High resolution measurement of neutron inelastic scattering and (n,2n ) cross-sections for 52Cr

Nuclear Physics A 786 (2007) 1–23

High resolution measurement of neutron inelastic scattering and (n, 2n) cross-sections for 52Cr L.C. Mihailescu a,b , C. Borcea a,b , A.J. Koning c , A.J.M. Plompen a,∗ a European Commission, Joint Research Centre, Institute for Reference Materials and Measurements,

B-2440 Geel, Belgium b “Horia Hulubei” National Institute for Physics and Nuclear Engineering,

P.O. Box MG-6, 76900 Bucharest, Romania c Nuclear Research Group Petten, Westerduinweg 3, 1755 ZG Petten, The Netherlands

Received 17 November 2006; received in revised form 15 December 2006; accepted 8 January 2007 Available online 12 January 2007

Abstract Cross-sections were measured for gammas produced by neutron inelastic scattering and (n, 2n) reactions on 52 Cr using the white neutron spectrum of GELINA with the time-of-flight technique at the 200 m flightpath station. The full energy range, from the inelastic threshold up to 18 MeV was covered in one experiment with an unprecedented neutron energy resolution of 1.1 keV at 1 MeV and 35 keV at 10 MeV. The gamma rays were detected with large volume HPGe detectors. The flux was determined with a 235 U fission chamber based on the 235 U(n, F ) standard cross-section. A Cr2 O3 sample was used with a 52 Cr/Cr concentration of 99.85% wt. Inelastic gamma production cross-sections were measured for 12 transitions, at least one transition from each level up to an excitation energy of 3.77 MeV. Based on the adopted level scheme of 52 Cr, the total inelastic and the level cross-sections were constructed. A total uncertainty smaller than 5% was obtained for the total inelastic cross-section up to 10 MeV. The (n, 2n) gamma production cross-section was measured for the 749.06 keV and 1164.4 keV transitions from 51 Cr. Results are compared with earlier experimental works and model calculations performed with the TALYS code. Calculations with the default parameters of TALYS show in general rather good agreement with the present data. © 2007 Published by Elsevier B.V. PACS: 29.30.Kv; 28.20.-v; 25.40.-h; 24.10.-i Keywords: Neutron inelastic and (n, 2n) cross-sections; Chromium; 52 Cr

* Corresponding author. Tel.: +32 14 571 381.

E-mail address: [email protected] (A.J.M. Plompen). 0375-9474/$ – see front matter © 2007 Published by Elsevier B.V. doi:10.1016/j.nuclphysa.2007.01.004

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1. Introduction Investigations in waste transmutation and the sustainable—closed fuel cycle—concepts of the Generation IV (GenIV) initiative show a renewed interest in nuclear reactors with fast neutron spectra. The recent study of Aliberti et al. [1] investigated the impact of nuclear data uncertainties on reactor parameter uncertainties for an accelerator driven system, showing, amongst others, the large impact of uncertainties of inelastic scattering on the uncertainty for the predicted keff in the case of lead and bismuth and structural materials. For fast reactors the importance of inelastic scattering was established earlier [2,3]. In inelastic scattering the energy loss is considerably larger than in elastic scattering. Because of this, inelastic scattering has an important impact on the neutron spectrum in applications with fast neutrons. In addition, neutron transport is affected by the difference in angular distribution between neutrons scattered inelastically or elastically. Thus, improved knowledge of the inelastic scattering process is of relevance to both radiation shielding and reactor criticality estimates. Following inelastic scattering gamma rays are emitted. The production cross-section of these gamma rays is important for dosimetry, radioprotection and heating calculations. Chromium is an important component of stainless steel that is used in reactors together with Fe and Ni for structural parts and the reflector. With 83.8% isotopic abundance 52 Cr is the most abundant isotope of chromium and in highly enriched form is an excellent case for our study of inelastic scattering effects. Here we present new measurements of gamma-ray production cross-sections for twelve transitions—at least one for each of the first eleven excited levels—resulting from neutron inelastic scattering on 52 Cr and for two transitions of the 52 Cr(n, 2n) reaction. The results are obtained with a new setup that is described in Ref. [4]. The excitation functions, that were obtained at the pulsed white neutron source GELINA using HPGe detectors and the time-of-flight (t.o.f.) technique, are continuous in incident neutron energy from threshold to 16–18 MeV. The neutron energy resolution is unprecedented and clearly reveals the resonance structures at low energy, as well as certain additional fine structure in the excitation functions. Level cross-sections and the total inelastic cross-section are deduced. Flux is measured conveniently with a fission chamber using the well-established 235 U(n, F ) cross-section and the impact of gamma-ray angular distributions is reduced to a minimum by a special combination of two detection angles [4]. Uncertainties for the gamma production cross-section of the main inelastic transition, which collects almost all the decay strength, were less than 5% up to 10 MeV and less than 10% up to 18 MeV. Thus, an important contribution is made to improve the understanding of inelastic scattering and, to a lesser extent, the (n, 2n) reaction on this nucleus. Although this paper’s primary focus is the presentation of new experimental results, the use of these new results for nuclear modelling is discussed by comparisons with calculations in the Hauser–Feshbach approach with Moldauer width fluctuation corrections, direct reaction contributions obtained in the distorted-wave Born (DWBA) and the coupled-channel (CC) approximations and pre-equilibrium estimates in the two-component exciton model. These calculations were performed with the TALYS code [5]. A recently established set of optical model parameters for 52 Cr was used together with a new global systematics for neutrons and protons for the other nuclei involved [6]. TALYS uses level density and strength function parameters from well established systematics [7,8], as well as a new set of pre-equilibrium parameters based on the above-mentioned optical model [9]. Neutron-inelastic scattering cross-sections for 52 Cr and natural Cr have been studied experimentally, either by measurements of the energy and angle distributions of the scattered neutrons

