Poenitz, W.

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Oktober 1966Institut für Angewandte KernphysikKFK 505The (n, y) Cross Section of 197Au at 30 and 64 keV Neutron Energyw. PönitzJournal ofNuclearEnergy Parts AlB. 1966. Vol. 20. pp. 825 to 834. Pergamon Press Ltd. Printed in NorthernIrelandTHE (U, y) CROSS SECTION OF 197Au AT30 AND 64 keV NEUTRON ENERGYW. PÖNITZInstitut für Angewandte Kernphysik, KernforschungszentrurnKarlsruhe, W. Germany(Received 2 March 1966)Abstract-The neutron capture cross section of 197Au was measured at 30 and 64 keV neutron energyusing the activation method. Two different methods were used at 30 keV for the absolute neutronfiux determination. The resuIts are (j~~ (30 keV) = (0'600 ± 0'009) barn and (j:'~ (64 keV) =(0·357 ± 0,009) barn.1. INTRODUCTIONTHE neutron capture cross sections in the keV energy region are of considerableinterest to nuclear theory in connexion with the optical model (LANE and LYNN,1957), to cosmological theories of element formation (BURBIDGE et al., 1957) andto the design of nudear reactors. These important applications have led to a largenumber of experiments by a variety of techniques which for the determination ofreaction rates fall mainly into two types: (i) The ~detection of prompt y-rays by alarge liquid scintillator tank (DIVEN et al., 1960; GIBBONS et al., 1961), a Moxon-Raedetector (MOXON and RAE, 1963) or a proportional counter (KONKS et al., 1964).(ii) The detection of the radioactivity which is induced by neutron capture in manynudei (MACKLIN et al., 1957; BOOTH et al., 1958). However, the main problem seemst<Y be the absolute neutron fiux strength determination. Only the shell transmissionmethod (SCHMITT, 1963; BELANOVA, 1960) ayoids any absolute measurements butthe corrections for the resonance self-shielding and for secondary neutron scatteringeffects are considerable.The (n, y) cross section of gold is of special interest as a standard. Existingmeasurements are shown in Fig. 1. The cross-section values measured by differentgroups disagree by a factor of about two.This measurement of the neutron capture cross section of gold is presented mainlyto give an absolute value at 30 keV for the renormalization of energy-dependent crosssections measured by other authors. To avoid systematic errors two different methodswere used for the determination of a~~ at 30 keV neutron energy.2. EXPERIMENTAL PROCEDURE AND RESULTSNeutrons far the irradiation of the gold sampIes were obtained from the reactions7Li(p, n)7Be and 3H(p, n)3He. The protons were accelerated by a 3 MeV Van deGraaff. A layer of LiF evaporated on a 0·06-em thiek Cu backing plate was used asthe target at 30 keV neutron energy. lust above the thresholds for the 7Li(p, nYBeand 3H(p, n)3He reaetions one gets neutrons of 30 and 64 keV average neutron energy.In this case the neutrons are kinematically eollimated in a forward cone. Therefore itwas possible' to use a water-eooling ring around the edge of the Cu backing platewhich did not interfere with the neutron fiux. This method enabled us to bombardthe target with a proton beam current of about 150 {tA.I 825826L VU ULW. PÖNITZyEc..0VL MU Ivuz-oA R.L. Macklin et 01., 1957B R.Booth et 01., 1958C A.E.Johnsrud et 01., 1959o A.T. Ferguson et 01., 1959E W.S.Lyon et 01., 1959F S.J.Bome et 01., \959G E.G"Bilpuch et 01.,19601·0 H T.S.Belanovo., 19601 J.H,Gibbons et oL,1960J J.H.Gibbons et 01..,1960K J.H.Gibbonset al., 1960L R.e. Block et 01., 1960MAl. Isakov et 01.,1960N B.C.Diven et oL,1960o L.W.Weston et 01., 196tP S.A.Cox, \961Q K.K. Hords, 1962R L.