Evaluation of resonance parameters for neutron induced reactions in cadmium

Nuclear Instruments and Methods in Physics Research B 300 (2013) 11–29

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Evaluation of resonance parameters for neutron induced reactions in cadmium K. Volev a,b, A. Borella a,c, S. Kopecky a, C. Lampoudis a, C. Massimi d, A. Moens a, M. Moxon e, P. Schillebeeckx a,⇑, P. Siegler a, I. Sirakov b, A. Trkov f,g, R. Wynants a a

European Commission, Joint Research Centre – IRMM, Retieseweg 111, B – 2440 Geel, Belgium Institute for Nuclear Research and Nuclear Energy, Sofia, Bulgaria c SCK-CEN, Boeretang 200, B – 2400 Mol, Belgium d Department of Physics, University of Bologna and Sezione INFN of Bologna, Via Irnerio 46, Bologna, 40126, Italy e Hyde Copse 3, Marcham, United Kingdom f Jozˇef Stefan Institute, Jamova Cesta 39, 1000 Ljubljana, Slovenia g International Atomic Energy Agency, NAPC/Nuclear Data Section, Vienna, Austria b

a r t i c l e

i n f o

Article history: Received 17 September 2012 Received in revised form 11 January 2013 Available online 8 February 2013 Keywords: Neutron cross section Neutron resonance parameters Capture cross section measurements Transmission measurements R-matrix analysis Evaluation

a b s t r a c t Resonance parameters for neutron induced reactions in 106,108,110,111,112,113,114,116Cd have been evaluated. The parameters are the result of an analysis of experimental data available in the literature together with a parameter adjustment to transmission and capture data obtained at the time-of-flight facility GELINA. The parameters derived from the GELINA data are in reasonable agreement with those quoted in the literature. From the analysis of the GELINA transmission data a thermal neutron total cross section equal to 2450 ± 40 b has been deduced for natCd at 300 K. This value is in agreement with results of previous measurements which have been performed at thermal reactor beams using different techniques. It differs by about 1.5% from the value 2413 b which was recently deduced from an adjustment to results of an integral experiment. The GELINA transmission and capture data in the low energy region are not fully consistent with resonance parameters recommended in evaluated data files. The impact of the resonance parameters obtained in this work on cadmium transmission factors and on the interpretation of an integral experiment is discussed. Ó 2013 Elsevier B.V. All rights reserved.

1. Introduction The interest in cadmium is primarily due to the presence of a very strong resonance at 0.178 eV, which was for the first time assigned to 113Cd by Moyer et al. [1]. A 1-mm thick sheet of natCd can be used to absorb almost all neutrons with an energy below about 0.25 eV but absorbing only a small fraction of the neutrons with an energy above about 0.5 eV, except in the region of the resonances present in natural cadmium. Therefore, the total cross section for neutron induced reactions in natCd is very important for a correct interpretation and analysis of neutron experiments using cadmium as an absorber. Nonetheless, the total, capture and scattering cross sections in cadmium have not been adequately studied. Experimental data covering the resolved resonance region are rather scarce. The most extensive experiments in the resonance region are those carried out by Liou et al. [2] and Frankle et al. [3]. Other measurements that can be used to determine resonance parameters in a wide energy region have been reported by Wasson and Allen [4] and Musgrove et al. [5]. Gunsing et al. [6] concentrated on spin assignments of p-wave resonances for 113Cd + n and Alfimen⇑ Corresponding author. E-mail address: [email protected] (P. Schillebeeckx). 0168-583X/$ - see front matter Ó 2013 Elsevier B.V. All rights reserved. http://dx.doi.org/10.1016/j.nimb.2013.01.030

kov et al. [7,8] and Frank et al. [9] on low energy p-wave resonances in 111,113Cd + n, all in support to parity violation studies. Also the measurements of Frankle et al. [3,10] have mainly been carried out to interpret results of parity violation measurements involving p-wave resonances of 113Cd. Since most of the above quoted experiments focused on more fundamental studies, such as parity violation [3,6–10] and a search for single particle effects [4,5], the experimental observables (i.e. transmission, capture and self-indication yields) have never been used in a combined resonance shape analysis (RSA) as part of an evaluation procedure. Resonance parameters for cadmium isotopes recommended in evaluated data files are primarily based on a compilation of parameters listed in Liou et al. [2], Musgrove et al. [5] and Wasson and Allen [4]. The ENDF/B-VII.0 [11] and JENDL 4.0 [12] evaluations also include the parameters of Frankle et al. [3] for 113Cd + n. The lack of a consistent evaluation for cadmium may be a source of a longstanding discrepancy between quantities resulting from integral measurements and results obtained from calculations using resolved resonance parameters. To provide data for a new evaluation, a set of capture and transmission measurements have been carried out at the time-of-flight (TOF) facility GELINA [13], which is installed at the EC-JRC-IRMM at Geel (B). The experiments have been carried out following the

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K. Volev et al. / Nuclear Instruments and Methods in Physics Research B 300 (2013) 11–29

recommendations in Ref. [14]. Results obtained from transmission measurements at GELINA, concentrating on the 0.178 eV resonance of 113Cd, have already been reported by Kopecky et al. [15] and were adopted in JENDL 4.0 [12]. In the present paper an evaluation for neutron induced reactions in cadmium covering the thermal and resolved resonance region is presented. The evaluation is based on an extensive study of parameters reported in the literature combined with a simultaneous RSA of GELINA data together with well documented experimental data from other facilities which are available in numerical form. The code REFIT [16,17], which is based on the Reich-Moore approximation [18] of the R-matrix theory [19], was used for the RSA. The results for the even Cd-isotopes and 111Cd have been included in ENDF/B-VII.1 [20]. However, the part for 113Cd as presented in this work was not adopted.

2. Experimental data in the literature Cross sections of neutron induced reactions in the resolved resonance region (RRR) are parameterized by the R-matrix nuclear reaction theory using resonance parameters of individual resonances [21]. For a non-fissioning nuclide a resonance is characterized by: the resonance energy (Er), neutron (Cn) and radiation width (Cc), total angular momentum (J) and orbital momentum of the neutron-nucleus system (‘). The latter defines the parity p = (1)‘ of a resonance. In addition, scattering radii are required to calculate the potential scattering cross section. The determination of resonance parameters requires a set of independent experimental observables. Ideally, transmission, elastic scattering, capture and self-indication measurements are performed using targets which are adapted to the resonance strengths [22,23]. In general, from a transmission measurement the parameter Kt = gJCn is deduced and from a capture measurement the capture Kernel Kc = gJCnCc/(Cn + Cc) is obtained, with gJ being the statistical spin factor. In case the width of an observed resonance profile is dominated by the total width C = Cn + Cc of the compound state, this width can also be obtained from a RSA of the observed profile. Table 1 compares resonance parameters for the 0.178 eV resonance that have been reported in the literature. The transmission data of Ref. [15] are incorporated in the final evaluation procedure. Kopecky et al. [15] performed a full uncertainty propagation and investigated the impact of various sources of uncertainties, i.e. uncertainties resulting from the data reduction and uncertainties due to systematic effects such as flight path length, sample characteristics and effective temperature. The flight path length was adjusted at the 6.674 eV resonance of 238U from Ref. [24]. The spin assignment obtained by Beeman [25] was confirmed by a simultaneous fit of thin and thick sample transmission data. Although the data in Table 1 seem to agree within their quoted uncertainties,

Kopecky et al. [15] noticed bias effects due to sample inhomogeneities, especially in case of thin powder samples. The work of Liou et al. [2] is the most comprehensive study of resonance parameters for Cd isotopes, with an emphasis on the even isotopes. This study was done at the Columbia University Nevis synchrocyclotron pulsed neutron beam. Transmission and selfindication measurements, at 200 m and 40 m, respectively, were carried out for natCd samples and samples enriched in 110Cd, 112 Cd, 114Cd and 116Cd. Resonance energies and neutron widths, which have been determined from an area analysis, are reported in Ref. [2]. For the even isotopes these parameters are given up to about 10 keV and for 111Cd and 113Cd up to 2.3 keV. Although the transmission data are available in EXFOR, the data cannot be used for a RSA due to a lack of experimental details. In the present work, the numerical transmission data have only been used for a consistency check of the final results. Capture measurements at a 40 m station of ORELA using samples enriched in even Cd isotopes, i.e. 106, 108, 110, 112, 114, and 116, have been performed by Musgrove et al. [5]. Resonance energies and capture areas for individual resonances above 2.6 keV are listed in Ref. [5]. For the even isotopes average parameters have been deduced from the data in both the resolved and unresolved resonance region. Unfortunately, the capture yields of Musgrove et al. [5] are not available in numerical form. Hence, only the reported parameters can be used in the evaluation. Capture areas for 111Cd have been obtained by Wasson and Allen [4] from measurements at a 40 m flight path station of ORELA using C6F6 detectors. In addition, parity assignments for 95 resonances below 1300 eV in 111Cd have been made based on differences in observed pulse-height spectra above 7.6 MeV. Also the capture yields of Wasson and Allen [4] are not available as numerical data. From experiments reported in the literature, only the data of Frankle et al. [3] can be used in a RSA. These authors performed transmission and capture measurements at ORELA on natural samples and samples enriched to 94.6% in 113Cd. For the transmission measurements a 6Li loaded glass scintillator was located at 79.710 m from the neutron producing target. The capture experiments were performed with the sample at a 40.110-m distance from the neutron target using a pair of C6D6 detectors, which were positioned at either side of the sample and at 90° with respect to the direction of the neutron beam. The total energy detection principle in combination with the pulse height weighting technique was applied. The transmission and capture data have been used in a RSA to determine gJCn values for resonances below 15 keV. These gJCn values have been used for a parity assignment (‘ = 0 or 1) applying an approach proposed by Bollinger and Thomas [36]. This approach is based on the Bayes’ theorem. Spin assignments of p-wave resonances for 113Cd + n have been made by Gunsing et al. [6]. These assignments were based on c-ray spectro-

Table 1 Comparison of resonance parameters of the 0.178 eV resonance of 113Cd + n reported in the literature. The data without uncertainties (placed between brackets) have been deduced from the values reported in the quoted references. For the calculations Eq. (1).23 in Mughabghab [34] was used. The peak cross section for natCd is denoted by (a ro), with a = 0.1222 the atomic abundance for 113Cd in natCd, which is taken from Ref. [35]. Reference

Er/meV

Rainwater et al. [26] Rainwater et al. [27] Brockhouse [28] Meservey [29] Shchepkin et al. [30] Akyüz et al. [31] Widder and Brunner [32] Harz and Priesmeyer [33] Kopecky et al. [15]

180 176 180 177 178 181 177.6 178.3 178.7

C/meV (8) (2) (3) (5) (2) (3) (0.6) (0.2) (0.1)

112 115 113 110 113.7 108.7 114.3 113.5 114.1

(6) (2) (2) (5) (3) (1) (1) (0.2)

Cc/meV

Cn/meV

(a ro)/b

111.4 114.4 112.4 109.4 113 108.7 113.7 112.9 113.5

0.646 0.599 0.648 0.608 0.65 0.791 0.618 0.650 0.640

7800 7200 7750 7600 7817 7847 7300 7814 7634

(5) (3)

(0.2)

(0.02) (0.032) (0.003) (0.005) (0.004)

(800) (200) (150) (300) (187) (50)