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([10–15]—(n, n )-technique) or by detection of the emitted gamma-rays ([16–30]—(n, n γ )technique). Most experimental work was carried out at single energies below 7 MeV or at 14 MeV, with the exception of the double-differential (n, n ) study by Schmidt and Mannhart [31] which addressed the range from 8 to 15 MeV. Three earlier studies used a pulsed white neutron source and the (n, n γ )-technique [23,25,28]. The second of these references measured integral gamma-ray spectra with a NaI detector. Refs. [23,28] used a Ge(Li) detector to determine gamma-ray production cross-sections for transitions uniquely identified by gamma-ray energy. The work of Ref. [23] has a resolution that is about two times worse than that of the present work. It demonstrated for the first time the resonance structure of the cross-section at low energies but it had energy-dependent normalisation problems [26]. Ref. [28] shows cross-sections with moderate resolution for gamma-rays from the first excited states populated in inelastic scattering and the (n, 2n)-reaction for En  40 MeV. Refs. [17] and [26] highlight the need of gammaray angular distribution corrections for cross-section determinations in case only one detector is employed. Comparisons with earlier measurements are made where appropriate. We note that fast neutron-induced reactions on 52 Cr in this energy range are rather well studied and refer to a recent paper by Han [32] for a comprehensive analysis. The present paper is structured as follows. In Section 2 the experimental setup and data analysis are shortly described. Section 3 contains a summary of the input parameters used in the TALYS calculation. Section 4 contains the experimental results compared with TALYS calculations and with other experimental data and is followed by conclusions in Section 5. Some prelimary results were given in Refs. [4,33,34]. 2. Experimental setup and data analysis A detailed description of the experimental setup, the measurement procedure and the data analysis procedure has been presented in Ref. [4]. Here we summarise the main points and the particularities of the measurement and analysis for 52 Cr. 2.1. Experimental setup Incident neutrons are produced by the pulsed white-neutron source GELINA [35–38]. Electrons are accelerated up to 140 MeV, produce bremsstrahlung on a uranium target and neutrons through the U(γ , xn) and U(γ , F ) reactions. The full width at half maximum (fwhm) of the pulse is less than 1 ns and the repetition rate is 800 Hz. The sample is placed at 90◦ with respect to the electron beam at 198.551 m. The beam diameter is 6 cm. Care is taken to avoid moderated neutrons by appropriate collimators and a 10 B filter (1.23 g/cm2 ). The gamma-flash is attenuated by a 36.8 g/cm2 nat U filter. Both filters are placed half-way source and sample. Two large volume HPGe detectors were used for the detection of the gamma rays; the first of 75.9% relative efficiency was placed at 150◦ and 15.5 cm from the sample, the second of 48.6% relative efficiency at 110◦ and 11.9 cm. These angles are zeroes of the fourth-degree Legendre polynomial (see below). Energy resolution for both detectors was 2.4 keV fwhm at 1.33 MeV and the time resolution was 4–6 ns fwhm. Dedicated shielding of these detectors is not required. Low background is achieved by shielding from the last collimator with a total of 25 cm of Pb. The neutron flux is determined, simultaneously with the gamma rays, using a 235 U fission chamber with eight deposits of 70 mm diameter that fully intercept the beam at about 1.3 m upstream from the sample (total thickness 3.066(6) mg-U/cm2 , 99.826(8)% 235 U/U).

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The sample consisted of 146.166 g of Cr2 O3 powder, pressed with 5 tonnes in a cylindrical aluminium can of inner diameter 6.86 cm, inner depth 2.3 cm and wall thickness 1.2 mm. The Cr mass was 100.007 g and the isotopic composition is 99.85% 52 Cr, 0.01% 50 Cr, 0.13% 53 Cr, 0.01% 54 Cr. The highly enriched sample of chromium was used to avoid contributions from the 53 Cr(n, 2n) reaction to the gamma-rays of the 52 Cr(n, n ) reaction. Conventional electronics were used. Good time-resolution was obtained for the HPGe detectors using a constant fraction discriminator with the Amplitude and Rise-time Compensation (ARC) scheme together with Slow Rise Time Rejection (SRTR). A strong gamma-flash precedes each neutron burst. Due to the collimation and the position of the HPGe detectors (out of the neutron beam), the number of direct gamma-rays from the flash detected with the present setup was negligible. Only gamma-rays scattered on the sample are detected and this amounted to 25% of all neutron pulses. The number of gamma-flash induced events depends on the detector efficiency, the detection angle and on the characteristics of the sample (atomic number and volume). The gamma-flash is scattered with higher probability at forward angles. Complicated dead time corrections are avoided by blocking the acquisition system for both HPGe detectors and fission chamber when such a scattered gamma flash is detected. The residual dead time is negligible since the typical count rate is less than one event per fifty neutron pulses. Thus, no dead time correction was required. 2.2. Data analysis The measurement procedure and the expressions for the various cross-sections are given in Ref. [4]. For clarity the relation for the angle-integrated gamma production cross-section σ (Ek ) is repeated, also because of a typing error in the previous publication where a factor of 2π was omitted:   2 2  1 1  Yi (Ek ) dσ tU As FC σU (Ek ) σ (Ek ) = 2π (θi , Ek ) = wi wi . (1) dΩ ts AU YFC (Ek ) cmsc (Ek ) 2 i i=1

i=1

Here Ek is the neutron energy for bin k, dσ/dΩ(θi , Ek ) is the differential gamma-production cross-section, θi is the detector angle, i = 1, 2 identifies the detector, s stands for sample, U for “235 U”, t is the material thickness and A is the atomic mass. FC is the fission chamber efficiency and i is the efficiency of the HPGe detector for the gamma ray of interest. σU is the 235 U(n, F ) standard cross-section obtained from Ref. [39]. Y (E ) is the yield of the gamma-ray i k of interest, YFC (Ek ) is the fission chamber yield, and cmsc (Ek ) is the multiple scattering and neutron attenuation coefficient that is calculated with MCNP [40]. The values of the angle integration coefficients wi are 0.6957 for 150◦ and 1.3043 for 110◦ . As argued in Ref. [4] this combination of angles and weights eliminates contributions of the second, fourth and sixth degree Legendre polynomials in the angular distribution. This corresponds to Gaussian quadrature specialised to even degree polynomials. For all transitions measured here the highest multipolarity is two, so that the highest degree involved is four [41] and thus our integration is exact. No correction is required for the finite opening angle of the detectors. It was verified by Monte Carlo integration that for 8 cm diameter detectors at 12 cm from the sample and unit intrinsic efficiency, finite opening angle effects are negligible for this angle integration procedure in the case of distributions that include terms up to degree six. The angular distribution (W(θ )) of the emitted γ -rays in inelastic scattering depends on the energy of the incident neutrons [41]. Such dependence was observed also in the present

