An analytical multigroup benchmark for (n, γ) and (n, n′, γ) verification of diffusion theory algorithms

The angular flux for the “rod model” describing coupled neutron/gamma (n, γ) diffusion has a particularly straightforward analytical representation when viewed from the perspective of a one-group homogeneous medium. Cast in the form of matrix functions of a diagonalizable matrix, the solution to the multigroup equations in heterogeneous media is greatly simplified. We shall show exactly how the one-group homogeneous medium solution leads to the multigroup solution.     

Measurement of L X-ray fluorescence cross-sections for elements with 45 ? Z ? 50 using synchrotron radiation at 8 keV

The L shell fluorescence cross-sections of the elements in range 45 ? Z ? 50 have been determined at 8 keV using Synchrotron radiation. The individual L X-ray photons, Ll, Lα, Lβ_I, Lβ_II, Lγ_I and Lγ_II produced in the target were measured with high resolution Si(Li) detector. The experimental set-up provided a low background by using linearly polarized monoenergetic photon beam, improving the signal-to-noise ratio. The experimental cross-sections obtained in this work were compared with available experimental data from Scofield [1] and [2] Krause [3] and [4] and Scofield and Puri et al. [5] and [6].These experimental values closely agree with the theoretical values calculated using Scofield and Krause data, except for the case of Lγ, where values measured of this work are slighter higher.     

Calculation and analysis of n+Zr reactions in the En ⩽ 250 MeV energy range

All of reaction cross sections, angular distributions, energy spectra, γ-ray production cross sections, and the double differential cross section for neutron, proton, deuteron, triton, helium and alpha emission are calculated and analyzed for n+^{90,91,92,94,96,nat}Zr at incident neutron energies from 0.1 to 250 MeV. The optical model, intranuclear cascade model, the unified Hauser–Feshbach theory and the exciton model which included the improved Iwamoto–Harada model are used. Theoretical calculated results are compared with existing experimental data and other evaluated data from ENDF/B-VI.8, ENDF/B-VII.0 and JENDL-3.3. The optical model potential parameters are obtained according to the experimental data of total, nonelastic cross sections and elastic scattering angular distributions.     

Excitation functions of (n, α) reaction cross-sections for some important isotopes from threshold to 20 MeV

The (n, α) reaction cross-sections from threshold to ∼20 MeV on some important nuclides ⁴²Ca, ^50,53Cr, ^56,57Fe, ^58,62Ni, and ^63,65Cu involved in the reactor shielding design have been calculated using the Hauser–Feshbach statistical model with preequilibrium effects by involving PCROSS option in Empire 2.19. The transmission coefficients for neutrons in the entrance channel are calculated using the optical model potential of Koning. In the exit channel optical model potential of Avrigeanu has been used. The experimental values have been chosen carefully for all the isotopes, from EXFOR data base. The calculations are compared with existing experimental data as well as with evaluated data files (ENDF/B-VI.0 and JENDL-3.3). A good agreement between the calculated and experimental data validates the nuclear model approaches with increased predictive power to supplement and extend the nuclear database that is required for several applications.     

Nuclear half-lives for α-radioactivity of elements with 100 ? Z ? 130

Theoretical estimates for the half-lives of about 1700 isotopes of heavy elements with 100 ? Z ? 130 are tabulated using theoretical Q-values. The quantum mechanical tunneling probabilities are calculated within a WKB framework using microscopic nuclear potentials. The microscopic nucleus-nucleus potentials are obtained by folding the densities of interacting nuclei with a density-dependent M3Y effective nucleon-nucleon interaction. The α-decay half-lives calculated in this formalism using the experimental Q-values were found to be in good agreement over a wide range of experimental data spanning about 20 orders of magnitude. The theoretical Q-values used for the present calculations are extracted from three different mass estimates viz. Myers-Swiatecki, Muntian-Hofmann-Patyk-Sobiczewski, and Koura-Tachibana-Uno-Yamada.     