Ä.Miskel ef al., 1962S R.L.Mocklin et 01., 1963T I. Ber~qvist, 1963U E.Hoddad et 01., 1963V VA.Konks et 01., 1963W H.W. Schmitt ,1963X J.F. Barry, 19640·2 i ~:~~~~~~~e~t ~~"~i~~965RR P"Cl R RRX T~:QpT Gy T NR QpI 11 fY cGy C1 I J300En , keVFIG. 1.-The (n, y) cross section of 197Au. Comparison of existing measurements.The proton beam energy was measured and controlled by a proton spin resonancespectrometer. It was calibrated by the thresholcl energies. of the 7Li(p, n)7Be and3H(p, n)3He reactions and the opening angle of the forward cone of the neutrons fromthe 7Li(p, n)7Be reaction. This cone was measured using long counters. The un-certainty in the primary energy is about 1 keV.The Au sampIes were 0·03-cm thick foils. In this case we have ätot. N. d ~ 1and the cross section can be determined by its definition equationC=a.N.d.Q (1)where Cis the reaction rate (activation) per sec. cm2 ; Q is the neutron flux strengthper sec. cm2 ; N is the number of atoms per cm3 and dis the thickness of the foil.However, for the application of equation (1) many corrections must be taken intoconsideration.2.1 The cross section at 30 keV (1st method)The principle of this method is to determine the neutron flux strength by theradioactivity of the reaction product 7Be in the LiF target (PERRY, 1960). In thiscase, it is of special advantage, that the y-ray energies occurring in the decays of 7Beand 198Au are very similar and therefore the ratio of the y-efliciencies of the usedNaI(Tl) detector is near to one.The experimental set-up is shown in Fig. 2. The proton beam is limited by anaperture to 0·9 cm diameter and strikes a LiF target. On the LiF a thin layer of Al isevaporated to avoid any loss of 7Be. The gold sampIe of 1·8-crn diameter is exposedto the neutron flux at the back of the Cu target backing. A second 0'005-cm thickThe (n, y) cross section of ,.7Au at 30 and 64 keV neutron energy 'ö27Au-Shield003mmTarget, LiF on Cu baeking plateAu-Sample0·3mmSampieSmm Plexiglas280 mg/em' AluminiumFm. 2.-Experimental set-up. (First method).gold foi1 is exposed to shie1d the samp1e from activation by thermal and e1ectronvolt resonance neutrons scattered back from the room. The aetivity of the externa1circ1e of this foi1, which was not struck by the kinematically collimated neutrons wasmeasured after the irradiation. No measurab1e activity was found showing thataetivation due to scattered neutrons was negligib1e.Two different experiments were earried out using 15 and 50-min irradiation times.The time dependenee of the neutron flux due to intensity variation of the proton beamcurrent was monitored by a 10ng counter 2 m distant from the target. Mter theirradiations the y-activities of the target CBe; 438 keV transition of 7*Li) and ofthe samp1e (l98Au; 411 keV transition of 198*Hg) were measured in the same geo-metrie arrangement using a 4 X 3 in. NaI(T1) deteetor. The y-ray spectra wereana1ysed by a mu1tichanne1 ana1yser. The experimental points of the photopeakswere fittedby gaussian curves.The quantitative eonnexion between the counts Z in the photopeak and theactivation C is easy to get from the differential equations of the radiative decayZAu = CAu' CAu ' FAuZBe = CBe • Q . FBeF = -1. (1 - e-ÄT). (1 - e-M) • e-Ät • TM' (2)C is the probability that a count occurs in the photopeak when a deeay takes p1ace.The faetor F