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experiment for different types of γ -ray transitions. Sheldon and van Patter [41] made modelindependent predictions for the γ -ray angular distributions in the inelastic scattering just above the threshold. Earlier works typically employed only one detector. Even when placed at 125◦ , Refs. [17,26, 41] show that energy-dependent corrections up to 10% are expected for stretched E2 transitions. The detection efficiency i for a particular γ -ray observed by detector i is the absolute photopeak efficiency including finite volume and self-absorption effects as well as the effect due to slow rise-time rejection—SRTR. The method of efficiency determination is illustrated in Fig. 1 for one detector. Experimental photo-peak efficiencies were measured with a 152 Eu point source with and without SRTR. Point-source Monte Carlo simulations with the MCNP code were made to adjust a detailed model of the detector until the simulated values agree with the measured ones without SRTR. The MCNP extended volume source simulation includes geometry, composition and density of the chromium sample. As illustrated, gamma-ray self-attenuation and the finite volume account for about 30% at 250 keV decreasing to about 5% at 1.4 MeV. Finally, the extended source estimates are corrected for the SRTR effect. 152 Eu is a convenient calibration source, however care must be taken that coincidences between gamma or gamma and X-rays do not require significant summing corrections. It was observed that the summing effect of gammarays with X-rays was negligible. As for gamma-rays summing, corrections of maximum 1% were required. The results were in agreement with calibration points obtained with single-line gamma-emitters. These small corrections justified ignoring this issue for the gamma’s emitted in the neutron-induced reactions on 52 Cr. For the analysis, mass numbers were taken from Ref. [42] and the branching ratios required for the construction of the inelastic and the level inelastic cross-sections were taken from Ref. [43]. The latter work reports no conversion coefficients different from zero and in view of the gamma-ray energies and transition multipolarities involved we have assumed a zero value, throughout. The uncertainties of the parameters involved in the cross-section calculations were estimated by the usual quadratic error propagation applied to the expressions for the gamma-ray production cross-section (Eq. (1)), the inelastic and the level cross-sections [4]. Input uncertainties were

Fig. 1. Efficiencies of the HPGe detector at 150◦ .

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taken from the databases mentioned above. Furthermore, uncertainties for the 52 Cr and 235 U thickness are given above. The uncertainty of the fission chamber efficiency FC is 1.6%. The 235 U(n, F ) standard crosssection has an uncertainty smaller than 1% up to 10 MeV, increasing to 1.5% at 20 MeV. During different experiments with the fission chamber used here, no changes in the neutron flux shape were observed. This allowed to apply a smoothing procedure on the fission chamber yield, YFC (Ek ), in order to reduce the statistical fluctuations. After the data smoothing the uncertainties of the YFC (Ek ) were smaller than 2% up to 10 MeV increasing up to 4% around 18 MeV. The HPGe yield Yi (Ek ) introduced the largest uncertainties except in the case of the first transition (1434 keV), where the HPGe yield uncertainties start to dominate only above 10 MeV. To reduce the statistical errors, a grouping of several energy bins (corresponding to 8 ns t.o.f. bin) was made for the strong transitions only at high energies and in the full range for the rest of the transitions. The grouping procedure was applied from the beginning of the data analysis, in the same way for all energy dependent parameters from Eq. (1), to avoid uncertainty correlation between neutron energy bins. The multiple scattering coefficient cmsc had a negligible statistical uncertainty from the MCNP calculation. A possible systematic uncertainty that may come from the cross-sections used for the simulation was not evaluated. The uncertainty of HPGe detectors efficiency, i was less than 3% for almost all gamma rays of interest. The major experimental component in this uncertainty was due to the calibration source activity, 1.5%, the rest was comming from the applied corrections. The statistical uncertainties from the efficiency measurement and from the MCNP simulations were less than 1%. The self-attenuation of the gamma ray and the effect of the finite extension of the chromium sample rely completely on the MCNP simulations. Special effort was made to reduce any systematic error of these MCNP simulations describing as realistically as possible the geometry of the detectors and of the sample (see also [4]). The above data unambiguously determine the uncertainty for the gamma production crosssections in the entire energy range. For the deduced inelastic and level inelastic cross-sections this is strictly speaking only true up to the incident energy that corresponds to the highest excited level for which a gamma is observed. 3. Input parameters for TALYS code The results obtained in the present experiment were compared with a calculation performed with the nuclear reaction code TALYS [5] version 0.64. TALYS is a recently developed code for analysis and prediction of nuclear reaction cross-sections induced by neutrons, protons, deuterons, tritons, 3 He-, α-particles and γ -rays for incident energies from 1 keV up to 200 MeV. TALYS generates a complete and self-consistent set of cross-sections for every target nucleus with 24  A  209. A set of default input parameters are built in, which are the result of recent evaluations. These default input parameters were used in this work on 52 Cr. The TALYS predictions are based on reaction models like the optical model, compound nucleus statistical theory, direct reactions and pre-equilibrium processes, in combination with databases and nuclear structure models. A detailed description of the theoretical modeling used in the TALYS 0.64 can be found in Refs. [5,44]. Neutron inelastic scattering has a compound and a direct-like component. The first one is described by the compound nucleus theory in the Hauser–Feshbach approach with Moldauer width fluctuation corrections and the second one by the coupled channels mechanism. Just above the inelastic threshold of 52 Cr, the compound com-

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Table 1 The optical model parameters for 52 Cr used as default in the TALYS 0.64 code. Ef is the Fermi energy in MeV. The reduced radii rv , rD , rvso and the diffuseness parameters av , aD , avso are given in fm. The parameters that enter in the potential well depths v1 , w1 , w2 , d1 , d3 , vso1 , wso1 , wso2 are given in MeV, v2 , d2 , vso2 , are given in MeV−1 , v3 in MeV−2 and v4 in MeV−3 rv

