J. Inorg. Nucl. Chem., 1965. Vol. 27, pp. 1175 to 1181. PergamonPress Ltd. Printed in Northern Ireland
N E U T R O N CAPTURE CROSS-SECTIONS OF 126Xe A N D 136Xe M. BRESESTI, F. CAPPELLANI, A. M . DEL TURCO, H . NEUMANN and E. ORVINI Chemistry Department, Nuclear Chemistry Laboratory, C.C.R. EURATOM, Ispra, Italy
(Received 10 September 1964) thermal neutron capture cross-section of l~6Xe, its resonance-capture integral (from 0.55 eV to co), and its effective cross-section in a reflector position of the Ispra 1 reactor have been found to be cr0, 12nxe = 2"20 4- 0"22 barns, RIl~sxe ~ 38"0 4- 3'8 barns, and do, 12exe = 2"45 4- 0"25 barns respectively. These values have been determined by irradiating natural xenon and measuring the activity of l~VXe. The thermal neutron capture cross-section of 13sXe has been found to be tr0,13axe = 0"281 4- 0"028 barns. This value has been determined by irradiating natural xenon in a well-thermalized position of the Ispra 1 reactor and measuring the activity of lavCs, the decay product of 187Xe, The neutron fluxes were measured with cobalt monitors. All values have been calculated according to the Westcott convention. Abstract--The
THERE appears to be no value in the literature for the neutron capture cross-section of ~2eXe. In the present work this has been determined from the activity of 127Xe formed in the reaction 126Xe (n, 7)127Xe. The neutron capture reaction can also produce 127raXe. This isotope, never observed in the neutron irradiation of 126Xe, has been studied only as a decay product of 127Cs.~1 Since 127mXe decays to ~2rXe with a 75-sec half life, the production ofl27mXe is not significant in calculating the neutron capture cross-section of a~6Xe. The activity of 127Xe has been evaluated by measuring the intensity of the 377 keV y-photopeak, the number of the 377 keV v-rays per 100 disintegrations being assumed to be 20.4. ~zl The half-life value of 36.4 ± 0.1 days (z) has been utilized in the calculations. For the neutron cross-section of x36Xe a value of 0.15 -~ 0.08 barns is reported, though without any experimental detail/4) 136Xe is a fission product with a high yield and therefore a more exact knowledge of its neutron capture cross-section would be useful. In the present work the neutron capture cross-section of 136Xe has been determined from the activity of ~3rCs formed through the following reactions : 13eXe (n, 7) 137Xe
~ > 137Cs fllzrmBa 3"8 rain 29"68 years ~"
The activity of ~37Cs has been evaluated by measuring the intensity of the 662 keV 7-photopeak of ~37~Ba. i1~ H. B. MATHUR and K. HYDE, Phys. Rev. 95, 708 (1954).
c2, R. N. FORRESTand H. T. EASTERDAY,Phys. Rev. 112, 950 (1958). ta~ M. BRESESTI, F. CAPPELLANIand A. M. DEL TURCO,Nucl. Phys. 58, 491 (1964). ,4, K. WAY and G. HAINES,AECD 2274 0948). 1
M. BRESESTI,F. CAPPELLANI,A. M. DEL TURCO, H. NEUMANN and E. ORVINI
T h e f o l l o w i n g d a t a were used i n the c a l c u l a t i o n s : f r a c t i o n o f laTCs d e c a y i n g via 1 3 7 ' ~ B a - - - - 9 2 ~ ; ratio e/y in the c o n v e r s i o n o f t37'~Ba ~-rays ---- 0-117 ; hence 82.4 ? - r a y s a n d "9.6 c o n v e r s i o n electrons per 100 d i s i n t e g r a t i o n s . A half-life o f 29.68 4 - 0 . 0 5 years '5~ has b e e n a s s u m e d , b e i n g the m o s t a c c u r a t e d e t e r m i n a t i o n r e p o r t e d in the literature. EXPERIMENTAL
a. Irradiations High purity natural xenon from "Air Liquide", containing 0.090 ~o l~eXe and 8.87 ~ aa6Xe was sealed in silica ampoules of 2 ~ cm a. Each ampoule was filled to a pressure of about 1 atm. with an amount of xenon measured in a high vacuum line. To determine the neutron capture cross-section of lzeXe, the ampoules were irradiated in a pneumatic carrier in the graphite reflector of the Ispra 1 reactor, close to the heavy water tank. The irradiation time was about 2 hr. For the 18eXe measurements some preliminary irradiations were made in the pneumatic tube. Owing to the weakness of the 187Cs activity obtained with the short irradiation periods possible in this position, measurements had to be made in another facility of the Ispra 1 reactor. This position, located in the graphite reflector far from the heavy water tank, is well thermalized. The irradiation time was several days (12 or 24). To evaluate the epithermal activation some xenon ampoules were enclosed in 1 mm thick cadmium boxes. In all irradiations a 1 mm dia. A1/Co alloy wire (1 ~ cobalt) was included to monitor the neutron flux.