depends on .the decay constant A, the irradiation time T, the countingtime (), the time t between the end of the irradiation and the beginning of the countingand on the eorrection factor TlJ,f ealcu1ated from the monitor counting rates. Thefaetors(3)828 W. PÖNITZeontain the transition intensity per decay a for the transition eonsidered. oc is theinterna1 conversion coefficient, 'YJ the total detection effieieney of the NaI(T1) crysta1and P its peak-ta-total ratio. The factors h' and h represent the y-ray absorption inthe cover of the NaI(Tl) detector and the y-ray self-absorption in the Au samp1e.'YJ and P were eva1uated using the calcu1ated va1ues of WEITKAMP (1963) andHEATH (1964). The y-absorption between the y-source and the NaI(T1) crysta1 wasealeu1ated using the formu1a(4)for y-rays crossing the cover perpendicu1ar to the crysta1 surfaee. fh is the totalabsorption coeffieient and b the thickness of the absorption material. Va1ues of fhwere taken from GRODSTEIN (1956). It shou1d be possib1e to get precise va1ues of thefactorw = -'.'YJ=.B.:...e_.P_B.:...e_.--:h_B.:....e''YJAu' PAu ' hAU'(5)(6)because of the simi1ar y-ray energies.The y-ray se1f-absorption in the Au samp1e was ealcu1ated using the assumptionof homogenous aetivation. This leads to the formu1ah = ~ . In LßO exp ( - ~) dfhX . dQfhb In dQThe integration limit Q is given by the maximum opening angle of the y-raysmeasured by the NaI(T1) detector.The aetivation CAu contains the cross sectionCAu = Q . N. dAu ' g(dcu) .f(dAu) . S(dAu) . ():;,~. (7)The factor g(deJ takes into account the 10ss of neutrons in the Cu target backingp1ate and the factor f(dAu) the correction for the 10nger neutron flight path in thesamp1e due to the divergence of the kinematically collimated beam. Va1ues wereealcu1ated using11exp (- Lfo1 deu) deos eg(deJ = eosa 1 cos e1 deos eeosa(8)and1f(dAu) = ,Au dktot· Au1:saLz;t~Au exp ( - !-:) dLfo1X . deos er deos eJeosa(9)Here e is the maxima opening angle of the neutron cone and ~tot the total macro-scopic cross section. The factor S(dAJ inc1udes the resonanee self-shie1ding of thefoi1 (DRESNER, 1962) and the activation by neutrons which are scattered within theThe (n, y) cross section of 197Au at 30 and 64 keV neutron energyTABLE l(a).-VALUES NEEDED FOR CROSS-SECTION CALCULATION829NotationaAu(J(AuaBe'rIAuPAu'rIBePBehAu'hBe'hAug(dCu)f(dA~S(dAu)Va1ue0·9980·0420·10320·26740·7520'25510·7020·9110·9160·9300·9750·9991·021RemarksNuclear Data Sheets (1958)LEWIN (1963), PETTERSON (1965)TAYLER and MERRITT (1962))Interpo1ated between va1uescalculated by WEITKAMP andHEATH}Calcu1ated usingequation (4)using equation (6)using equation (8)using equation (9)MACKLINTABLE l(b).-MEASURED VALUES FOR THE CROSS-SECTION CALCULATION AT 30 keV NEUTRON ENERGYNotationMeasurement No. 1ValuesNo. 2ZAuZBeFBe/FAuAu weightGn,y2·214 1061.0281064·914 10-31·533 g0'5913 barn1·346 1051'500 10"1-14110-21·463 g0·5942 barnTABLE 1(c).-EsTIMATED ERRORS OF THE VARIOUS VALUESUSED FOR THE CROSS-SECTION CALCULATIONError ErrorNotation (%) Notation (%)aAu 0·1 ZAU/ZBe 0·61 + (J(Au 0·2 FBe/FAu 0·4aBe 1·6 hAu 0·5W 0·8 S(dAu) 0·5g(dcu) 0·3 N.dAu 0·1foil (SCHMITT, 1960) and was calculated using the simplified relations for S(t!) ofMACKLIN.Table l(a) contains all values which are needed for the calculation of the crosssection. Table leb) contains the measured values and Table l(c) the errors of thevalues given in Tables l(a) and (b). The result for the cross seetion isa~,~ (30 