av

v1

v2

v3

v4

w1

w2

rD

aD

1.190

0.667

56.2

0.0071

1.9 × 10−5

7 × 10−9

12.8

78.0

1.282

0.535

d1

d2

d3

rvso

avso

vso1

vso2

wso1

wso2

Ef

11.6

0.0215

11.00

1.010

0.600

6.2

0.0040

−3.1

160.0

−9.99

ponent increases rapidly up to about 3 MeV and then decreases. Above 8 MeV the inelastic scattering cross-section is dominated by the direct-like component. The latter has a smooth and almost constant behaviour from the threshold up to 20 MeV. In the present calculation, the first 20 excited levels in 52 Cr were considered as discrete levels (up to about 4.6 MeV excitation energy). For higher incident energies the pre-equilibrium processes are taken into account using the two-component exciton model [9]. The optical model plays a central role in the cross-sections prediction. TALYS 0.64 uses as default the model of Koning and Delaroche [6] for the optical model parameters. The modeling and the formulae are given in Refs. [6,44]. The local optical model parameters for 52 Cr are shown in Table 1, as used in the present calculation. For 52 Cr nucleus the experimental deformation parameter for the ground state is β2 = 0.223. In the present calculations using TALYS 0.64, nuclei with β2  0.15 are considered deformed and consequently, a rotation-vibration model was adopted, including in the coupling scheme the first excited 0+ , 2+ and 4+ states as members of the ground state rotational band and also three vibrational states, i.e. two β- and one octupole vibrational state. This allowed a good description of the cross-section of the first excited level. Therefore, the only difference with the parameters of Ref. [6] is that the d1 parameter of that work was multiplied with 0.85 to take the coupling into account. For deuterons, tritons, helions and alpha particles, we use a simplification of the folding approach of Watanabe [45] (see also Ref. [46]). The level densities are described using a combination of two models. The constant temperature model is used at low excitation energies and the back shifted Fermi gas model with shell and energy dependent level density parameter a is used at high energies. The two models and the procedure to obtain the matching excitation energy (Exmatch ) between the models is given in details in Ref. [44]. Using the same notations as in Ref. [44], the level density parameters are shown in Table 2. The gamma-ray transmission coefficients are calculated through the energy-dependent gamma-ray strength function according to Kopecky and Uhl [47], for E1 radiation, or Brink– Axel [48,49], for all transition types other than E1. We renormalise the gamma-ray transmission coefficients [50] through the (often available) average radiative capture width, by integrating the gamma-ray transmission coefficients over the density of final states that may be reached in the first step of the gamma-ray cascade. The comparison of the present experimental results with the TALYS 0.64 predictions using the default input parameters may be considered as a “blind” comparison in the sense that the present experimental results were not used to adjust the input parameters. Through further adjustment of level density and pre-equilibrium parameters even better agreement can be obtained, but our main

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Table 2 The default level density parameters used in the TALYS 0.64 code. The level density parameters at the separation energy (Sn ) and average level spacing D0 are given in MeV−1 . The shell correction energy δW , the temperature T , the backshift energy E0 , the pairing energy Δ and the matching energy Exmatch are given in MeV. The shell damping parameter is given by γ = 0.459/A1/3 , and the asymptotic level density parameter by a˜ = 0.0666A + 0.2587A2/3 Nuclide

a(Sn )

δW

T

E0

Δ

D0

Exmatch

51 V

6.61 6.71 6.34 6.36 6.48

−0.64 −0.61 −1.09 −1.32 −1.13

1.39 1.37 1.41 1.48 1.38

−1.295 −2.902 −1.103 −0.074 −1.123

1.68 0.00 1.68 3.33 1.65

2.70 4.10 15.00 8281.26 11076.38

10.39 8.49 10.62 13.80 10.53

52 V 51 Cr 52 Cr 53 Cr

aim is here to demonstrate the predictive power of default model calculations. This comparison may be a starting point for the future improvements in the theoretical models. 4. Results and discussion The results of the present experiment are given in detail in this section compared with existing experimental results found in the literature and with the TALYS code (version 0.64) calculation that uses the default input parameters (Section 3). The differential gamma production cross-sections at two angles 110◦ and 150◦ are the first measured quantities. These will be shown only for few gamma transitions as an evidence of the dσ angular distribution together with the ratio between the angular distributions W (θ ) = 4π σ dΩ (θ ) ◦ ◦ at the two angles 150 and 110 . The integral gamma production cross-section was obtained as described in Section 2.2. Using the so measured integral gamma production cross-sections and the evaluated level scheme of 52 Cr [43], the total inelastic and the level cross-sections were constructed. These quantities rely entirely on the precision of the evaluated level scheme. Moreover, for incident neutron energies higher than 3.77 MeV (that correspond to the maximum observed excitation energy in this experiment) the values obtained here for the total inelastic and for the level cross-sections are only limits to these quantities as explained in detail in Ref. [4]. 4.1. Gamma production cross-sections 4.1.1. 1434.07 keV The differential gamma production cross-section for the main transition of 52 Cr, 1434.07 keV, is given in Fig. 2(Left). The data were smoothed with a moving average window filter only for a better comparison. Fig. 2(Right) shows the ratio between the differential gamma production at 150◦ and 110◦ as a function of incident neutron energy. This ratio is equal to the ratio of the angular distributions W (θ ) at the two angles. The value predicted in Ref. [41] for a stretched E2 γ -ray transition from an initial level 2+ to a level 0+ is 1.61 at the threshold. The representative uncertainty of the experimental ratio is about 6% (Fig. 2) and consists of roughly equal systematic and statistical components. The experimental value of this ratio immediately above the threshold is in good agreement though lower than the theoretical prediction for an E2 transition. With the increase of the neutron energy the observed ratio W (150)/W (110) decreases, becoming a constant different from unity at about 2.5 MeV neutron energy. Using the code CINDY of

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Sheldon and Rogers [51] with transmission coefficients from the present TALYS calculations the initial trend is well reproduced and is mainly the result of the energy dependence of the transmission coefficients involved (Fig. 2). Quantitatively the estimated anisotropy is too large. However, an estimate of the attenuation of the angular distribution as a result of the finite extent of the gamma-ray source and the detectors made with the MCNP code shows closer agreement with the experimental data (CINDY+attenuation). As this calculation only considers the first excited level it does not represent the physical situation above the second excited level at 2.4 MeV. The precise value and trend of the residual anisotropy above this energy is therefore not well reproduced as a consequence of the impact of these higher lying states. Fig. 3 shows the differential gamma production cross-sections of the 1434.07 keV transition with the full energy resolution of this experiment. The high neutron energy resolution of the setup allowed the observation of the resonance structures at low energies above the inelastic threshold.