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K. Volev et al. / Nuclear Instruments and Methods in Physics Research B 300 (2013) 11–29

of 35 mm at the sample position. Neutrons were detected by a 6.35-mm thick and 101.6-mm diameter NE912 Li-glass scintillator enriched to 95% in 6Li, which was coupled to a boron-free quartz windowed EMI9823-QKB photomultiplier (PMT). The detector was placed at a distance of 49.34 m from the exit face of the moderator. Transmission measurements at the 25-m station have been performed with the accelerator operating at 50 Hz, 400 Hz and 800 Hz. The samples were placed at 9 m from the neutron target in a multiposition sample changer. The aperture of the last collimator before the samples resulted in a 15-mm diameter neutron beam at the sample position. A 5-mm thick Pb filter was placed in front of the sample changer to reduce the intense gamma-ray flash. Neutrons were detected by a NE905 Li-glass scintillator, enriched to 95% in 6Li. The Li-glass (110.0 mm diameter and 12.7 mm thick) was placed in a thin-walled aluminum can and viewed by two EMI9823-QKB PMTs, which were placed outside the neutron beam and perpendicularly to its axis. The inside of the aluminum canning was lined with a thin Teflon foil to enhance the light reflection. The anode pulses of both PMTs were fed into a constant fraction discriminator to create fast logic signals. To separate a valid neutron event from background noise, a coincidence between two fast signals was required with a 30 ns resolving time. The time-of-flight transmission data at 25 m and 50 m were recorded in histograms. The transmission Texp was obtained from the ratio of a samplein measurement Cin and a sample-out measurement Cout, both corrected for their background contributions Bin and Bout, respectively [14]:

scopic measurements with Ge-detectors using the intensity of both primary and low energy transitions. 3. Experiments at GELINA Transmission and capture experiments on natural cadmium have been carried out at the neutron TOF facility GELINA. A detailed description of the accelerator and its neutron producing target can be found in Ref. [13,37]. All measurements described in this paper have been performed at a moderated neutron beam. Therefore, a shadow bar made of Pb and Cu is placed close to the uranium target to reduce both the c-ray flash and the fast neutron component. BF3 proportional counters, placed at different locations around the target hall, are used to monitor the stability of the accelerator and to normalize TOF-spectra to the same total neutron intensity. The measurement stations are equipped with air-conditioning to reduce electronic drifts in the detection chains due to temperature changes and to keep the sample at a constant temperature of about 20 °C. The temperature at the sample position is continuously monitored. The average temperature is used in the RSA to account for the Doppler broadening. The characteristics of the natCd samples are given in Table 2. All samples were in the form of a metallic disc or foil. The areal density was derived from a measurement of the weight and the effective area. The latter was deduced from a non-contact optical surface inspection with a microscope-based system from Mitutoyo. The thicknesses of the samples, ranging from 30 lm up to 25 mm, have been chosen to find a good compromise between counting statistics and the characteristics of the resonances. Also the accelerator operating frequencies (50 Hz, 400 Hz or 800 Hz) have been adapted to cover an energy region from thermal up to about 10 keV. The data processing was carried out with the AGS-package [38,39]. This package includes the most important spectra manipulations. The package performs a full uncertainty propagation accounting for both correlated and uncorrelated uncertainty components. In AGS the covariance matrix is split in two parts. The uncorrelated part is represented as a diagonal matrix and the correlated part is expressed as the product of a rectangular matrix with its own transpose. The AGS structure results in a substantial reduction of space for data storage and is very convenient to document the various uncertainty components involved in the reduction process.

T exp ¼ NT

C in  Bin : C out  Bout

ð1Þ

All TOF-spectra (Cin, Bin, Cout and Bout) in Eq. (1) were corrected for dead time effects. The dead time of the detection chains was monitored by registering the time-interval distribution between successive events and gave a dead time of 2850 ns and 100 ns for the 50 and 25 m station, respectively. At the 25 m station the energy deposited in the 6Li-detector was not recorded and only the time-of-flight signal was processed. This is the main reason for the difference in the dead time of the detection systems. Only TOF-regions with a dead time correction below 10% have been taken into account for further analysis to avoid systematic bias effects due to the dead time correction. The dead time correction for neutron energies below 500 eV was smaller than 2%. The normalization constant NT accounts for the ratio of the integrated intensities of the incident neutron beam during the in and out cycles. Alternating sequences of sample-in and sample-out measurements reduced the uncertainty on the normalization NT to less than 0.5%. The background was determined by an analytical expression applying the black resonance technique [14]. The analytical function was a sum of a time independent and two time dependent components:

3.1. Transmission experiments Transmission measurements have been performed at a 25 m and 50 m flight path station, forming an angle of 9° and 9°, respectively, with the direction normal to the exit face of the moderator. The experiments at the 50 m station have been performed with the accelerator operating at 800 Hz. A 10B overlap filter, with an areal density of 0.008 at/b, was used to eliminate neutrons from a previous burst. A combination of Li-carbonate plus resin, Pb and Cu-collimators was used to reduce the neutron beam to a diameter

Table 2 Characteristics of the samples used for the transmission and capture measurements performed at GELINA. Weight

Form

Diameter or length  width

g 1.281 3.184 87.460 1.979 17.1120 414.646 447.216

Disc Disc Disc Disc Disc Disc Foil

/ = 80.40 mm / = 80.04 mm / = 80.00 mm / = 50.08 mm / = 50.00 mm / = 50.00 mm 100  100 mm2

Thickness

Areal density

Cd-purity

Transmission

Capture

mm

at/b

wt.%

25 m

12.5 m

99.9975 99.9975 99.9975 >99.99 99.999 99.999 99.99

X X

0.03 0.08 2.06 0.12 1.02 25.00 5.09

4

1.363 10 3.390 104 93.406 104 5.382 104 46.698 104 1.205 101 231.020 104

50 m

30 m

X X X

X X

X X

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K. Volev et al. / Nuclear Instruments and Methods in Physics Research B 300 (2013) 11–29 2

10

Cin(t) Bin(t) = Bo + Bγ(t) + Bn(t)

1

10

Bo

Response / (1/ns)

Bγ(t) Bn(t)

0

10

-1

10

-2

10

Bo -3

10

Bn(t)

Bγ(t) -4

10

3

10

4

10

5

10

6

10

7

10

Time-of-flight / ns Fig. 1. Dead time corrected TOF-spectrum resulting from a 25-mm thick natCd sample-in measurement at the 50-m station with GELINA operating at 50 Hz. The time independent and time dependent background components due to the 2.2 MeV c-rays and scattered neutrons are given.

BðtÞ ¼ Bo þ Bc ðtÞ þ Bn ðtÞ:

ð2Þ

This function reflects the different background contributions in a TOF transmission experiment. The contribution Bc(t) due to the 2.2 MeV c-ray resulting from neutron capture in hydrogen dominates the background for t < 100 ls at 25 m and 50 m flight path lengths. Since the energy deposited by a 2.2 MeV c-ray is comparable to the energy deposited by the charged particles produced in the 6Li(n,a) reaction, this background component is hard to suppress by pulse-height discrimination. The time distribution of the 2.2 MeV c-rays is described by an exponential decay with a decay time of about 25 ls. A second time dependent component Bn(t) originates predominantly from neutrons which are scattered inside the detector station. A small background component is due to neutrons scattered at other flight paths. The sum of these two contributions can be described by a power function or by an exponential decay. The free parameters in the analytical expression were determined by a least square fit to saturated resonance dips observed in the TOF-spectra resulting from measurements with black resonance filters. The background level was continuously monitored by performing all measurements with at least one fixed black resonance filter in the beam. The resonance dips of the fixed filters were also used to determine the impact of the sample on the background level for a sample-in measurement. An example of a dead time corrected TOF-spectra obtained at the 50 m station with a 25-mm thick natCd sample together with the different background contributions is shown in Fig. 1. 3.2. Capture experiments Capture measurements have been carried out at a 12.5-m and 30-m flight path, forming an angle of 18° and 0°, respectively, with the direction normal to the emitting face of the moderator. The accelerator was operated at 50 Hz and 400 Hz. The moderated neutron beam at the two stations was collimated to about 75 mm diameter at the sample position. The collimating system was composed of Li-carbonate, Cu- and Pb-collimators. The detection systems (i.e. c-ray detectors, neutron flux detector, electronics and data acquisition systems) at the two stations were very similar. The c-rays were detected by a pair of C6D6 detectors. Each detector was positioned at an angle of 125° with respect to the direction of the neutron beam. This geometry minimizes systematic effects due

to the anisotropy in the primary dipole c-ray emission from resonances which can be spin and orbital momentum dependent. The detection of scattered neutrons was minimized by coupling each scintillator to a boron-free quartz windowed PMT. For each detector the anode signal from the PMT was used to determine the arrival time of the neutron and the signal of the 9th dynode to determine the energy deposited by the c-ray in the detector. The discrimination level of the capture detection systems at 12.5 m and 30 m corresponded to 200 keV and 150 keV deposited energy, respectively. The total energy detection principle in combination with the pulse height weighting technique was applied to arrive at a detection efficiency for a capture event directly proportional to the total c-ray energy liberated in the capture event [14]. For each target-detection system combination weighting functions were calculated by Monte Carlo simulations and validated by experiment as discussed in Ref. [40]. In the calculation of the weighting functions the effective discriminator level on the energy deposited in the C6D6 detector was taken into account. To account for the gamma-ray attenuation in the sample, the procedure proposed in Refs. [14,40] has been applied. In this approach the weighting functions are applied for a homogeneous distribution of the c-rays in the sample and a correction factor for the c-ray attenuation is applied as part of the RSA. The energy dependent neutron spectrum below 150 keV was measured in parallel with a 10B Frisch gridded ionization chamber placed at about 80 cm before the sample. At each station a double chamber was used with a cathode loaded with two back-to-back layers of 10B. The 10B layers, with an effective diameter of 84 mm and areal density of about 40 lg/cm2, were evaporated on a 30lm thick aluminum backing and the entrance and exit windows of the chambers had a thickness of 40 lm. The chambers were operated with a continuous flow of a mixture of argon (90%) and methane (10%) at atmospheric pressure. The time-of-flight and pulse height of each detected event were recorded in list mode. The list mode recording allowed a continuous stability check of the detection systems and an off-line application of the weighting function for the C6D6 detection systems. The stability of both the detection systems and the accelerator operating conditions were verified in cycles of 1 h. The linearity and resolution of the C6D6 detectors were monitored on a weekly basis by measurements of the 2.6 MeV c-ray from the 232Th decay chain. The dead time of the capture and neutron detection chains were monitored continuously. For the flux measurements the dead time was 3500 ns. The maximum correction for the dead time was less than 1% at all measurements stations. The dead time for the capture measurement systems was 2800 ns. For the measurements at 12.5 m and 30 m the maximum dead time corrections were less than 20% and 5%, respectively. Mihailescu et al. [41] and Schillebeeckx et al. [14] have demonstrated that possible bias effects due to such dead time corrections are less than 1.0%. The experimental yield Yexp, which represents the fraction of the neutron beam that undergoes a reaction in the sample and generates a signal in the capture detection system, was deduced from the ratio of the observed response of the capture detectors and the neutron detector [14]:

Y exp ¼

Nc C w  Bw Y u : e C u  Bu T u

ð3Þ

The dead time corrected weighted response is denoted by Cw and its background contribution by Bw. The dead time corrected TOF-spectrum resulting from the flux measurement is Cu and the background contribution is Bu. The theoretical yield of the flux detector Yu is given by:

Y u ¼ ð1  enu rtot Þ

ra ; rtot

ð4Þ

K. Volev et al. / Nuclear Instruments and Methods in Physics Research B 300 (2013) 11–29 1

10

Cϕ(t) Bϕ(t)

0

Response / (1/ns)

10

-1

10

-2

10

Na

Co

Ag

-3

10

-4

10

4

10

5

6

10

10

7

10

Time-of-flight / ns Fig. 2. TOF spectrum obtained with a 10B-ionization chamber for measurements at 12.5 m and GELINA operating at 50 Hz. The background contribution resulting from an adjustment to the black resonance dips is shown.

