin target used,∆lab = 2.9 keV at Ep = 2 MeV,the effective beam energy is given by the relation (9) and thetotal cross section was determined using again expression (8).Cross section vs. effective beam energy for this energy rangeis shown in Fig. 7.

3.4 S-factor calculation

The astrophysical S-factor was calculated using the expressionS(Ecm) = σ(Ecm) · Ecm · exp(275.49 · E−0.5

cm ), with Ecm inunits of keV. The results are presented in Table 3 and displayed

in Fig. 8. Taking into account all the sources of errors, anoverall error of± 11 % was calculated for the S-factor valueswhile the effective energy is accurate within an error of 0.7keV.

4 Conclusions

The present work gives complete quantitative information onthe total cross section for the19F (p, αγ)16O reaction over theenergy rangeEp = 800 - 3600 keV. The results have beenpresented in terms of resonance strengthωγ for ten narrowresonances. The total cross section and thus the astrophysicalS factor vs. effective proton energy has been determined forthe rest of the excitation curve and presented in a tabular form.Similar measurements covering the low energy region, Ep <800 keV, are needed for the complete determination of thereaction rate vs. temperature.

289

Fig. 7. Cross section vs effective proton energy for the energy range 1680 to3600 keV

Fig. 8. S-factor vs effective center of mass energy of protons combining theresults from both parts of the experiment, Ep=1000-3600 keV

The authors would like to thank M. Kokkoris for his help during the develop-ment of the Monte-Carlo simulation programs and the RBS measurements ofthe targets. This work was partly supported by EU grant ERBCHRX-CT93-0339.

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