Fig. 2. Left: Differential gamma production cross-section for the 1434.07 keV transition from 52 Cr at 110◦ and 150◦ . The data were smoothed with a moving average window for an easier comparison. The width of the window was 88 ns. Right: The ratio between the angular distribution at 150◦ and 110◦ for the 1434.07 keV. The angular distribution is defined by dσ the relation W (θ) = 4π σ dΩ (θ). The data were smoothed with a Bezier curve to reduce the statistical fluctuation. Generic error bars are shown for the present results.

Fig. 3. The differential gamma production cross-section of the 1434.07 keV transition with the full energy resolution of this experiment at 150◦ and 110◦ . In this energy interval, a total uncertainty of 6% was obtained for both indicated angles.

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The integral gamma production cross-section obtained by integrating the differential crosssections through the Gauss quadrature is given in Fig. 4. At 14 MeV the present results agree well with the other measurements. A significant difference can be observed in the comparison with the data of Tessler et al. [52] and Voss et al. [23]. These data are lower than the present ones. The normalisation of the present data is supported by the good agreement with the more recent data of Karatzas et al. [26] and Lashuk et al. [52] at low energies (Fig. 4(Right) and Fig. 5(Left)). Despite the difference in the normalisation with the Voss results (difference mentioned first time in Ref. [26]) the same resonance structures are observed (Fig. 5(Left)). The net advantage of the present results is a factor 2 gained in the neutron energy resolution, 1.1 keV at 1 MeV for the present results, compared with 2.2 keV in the experiment of Voss et al. The calculation done with the TALYS code version 0.64 in general describes well the present data, except for the two broad peaks at 6 MeV and respectively 12.5 MeV. At these energies the TALYS calculations are below the present experimental values. It may be noted that the optical model parameters used here fail to describe well the angular distribution of the elastic scattering between 8 and 12 MeV as observed in Ref. [6]. However, on the whole the model calculations clearly support the gamma-production cross-sections measured in the present work for this important transition and disagrees with the data of Tessler et al. and Voss et al.

Fig. 4. Integral gamma production cross-section for the 1434.07 keV transition in 52 Cr. Left: Full energy scale from the threshold up to 18 MeV. Right: A detailed plot at low neutron energies.

Fig. 5. Left: Integral gamma production cross-section for the 1434.07 keV transition in 52 Cr with the full energy resolution. The present data are compared with the results of Voss et al. [23]. Right: The total uncertainty of the integral gamma production cross-section for the 1434.07 keV transition.

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The total uncertainty of the integral gamma production cross-section for the 1434.07 keV is given in Fig. 5(Right). Below 10 MeV neutron energy, the total uncertainty was less than 5%. With the increase of the neutron energy, the total uncertainty increased up to 10% at 18 MeV because of the statistical uncertainty that became the dominant component. The large fluctuations in the total uncertainty at energies immediately above the inelastic threshold are due to the observed resonance structures (between two consecutive resonances a small number of counts was recorded). The steps in the total uncertainty at 10 MeV and about 13 MeV are due to the grouping of few energy bins to keep a reasonable statistical uncertainty (Section 2.2). 4.1.2. 935.54 keV The 935.54 keV γ -ray transition from the decay of the second excited level at 2.369 MeV to the first exited level at 1.434 MeV has the same multipolarity as the 1434.07 keV transition (E2). The differential gamma production cross-sections at the two angles 150◦ and 110◦ and their ratio is given in Fig. 6. The representative uncertainty of 6.5% is shown, which consists of roughly equal statistical and systematic components. Near threshold the statistical error is larger. Therefore, within the present uncertainties the ratio between the angular distributions at the two angles does not show a clear neutron energy dependence as in the case of the 1434.07 keV transition. This may result from the feeding of the higher excited levels and the much smaller energy range between the threshold for this level and that of the next excited level. Nevertheless, a value clearly different from one is observed, despite the relatively large uncertainties of the measurement. The integral gamma production cross-section for the 935.54 keV is given in Fig. 7. Within the stated uncertainties the present data agree very well with the experimental data at 14 MeV and with the results of Karatzas et al. [26] and Lashuk et al. [52] at low energies. As in the case of the 1434.07 keV transition, the same difference in the amplitude can be observed between the present data and the data of Voss et al. [23]. Also for this transition, 935.54 keV, some small resonance structures can be observed below 4 MeV (Fig. 7(Right)). The TALYS calculation describes reasonably the present experimental integral gamma production cross-section for the 935.54 keV transition on the full energy range, from the threshold (2.41 keV) up to 18 MeV. Two weak points can still be observed. The calculation is higher than the measured values with about 15% around 8 MeV neutron energy and above 14 MeV (Fig. 7). The calculations clearly favour the present measured data over the results of Tessler et al. and Voss et al.

Fig. 6. Left: Differential gamma production cross-section for the 935.54 keV transition in 52 Cr at 110◦ and 150◦ . Right: The ratio between angular distributions at 150◦ and 110◦ . Generic error bars are shown for the present results. The data were smoothed in both panels.

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4.1.3. 1530.67 keV A different example of a γ -ray angular distribution is given in Fig. 8 for the 1530.67 keV transition (M1 + E2). This γ -ray results from the decay of the 5th excited level, at 2964.78 keV. For this transition the ratio between angular distribution at 150◦ and 110◦ is smaller than unity. Representative uncertainties are about 6.5% and consist of roughly equal statistical and systematical uncertainties. Near threshold the statistical threshold is larger. According to Eq. (64) from Ref. [41], for an M1 + E2 (2+ → 2+ ) transition with a mixing ratio δ = −6.25 ± 0.15 obtained from Ref. [43], the predicted value of the ratio W (150)/W (110) = 0.758 ± 0.003 for incident neutron energies just above the threshold. The uncertainty of the mixing ratio produces a negligible uncertainty on the W (150)/W (110) ratio in comparison with the present experimental uncertainties for this gamma transition. The calculated W (150)/W (110) ratio at threshold agrees with the experimental ratio shown in Fig. 8(Right). The ratio W (150)/W (110) has a small increase above the threshold and then within the experimental uncertainties is a constant about three standard deviations less than unity. The integral gamma production cross-section of the 1530.67 keV is given in Fig. 9. Different from the case of the first two gamma transitions, the TALYS code calculation underestimates the integral gamma production cross-section in the

Fig. 7. Integral gamma production cross-section for the 935.54 keV transition in 52 Cr. Left: Full energy scale from the threshold up to 18 MeV. Right: A detailed plot at low neutron energies.