4

10

nat

Cd (0.03 mm) Pb (0.5 mm) no sample ambient 208

3

Response / (1/ns)

10

2

10

1

10

15

The time dependent background for the flux measurements was expressed as an analytical expression, i.e. a sum of a constant term, a power function and a contribution due to overlap neutrons. The free parameters in the analytical expression were derived from saturated resonance dips created by black resonances. Fig. 2 shows the results of a TOF spectrum for the flux measurements at the 12.5 m station and the accelerator operating at 50 Hz together with the background contribution, resulting from a fit through the black resonance dips. In the whole region the background is less than 1%. The background for capture measurements consists of three components [14]: (1) a time independent component due to ambient radiation and possible radioactivity in the sample and its surroundings; (2) a time dependent component independent of the sample and (3) a time dependent component depending on the sample characteristics. The first component was estimated from measurements when the accelerator was switched off. The second component was deduced from measurements without a sample in the beam. The third component is due to neutrons and c-rays which are scattered from the sample and produce a signal in the detection system. For the energy region considered in this paper the third component is primarily due to scattered neutrons and depends on the neutron sensitivity of the detection system. The smooth part of this time-dependent background component, which is mainly due to potential scattering in the sample, was determined from measurements with a 0.5-mm thick 208Pb sample. The correction due to resonance scattering in the sample, which was almost negligible, was included in the RSA as explained in Ref. [14,17]. The neutron sensitivities of the two capture detection systems have been determined by Monte Carlo simulations which have been verified by experiment in Ref. [40]. The weighted TOF-spectrum for a 0.03-mm thick natCd sample together with results of measurements with a 0.5-mm thick Pb sample and with no sample are compared in Fig. 3. The spectra were taken at 12.5 m with the accelerator operating at 50 Hz. This figure reveals that there is almost no difference between the response with no sample in the beam and the one obtained with a 0.5-mm thick 208Pb. Hence, the impact of the sample dependent background components, including the neutron sensitivity, is very small and can almost be neglected.

0

10 4 10

5

10

6

10

7

10

Time-of-flight / ns Fig. 3. TOF spectrum from capture measurements on a 0.03-mm thick natCd sample. The different background components are also shown: the response of a measurement without sample, of a measurement with a 0.5-mm thick 208Pb sample and of a measurement when the accelerator was not in operation.

where nu is the areal density of the 10B layer in the ionization chamber, ra is the cross section for the 10B(n,a) reaction and rtot is the total cross section for neutron induced reactions in 10B. The factor Tu corrects for the attenuation in the exit window of the ionization chamber and the attenuation due to the 80 cm air between ionization chamber and target. The efficiency to detect a capture event is denoted by e. This efficiency was taken to be proportional to the neutron separation energy of 113Cd. For a correct interpretation of the yield in REFIT the detection efficiency for each isotope was defined as its neutron separation energy divided by the one of 113Cd. The normalization NC accounts for energy independent factors such as the absolute neutron flux, the efficiency of the flux detector and the solid angle subtended by the target and the C6D6 detectors [14]. In this work the normalization constant was considered as a free parameter in the RSA and was defined by resonances for which the parameters were determined from the transmission data.

4. Resonance analysis of GELINA data 4.1. Experimental input parameters Resonance parameters were extracted by a simultaneous least squares adjustment of the capture and transmission data using REFIT [16]. The code accounts for various experimental effects [17] such as, the Doppler broadening, self-shielding and scattering in the sample, the attenuation of c-rays in the sample, the response of the TOF-spectrometer and the neutron sensitivity of the capture detection system. The code also accounts for the target characteristics [14], i.e. inhomogeneities, isotopic composition and impurities. Nuclear data of Cd-isotopes required in the RSA are given in Table 3. The free gas model with an effective temperature of 298 K, corresponding to a 186 K Debye temperature, was used to describe the Doppler effect. Hence, the parameters determined in this work do not account for solid state effects. The time response of GELINA, which is mainly due to the neutron transport in the moderator, was obtained from Monte Carlo calculations [42] and introduced numerically. For the analysis of the transmission data the time response of the detector was accounted for by an analytical model. The correction factor for the c-ray attenuation in the sample was obtained by using c-ray emission spectra that were calculated with a statistical code based on

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K. Volev et al. / Nuclear Instruments and Methods in Physics Research B 300 (2013) 11–29

Table 3 Nuclear data of Cd-isotopes used in and deduced from a RSA. The nuclear cross sections r(nth,tot) and r(nth,c) (at 0 K i.e. without Doppler broadening) are calculated at 2200 m/s using the resonance parameters obtained in this work. The adopted average radiation widths are mainly based on the analysis of GELINA data and the results of Musgrove et al. [5]. The upper limit on the p-wave reduced neutron width for the separation between s- and p-waves similar to the Bollinger and Thomas [36] approach is given in the last column. The neutron separation energy Sn for the ACd + n system is from Ref. [44], the effective scattering radius is denoted by R’ and Ip is the ground state spin and parity of the target nucleus. nat

Isotope

Ip

Cd

at.% [35] 106

Cd 108 Cd 110 Cd 111 Cd 112 Cd 113 Cd 114 Cd 116 Cd

Sn

ma

r(nth,tot)

r(nth,c)

R’

Cc

keV

u

barn

barn

fm

meV

5.527 4.236 15.233 12.457 7.273 20185.203 5.991 5.019

0.986 0.906 10.999 6.870 2.198 20163.670 0.305 0.076

6.0 5.79 5.80 6.15 6.6 6.5 6.9 6.24

[44] 0+ 0+ 0+ ½+ 0+ ½+ 0+ 0+

1.25 0.89 12.49 12.80 24.13 12.22 28.73 7.49

[44]

7924.0 7327.0 6975.85 9394.32 6540.10 9042.98 6140.9 5777.2

(8.0) (6.0) (0.19) (0.30) (0.60) (0.14) (0.6) (1.0)

105.906461 107.904176 109.903005 110.904182 111.902757 112.904400 113.903357 115.904755

112

Cd Cd

113

Fc

1.04

1.02

1.00 -1 10

0

1

10

10

2

10

nσtot Fig. 4. Correction factor Fc to account for the c-ray attenuation in the sample. The factor for 112Cd and 113Cd is given as a function of the product of the areal density and the total cross section.

the same principle as the code DICEBOX [43]. The correction factor for 112Cd(n,c) and 113Cd(n,c) in a 2-mm thick metal sample are compared in Fig. 4. This comparison shows that even for a 2-mm thick sample the maximum correction is less than 5%. The flight path length of the 50 m transmission station at GELINA, which has been determined from the transmission dip of the 6.673 ± 0.001 eV resonance in 238U + n [24], was used as a reference to determine the resonance energies. The flight path lengths for the capture measurements and the other transmission station have been adjusted in the RSA together with the resonance energies. The transmission data were analyzed without applying any additional normalization or background corrections. The flight path length and normalization of the capture data were considered as adjustable parameters. No additional background corrections on the capture data were required during the RSA process. This confirms the correct treatment of the background during the data reduction. By performing a simultaneous analysis with the transmission data the capture data are effectively normalized to strong resonances with Cc  Cn. For these resonances the parameters are determined from the transmission data. 4.2. Results Table 4 lists the parameters of resonances for which at least the resonance energy and gCn have been determined from the GELINA data. For certain resonances also the radiation width was deduced

g J C1n meV

‘=0

‘=1

150.0 103.0 70.0 130.0 77.5 113.5 54.0 47.2

172.5 123.0 79.0 165.0 90.5 145.0 71.5 70.0

190 640 300 56 280 47 430 560

and a spin assignment was made based on a simultaneous analysis of thin-thick transmission and/or capture data. Results of the least squares adjustment are given in Figs. 5–7. It was not possible to obtain a consistent fit of all the transmission and capture data in the thermal region together with the region covering the first resonance, even not by adding negative resonances with completely free parameters. A consistent description of the experimental data covering a broad energy region was obtained by allowing for a small bias between the experimental and fitted data in the thermal energy region. Since the deviation in the capture and transmission data was fully consistent, this might suggest an impact of interference effects. Unfortunately such effects cannot be included in an ENDF compatible evaluation file. Therefore, it was decided to adopt the parameters of the 0.178 eV resonance determined by Kopecky et al. [15] and include one negative resonance in 113Cd + n. The parameters of this resonance were adjusted to the data in the thermal region taking into account the coherent scattering length b = -8.0 ± 0.1 fm determined by Knopf and Waschkowski [45]. This results in a full consistent description of all the data above 0.05 eV to the expense of an overestimation of the thermal cross section of about 1%, as can be seen in Fig. 5. In addition, below 20 meV both the total and capture cross section data revealed structures which cannot be described by the current state of resonance shape analysis codes due to the lack of a treatment for solid state effects. The Doppler broadened total cross section for natCd + n at thermal energy (or v = 2200 m/s) and room temperature resulting from the total cross section data is r(nth,tot) = 2450 ± 40 b. The value deduced from the resonance parameters is 2487 b, with a total absorption cross section of 2480 b. These cross sections are 99.1% dominated by neutron absorption in 113Cd due to the 0.178 eV resonance. Neutron capture by the other Cd-isotopes and the contribution of the bound state in 113Cd account for approximately 0.4% and 0.5%, respectively. The energy dependence of the cross sections of the 0.l78 eV resonance explains the difference between the nuclear cross section at T = 0 K and Doppler broadened cross section at 300 K which are given in Table 5. Table 5 reveals that our value is in very good agreement with results from measurements performed at a thermal neutron beam applying different measurement techniques [32,46–50]. It should be noted that in the literature often reference is made to the value r(nth,c) = 2537 ± 9 b of Meadows and Whalen [48]. However, this value has been corrected in Ref. [49]. Our value is also in agreement with more recent capture and transmission measurements performed at RPI [51] and is close to the one recommended in IRDF-2002, JENDL-4.0 and ENDF/B-VII.1. However, JENDL-4.0 already includes the 0.178 eV parameters of Kopecky et al. [15]. The thermal cross sections deduced from the GELINA data deviate by

17

K. Volev et al. / Nuclear Instruments and Methods in Physics Research B 300 (2013) 11–29

Table 4 Resonance parameters which have been deduced from a simultaneous resonance shape analysis of transmission and capture data obtained at GELINA. The analysis was performed with REFIT. Isotope 106

108

110

Energy/eV

Jp

gCn/meV

1/2+

102.0 794.0

(5.1) (15.0)

349.0 539.0

(6.0) (7.0)

162.7 6.7 19.60 452.0 2.89 17.08 66.8 39.1 962 342.2 1877 1896 1281 1144 3518

Cc/meV

Cd 456.657 635.087

(0.017) (0.014)

233.704 311.653

(0.010) (0.007)

89.549 231.026 369.684 800.145 824.575 917.598 921.180 1117.852 1347.109 1828.557 2067.150 2377.926 3956.386 5987.225 8832.493