b. Source preparation and counting procedure For measurement of the 127Xe activity the irradiated ampoules were opened in a vacuum line and the xenon was frozen into flat cylindrical glass containers using liquid nitrogen. The containers were then sealed. The 377 KeV y-ray intensity was evaluated about 1 month after the end of the irradiation with a 3 in. × 3 in. NaI(T1) crystal connected with a multichannel pulse analyser. The crystal had been previously calibrated with standard sources of 5tCr (E;, = 320 KeV) and 198Au (Ee = 411 KeV). The efficiency for the 377 keV ?-photopeak was determined by interpolating between the two experimental points using the outline of the calculated efficiency curves for a 3 in. × 3 in. NaI(TI) crystal. <6~ The purity of the 377-keV ?-photopeak was checked by following the decay. The t27Xe 7 spectrum is shown in Fig. 1. The small contribution of the 173 keV and 204 keV sum to the 377 keV peak has been evaluated and the correction introduced. In the determination of the 13+Xe neutron capture cross-section, the irradiated ampoules were opened to remove all xenon activities, and 137Cs was recovered from the ampoule walls by repeated washings with a hot (CsC1 + KI) solution. This solution would also contain m I and 12q, formed in neutron capture by l~4Xe and 1~6I. 125I does not interfere with the 662-keV ?-rays of tST'~Ba, but m I (h/~ 13"3 days, E v = 380 and 650 keV) is very troublesome. It was necessary therefore to wait about 3 months before counting. The intensity of the 662 keV 137Cs~,-ray was evaluated by a 3 in. × 3 in. NaI(T1) crystal previously calibrated with a standard 187Cs source. The activity of the flux monitors was determined by counting the 1.17 and 1.33 MeV ~-photopeaks of 6°Co with a 3 in. × 3 in. NaI(TI) crystal, the crystal in this case being calibrated with standard °°Co sources.
METHOD OF CALCULATING CROSS-SECTIONS AND RESONANCE INTEGRALS The calculations were made following the procedure of EASTWOODet al.tT~ based on the convention described by WESTCOTTet al. '8~ ,5~ S. G. GortalCS, W. E. KtrNz and A. E. NASH, Nucleonics, 21, 1, 63 (1963). te~ R. L. HEAT, IDO 16408. ~7>T. A. EASTWOOD,A. P. BAERG,C. B. BIGHAM,F. BROWN, M. J. CABELL,W. E. GRUMMIT,J. C. Roy, L. P. RoY and R. P. SCHUMAN,Proc. 2ndlnt. Conf. Peaceful Uses of Atomic Energy, Geneva 1958, 16, p. 54. United Nations (1959). ~al C. H. WESTCOTT,W. H. WALKERand T. K. ALEXANDER,Proc. 2nd Int. Conf. Peaceful Uses of Atomic Energy, Geneva 1958, 16, p. 70 United Nations (1959).