Fig. 8. Left: Differential gamma production cross-section for the 1530.67 keV transition in 52 Cr at 110◦ and 150◦ . Right: The ratio between angular distributions at 150◦ and 110◦ . Generic error bars are shown for the present results. The data were smoothed in both panels.

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Fig. 9. Integral gamma production cross-section for the 1530.67 keV and 1333.65 keV transitions in 52 Cr.

energy range between 5 MeV and 13 MeV and appears to favour the results of Voss et al. in this energy range. 4.1.4. The transitions from higher lying levels The integral gamma production cross-section for 9 other γ -ray transitions that were observed are shown in Figs. 9 and 10. In general, good agreement can be noted between the present data and the data of Karatzas et al. [26] at low energies and the data of Oblozinsky et al. at 14.6 MeV. For the transitions for which Voss et al. [23] data were available a systematic difference in the normalisation can be observed as in the case of the main transitions. This difference in the normalisation is energy dependent and may come from the determination of the response function of the scintillator used by Voss et al. [23] for the neutron flux measurement. Despite the difference in the normalisation, the shape of the integral gamma production cross-section is similar in the present data and in the data of Voss et al. [23]. The data of Tessler et al. [52] are systematically lower. The TALYS code calculation describes fairly well the experimental cross-section of the 704.6 keV and 744.23 keV transitions on the full energy range. For the other measured transitions the agreement with the calculation is good at incident energies below about 4–5 MeV. However, it underestimates the present experimental data in the energy interval between 4 MeV and 14 MeV for the following transitions: 647.53 keV, 1246.28 keV, 1333.65 keV, 1727.53 keV and 2038.0 keV. In the case of the 1212.8 keV and 2337.44 keV the TALYS calculations are higher than the experimental values. Although in some cases the TALYS calculations match the Voss data at higher energies better than the present data, the mixed success at representing these data is attributed to the difficulties associated with modeling of the decay of the compound nucleus at the involved higher incident and excitation energies. 4.1.5. Branching ratio for the level at 3472 keV The excited level of 3472.24 keV was the only level from which two γ -ray transitions were observed with sufficient statistics to build the gamma production cross-sections. According to the adopted level scheme the transitions by which the level decays are 704.6 keV and 2038.0 keV. Within the uncertainties, the thresholds of the gamma production cross-section for these two transitions were the same. The ratio between their gamma production cross-sections is constant as a function of the neutron energy, bringing an additional support to the gamma ray identification. The relative gamma intensities found in this experiment are 100% for 704.6 keV and 44.2 ± 12% for 2038.0 keV. This relative intensity for the 2038.0 keV transition is two times higher than

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Fig. 10. Integral gamma production cross-section for transition that decay from higher excited levels of 52 Cr. For the 704.60 keV and 2038.00 keV transitions from the level at 3472.24 keV the branching ratio obtained in Section 4.1.5 were used to adjust the TALYS 0.64 calculation (TALYS “corrected”).

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the adopted value (Ref. [53]). On the other hand Karatzas et al. [26] found a relative intensity of 66% for the 2038.0 keV transition (with respect to the 704.6 keV transition), which is about 50% larger than the present value. The effect of the difference between the measured and the evaluated branching ratio on the gamma production cross-section is shown in Fig. 10 for the gamma production cross-section. With the new measured values for the branching ratios (the “corrected” curve in Fig. 10) the calculation describes slightly better the production cross-section of the 2038.00 keV transition. For the 704.60 keV transition the difference between the measured production cross-section and the TALYS calculation becomes larger around 6 MeV and smaller at energies above 10 MeV. 4.1.6. (n, 2n) gamma production cross-sections The relatively high threshold of the 52 Cr(n, 2n)51 Cr reaction (12.27 MeV) and the low neutron flux at high energies resulted in poor statistics for the gamma ray peaks from the (n, 2n) channel. Fig. 11 shows the amplitude spectrum of the detector at 150◦ integrated over the neutron energies from just below the (n, 2n) threshold up to 20 MeV. This procedure allowed an easier identification of the 51 Cr peaks. Only two transitions, 749.06 keV and 1164.4 keV, were observed with enough statistics to construct the gamma production cross-sections. The transition of 27.8 keV from the decay of the second excited level was not observed in this experiment because of its very low energy, below the thresholds of the electronics. Another limitation for this transition is its internal conversion factor of 0.905 [53]. The 603.5 keV and 1480.3 keV transitions were too weak to be separated from the background with a reasonable statistical error. The resulting gamma production cross-sections for the two transitions from 51 Cr are shown in Fig. 12. The observed reaction threshold for each transition is the same as the calculated one and this fact confirms the correct identification of the gamma rays. The 52 Cr(n, 2n)51 Cr gamma production cross-section presented here were not corrected for the neutron attenuation and multiple scattering. For the (n, 2n) cross-sections the multiple scattering is expected to be negligible and the attenuation correction with the 52 Cr sample is of the order of 1.5–2%. The total uncertainty for the derived (n, 2n) gamma production cross-section was around 25% (Fig. 13). Higher values for the total relative uncertainty were obtained immediately above the threshold because of the

Fig. 11. HPGe yield integrated over neutron energies between 12 MeV and 20 MeV. The 749 keV and 1164 keV peaks from the 52 Cr(n, 2n)51 Cr reaction are better observed with such a selection on the neutron energy.

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Fig. 12. 52 Cr(n, 2n)51 Cr gamma production cross-sections.

Fig. 13. Total uncertainty for the gamma production cross-section of the 749 keV transition from the 52 Cr(n, 2n)51 Cr reaction.

poor statistics. The neutron energy resolution ranged between 120 keV immediately above the threshold and 180 keV at 18 MeV. The present data agree very well with the TALYS calculation and with the measurement of Oblozinsky et al. [30] at 14.6 MeV. 4.2. Total inelastic and level cross-sections 4.2.1. Total neutron inelastic cross-section The total inelastic cross-section was obtained as described in Ref. [4] using the measured integral gamma production cross-sections. Up to 3.771 MeV excitation energy, only four transitions contribute to the total inelastic cross-section: 1434.07 keV, 1530.67 keV, 1727.53 keV and 2337.44 keV (Ref. [43]). The 1530.67 keV, 1727.53 keV and 2337.44 keV transitions were used with the appropriate branching factor to compensate for the fact that the transitions 2965.0 keV, 3161.8 keV and 3771.7 keV are too weak to be observed in our experiment. According to the adopted level scheme, the next excited level above 3771.7 keV that decays directly to the ground state is at 3951.2 keV. This leads to the conclusion that the total inelastic cross-section shown here (Fig. 14) is exact up to about 4.0 MeV neutron energy. Above this value it has to be consid-