(0.001) (0.006) (0.005) (0.007) (0.300) (0.018) (0.011) (0.415) (0.013) (0.020) (0.023) (0.031) (0.062) (0.154) (0.211)

1/2+

66.7800 226.5090 443.1000 565.944 737.738 884.841 895.029 909.220 1052.936 1116.124 1208.097 1640.327 2036.695 2338.535 2574.840 4561.319 5578.370

(0.0010) (0.0030) (0.0040) (0.029) (0.020) (0.070) (0.061) (0.007) (0.039) (0.010) (0.088) (0.056) (0.020) (0.019) (0.032) (0.048) (0.217)

1/2+ 1/2+ 1/2+

120.1300 392.550 671.190 752.4400 962.388 1100.2340 1327.484 1426.722 1605.28 2134.030 3822.665 5362.34 5517.404 6411.893 7845.02 8376.25

(0.0010) (0.010) (0.010) (0.0060) (0.067) (0.0080) (0.055) (0.023) (0.11) (0.039) (0.068) (0.13) (0.081) (0.099) (0.22) (0.20)

1/2+ 1/2+ 1/2+ 1/2+

676.691 889.230 1048.800 1384.542

(0.082) (0.018) (0.017) (0.068)

27.57000 69.590 86.1850 99.4910 138.1660 164.2450 225.1460

(0.00064) (0.022) (0.0036) (0.0024) (0.0022) (0.0015) (0.0028)

110.0

(5.0)

(0.4) (0.1) (0.21) (4.6) (0.28) (0.34) (1.5) (4.3) (11) (7.2) (26) (34) (48) (68) (121)

73.2

(0.5)

89.0 69.0

(1.5) (1.0)

83.0

(6.0)

82.8

(2.5)

8.480 20.57 61.31 2.430 353.4 11.8 5.74 277.0 8.65 657.0 18.8 22.1 1492 679 1525 1588 857

(0.050) (0.17) (0.56) (0.090) (2.9) (2.0) (0.48) (3.3) (0.32) (7.5) (1.4) (1.0) (17) (13) (25) (66) (51)

62.8 56.0 61.6

(1.5) (3.0) (2.0)

67.4

(1.0)

68.7

(1.0)

60.6

(1.1)

83.5

(3.2)

(0.48) (5.6) (5.3) (2.9) (0.68) (3.3) (1.5) (15) (1.9) (7.8) (29) (26) (31) (44) (94) (79)

50.0 55.2 56.4 53.7

(0.5) (0.4) (1.0) (1.0)

50.7

(0.7)

48.0

(1.1)

1/2+

60.81 936.2 402.3 367.5 11.03 302.4 37.3 1812 31.7 279.4 1200 482 783 829 1793 1572

1/2+ 1/2+ 1/2+

21.1 53.7 511.7 119.1

(1.6) (1.8) (8.0) (6.1)

73

(10)

170

(16)

3.684 0.132 2.516 10.930 7.125 51.44 24.08

(0.017) (0.010) (0.033) (0.090) (0.046) (0.36) (0.19)

131.1

(3.0)

130.1 129.6

(9.0) (5.0)

127.0 130.5

(4.0) (8.0)

Cd

Cd

112

114

116

111

+

1/2 1/2+

1/2+ 1/2+ 1/2+

1/2+

Cd

1/2+

1/2+ +

1/2

1/2+ 1/2+ 1/2+

Cd

1/2+ 1/2+

Cd

Cd 1+ 1+ 1+ 1+ 1+

(continued on next page)

18

K. Volev et al. / Nuclear Instruments and Methods in Physics Research B 300 (2013) 11–29

Table 4 (continued) Isotope

113

Jp

Energy/eV 233.4660 275.6938 332.085 356.2102 389.1695 422.94 478.217 483.071 484.931 540.460 576.184 603.834 622.773 706.68 790.917 809.768 861.311 878.714 882.543 965.786 1042.354 1048.331 1068.41 1252.819 1261.862 1308.590 1449.166 1468.679 1523.315 1565.488 1582.349 1597.576 1618.290 1631.895 1743.411 1766.678

(0.0028) (0.0039) (0.041) (0.0036) (0.0062) (0.71) (0.022) (0.072) (0.034) (0.025) (0.017) (0.010) (0.021) (0.24) (0.032) (0.028) (0.094) (0.037) (0.040) (0.047) (0.064) (0.049) (0.12) (0.042) (0.027) (0.034) (0.052) (0.040) (0.062) (0.054) (0.042) (0.025) (0.055) (0.040) (0.041) (0.051)

0.17870 63.7091 84.8740 108.3320 143.0974 158.7720 192.8711 215.2592 261.1192 269.3491 291.6503 414.1187 432.0578 551.9610 841.849 851.9014 901.689 911.831 965.64 1051.52 1068.475 1120.405 1252.136 1267.632 1318.290 1364.75 1468.20 1628.34

(0.00010) (0.0014) (0.0092) (0.0017) (0.0054) (0.0029) (0.0022) (0.0024) (0.0028) (0.0038) (0.0095) (0.0036) (0.0062) (0.0053) (0.011) (0.0075) (0.019) (0.030) (0.12) (0.37) (0.055) (0.016) (0.023) (0.031) (0.035) (0.15) (0.11) (0.12)

0+

1+ 0+ 1+ 1+

gCn/meV

Cc/meV

38.48 15.32 5.81 36.12 19.91 0.70 3.88 1.28 2.33 18.51 35.87 25.88 35.90 3.22 40.3 41.4 14.9 31.1 6.42 44.0 46.7 15.29 5.28 110.8 27.15 23.97 15.65 49.4 17.60 21.32 161.4 61.2 172 185.0 372.0 15.43

(0.35) (0.13) (0.38) (0.32) (0.23) (0.26) (0.20) (0.10) (0.11) (0.60) (0.83) (0.35) (0.98) (0.73) (1.4) (1.4) (1.2) (1.3) (0.26) (2.1) (2.2) (0.54) (0.28) (4.2) (0.71) (0.62) (0.52) (1.3) (0.68) (0.83) (4.7) (1.5) (17) (5.3) (9.8) (0.68)

0.4800 2.375 24.59 8.175 2.250 6.068 47.25 19.05 23.36 15.44 4.073 93.15 19.29 80.25 53.49 389.3 13.95 17.14 16.9 13.8 12.26 93.1 36.98 139.5 77.0 102.6 91.0 65.0

(0.0015) (0.015) (0.11) (0.050) (0.032) (0.052) (0.30) (0.14) (0.18) (0.17) (0.087) (0.90) (0.24) (0.98) (0.97) (4.4) (0.75) (0.79) (1.9) (0.9) (0.51) (2.3) (0.83) (3.5) (4.8) (1.0) (5.5) (6.0)

176

(20)

152.0

(6.0)

121.0

(4.0)

113.5

(0.1)

123.3

(4.5)

112.3 129.9 144.5 120.3

(1.5) (5.0) (6.5) (7.0)

111.4

(2.5)

129.5

(4.0)

103.0 110.8

(5.0) (5.0)

Cd 1+

1+

0+ 1+ 1+ 0+ 1+ 1+ 1+ 1+

1+ 1+ 1+ 0+ 1+ 1+ 0+

almost 4% from the values recommended in the other evaluated data files (JEFF-3.1.2, ENDF/B-VII.0 and JENDL-3.3) and by 1.5% from the one suggested by Mosteller et al. [52]. In Ref. [52] the neutron width Cn = 0.622 meV has been adjusted to match results of integral measurements performed by Lloyd et al. [53]. This adjustment resulted in a change of approximately 3% to the neutron width derived by Kopecky et al. [13].

The parameters of the bound states for the other isotopes were initially adjusted to match the thermal capture cross sections of Mughabghab [34] and coherent scattering lengths recommended by Knopf and Waschkowski [45], with an absolute energy close to the first strong s-wave resonance. To avoid the use of strong bound states in some cases small changes to the initial scattering radius were made. To describe the transmission data of the

19

K. Volev et al. / Nuclear Instruments and Methods in Physics Research B 300 (2013) 11–29

1.0

0.6

0.60

0.55 0.14

Yexp (2 mm)

This work ENDF/B - VII.0 ENDF/B - VII.1

0.16

0.18

This work JEFF 3.1.2 JENDL 4.0 ENDF/B-VII.1

Yield

Yield

0.8

0.2

Yexp (0.03 mm)

0.65

0.20

0.1

0.4

0.2

0.0 0.8

0.0 Texp (0.03 mm)

1.0

Texp ( 25 mm)

This work ENDF/B - VII.0 ENDF/B - VII.1

0.6

Transmission

Transmission

0.8

0.6

This work JEFF 3.1.2 JENDL 4.0 ENDF/B-VII.1

0.75

0.4

0.70

0.2

0.4 0.65 0.02

0.04

0.2 0.01

0.06

0.08

0.1

1

Neutron energy / eV

Transmission

0.6

0.4

Texp (25 mm) This work JEFF 3.1.2 JENDL 4.0 ENDF/B-VII.0 ENDF/B-VII.1

0.0 1

380

400

420

440

Neutron energy / eV

Fig. 5. Results of a RSA of transmission and capture data obtained at GELINA in the thermal energy region. The theoretical transmission and yield using the resonance parameters of ENDF/B-VII.0 and ENDF/B-VII.1 are also shown.

0.2

0.0 360

10

Neutron energy / eV Fig. 6. Transmission data obtained with a 25-mm thick natCd sample at GELINA. The theoretical transmissions using the resonance parameters obtained in this work and those recommended in ENDF/B – VII.0, ENDF/B – VII.1, JENDL 4.0 and JEFF 3.1.2 are also shown.

25-mm thick sample a coherent scattering length of b = 6.72 fm together with a scattering radius of 6.9 fm for 114Cd was adopted. This length deviates from the length b = 7.48 ± 0.05 fm in Ref.

Fig. 7. Result of a RSA of transmission and capture data measured with a natural Cd-sample at GELINA. The theoretical transmission and yield based on JEFF 3.1.2, ENDF/B – VII.1 and JENDL 4.0 are also shown.