keV) = (0'593 ± 0·012)barn. (10)The error in this first method is mainly due to the error of aBe •2.2 The cross section at 30 keV and 64 keV (2nd methot!)The principle of this method is to determine the neutron flux by the manganesebath method (PERRY). The radioactivity of the Au sampie was determined absolutelyby the coincidence method.830 W. PÖNITZThe experimental set-up is shown in Fig. 3. The kinematically collimated neutronsentered a glass sphere through an entrance channel made of quartz. The neutronsslowed down in the MnS04 solution and were captured at thermal energies by thevarious components of the manganese bath. The integration over the space-dependentneutron fiux was performed after the irradiation by stirring the solution. A well-defined quantity of the solution was filled into a container of Plexiglas and its activitywas measured using a 4 X 3 in. NaI(Tl) crystal detector. The y-activity of the AuGlass SphereChannel(Quartz}54·45 LitreMnSO.-H20 solutionO·3mlD-Au-Sample----O·03mmAu- ShieldSEV XP104050mm pb-ShieldÜ'5mm Cd- Shield=p=r=ot=o=n=b=e===er=t=ur::j:et==li F_~~~~-r-r;zzzm~~;ZZZ;;~Z22:i~itZZ:t.:zz::22:2:l:Z:Z:;:.zz:;~4)(3 in.NaI (Tl) Plexiglas ContoinerFIG. 3.-Experimental set-up (Second method).sampIe was measured also by the NaI(Tl) detector. The counts in the photopeaksare given by the following relations:ZAn = EAn' Q. N. dAn' FAn.' gAuCdoJ .f(dAn). S(dAJ. (J~~ZMu = EMu' CMu · FMu • gAn(dcn) . gMu(dAn, dOd)' (11)The meaning of all factors is the same as in Section 2.l.The relations CMu!Q needed for cross-section calculation follows from a fewwell-known simple considerations: The 'source' strength of the neutron beam isQ = L00 Iv P::H(E) + L,o(E) + L,s(E) + L,Mu(E)] . ep(E, r) dV dE + QL + Qc'(12)~(E) is (he macroscopic absorption cross section at the energy E, ef;(E, r) is the neutronfiux in the manganese bath solution at the point rand V is the volume of the sphere.QL is the loss of neutrons due to the leakage at the edge of the sphere and Qo is theloss of neutrons due to the capture in the entrance channel. Vsing the well-knownThe (n, y) cross section of 197Au at 30 and 64 keV neutron energy 831thermal cross sections (BECKURTS and WIRTZ, 1964) or their ratios (AxToN et al.,1965) and regarding the resonance contribution of the Mn activation one getsQ1·011 - QL/Q - Qc/Q1·040 + 0·02497 . NH/NMU(13)Qa/Q was calculated using thermal neutron fiux values measured bygold foils in theneighbourhood of a Sb-Be source in the solution. QL/Q was determined usingrelative long counter measurements and absolute neutron fiux values measured bygold foils in the solution near the edge of the glass sphere.EAu and EMu were determined using sampies ofknown absolute disintegration ratesmeasured by the 47Tß-y coincidence apparatus (CAMPION, 1958). The determinationof the absolute activity of the thick Au foils was described in an earlier paper(PÖNITZ, 1963). To get a well-known 56Mn activity MnS04 powder was activatedby thermal neutrons and its activity determined by the 47Tß-y coincidence method.To avoid errors an extrapolation method was used (PÖNITZ and PÖNITZ andBRUDERMüLLER, 1963).Ta-Ples 2(a), (b), (c) contain the factors needed for the cross-section calculation,TABLE 2(a).-VALUES NEEDED FOR CROSS-SECTION CALCULATIONNotationEAuEMugMu(dAu, dCd)S(dA~, (30 keV)S(dA~, (64 keV)QL!QQc!QValue0·19220·969 x 10-30·9541·0211·0230·0690·005Remarks47Tß-y coincidence47Tß-y coincidenceCalculated using equation (8)MACKLINMACKLINMeasured (see text)Measured (see text)TABLE 2(b).