Mi (i = 1-5) subshell fluorescence and Coster-Kronig yields for elements with 67 ? Z ? 92

A complete set of the M_i (i = 1-5) subshell fluorescence and Coster-Kronig (CK) yields has been generated by interpolation for elements with 67 ? Z ? 92 from the Dirac-Hartree-Slater (DHS) model based values tabulated for a limited number of elements, considering the cutoff/onset of different CK transitions in accordance with the CK transition energies evaluated in the present work. The CK transition energies have been deduced from tabulated values of the Dirac-Hartree-Fock-Slater model based neutral atom binding energies [K. Huang, M. Aoyagi, M.H. Chen, B. Crasemann, H. Mark, At. Data Nucl. Data Tables 18 (1976) 243] and the L_i (i = 1-3) subshell CK transition energies [M.H. Chen, B. Crasemann, K. Huang, M. Aoyagi, H. Mark, At. Data Nucl. Data Tables 19 (1977) 97] in order to establish the cutoff/onset of different CK transitions at specific atomic numbers. A second set of the M_i (i = 1-5) subshell fluorescence yields have also been deduced using radiative widths computed from the Dirac-Fock (DF) model based X-ray emission rates, and the total widths reevaluated to incorporate the DF model based radiative widths in place of those based on the DHS model. Further, the CK-corrected (ν_i) and average fluorescence (?_M) fields, which are experimentally important, have been evaluated from the generated set of CK yields and two sets of fluorescence yields.     

Li (i = 1-3) subshell X-ray production cross sections and fluorescence yields for some elements with 56 ? Z ? 68 at 22.6 keV

The L_k (k = l, α, β_1,4, β_3,6, β_2,15,9,10,7, γ_1,5 and γ_2,3,4) X-ray production (XRP) cross sections have been measured for six elements with 56 ? Z ? 68 at 22.6 keV incident photon energy using the EDXRF spectrometer. The incident photon intensity, detector efficiency and geometrical factors have been determined from the K X-ray yields emitted from elemental targets with 22 ? Z ? 42 in the same geometrical setup and from knowledge of the K XRP cross sections. The L₁ and L₂ subshell fluorescence yields have been deduced from the present measured L_k XRP cross sections using the relativistic Hartree-Fock-Slater (HFS) model based photoionization cross sections. The present deduced ω₁ (exp) values have been found to be, on an average, higher by 15% and 20% than those based on the Dirac-Hartree-Slater (DHS) model and the semi-empirical values compiled by Krause, respectively, for elements with 60 ? Z ? 68.     

Interaction of 〈1 0 0〉 and ½〈1 1 1〉 dislocation loops with point defects in ferritic alloys

The interaction between dislocation loops of interstitial nature with ½〈1 1 1〉 and 〈1 0 0〉 Burgers vectors and point defects in Fe has been studied molecular dynamics. Comparative calculations have been carried out using two interatomic potentials for pure Fe ([G.J. Ackland, M.I. Mendelev, D.J. Srolovitz, S. Han, A.V. Barashev, J. Phys.: Condens. Mater. 16 (2004) 1; S. Dudarev, P. Derlet, J. Phys.: Condens. Mater. 17 (2005) 7097]). The results of this study are range and energy of the interaction as functions of size and mutual position of defects. The applied potentials predict somewhat different strain field structure for 〈1 0 0〉 loops and therefore different lengths of interaction. However, both potentials suggest that, contrary to common belief, the distance of cluster-defect interaction within the glide prism of a ½〈1 1 1〉 cluster is significantly longer than that of a 〈1 0 0〉 cluster of similar size, in spite of the longer Burgers vector in the latter case.     

L1 and L2 sub-shell fluorescence yields for elements with 64 ? Z ? 70

The L₁ and L₂ sub-shell fluorescence yields have been deduced for elements with 64 ? Z ? 70 from the L_k(k = l, α, β_1,4, β_3,6, β_2,15,9,10,7, γ_1,5 and γ_2,3,4) X-ray production cross sections measured at 22.6 keV incident photon energy using a spectrometer involving a disc type radioisotope of Cd¹⁰⁹ as a photon source and a Peltier cooled X-ray detector. The incident photon intensity, detector efficiency and geometrical factor have been determined from the K X-ray yields emitted from elemental targets with 20 ? Z ? 42 in the same geometrical setup and from knowledge of the K shell cross sections. The present deduced ω₁(exp) values, for elements with 64 ? Z ? 70, are found to be in good agreement with those tabulated by Campbell (J.L. Campbell, Atom. Data Nucl. Data Tables 95 (2009) 115), where as these are, on an average, higher by 19% and 24% than those based on the Dirac-Hartree-Slater model (S. Puri et al., X-ray Spectrometry 22 (1993) 358) and the semi-empirical values compiled by Krause (M.O. Krause, J. Phys. Chem. Ref. Data 8 (1979) 307), respectively. The present deduced ω₂(exp) values are found to be in good agreement with those based on the Dirac-Hartree-Slater model and are higher by up to ∼13% than the semi-empirical values for the elements under investigation.     