[45] but is very close to the value b = 6.4 ± 0.2 fm obtained by Vertebnyi et al. [55]. Also the scattering radii for 112Cd and 110Cd have been adjusted to match the interference profiles between potential and resonance scattering observed in the GELINA transmission data. The final scattering radii adopted in the file are given in Table 3. It should be noted that these values are completely linked to the resonance parameters, including spin and parity, presented in this paper together with the coherent scattering lengths in Table 3. Hence, they are effective scattering radii for the energy region covered in our transmission data. The deviations between the experimental data and the calculated transmissions and yields based on recommended resonance parameters observed in Figs. 5–7 demonstrate that the data obtained at GELINA with natural samples cannot be described by using resonance parameters in the evaluated data files. Fig. 5 illustrates the deviations of the GELINA data in the low energy region with respect to ENDF/B-VII.0 and ENDF/B-VII.1. The relative good agreement with the latest version ENDF/B-VII.1 is not surprising since part of this file is based on results described in this work. However, discrepancies around the peak/dip of the first resonance energy suggest that parts of the file have not been adopted. This is confirmed by the results of transmission measurements with the 25-mm thick sample shown in Fig. 6. This figure also illustrates that the parameters in JENDL 4.0, which include parameters of the resonance at 0.178 eV given by Kopecky et al. [15], are not fully consistent with energy dependent

20

K. Volev et al. / Nuclear Instruments and Methods in Physics Research B 300 (2013) 11–29 Table 5 Comparison of literature values for the total and capture cross section of natCd + n at 2200 m/s with results obtained in this work. The values recommended in the evaluated data libraries (for 300 K) and the one suggested by Mosteller et al. [52] are also given. Reference

Method

This work (experiment) Widder and Brunner [32] Tattersall et al. [46] Sokolowski et al. [47] Sokolowski et al. [47] Meadows [48,49] Albert et al. [50]

TOF TOF Pile oscillator TOF Pile oscillator Pulsed-source Pile oscillator

Total Total Absorption Absorption Absorption Absorption Absorption

2450 2455 2430 2445 2390 2484 2430

Mosteller et al. [52]

Adjustment to [53]

Total

2413

This This This This

TOF TOF TOF TOF

Total Total Absorption Absorption

2474 2487 2467 2480

Total Total Total Total Total Total

2547 2543 2450 2549 2475 2471

evaluation evaluation evaluation evaluation

(T = 0 K) (T = 300 K) (T = 0 K) (T = 300 K)

JEFF 3.1.2 ENDF/B-VII.0 ENDF/B-VII.1 JENDL-3.3 JENDL-4.0 IRDF-2002 = ENDF/B-VI.8

Evaluation Evaluation Evaluation Evaluation Evaluation Evaluation

Cross section Barn

(300 K) (300 K) (300 K) (300 K) (300 K) (300 K)

(40) (10) (40) (25) (45) (14) (50)

Table 6 Average ratios of resonance energies deduced from results obtained in this work, Liou et al.[2], Musgrove et al. [5], Allen and Wasson [4] and Frankle et al. [3]. The values between brackets are standard deviations. GELINA

Liou

GELINA

Liou

Liou

Liou

Musgrove

Frankle

Frankle

Allen and Wasson

106

Cd 108 Cd 110 Cd 111 Cd 112 Cd 113 Cd 114 Cd 116 Cd Average

1.00051 1.00080 1.00040 1.00045 1.00055 1.00026 1.00049

(0.00029) (0.00065) (0.00056) (0.00017) (0.00031) (0.00025) (0.00040)

0.99740 (0.00051) 0.9967 (0.0010) 0.99987 0.99985 0.99986 0.99986 0.99985

(0.00021) (0.00030) (0.00026) (0.00023) (0.00023)(without

1.00014 (0.00014)

110

1.00023 (0.00041)

Cd)

[45], which has been adopted in this work. The results in Fig. 6 illustrate the importance of thick transmission measurements to adjust the parameters (i.e. bound state parameters and scattering radii) which influence the cross sections between resonances. Examples of typical discrepancies in other regions are shown in Fig. 7.

cross section data obtained in this work. The large discrepancies in Fig. 6 for the theoretical estimate obtained with the JEFF 3.1.2 file is primarily due to the overestimation of the scattering cross section between resonances. For 110Cd a thermal scattering cross section of 18.2 b is adopted in JEFF 3.1.2, compared to the value 4.2 b deduced from the data of Knopf and Waschkowski

1.0010

1.005

113

Cd

Er,GELINA / Er,Frankle

Er,GELINA / Er,Liou

1.0005

1.000 110

Cd 112 Cd 114 Cd 116 Cd 111 Cd 113 Cd

0.995 1 10

1.0000

0.9995

0.9990 2

10

10

3

Neutron energy / eV

10

4

0

500

1000

Neutron energy / eV

Fig. 8. Ratio between resonance energies obtained at GELINA with those reported by Liou et al. [2] (left) and Frankle et al. [3] (right).

1500

21

K. Volev et al. / Nuclear Instruments and Methods in Physics Research B 300 (2013) 11–29

1.2

1.5

113

gΓn,GELINA / gΓn,Frankle

gΓn,GELINA / gΓn,Liou

Cd

1.0 110

Cd Cd 114 Cd 116 Cd 111 Cd 113 Cd 112

1.1

1.0

0.9

0.5 1

2

10

10

10

3

4

0

10

500

Neutron energy / eV

1000

1500

Neutron energy / eV

Fig. 9. Ratio between gJCn-values obtained at GELINA with those reported by Liou et al. [2] (left) and Frankle et al. [3] (right).

4

10

3

2

10

J 0 1 0 1 2

1

10

1

Γγ,s / meV

150

l 0 0 1 1 1

10

gΓn / eV

200

Musgrove, s-wave Musgrove, p-wave (URR) IRMM, s-wave (even) IRMM, s-wave (odd) 113 Frankle, p-wave ( Cd)

100

0

10

gΓ1 n = 0.047 eV

-1

10

50 -2

10

0 0

-3

10

2000

4000

6000

8000

10000

Neutron separation energy / keV Fig. 10. Average radiation width for the Cd-isotopes deduced from the data of Musgrove et al. [5], Frankle et al. [3] and the parameters obtained in this work. The full lines, which are based on a power function, are only given to guide the eye.

-1

10

0

10

1

10

2

10

3

10

4

10

Neutron energy / eV Fig. 11. Reduced neutron width for 113Cd + n as a function of neutron energy supposing that all resonances have ‘ = 1. The selection k = 0 or 1 based on the Bollinger and Thomas [36] approach is compared with a selection based on an upper level g J C1n 6 0.047 eV for ‘ = 1.

4.3. Comparison with literature data In general there is a reasonable agreement between the resonance parameters obtained in this work and those deduced by Liou et al. [2], Musgrove et al. [5] and Frankle et al. [3]. The largest discrepancies are observed when comparing our results with those of Wasson and Allen [4]. A systematic relative difference between the resonance energies is observed. This is illustrated in Fig. 8 showing the ratio between the resonance energies obtained at GELINA with the energies given by Liou et al. [2] and Frankle et al. [3]. The average ratios per isotope are summarized in Table 6. This table gives also ratios deduced from the energies reported by Wasson and Allen [4] and Musgrove et al. [5]. Ratios of gCn-values are shown in Fig. 9. There is a reasonable agreement between the data obtained in this work and those of Frankle et al. [3]. No obvious systematic difference is observed. A similar agreement exists between our data and the data of Liou et al. [2].

The average radiation widths for the different isotopes are plotted in Fig. 10 as a function of the neutron separation energy. There is a good agreement with the values obtained by Musgrove et al. [5] and the average radiation width for s-wave resonances adopted by Frankle et al. [3]. Our data confirm the strong dependence on the separation energy observed by Musgrove et al. [5]. This behaviour is in disagreement with Liou et al. [2]. In Ref. [2] a radiation width of 100 meV independent of the isotopes is quoted. From our data we were not able to deduce radiation widths of p-wave resonances in 113Cd in order to verify the difference in average radiation widths between sand p-wave resonances quoted by Frankle et al. [3]. The results of Musgrove et al. [5] also indicate a systematic difference between the radiation width of s- and p-wave resonances for the even isotopes.

22

K. Volev et al. / Nuclear Instruments and Methods in Physics Research B 300 (2013) 11–29

5. Recommended resonance parameters

200

λ 0 1 1

106,108,110,111,112,113,114,116

Cc ¼

1 KtKc gJ K t  K c

and Cn ¼

Kt gJ

ð5Þ

together with the radiation width closest to the average radiation width Cc was chosen. This is illustrated in Fig. 12 for 110Cd, where the capture Kernel is plotted as a function of gJCn together with the estimate for gJ = 1 and gJ = 2 based on the average widths in Table 3. For the even isotopes such a spin assignment results directly in a parity assignment k = 1 in case gJ = 2 is preferred. This spin and parity assignment (for the even isotopes) overruled both the most probable spin assignment and ‘-assignment based on the Bollinger and Thomas [36] approach. The corresponding radiation width was preferred in case the width deviated by less than 50% from the average width. When the radiation width deviated by more than 50% from the average width the average width was preferred and only the result from the transmission measurement (i.e. gJCn) was considered. When only the capture Kernel Kc was reported, the average radiation width Cc was adopted and the neutron width was obtained from:

Cn ¼

Cc K c g J Cc  K c

ð6Þ

and preference was given to a gJ –value or spin J based on the condition:

gJ >

Kc

Cc

:

ð7Þ

When only gJCn was available the average radiation width was adopted and the neutron width was deduced by assuming the most probable spin and parity from the Bollinger and Thomas [36] approach.

Γγ = 73 meV Γγ = 77 meV Γγ = 77 meV

Kγ / meV

150

100

50

0 0

1000

2000

gΓn / meV Fig. 12. Capture Kernel Kc as a function of gJCn for 110Cd. The lines are based on Eq. (6) using an average radiation width Cc = 70 meV and 79 meV corresponding to ‘ = 0 and ‘ = 1, respectively.

The resonance parameter files were verified and a final adjustment in the whole resonance region was made by a simultaneous analysis with REFIT using the GELINA data together with the transmission and capture data of Frankle et al. [3]. An analytical response function for ORELA, based on the work of Koehler et al. [59] and Coceva et al. [60], was used. In the analysis the flight path length for the ORELA data was adjusted to match the resonance energies of GELINA. The consistency with the transmission data of Liou et al. [2] was verified using a Gaussian response function for their TOF-spectrometer. The result of the final adjustment procedure is shown in Figs. 13 and 14, which also include the results of measurements on an enriched 113Cd sample performed by Frankle et al. [3,10]. Parameters of resonances for 113Cd that were adjusted or added based on the simultaneous analysis of GELINA and ORELA data are given in Table 7. Fig. 13 clearly illustrates how the results of measurements on natural samples have improved the quality of

1.0

0.8

Transmission

Resonance parameter files for Cd were constructed based on the parameters of resonances which were observed in the work of Liou et al. [2], Musgrove et al. [5], Wasson and Allen [4], and Frankle et al. [3] together with the parameters in Table 4. The low energy parameters of 106Cd and 108Cd were taken from Ref. [56] and [57], respectively. The capture areas of Musgrove et al. [5] have been corrected using the factors published by Allen et al. [58]. For the strong s-wave resonances of 113Cd the resonance parameters obtained from non-saturated thin sample transmission data obtained at GELINA were preferred instead of the parameters of Frankle et al. [3]. The resonance energies obtained at GELINA were considered as a reference and the ratios in Table 6 were used to correct the energies in Liou et al. [2], Musgrove et al. [5], Wasson and Allen [4], and Frankle et al. [3]. For 106Cd and 108Cd the isotope independent average ratios in Table 6 were used. Preference was always given to gCn – values deduced from transmission measurements. The choice of orbital angular momentum (‘ = 0 or 1) was based on the Bayes’ theorem approach of Bollinger and Thomas [36] and for the spin the most probable spin (largest possible) was chosen. This spin choice was overruled by specific spin assignment measurements in the literature, as those reported by Gunsing et al. [6] and Wasson and Allen [4], or by spin assignments based on our data in Table 4. The Bollinger and Thomas [36] approach is almost identical to a selection based on an upper threshold level for the reduced neutron widths of p-wave resonances. Fig. 11 shows the reduced neutron width supposing that all resonances for 113Cd + n are p-waves. Defining an upper level for the p-wave reduced neutron width of 0.047 eV results in almost the same choice of orbital angular momentum as with the Bollinger and Thomas [36] approach as illustrated in Fig. 11. The upper limits corresponding to the Bollinger and Thomas [36] approach for the other isotopes are given in Table 3.When both Kc and Kt are given the combination (gJ, Cn, Cc) resulting from:

J 1/2 3/2 3/2

0.6

0.4 Texp (2 mm)

0.2

Texp (5 mm) Frankle et al. This work ENDF/B-VII.1

0.0 430

432

434

Neutron Energy / eV Fig. 13. Result of a RSA of GELINA transmission and capture data around the 432.06 eV resonance for 113Cd + n. The experimental transmission is compared with the transmission data of Frankle et al. [3,10] and with the transmission calculated with resonance parameters from the ENDF/B-VII.1 library.