-MEASURED VALUES FOR TElE CROSS-SECTION CALCULATIONNotation ValuesEnZAuZMUFAu!FMUAu weightO'n,y30keV4·378 x 1056·991 X 1050·9401·465 g0·6037 barn64keV1·403 x 10·2·606 X 1051·422l-468g0·360 barnTABLE 2(c).-EsTIMATED ERRORS OF TElE VARIOUS VALUES. GIVEN IN TABLES 2(a) AND (b)Error ErrorNotation (%) Notation (%)EAu 0·8 1 + Qc!Q 0·2EMu 0·8 ZAu!ZMu 0·6g~Iu(dAU, dCd) 0·4 FAu!FMU 0·5S(dAu) 0·5 N.dAu 0·11 + QL!Q 1·3832 w. PÖNITZAuthorWESTON et al. (1961)HARRIS et al. (1965)This workAverage value1·6821·6801·6761·679200 300100503020,I (T ~l~r,"~~ ..'.l~ ~'!<"lI'l' ......... f.....~"l.. .....!-t_t~I-I_r<'> HW.Schmittt,x K.K. Harris et al. "1-!'• J.F.Barry• J.C.Robertson (see text) "0 This workI II I1·00'90·80·70·60·50·2o· 10b 0·3Eo 0·4.QEn • keVFIo. 4.-Comparison of our result with other absolute measurements.The (n, y) cross section of '·'Au at 30 and 64 keV neutron energy 833Table 3 contains a few ratios for cross-section values at 30 and 64 keV. Theaverage value .and equation (16) lead to the resulta~~(64 keV) = (0,357 ± 0'014)barn (17a)a~~(64 keV) = (0'357 ± 0·009)barn. (17b)The meaning of equation (17a) and (17b) is the same as equation (16a) and (16b).In Fig. 4 we compare our results with other absolute measurements in the energyregion 10-300 keV. Our result is in agreement with the values measured by HARRISet al. (1965) as far as the error limits overlap. The results of BARRY (1964) are about20 per cent higher and those of SCHMITT (1963) about 25 per cent lower than the presentones. ROBERTSON (1965) has measured the (n, y) cross section of 1271 at 24 keVneutron energy. His result is (0'832 ± 0,026) barn. We have used this value and theaverage ratio (J~ja~~ = 1·41 ± 0·10 (GIBBONS et al., 1961; KONKS et al., 1964;CHAUBEY and SEHGAL 1965; SCHMITT, 1963) to determine a further a~~ value withan accuracy < 10 per cent. This value is also inc1uded in Fig. 4.Acknowledgment-In conclusion the author th~nks Prof. K. H. BECKURTS for valuable discussions.REFERENCESAxTON E. J., CROSS P. and ROBERTSON J. C. (1965) J. nucl. Energy (parts AlB Reactor Sei. 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Meth. 26, 213.FERGUSON A. T. G. and PAUL E. B. (1959) Reactor Sei. (J. nucl. Energy Part A) 10, 19.GIBBONS J. H., MACKLIN R. L., MILLER P. D. and NEILER J. H. (1961) Phys. Rev. 122, 182.GRODSTEIN G. W. (1956) NBS Circular 583.HADDAD E., WALTON R. B., FRIESENHAHN S. J. and LoPEZ W. M. (1963) Report EANDC-33 "U".HARRIS K. K. (1963) Thesis, Stanford University, Calif.HARRIS K. K., GRENCH H. A., JOHNSON R. G., VAUGHN F. J., FERZIGER..J. H. and SHER R. (1965)Nucl. Phys. 69, 37.HEATH R. L. (1964) Report IDO-16880.ISAKov A. I., Popov Y. P. and SHAPIRO F. L. (1960) Soviet Phvs. JETP 11, 712.JOHNSRUD A. E., SILBERT M. G. and BARSCHALL H. H. (1959j'Phys. Rev. 116, 927.KONKS V. A., Popov Y. P. and SHAPIRO F. L. (1964) Soviet Phys. JETP 19, 59.LANE A. M. and LYNN J. E. (1957) Proc. phys. Soc. Lond. 70a, 557.LEWIN W. H. G. (1963) Nucl. Phys. 48, 159.LYON W. S. and MACKLIN R. L. (1959) Phys. Rev. 114, 1619.MACKLIN R. L. (1964) Nucl. lnstrum. Meth. 26, 213.MACKLIN R. L., LAZAR N. H. and LYON W. S. 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The (n,γ)-cross-section of Au¹⁹⁷ at 30 and 64 keV neutron energy

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The (n,γ)-cross-section of Au¹⁹⁷ at 30 and 64 keV neutron energy

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