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Fig. 14. Total inelastic cross-section of 52 Cr. Left: Comparison with other experimental data and with the TALYS calculation. The corresponding total uncertainty is given as inset. Right: Comparison of the full resolution total inelastic cross-section with the total neutron cross-section measured at ORELA et al. [54].

ered as a lower limit. In the case of the 52 Cr, the majority of the excited levels decay through the first excited level so this limit is very close to the exact value. For a better comparison of the total cross-section with the existing data in Fig. 14(Left) the present data were smoothed . The inset of Fig. 14(Left) represents the total uncertainty for the total inelastic cross-section. Because the 1434.07 keV transition is the dominant component in the construction of the total inelastic cross-sections, the uncertainty of the total inelastic crosssection is very similar to the uncertainty of the 1434.07 keV transition. At the extremities of the energy interval the total uncertainty is dominated by the statistical fluctuations. The steps in the uncertainty at 10 MeV and 13 MeV are due to the grouping together of few energy bins. The total inelastic cross-section agrees very well with the experimental data of van Patter et al. [17] at low energies and that of Simakov et al. [52] at 14 MeV. Despite the fact that the TALYS calculation underestimates almost all the gamma production cross-sections that contribute to the total inelastic cross-section, the latter is well described in the whole energy range. This shows that although details of the decay of the compound nucleus are not modeled to full satisfaction, the overall inelastic cross-section is very well described. As the gamma-production results of Voss et al. and Tessler et al. are consistently below the corresponding results of the present work, they are implicitly in disagreement with the predicted total inelastic cross-section. In particular so, because this cross-section is close to that of the gamma production cross-section of the 1434.07 keV transition. In Fig. 14(Right), the full resolution total inelastic cross-section is compared with the total neutron cross-section measured in a transmission experiment at ORELA [54]. Many structures are common to both data sets even if the resolution of the inelastic measurement is worse compared with the transmission measurement. At the same time it is clear that the resonance integrals in the inelastic cross-section are not a fixed fraction of the resonance integrals in the total neutron cross-section. This is in accord with the random nature of the partial widths for resonances of the compound system. 4.2.2. Level 1434.09 keV The cross-section of the first excited level is given in Fig. 15 together with the corresponding total uncertainty. As described in Ref. [4], this cross-section was obtained subtracting from the gamma production cross-section of the 1434.07 keV transition the contributions of the following transitions: 935.54 keV, 1212.80 keV, 1333.65 keV, 1530.67 keV, 1727.5 keV, 647.47 keV,

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Fig. 15. Cross-section of the 1434.09 keV level (Left) and its corresponding total uncertainty (Right).

Fig. 16. Cross-section of the 2369.63 keV (Left) and 2646.9 keV (Right) levels. Generic uncertainty bars are given at the extremities of the energy range for the graphs with a continuum line.

2038.0 keV and 2337.44 keV. From the evaluated level scheme, the next level that decays directly to the 1434.09 keV level has an energy of 4563.0 keV. From this it results that the constructed cross-section of the 1434.09 keV level is exact up to about 4.5 MeV neutron energy. The present cross-section for the 1434.09 keV level agrees very well with the data of van Patter et al. [17] and Korzh et al. [13]. The results of Degtjarev et al. [12] are below the present values. The level cross-section given by Broder et al. [52] is significantly higher above 3.2 MeV, likely because of an insufficient correction for the feeding from the higher excited levels. The TALYS calculations match very well the present results. For the TALYS calculations, the good agreement with the measured data in the case of the level cross-sections can be understood also from the good agreement of almost all the gamma production cross-sections at energies below 4–5 MeV. The total uncertainty for the cross-section of the 1434.09 keV level increases with the neutron energy up to about 20% at 4.5 MeV. The larger uncertainty for this level cross-section is due to the fact that 9 different γ -ray transitions feed this excited level. 4.2.3. Levels with higher excitation energy The cross-sections for the excited levels up to 3771 keV are given in Figs. 16 and 17. All these cross-sections were constructed only up to about 4 MeV. Generic uncertainty bars were plotted on the graphs at the extremities of the energy range. Where other experimental data exist, a good agreement with the present data was found.

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Fig. 17. Cross-section of the higher energy levels. Generic uncertainty bars are given at the extremities of the energy range for the graphs with a continuum line.

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In general the default calculation of TALYS describes well the level cross-sections presented here. For the levels at 2646.9 keV and at 3113.86 keV, the calculation shows slightly higher results above 3 MeV and respectively 3.5 MeV. For the level at 3771.7 keV, the calculation is slightly lower, but still at the limits of the error bars. 5. Conclusions Using a highly enriched sample of 52 Cr, 12 γ -ray transitions from the inelastic scattering channel and two γ -ray transitions from the (n, 2n) reaction channel were observed. For all these transitions the differential gamma production cross-section at two angles, 110◦ and 150◦ , were measured from the threshold up to about 18 MeV. The angle-integrated gamma production crosssections were obtained for the same energy range in a manner that is insensitive to the gamma-ray angular distribution. For each level up to 3771 keV excitation energy at least one gamma-ray was observed. The inelastic total and level cross-sections were constructed based on the evaluated level scheme of 52 Cr from the angle integrated gamma production cross-sections. Above 4 MeV neutron energy, the total inelastic cross-section presented here is only a lower limit but is close to the exact value. The same 4 MeV represents the maximum neutron energy up to which the level cross-sections were given. Neutron energy resolutions of 1.12 keV at 1 MeV up to 35 keV at 10 MeV were obtained for the main transitions and for the total inelastic scattering cross-section. The total uncertainty on the gamma production cross-section of the main transition and on the total inelastic scattering cross-section was smaller than 5% up to 10 MeV and less than 10% up to 18 MeV. In comparison with the previous experiments for 52 Cr, the set of cross-sections measured in the present experiment have the advantage of covering the full energy range from threshold up to about 18 MeV in only one run. Systematic uncertainties are substantially reduced resulting in a small overall uncertainty. Moreover the present results have a better neutron energy resolution than the existing experimental data. In general, the TALYS code calculation with the default input parameters describes relatively well the measured cross-sections presented here. We stress that the present experimental results were not used to adjust the input parameters of the TALYS calculation. The gamma production cross-sections are described well at energies below about 4 MeV, but significant differences with the measured data are visible above this energy. The total inelastic cross-section is better described by the default TALYS calculation on the full energy range. This is valid despite the fact that the gamma production cross-sections of the most intense transitions that are used to construct the total inelastic cross-section (1434.07 keV, 1530.67 keV and 1727.53 keV) are underestimated by the calculation. Anyway, the calculation gives higher values for the total inelastic cross-section around 9 MeV and above 14 MeV. These differences are higher than the experimental uncertainties. The good agreement of the calculated level cross-section with the measured values can be understood also from the good agreement of almost all the gamma production cross-sections at energies below 4–5 MeV. The good agreement of TALYS with the experimental total inelastic cross-section of Fig. 14 suggests that the compound nucleus and direct reaction modeling, including the associated optical model and level density parameters, is well under control. The failure to describe particular gamma-ray transitions may be due to either wrong branching ratios in the discrete level database or an incorrect model for the level density spin distribution (in particular the spin cutoff parameter). The current, and similar, measurements may form the starting point for a study to resolve these problems in a systematical manner.