23

K. Volev et al. / Nuclear Instruments and Methods in Physics Research B 300 (2013) 11–29

the resonance parameter file. Fig. 14 demonstrates that even without additional information from other data, the data of Frankle et al. [10] is better described using the file produced in this work. At present the resonance parameters have been transferred into a full compatible ENDF format without producing a covariance matrix. The uncertainties on the resonance parameters listed in Tables 4 and 7 are limited to the uncorrelated component due to counting statistics. The production of covariance data accounting for all uncertainty components is in progress. Only parameters of resonances that have been observed in experiments have been included and no attempt has been made to account for missing resonances based on level statistical theories. A few resonances that were not reported before were observed in the GELINA capture data, but not in the transmission data. Since no isotope assignment could be made, the capture area could not be deduced from the data and only the resonance energy was determined. Therefore, these resonances have not been included in the final files.

FCd-factors do not significantly differ from unity. However, FCdfactors can be smaller than unity when resonances of Cd overlap with those of the irradiated material [65]. They can be larger than unity when the energy of neutrons scattered by Cd overlaps with a lower energy resonance of the irradiated material [66]. The magnitude of FCd depend on the Cd cover thickness and its assumed cut-off energy ECd, which in turn depends on the Cd cover thickness. Since it is hard to determine this factor experimentally mostly theoretical estimates are used. The impact of the resonance parameter file on theoretical estimates has been studied by comparing FCd-factors using the Cd data from the present work with those resulting from calculations with ENDF/B-VII.0 and the IRDF-2002 file. In the calculations a parallel beam was considered and the effect of the scattering neglected. The FCd-factor was expressed as:

6. Impact of the parameter file on integral quantities

where T(E) is the exponential attenuation due to the Cd-cover, u(E) is the neutron flux, r(E) is the capture cross section and values ECd = 0.55 eV and Em = 2 MeV are assumed. Table 8 lists nuclides for which substantial differences have been observed. The largest difference is observed for 130Ba(n,c). This is due to a spurious resonance at 59 eV present in the IRDF2002 file. This resonance is not present if the natural cadmium cross sections are reconstructed from the isotopic data in evaluated data libraries (e.g. ENDF/B-VII.0 or JENDL-4.0).

6.1. Cadmium transmission factors The cadmium transmission factor FCd is a quantity that is used in the analysis of neutron activation data in case epicadmium irradiation is performed by covering a foil or sample with a cadmium sheet. Epicadmium activation is used to measure resonance integrals [61], to determine the neutron flux [62] or to determine k0 and Q0 factors for Neutron Activation Analysis (NAA) by the Cd-ratio method [63]. Epithermal Neutron Activation Analysis (ENAA) [64] is also employed as an alternative to classical NAA to enhance the signal of trace elements. The FCd-factor, which accounts for the fact that the activity resulting from an irradiation under a cadmium cover (ACd) is different from the activity by a pure epithermal neutron beam (AEp), is defined as the ratio of these activities:

F Cd ¼

ACd : AEp

ð8Þ

With a pure epithermal neutron beam is intended a neutron spectrum that is inversely proportional to the velocity between a lower (ECd) and upper limit (Em) and zero elsewhere. For a 0.1 mm thick Cd cover the lower limit is assumed to be 0.55 eV and the upper limit is usually supposed to be 2 MeV. Usually

R Em F Cd ¼

1.0

Exp. (Frankle et al.) This work ENDF/B-VII.1

0.8

Transmission

Transmission

0.4

ð9Þ

To study the effect of the resonance parameters obtained in this work on the interpretation of the integral experiments reported by Lloyd et al. [53], the exercise performed by Kopecky et al. [15] was repeated. The results are given in Table 9. Details of the integral experiments can be found in the handbook of evaluated criticality safety benchmark experiments with reference HEU_SOL_THEM_049 [67]. The experiments consisted of a cylindrical stainless-steel vessel surrounded by an effectively infinite reflector of water around and beneath it. The vessel contained a high enriched uranium solution, with or without cadmium nitrate in the solution. In some cases additional soluble cadmium absorbers were added to the reflector. In Table 9 results of calculations

Exp. (Frankle et al.) This work ENDF/B-VII.1

0.6

TðEÞrðEÞuðEÞdE ; R Em rðEÞuðEÞdE ECd

6.2. Integral experiments

1.0

0.8

0

0.6

0.4

0.2

0.2

0.0 2220

2240

Neutron energy / eV

2260

0.0 7460

7480

7500

7520

7540

Neutron energy / eV

Fig. 14. Examples for simultaneous analysis of GELINA and ORELA data in the energy intervals around 2.24 and 7.5 keV. The experimental transmission data of Frankle et al. [3,10] are compared with the stransmission calculated with resonance parameters from the ENDF/B-VII.1 library.

24

K. Volev et al. / Nuclear Instruments and Methods in Physics Research B 300 (2013) 11–29

Table 7 Resonance parameters for 113Cd + n which have been adjusted or added as a result of a simultaneous analysis of GELINA and ORELA data. The change in spin assignments of analyzed resonances is with respect to those reported by Frankle et al. [3]. Energy/eV 21.830 49.767 81.551 196.180 211.864 232.3042 281.796 376.767 446.9354 457.612 495.027 629.820 677.0862 758.942 760.844n 824.465 870.523 919.586 936.39n 939.655 975.971 1063.19 1081.455 1089.0819 1146.780 1169.546 1174.824 1288.98 1310.6460 1356.926 1368.82n 1410.19 1423.530n 1461.051 1471.42n 1511.462 1516.10 1563.49n 1567.214 1578.22 1602.30 1622.743 1646.075 1653.72n 1660.5164 1734.258 1746.86 1772.122 1787.508 1822.547 1867.590 1873.78 1889.73 1909.215 1916.592 1994.78 2008.474 2014.59 2022.56n 2034.324n 2043.554 2046.51 2053.8133 2065.63n 2078.925 2091.52 2098.39 2115.576 2161.682 2200.637 2228.69n 2238.112n

(0.014) (0.020) (0.045) (0.082) (0.087) (0.0071) (0.026) (0.015) (0.0085) (0.012) (0.027) (0.037) (0.0035) (0.019) (0.080) (0.033) (0.098) (0.094) (0.24) (0.021) (0.012) (0.47) (0.088) (0.0049) (0.086) (0.045) (0.048) (0.12) (0.0083) (0.039) (0.27) (0.18) (0.024) (0.029) (0.18) (0.067) (0.10) (0.13) (0.081) (0.36) (0.24) (0.058) (0.011) (0.14) (0.0095) (0.021) (0.10) (0.090) (0.015) (0.077) (0.019) (0.29) (0.16) (0.077) (0.053) (0.13) (0.026) (0.17) (0.21) (0.011) (0.061) (0.10) (0.0096) (0.18) (0.060) (0.78) (0.45) (0.017) (0.087) (0.014) (0.20) (0.063)

Jp

gCn/meV

212221+ 1-* 10+ 1+ 2-* 2- * 1+ 1+ 22-* 2221+ 1+ 220+ 21+ 1+ 21+ 1+ 221+ 1+ 22-* 221+ 222-* 1+ 21+ 1+ 22-* 1+ 2- * 1+ 221+ 1+ 21+ 221+ 1+ 2-* 1+ 21+ 221+ 2- * 1+ 21+

0.00662 0.0144 0.0138 0.0599 0.0670 1.007 0.474 0.827 2.110 1.529 0.873 1.183 14.655 3.560 1.007 2.601 0.976 1.210 0.470 5.62 10.66 0.279 1.93 40.41 2.02 4.61 4.37 0.404 24.02 5.49 0.764 1.25 9.59 8.87 1.47 4.29 2.79 2.24 40.98 0.847 1.34 6.00 33.81 2.48 38.80 19.81 4.06 4.88 28.76 6.15 27.20 1.72 3.27 76.58 10.20 4.57 23.94 3.68 3.01 70.5 13.17 8.16 74.08 3.78 12.70 0.720 1.34 41.63 8.64 61.70 4.12 12.28

(0.00038) (0.0010) (0.0011) (0.0053) (0.0056) (0.014) (0.019) (0.018) (0.026) (0.027) (0.030) (0.048) (0.071) (0.076) (0.064) (0.084) (0.069) (0.081) (0.044) (0.11) (0.14) (0.027) (0.12) (0.28) (0.14) (0.17) (0.16) (0.039) (0.20) (0.17) (0.069) (0.10) (0.18) (0.20) (0.12) (0.19) (0.17) (0.15) (0.31) (0.079) (0.12) (0.24) (0.32) (0.16) (0.35) (0.30) (0.14) (0.26) (0.37) (0.29) (0.38) (0.15) (0.22) (0.62) (0.34) (0.29) (0.43) (0.26) (0.24) (1.4) (0.47) (0.41) (0.69) (0.28) (0.41) (0.063) (0.12) (0.53) (0.40) (0.64) (0.31) (0.45)

Jp

Energy / eV 2241.973 2258.024 2306.38 2331.319 2346.687 2356.94 2451.089 2489.13 2526.39n 2528.682 2535.069 2544.21 2604.744 2610.80n 2615.78 2638.172 2651.288 2677.613n 2697.19 2708.22 2719.56 2744.28 2754.71 2773.339 2793.454 2828.614 2850.50 2863.31 2905.74 2921.87 2929.675 2978.50 2987.90 3022.35 3040.61 3055.496 3062.97 3068.10n 3074.381 3088.921n 3091.687 3095.329n 3210.717 3227.23 3242.525 3273.938n 3276.307 3321.57 3327.310 3362.33 3370.91n 3377.716 3424.31 3458.570 3473.58 3482.830n 3499.891 3580.803 3607.59 3621.96 3627.57 3651.88 3671.775 3678.662 3685.828 3710.14n 3725.03 3737.42 3758.93 3774.95 3798.45 3829.82 3847.73 3915.688 3927.421 3975.35 3980.31n 3994.193

(0.023) (0.091) (0.11) (0.055) (0.029) (0.10) (0.015) (0.13) (0.17) (0.076) (0.036) (0.46) (0.010) (0.17) (0.28) (0.080) (0.014) (0.021) (0.31) (0.45) (0.99) (0.60) (0.15) (0.015) (0.030) (0.037) (0.57) (0.69) (0.34) (0.11) (0.053) (0.14) (0.19) (0.10) (0.20) (0.059) (0.12) (0.23) (0.073) (0.087) (0.033) (0.053) (0.055) (0.15) (0.024) (0.092) (0.030) (0.13) (0.054) (0.13) (0.27) (0.025) (0.22) (0.014) (0.51) (0.080) (0.022) (0.060) (0.53) (0.33) (0.12) (0.64) (0.071) (0.026) (0.049) (0.72) (0.69) (0.50) (0.99) (0.14) (0.58) (0.38) (0.23) (0.059) (0.052) (0.23) (0.38) (0.049)