Ga NMR and magnetic susceptibility in δ-phase of Pu1−xGax (x = 0.05, x = 0.08) alloys

⁶⁹Ga nuclear magnetic resonance spectra, line shifts (⁶⁹K) and nuclear spin-lattice relaxation rate have been measured in the 20 years aged Pu_0.95Ga_0.05 and in fresh prepared Pu_0.92Ga_0.08 alloys, stabilized δ-phase, at magnetic field of 9.4 T in the temperature range (10-500) K. The line shift and are determined correspondingly by the static and fluctuating-in-time parts of the local magnetic field that originates in transferred hyperfine coupling the Ga nuclear spin with the nearest f-electron environment of more magnetic Pu.Temperature behavior of the resonance properties is found the same in fresh Pu_0.92Ga_0.08 and aged Pu_0.95Ga_0.05 alloy. The NMR results are in favor that δ-phase of Pu_1−xGa_x alloys represents at T > 200 K the Kondo lattice, in which the localized electronic spins fluctuate independently from each other without any macroscopic coherence. The coherent state like in heavy-fermion liquids emerges in Pu_0.95Ga_0.05 below T^∗ = 200 K. A little bit higher estimate of crossover temperature T^∗ = 250 K was founded for Pu_0.92Ga_0.08.     

Stopping power measurements of heavy ions (3 ? Z1 ? 14) in Mylar foil by time-of-flight spectrometry

Heavy ions elastic recoil detection analysis coupled with time of flight spectrometer (HIERDA_ToF-E) have been used to measure energy loss of charged particles in thin absorber. The stopping power of heavy ions has been determined in Mylar for ²⁸Si, ²⁷Al, ²⁴Mg, ¹⁹F, ¹⁶O, ¹²C and ⁷Li ions over a continuous range of energies 0.14-0.80 MeV/nucleon. The ions were recoils from the bombardment of different samples (Si, MgO, Al₂O₃, LiF and C) with a 27.5 MeV Kr⁺ beam. The energy loss of the recoil atoms is measured with and without additional foils placed in front of a Surface Barrier Detector (SBD). The energy of individual ions is determined from its ToF data; the exit energy after the stopping foil is measured using the SBD detector. We have compared our stopping values to those predicted by SRIM-2008 computer code, ICRU-73 stopping data tables, MSTAR calculations and to the published data from literature. The results show good agreement with limited existing data but indicate a large deviation among the predicted theoretical values at the low energy side of the stopping maximum peak.     

Energy levels in Ag-like (4d4f, 4d5? (? = 0-3)), Pd-like (4d4f [J = 1], 4d5p [J = 1], 4d5f [J = 1]), and Rh-like (4d [J = 5/2, 3/2]) ions with Z ? 86

Relativistic perturbation theory with a model potential is used for the calculation of energy levels of the states 4f_5/2, 4f_7/2, 5s_1/2, 5p_1/2, 5p_3/2, 5d_3/2, 5d_5/2, 5f_5/2, and 5f_7/2 above the 1s²2s²2p⁶3s²3p⁶3d¹⁰4s²4p⁶4d¹⁰ core, with one vacancy , in the same core, in the silver and rhodium isoelectronic sequences with the maximum nuclear charge Z = 86. The method of extrapolation of the model potential parameter is applied to calculate one-electron and one-vacancy wavefunctions. The wavefunctions of Ag- and Rh-like ions were used to calculate the energies of resonance transitions to the ground state ¹S₀ in Pd-like ions. Good agreement between the theoretical and the experimental energies of the resonance transitions in Pd-like ions indicates the reliability of the results obtained.     

Post-annealing temperature dependence of blistering in high-fluence ion-implanted H in Si 〈1 0 0〉

This study examined the influence of post-annealing temperature on blister formation and growth in ion-implanted H in Si 〈1 0 0〉. Ion energy levels of 40 and 100 keV and fluences of 2 × 10¹⁶ and 5 × 10¹⁶ cm⁻² were investigated. Post-annealing treatments were performed using the furnace annealing (FA) method with temperatures ranging from 200 to 600 °C for a duration of 1 h. Raman scattering spectroscopy (RSS), optical microscopy (OM), secondary ion mass spectrometry (SIMS), atomic force microscopy (AFM), and cross-sectional transmission electron microscopy (XTEM) were employed to explore the mechanisms behind the smart cut technique. The results revealed that variations among the transformation of the VH₃ (or V₂H₆) defect complex phase into the Si(1 0 0):H bonding configuration phase (RSS results), the appearance of optically detectable blisters and craters (OM results), the average depth of craters (AFM results), the trapping of hydrogen atoms and gettering of oxygen atoms (SIMS results), and the damaged microstructures (XTEM results) against post-annealing temperature were in close correspondence. It was also found that the optimal post-annealing temperature for blister formation and growth was 550 °C.     