Neutron capture cross-sections of l~6Xe and 13sXe
9~, Ke V
ioooo 173 KeY
FIG. 1.--~27Xe ~-spectrum [3 in. × 3 in. NaI (TI) crystal]. In a well-moderated thermal reactor the neutron spectrum is assumed to consist of a Maxwellian distribution with a characteristic temperature T°K, plus a d E [ E flux distribution in the epithermal region subject to a lower limit, E , but overlapping the Maxwellian distribution. The measured reaction rate, R, in this neutron flux is equated to the product of the effective cross section, iS, and the conventional flux, nvo, where n is the total neutron density and v0 is 2200 m/sec. Thus (1)
R = ~rnvo
The effective cross-section is defined by the relation: (r = tro(g + rs)
where tr0 = cqz00m/see, r is a measure of the relative density of the epithermal component of the neutron spectrum,g and s are factors which depend on the departure of the cross section from the 1Iv law. For a pure Maxwellian neutron spectrum r is 0. For most substances, including Co 59, which follow the 1/v law closely in the Maxwellian region, g = 1. Values of the factorsg and s for the most important nuclides, including Co 59, have been tabulated over a range of temperatures. ~9~ The factor s is proportional to the square root of the temperature T. Since the neutron temperatures are not usually known a temperature-independent term so is introduced, such that So = s where To = 293'6°K. Equation (2) can now be written:
~9~C. H. WESTCOTT, Report AECL 1101 (1960).
M. BRESESTI,F. CAPPELLANI,A. M. DEL TURCO, H. NEUMANN and E. ORVINI
Following the convention, r ~/(T[To) is related to the cadmium ratio CR and so as follows:
= CR(s0 + l/K) -- So The factor K is a coefficient calculated from the variation of the cadmium cross-section with neutron energy and the thickness of cadmium used in the irradiation. Values of K for thicknesses of cadmium in common use have been tabulated, cs~ F o r l m m of cadmium, the thickness usedin this experiment, with an isotropic incidence of neutrons K = 2.29. Thus, from a measurement of the cadmium ratio for the irradiation position used and application of Equations (4) and (5), • for cobalt can be deduced, and nvo follows from Equation (1). With the conventional flux known, the effective cross-section follows from its measured reaction rate using Equation (1). In certain experiments it is possible to measure the cadmium ratio. In these instances the 2200 m]sec cross-section, go, and the resonancecapture integral can be calculated if it is assumed that the isotope is a l[v absorber in the thermal region. In this case g = 1. The factor So can be calculated using Equation (5), where r ~/(T/To) has been already determined. The 2200 m/see cross-section can now be calculated from the values of 6, So and r~/(T/To) by application of Equation (4). The resonance-capture integral can be defined as RI =
a ( e ) -~-. Cd
where Eta is the cadmium cut-off energy. The cadmium cover in our experiment was a cylindrical box with 1 m m thick walls; for this geometry and thickness the effective energy for the cadmium cut-off in a 1/v detector has been calculated as 0.55 eV. ~1°~ The resonance integral of an isotope, designated with a subscript x, can be obtained by reference to a standard (cobalt in this experiment) from the relationship (CR-1)5°co ao.~ RI~ = RIr°co (CR-1)~ " °0,°co The data for 59Co used in the calculation were taken from Ref. (9): cr0,09co = 37'3 barns RI59co = 75 barns s0,59co = 1.736 A value of 5.24 years for the 6°Co half life has been used. No self-shielding correction had to be applied to the thermal and epithermal activities induced in 5aCo. xsaXe C R O S S - S E C T I O N
The experimental activation data for the A1/Co alloy m o n i t o r s were very similar in all the irradiations a n d lead to the following results: R59co = reaction rate of ~9Co ---- 8.20 × 10 -1° sec -1 R~.co(Cd ) = reaction rate of 59Co ---- 1.11 × 10-11 sec -1 under Cadmium CRs0co = C a d m i u m
R a t i o o f C o - 5 9 ---- 74
r~/(T/To) = 0 . 0 0 6 3 ~09co =- effective c r o s s - s e c t i o n o f 59Co ---- 37.7 b a r n s
nv o ---- c o n v e n t i o n a l flux ---- 2.17 × 1013 n / c m ~ . s e c ~o~ R. W. STOUGItTON and J. HALPEPaN, Nucl.
Sci. Engng. 6, 100 (1959).