+

1 2-* 2-* 1+ 1+ 2-* 1+ 2-* 21+ 1+ 21+ 221+ 1+ 1+ 22222-* 1+ 1+ 1+ 2221+ 1+ 2-* 2-* 1+ 21+ 1+ 21+ 1+ 1+ 1+ 1+ 2-* 1+ 1+ 1+ 1+ 1+ 1+ 21+ 21+ 221+ 1+ 221+ 21+ 1+ 1+ 22221+ 222-* 1+ 1+ 2-* 21+

gCn / meV 41.34 9.55 8.31 16.42 33.04 9.51 73.4 8.32 9.08 19.3 33.26 2.38 276.0 6.54 4.53 16.43 105.9 65.90 4.39 2.97 1.060 2.21 9.69 115.2 52.50 42.79 2.56 1.26 4.92 16.29 33.50 13.47 10.08 19.91 9.24 33.68 17.58 9.03 27.63 37.2 122.9 41.3 42.8 15.44 107.3 65.0 102.7 20.28 48.8 20.5 9.48 118.3 12.02 928.6 5.35 3.79 152.0 53.9 5.94 10.36 27.4 5.21 50.1 312.8 77.9 4.30 4.66 7.07 2.47 25.1 6.09 9.66 17.3 72.1 83.1 19.4 12.6 132.3

(0.61) (0.44) (0.45) (0.54) (0.62) (0.48) (0.9) (0.50) (0.76) (0.8) (0.69) (0.23) (2.5) (0.45) (0.27) (0.65) (1.2) (0.98) (0.38) (0.27) (0.093) (0.21) (0.60) (1.4) (0.98) (0.90) (0.25) (0.13) (0.42) (0.75) (0.90) (0.75) (0.68) (0.83) (0.66) (0.98) (0.87) (0.64) (0.97) (1.7) (2.6) (1.1) (1.2) (0.88) (1.7) (3.1) (1.6) (0.97) (1.3) (1.1) (0.73) (1.9) (0.85) (5.5) (0.48) (0.38) (2.3) (1.5) (0.54) (0.82) (1.3) (0.48) (1.7) (3.2) (2.1) (0.41) (0.44) (0.63) (0.25) (1.3) (0.56) (0.81) (1.2) (1.9) (2.0) (1.3) (1.0) (4.2)

25

K. Volev et al. / Nuclear Instruments and Methods in Physics Research B 300 (2013) 11–29 Table 7 (continued) Energy/eV 3997.84n 4021.36n 4055.70n 4082.77 4089.87 4099.636 4129.90 4151.42 4194.712 4215.58n 4222.50 4275.43 4280.80n 4286.93 4308.985 4313.31n 4366.50 4374.60n 4406.57 4422.08 4458.0n 4483.05 4492.545 4511.68 4557.945n 4562.639n 4590.734 4607.70 4611.59n 4626.23 4677.02 4688.65 4734.01 4748.92 4775.587 4802.55n 4809.732 4814.09n 4821.99 4845.92 4860.21 4869.26 4908.17n 4928.44 4940.75 4952.49n 4959.28 4968.38 4998.46n 5002.60 5022.38n 5040.65n 5043.880 5048.26n 5070.71 5088.41 5104.991 5112.272 5146.38 5163.43 5175.87 5232.69 5268.16 5274.29 5289.62 5305.01n 5320.57 5331.857 5371.80 5377.79 5387.93 5397.53 5424.45 7484.34 7491.44n

Jp

Energy / eV p

(0.31) (0.46) (0.37) (0.35) (0.35) (0.093) (0.23) (0.41) (0.043) (0.55) (0.49) (0.14) (0.68) (0.21) (0.057) (0.24) (0.35) (0.47) (0.11) (0.14) (1.3) (0.24) (0.048) (0.33) (0.064) (0.024) (0.025) (0.40) (0.37) (0.36) (0.44) (0.26) (0.19) (0.34) (0.081) (0.15) (0.068) (0.45) (0.10) (0.15) (0.21) (0.15) (0.14) (0.55) (0.25) (0.43) (0.15) (0.32) (0.11) (0.12) (0.61) (0.27) (0.046) (0.12) (0.13) (0.18) (0.066) (0.096) (0.16) (0.19) (0.07) (0.17) (0.12) (0.11) (0.42) (0.27) (0.15) (0.056) (0.14) (0.11) (0.13) (0.13) (0.25) (0.11) (0.39)

J

gCn/meV

2222-* 2-* 1+ 2-* 21+ 22-* 1+ 22-* 1+ 22-* 21+ 1+ 22-* 1+ 2-* 1+ 21+ 2-* 22-* 2-* 2-* 1+ 2-* 1+ 1+ 1+ 21+ 1+ 1+ 1+ 1+ 2-* 2-* 21+ 2-* 1+ 1+ 221+ 21+ 2-* 1+ 1+ 1+ 2-* 1+ 1+ 1+ 1+ 2-* 21+ 1+ 1+ 1+ 1+ 1+ 2-* 1+ 2-

21.4 9.18 11.32 13.0 11.5 50.2 20.3 11.03 188.9 8.75 10.53 35.8 7.44 26.2 100.8 29.0 15.6 11.44 52.7 42.4 3.64 24.2 138.5 18.8 95.3 18.5 340.6 18.3 19.8 17.2 15.3 25.4 37.1 21.0 92.1 49.0 128.8 16.7 77.3 51.7 35.9 52.5 56.5 13.40 32.5 18.7 54.9 25.6 80.2 86.8 9.09 30.9 137.8 35.1 46.8 33.1 99.4 65.1 38.2 32.2 89.2 39.6 58.4 59.3 15.5 24.5 46.7 170.5 58.1 75.3 56.0 51.9 27.8 298.7 57.7

(1.6) (0.80) (0.94) (1.0) (1.0) (1.9) (1.4) (0.94) (3.0) (0.79) (0.91) (1.8) (0.69) (1.6) (2.9) (1.8) (1.2) (0.99) (2.2) (2.0) (0.35) (1.6) (3.2) (1.4) (2.7) (1.9) (4.8) (1.6) (1.7) (1.4) (1.3) (1.7) (2.1) (1.6) (3.0) (2.4) (3.8) (1.6) (2.8) (2.5) (2.2) (2.5) (2.6) (1.2) (2.1) (1.5) (2.6) (1.9) (3.4) (3.9) (0.73) (2.7) (2.5) (2.7) (2.0) (1.8) (2.5) (2.3) (1.9) (1.8) (2.4) (1.9) (2.3) (2.2) (1.2) (1.6) (2.1) (3.4) (2.4) (2.7) (2.3) (2.3) (1.8) (9.6) (4.5)

5456.62 5502.844 5522.11 5564.55 5611.30n 5615.70 5662.44 5720.22 5729.91 5735.46 5766.48 5769.26 5787.02 5805.755 5811.56n 5826.69 5855.32 5901.54 5908.06n 5925.51n 5942.157 5963.15n 6000.64 6033.18 6095.82 6165.10 6188.60 6222.09n 6227.330 6239.08n 6247.97n 6265.34 6275.66n 6295.12 6334.68 6349.73n 6434.55 6467.10 6503.07 6541.37n 6560.26n 6567.103 6600.793 6632.87 6659.68n 6664.39 6686.49 6693.92n 6716.22n 6729.17 6742.47n 6771.45n 6788.71 6800.015 6809.853 6838.40 6899.68 6915.19n 6949.40 6967.28 6995.99n 7001.87 7061.01 7081.32 7093.22n 7106.37 7243.18 7303.29n 7318.35n 7341.44n 7377.40 7397.50 7416.03 7429.74n 7449.91 7476.62n 7504.98n 7509.86

(0.15) (0.034) (0.54) (0.16) (0.47) (0.14) (0.39) (0.31) (0.43) (0.29) (0.18) (0.17) (0.23) (0.026) (0.13) (0.12) (0.18) (0.15) (0.16) (0.33) (0.077) (0.49) (0.12) (0.29) (0.15) (0.31) (0.24) (0.16) (0.086) (0.48) (0.61) (0.11) (0.23) (0.16) (0.42) (0.29) (0.10) (0.31) (0.30) (0.73) (0.26) (0.057) (0.073) (0.24) (0.35) (0.19) (0.11) (0.21) (0.45) (0.28) (0.54) (0.68) (0.17) (0.061) (0.076) (0.23) (0.11) (0.51) (0.43) (0.30) (0.52) (0.21) (0.23) (0.29) (0.57) (0.15) (0.41) (0.83) (0.72) (0.81) (0.44) (0.33) (0.13) (0.64) (0.46) (0.34) (0.24) (0.19)

1+ 1+ 2-* 1+ 21+ 2-* 2-* 2-* 2-* 1+ 1+ 2-* 1+ 21+ 1+ 1+ 1+ 21+ 21+ 2-* 1+ 2-* 21+ 1+ 221+ 21+ 2-* 22-* 2-* 2-* 221+ 1+ 1+ 21+ 1+ 1+ 22-* 221+ 1+ 1+ 1+ 1+ 22-* 2-* 21+ 2-* 2-* 21+ 2-* 2222-* 2-* 1+ 22-* 21+ 1+

gCn / meV 48.5 283.4 13.3 48.8 21.9 78.5 21.2 27.6 23.7 34.8 64.5 80.2 38.8 447.9 61.2 76.5 46.8 69.3 67.8 28.7 127.0 18.9 79.2 34.3 66.4 34.0 46.1 94.9 264.8 23.8 17.9 96.9 47.5 72.8 25.6 39.1 17.2 38.4 43.3 18.2 52.0 257.9 196.1 55.9 23.2 102.3 151.5 73.7 30.0 52.0 25.9 20.7 84.0 277.4 214.1 61.4 151.4 27.9 34.8 56.3 27.4 76.0 74.9 59.0 27.3 117.7 43.7 20.4 24.0 20.8 24.8 55.7 142.1 29.6 43.4 60.0 108.5 127.1 (continued on next

(2.2) (4.7) (1.1) (2.3) (1.9) (3.4) (1.6) (1.9) (1.8) (2.3) (4.9) (4.5) (2.2) (7.5) (2.3) (3.0) (2.5) (3.0) (3.0) (2.0) (3.4) (1.6) (3.0) (2.3) (2.9) (2.3) (2.6) (4.5) (8.3) (1.9) (1.6) (3.6) (2.8) (3.2) (2.4) (2.5) (1.7) (2.6) (2.8) (1.8) (2.9) (5.6) (5.2) (3.1) (2.3) (4.7) (5.0) (3.8) (2.3) (3.1) (2.1) (1.8) (3.9) (6.6) (5.8) (3.4) (4.9) (2.3) (2.6) (3.3) (2.2) (3.8) (3.8) (3.5) (2.3) (4.6) (3.1) (2.3) (2.6) (2.4) (3.0) (3.7) (5.4) (2.5) (3.2) (3.6) (7.4) (8.1) page)

26

K. Volev et al. / Nuclear Instruments and Methods in Physics Research B 300 (2013) 11–29

Table 7 (continued) Energy/eV 7535.72n 7556.97n 7573.01n 7580.545 7588.51n 7605.98n 7613.37 7621.30n 7704.497 7714.933n 7761.74 7785.15n 7805.49 7820.9n 7853.52n 7862.67 7909.80n 7915.06 7922.60n 7942.25n 7949.64 7958.6n 7975.23 7998.04n 8003.06 8024.18n 8065.78 8088.28n 8100.89n 8105.99 8112.85n 8121.56 8130.48n 8168.90 8179.87 8187.84n 8219.99 8239.09 8276.70 8285.58n 8295.01 8340.3n 8348.86 8382.72 8429.18 8468.57 8479.57n 8490.75 8498.02n 8534.94 8564.17 8601.91 8627.35n 8656.23n 8710.83 8818.64 8847.19n 8857.95 8906.35n 8929.77 8957.23 8986.21 8998.06n 9059.08 9113.31 9127.10 9148.36 9213.47n 9230.70n 9247.57n 9253.62 9271.60n 9279.69 9287.96n 9300.28n 9341.695