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The large cross-sections data set that was obtained in this experiment for the neutron inelastic scattering and (n, 2n) reaction on 52 Cr can be used as benchmark for new studies. As was shown, it would be of interest to further investigate the modeling of the decay for a better description of the gamma production cross-sections at incident energies above 5 MeV and for precompound estimates above 14 MeV. To facilitate such studies the numerical results of this work are available from the EXFOR database [52]. Acknowledgements The authors thank the team of operators of the GELINA facility for the preparation of the neutron beam. L.C.M. and C.B. are grateful to the EC/JRC for financial support (contract number 20207). References [1] G. Aliberti, G. Palmiotti, M. Salvatores, C.G. Stenberg, Impact of nuclear data uncertainties on transmutation of actinides in accelerator-driven assemblies, Nucl. Sci. Eng. 146 (2004) 13. [2] M. Salvatores, G. Palmiotti, LMFBR design parameter uncertainties and target accuracies, Ann. Nucl. Energy 12 (1985) 291. [3] G. Palmiotti, M. Salvatores, Use of integral experiments in the assessment of large liquid–metal fast breeder reactor basic design parameters, Nucl. Sci. Eng. 87 (1984) 333. [4] L.C. Mihailescu, L. Oláh, C. Borcea, A.J.M. Plompen, A new HPGe setup at Gelina for measurement of gamma-ray production cross sections from inelastic neutron scattering, Nucl. Instrum. Methods Phys. Res. A 531 (2004) 375. [5] A.J. Koning, S. Hilaire, M.C. Duijvestijn, TALYS: Comprehensive nuclear reaction modeling, in: Proceedings of the International Conference on Nuclear Data for Science and Technology—ND2004, Santa Fe, USA, 26 September– 1 October, 2004, in: AIP Conference Proceedings, vol. 769, American Institute of Physics, Melville, NY, 2005. [6] A.J. Koning, J.P. Delaroche, Local and global nucleon optical models from 1 keV to 200 MeV, Nucl. Phys. A 713 (2003) 231. [7] IAEA–NDS, Handbook for calculations of nuclear reaction data: RIPL-2, IAEA, Vienna, Austria, available online at, www-nds.iaea.org/RIPL-2, 2005. [8] IAEA–NDS, Handbook for calculations of nuclear reaction data: Starter file, Reference Input Parameter Library, IAEA-TECDOC-1034, IAEA, Vienna, Austria, available online at www-nds.iaea.org/ripl, 1998. [9] A.J. Koning, M.C. Duijvestijn, A global pre-equilibrium analysis from 7 to 200 MeV based on the optical model potential, Nucl. Phys. A 744 (2004) 15. [10] L. Cranberg, J.S. Levin, Neutron scattering at 2.45 MeV by a time-of-flight method, Phys. Rev. 103 (1956) 343. [11] P.H. Stelson, R.L. Robinson, H.J. Kim, J. Rapaport, G.R. Satchler, Excitation of collective states by the inelastic scattering of 14 MeV neutrons, Nucl. Phys. 68 (1965) 97. [12] Y.G. Degtjarev, V. Protopopov, Excitation of low-lying levels of 27 Al, 52 Cr, 56 Fe and 209 Bi in the inelastic scattering of 1–4 MeV neutrons, At. Energ. 23 (1967) 568. [13] I.A. Korzh, V.A. Mishchenko, E.N. Mozhzhukhin, N.M. Pasechnik, N.M. Pravdivyj, I.E. Sanzhur, Neutron scattering in energy range 1.5–3.0 MeV on the even isotopes of Cr, Ni, Zn, Sov. J. Nucl. Phys. 26 (1977) 608. [14] N. Olsson, E. Ramstrom, B. Trostell, Neutron elastic and inelastic scattering from Mg, Si, S, Ca, Cr, Fe and Ni at E(n) = 21.6 MeV, Nucl. Phys. A 513 (1990) 205. [15] Y.G. Degtjarev, Experience of semiconductor detectors application for fast neutron spectrometry, Bull. Russ. Acad. Sci. 66 (2002) 790. [16] R.M. Kiehn, C. Goodman, Neutron inelastic scattering, Phys. Rev. 95 (1954) 989. [17] D. van Patter, N. Nath, S.M. Shafroth, S. Malik, M. Rothman, Gamma rays from inelastic neutron scattering in chromium, Phys. Rev. 128 (1962) 1246. [18] D.L. Broder, V.E. Kolesov, A.I. Lashuk, I.P. Sadokhin, A.G. Dovbenko, The excitation cross section of the levels of Mg, Cr-52, Ni-58, Ni-60 and Nb-93 by the inelastic scattering of neutrons, At. Energ. 16 (1964) 103. [19] M.V. Pasechnik, M.B. Fedorov, T.I. Jakovenko, I.E. Kashuba, V.A. Korzh, Neutron scattering with initial energy of 2.9 MeV by titanium and chromium nuclei, Ukr. Phys. J. 14 (1969) 1874. [20] E.M. Burymov, Measurement of level-excitation cross sections for cross-section determination induced by 14.6 MeV neutrons, Yad. Fyz. 9 (1969) 933.

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