Neutron capture cross-sections of lZnXeand 136Xe
The expressions for calculating the reaction rate and the effective cross-section of 126Xe are: A R126xe - -
N(1 -- e -~)
R12+Xe HU0 where
A = 127Xe activity at the end of the irradiation N = number of ~28Xe atoms 2 = decay constant of 127Xe t = irradiation time
The experimental values of Rl~6xe and ~ " x e are given in Table 1. TABLE 1.--REACTION RATE AND EFFECTIVE CROSS-SECTION OF 126Xe
Experiment without Cd cover
Rl~exe (sec-1) (× 10 11)
1 2 3 4 5 6 Average value
4"95 5"26 5"33 5"54 5"41 5'41 5.32
2'28 2'42 2'46 2-55 2"49 2"49 2-45
The average values of Table 1 have been used to calculate the Cadmium Ratio CRl~exe the thermal cross-section %,l~xe, and the resonance integral RIl~x~ reported in Table 2. TABLE 2.--THERMAL CROSS-SECTION AND RESONANCE INTEGRAL OF 126Xe
Experiment under Cd
Rl-o6xe(Cd)(sec-1) (× 10 12)
7 8 9
5"71 5-56 5.57
CRI~6x~ 9'32 9'57 9.55
so 18.6 18.0 18.1
O'o12exe (barns) 2'19 2.20 2'20
Rl126xe (barns) 38'6 37.7 37.8
Although the agreement of the experimental results is extremely good, considering the complexity of the operations, an error of ± 10 per cent is assumed because of possible systematic errors in evaluation of the 127Xe activity and the neutron flux. This error does not take into account the uncertainties in the decay scheme of 127Xe and in the nuclear parameters of 59C0. Other sources of uncertainty are the assumptions of 1/v variation of the cross-section in the thermal region and in the cadmium cutoff region, and of the dE/Eneutron distribution in the epithermal region. Deviations from the dE/E distribution can be expected in a reactor mainly because of
M. BRESESTI, F. CAPPELLANI, A. M. DEL TURCO, H. NEUMANN and E. ORVIr~I
resonance capture in uranium and of the spatial non-uniformity of the fission source distribution, which causes an excess of high energy neutrons close to the uranium rods and a deficit far from the rods. In the irradiation position utilized measurements of the epithermal neutron spectrum have been made by resonance detectors/n) and a deviation from the d E / E distribution has been observed, with an excess of neutrons in the low energy part of the spectrum. The average of the determinations, including the estimated errors, leads to the values" ~2exe = 2"45 -4- 0"25, a0,~2~x, = 2"20 -4- 0"22 and Rh~exe = 38"0 ~ 3"8 barns. 138Xe C R O S S - S E C T I O N
The irradiations for the 13nXe cross-section determination were made in a very well thermalized position where a Cadmium Ratio of about 1000 has been measured for the reaction 59Co (n, y)6°Co. Some preliminary experiments made in the pneumatic tube have shown that for CRy,co ---- 70, the value of CRI~x~ is ~ 50. Therefore, in the position with C R , co ---= 1000 the epithermal contribution for the reactlon xSeXe (n, y)x3~Xe can be neglected. Under these flux conditions the term r of Equation (2) can be assumed to equal 0. Moreover, the factor g is 1 for ~9Co. We deduce from Equation 2 that ~ = a0, and Equation 1 can be written in the form" R = aonv o
so that the conventional flux nv o follows from the thermal cross-section value of 59Co (a0 = 37.3 barns). Assuming that ~a6Xe is a 1/v absorber in the thermal region, its thermal crosssection has been calculated from the expressions: A Rla~x~ -- N 2 t R186xe G0,1a6Xe =
.4 = 1arCs activity at the end of the irradiation N = number of aZSXe atoms ;t = decay constant of laTCs t = irradiation time
The experimental values of Rx~xe and ao,~x~ are given in Table 3. TABLE 3.--REACTION RATE AND THERMAL CROSS-SECTION OF lS6Xc nVo
Experiment without Cd
n/cm ~. see ( × 10TM)
(see-X) ( × 10-~2)
ao, ~seXe (barns)
1 2 3 4
3"38 3"01 6'46 6'17
0"939 0-780 1-89 1'82
0"277 0"259 0"293 0"296
~u~ M. BRESES~, A. M. BRES~S~ and A. ROTA, E U R 1643. e
Neutron capture cross-sections of a~nXeand ~aeXe
In this determination the error has been estimated as 4- 10 per cent. This is mainly due to systematic errors in the evaluation of the activity and does not take into account uncertainties in the 137Cs and 59Co nuclear parameters. The average value of the thermal neutron capture cross-section of 136Xe is a013~xe ----0"281 ! 0"028 barns and it is seen to be very different from the value previously reported, a01,6xe ----0.15 ± 0.08 barns. 141
Acknowledgements--Theauthors wish to thank Prof. G. BERTOLINIof this laboratory for the helpful discussions.