(0.59) (0.57) (0.34) (0.092) (0.65) (0.28) (0.20) (0.27) (0.090) (0.026) (0.36) (0.74) (0.13) (1.1) (0.39) (0.34) (0.68) (0.28) (0.82) (0.30) (0.31) (1.1) (0.33) (0.15) (0.23) (0.90) (0.17) (0.24) (0.39) (0.37) (0.48) (0.32) (0.12) (0.49) (0.21) (0.52) (0.24) (0.71) (0.18) (0.21) (0.13) (1.6) (0.45) (0.29) (0.16) (0.10) (0.72) (0.22) (0.10) (0.38) (0.26) (0.34) (0.12) (0.63) (0.23) (0.26) (0.66) (0.56) (0.97) (0.33) (0.43) (0.28) (0.65) (0.50) (0.38) (0.33) (0.50) (0.44) (0.48) (0.37) (0.22) (0.46) (0.24) (0.50) (0.57) (0.097)

Energy / eV

Jp

gCn/meV

2221+ 221+ 21+ 22-* 21+ 222-* 21+ 21+ 1+ 21+ 21+ 21+ 221+ 21+ 22-* 1+ 21+ 2-* 1+ 1+ 1+ 22-* 1+ 1+ 1+ 21+ 22-* 1+ 1+ 221+ 1+ 22-* 21+ 1+ 1+ 22-* 1+ 1+ 1+ 2221+ 1+ 1+ 221+

31.9 35.0 57.8 371.5 34.1 68.9 90.1 43.8 298.1 16.7 63.2 27.8 181.7 18.5 55.9 63.6 40.1 112.4 33.4 79.5 95.4 21.6 71.5 46.2 133.1 25.4 141.9 18.8 60.1 108.5 49.2 83.1 34.9 49.6 144.9 57.5 110.2 35.8 164.8 151.5 244.5 14.6 59.0 93.9 179.0 649 37.4 131.3 27.8 75.8 117.2 83.7 31.3 53.6 139.8 125.1 52.2 59.8 32.7 97.9 88.5 119.4 14.6 78.6 97.1 108.5 94.8 86.7 74.4 90.8 172.5 114.1 292 58.6 74.8 510

n

(2.6) (2.8) (4.1) (9.8) (3.0) (2.4) (4.4) (4.2) (9.8) (1.6) (4.1) (2.5) (6.5) (1.7) (3.8) (4.1) (3.7) (6.8) (3.0) (5.2) (5.8) (2.0) (4.4) (4.6) (5.9) (2.3) (6.2) (1.9) (4.0) (7.2) (3.6) (5.1) (3.5) (3.8) (7.3) (4.5) (5.7) (3.0) (7.2) (6.9) (8.3) (1.4) (4.2) (5.6) (7.4) (14) (3.2) (6.3) (2.8) (5.0) (6.1) (5.3) (2.8) (3.5) (6.7) (6.7) (4.2) (4.6) (3.0) (5.9) (5.2) (6.7) (1.4) (5.5) (6.1) (6.5) (5.7) (5.9) (5.5) (6.6) (8.0) (9.0) (15) (5.0) (5.5) (14)

9356.25 9368.80n 9403.63n 9412.765 9441.44 9461.97n 9504.25 9526.53n 9536.06n 9544.37 9569.30n 9577.46 9612.9n 9632.51 9698.89 9736.74 9790.74n 9848.1n 9882.66 9912.89 9973.86 9987.8n 10000.22n 10014.86n 10022.60n 10045.10n 10052.71n 10060.69 10074.09n 10102.44n 10114.91n 10123.25 10153.84 10212.11n 10221.12

(0.41) (0.73) (0.38) (0.081) (0.42) (0.66) (0.38) (0.44) (0.47) (0.34) (0.59) (0.30) (1.2) (0.27) (0.20) (0.34) (0.96) (1.2) (0.53) (0.14) (0.36) (1.5) (0.59) (0.85) (0.71) (0.29) (0.46) (0.51) (0.58) (0.11) (0.99) (0.68) (0.35) (0.10) (0.11)

Jp

gCn / meV

221+ 1+ 1+ 21+ 1+ 1+ 1+ 21+ 21+ 1+ 1+ 222-* 1+ 1+ 222221+ 1+ 2222-* 1+ 21+

55.1 51.3 101.9 136.9 94.3 58.4 114.2 106.7 122.0 164.7 26.3 141.8 35.3 157.0 234 127.3 44.7 37.2 83.2 410 139.3 18.8 52.3 60.4 76.2 37.8 126.0 117.4 86.1 40.3 56.6 80.6 157.5 53.0 669

(4.5) (4.3) (6.5) (7.9) (6.3) (4.7) (7.1) (7.3) (8.3) (9.7) (2.4) (7.9) (3.2) (8.3) (10) (7.6) (4.0) (3.4) (6.2) (14) (8.3) (5.3) (6.6) (5.4) (6.3) (3.8) (9.1) (8.2) (6.6) (4.0) (5.0) (6.5) (8.6) (5.3) (19)

n *

New resonance. Spin change.

Table 8 FCd-factors based on the IRDF-2002 file [54]. The data are given when FCd based on IRDF-2002 differs by more than 1% from the one based on ENDF/B-VII parameters and the parameters derived in this work. Nuclide

IRDF-2002 FCd

ENDF/B-VII.0 Diff. (%)

This work Diff. (%])

56-Ba-130 56-Ba-140 37-Rb-86 34-Se-78 46-Pd-107 54-Xe-132 90-Th-232 96-Cm-242 27-Co-58 58-Ce-144 58-Ce-136 91-Pa-231 63-Eu-151

0.862 0.882 0.951 0.952 0.958 0.960 0.976 0.972 1.504 0.972 0.937 1.425 1.798

15.8 2.3 1.6 2.1 1.8 1.3 1.7 1.4 <1 1.1 <1 1.0 <1

15.8 2.7 2.2 2.0 2.0 1.8 1.7 1.6 1.5 1.2 1.1 1.1 1.1

using seven resonance parameter files are compared. The files considered are: (1) The reference library of Ref. [67] (2) JEFF 3.1.2 (3) JEFF 3.1.2 with the 0.178 eV parameters of Kopecky et al. [15] (4) ENDF/B-VII.0 (5) ENDF/B-VII.0 with the 0.178 eV parameters of Mosteller et al. [52] (6) ENDF/B-VII.0 with the 0.178 eV parameters of Kopecky et al. [15] (7) ENDF/B-VII.0 and the Cd parameter files recommended in this work.

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K. Volev et al. / Nuclear Instruments and Methods in Physics Research B 300 (2013) 11–29

Table 9 Results of calculated keff for the integral experiment of Lloyd et al. [53], with reference HEU-SOL-THERM-049 in Ref. [67], using different nuclear data libraries. The indexes of the libraries are explained in the text. The reference benchmark is kref = 1.0012 with uncertainties ranging from ±0.0019 to ±0.0029. Case

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 19 20 21

U density

Cd density In-vessel

Cd density in reflector

105 x (keff–kref) for different libraries

(mg/g)

(mg/g)

(mg/g)

(1)

(2)

293.85 294.17 292.98 291.34 290.58 306.43 306.79 306.93 298.38 298.76 301.17 303.48 302.03 301.84 300.94 300.75 301.14 301.55 300.83 303.06

0.0 0.0 1.208 2.393 3.897 4.067 4.196 4.279 0.0 0.0 1.240 2.250 3.362 4.189 4.577 4.897 5.049 5.032 5.937 6.262

0.0 14.848 0.0 0.0 0.0 0.0 0.0 0.0 0.0 10.596 10.60 10.60 10.60 10.60 10.60 10.60 9.519 0.0 0.0 0.0

1310 1150 720 850 900 500 510 600 340 1050 1110 1020 1170 1250 1030 1160 1270 1130 1080 1330

280 1190 750 840 890 580 520 750 450 1120 1140 1030 1220 1280 1030 1190 1340 1120 1140 1340

Comparing the results in Table 9 the same conclusion as in the work of Kopecky et al. [15] can be drawn. The changes in the parameters, in particular the neutron width of the resonance at 0.178 eV, have an impact on the results and improve the agreement between calculations and experiment. However, the changes are not enough to bring the calculations in agreement with the results of the experiment. It should be noted that for case 21, which according to Mosteller et al. [52] was the most sensitive to the thermal neutron absorption in cadmium, the result based on the file produced in this work is in better agreement compared with the one obtained by Mosteller et al. [52]. Based on different differential neutron scattering tables, i.e. S(a,b) tables, we verified that the results of the experiments of Lloyd et al. [53] are more sensitive to the scattering treatment than to the resonance parameters of Cd. Therefore, this integral experiment cannot be used to validate the resonance parameters of the 0.178 eV resonance, as in the work of Mosteller et al. [52].

(3) 1150 750 770 720 410 330 500 1100 1280 1160 1070 1230 950 1040 1210 940 980 1140

(4)

(5)

(6)

290 1270 450 650 510 220 60 320 300 1060 1050 920 810 1060 720 870 1020 810 1020 1010

200 580 520 590 510 120 100 250 360 1210 1040 880 930 890 710 910 970 760 730 940

290 1060 620 540 350 10 30 180 300 1100 1240 1010 910 910 650 810 930 580 490 640

(7) 1040 630 580 410 10 30 130 1110 1290 1030 930 1010 690 910 1020 610 540 730

the IRDF-2002 file are significant. Considering the low abundance of 106,108,116Cd the resonance parameters recommended in this work seem more than adequate for applications in which natural cadmium is used. An overall improvement on the cadmium files might be achievable if measurements with samples enriched in 114 Cd and 111Cd would be available.

Acknowledgements We are grateful to the Nuclear Data Section of the IAEA and the Nuclear Energy Agency of the OECD for their interest in this work. This work was supported by the European Commission within the Sixth Framework Program through NUDAME (EURATOM contract no. FP6-516487) and within the Seventh Framework Program through the project EUFRAT (FP7-211499). The authors are grateful to the GELINA operators for the dedicated and skilful running of the accelerator.

7. Summary References New resonance parameter files for 106,108,110,111,112,113,114,116Cd have been presented. These files are the result of a combined analysis of available experimental data together with a RSA of transmission and capture data on natCd at GELINA. The importance of thick transmission data to adjust parameters of bound states and effective scattering radii has been demonstrated. From a RSA of the GELINA data a Doppler broadened thermal total cross section of 2450 ± 40 b for natCd at 300 K is deduced. This value is in very good agreement with results of previous measurements performed at a thermal neutron beam using different techniques. However, the cross section data obtained in this work are in disagreement with most of the evaluated data files, especially in the low energy region. It was also shown that an adjustment of resonance parameters to an integral experiment might result in misleading conclusions. The parameter file recommended in this work, which has not been adjusted to any integral experiments, produces results which are even in better agreement with results of integral tests compared to a file which was adjusted to this experiment. The impact of the resonance parameters on cadmium transmission factors has been verified. For certain nuclides changes compared to

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