Measurement of cross sections for (n, 2n), (n, p) and (n, α) reactions on germanium isotopes induced by 14 MeV neutrons

Activation cross sections at the neutron energy about 14 MeV on germanium isotopes have been measured, employing the activation technique and γ-ray spectrometry. The data of the cross section are reported for the (n, 2n), (n, p) and (n, α) reactions. The neutron flux was determined using the monitor reactions ²⁷Al (n, α) ²⁴Na and the neutron energies were measured by the method of cross section ratios for ⁹⁰Zr (n, 2n) ⁸⁹Zr to ⁹³Nb (n, 2n) ^92mNb reactions. The measured results were compared with the other measurements.     

Influence of post-annealing time on blistering evolution in Si 〈1 0 0〉 implanted with high-fluence H ions

The influence of post-annealing time on blistering characteristics induced by 5 × 10¹⁶ cm⁻² ion-implanted H in Si <1 0 0> was studied in terms of the formation and growth of blisters. Ion energies consisted of 40 and 100 keV. Post-annealing treatments were carried out using furnace annealing (FA) at 400 and 500 °C for a duration of 0.25-3 h in a nitrogen ambient. Raman scattering spectroscopy (RSS), optical microscopy (OM), atomic force microscopy (AFM), and secondary ion mass spectrometry (SIMS) were utilized to analyze the defect complex phases, the appearance of optically-detectable blisters and craters, the average depth of craters, and the hydrogen and oxygen depth profiles in the implanted layer, respectively. Furthermore, a characteristic time for the growth of optically-detectable blisters which was determined from the blister-covered fractions for various post-annealing times is proposed and used as a criterion to identify the effectiveness in the formation and growth of optically-detectable blisters. The results revealed that the characteristic time for the 400 °C-annealed specimens in the 40 keV implant is much shorter than it is in the 100 keV one. However, the characteristic time for the 500 °C-annealed specimens in the 40 keV implant is slightly longer than it is in the 100 keV implant. In addition, both the characteristic times for the 500 °C-annealed specimens are much shorter than those for the 400 °C ones. The above-mentioned phenomena hold true for craters.     

Thermal neutron cross-section and resonance integral of the W(n, γ)W reaction

We measured the thermal neutron cross-section and the resonance integral of the reaction ¹⁸⁶W(n, γ)¹⁸⁷W by the activation method using a ¹⁹⁷Au(n, γ)¹⁹⁸Au monitor reaction as single comparator. The high-purity natural W and Au metallic foils with and without a cadmium shield case of 0.5 mm thickness were irradiated in a neutron field of the Pohang neutron facility. The induced activities in the samples were measured by high-resolution γ-ray spectrometry with a calibrated p-type high-purity Ge detector. The necessary correction factors for γ-ray attenuation (F_g), thermal neutron self-shielding (G_th), and resonance neutron self-shielding (G_epi) effects, and the epithermal neutron spectrum shape factor (α) were taken into account. The thermal neutron cross-section for the ¹⁸⁶W(n, γ)¹⁸⁷W reaction has been determined to be 37.2 ± 2.1 barn, relative to the reference value of 98.65 ± 0.09 barn for the ¹⁹⁷Au(n, γ)¹⁹⁸Au reaction. The present result is, in general, in good agreement with most of the experimental data and the recently evaluated value of ENDF/B-VII.0 by 5.7%. By assuming the cadmium cut-off energy of 0.55 eV, the resonance integral obtained is 461 ± 39 barn, which is determined relative to the reference values of 1550 ± 28 barn for the ¹⁹⁷Au(n, γ)¹⁹⁸Au reaction. The present resonance integral value is in general good agreement with the recently measured values by 9%. The present result is lower than the evaluated ones by 10-13%.     

Energy loss straggling in thick mylar polymeric foils for swift heavy ions in fractional energy loss limits ΔE/E ∼ 5-80%

The energy loss straggling in thick mylar (monomer composition: C₁₀H₈O₄) polymeric foils has been measured for swift heavy ions covering Z = 3-22, in the fractional energy loss limits ΔE/E ∼ 5-80%. These measured straggling values have been compared with the most commonly used Bethe-Livingston collisional straggling formulation after modifying it suitably for thick targets. Further, the charge-exchange straggling values have been extracted from the measured values and were found to be consistently higher than the corresponding values deduced from Yang’s et al. formulation. Finally, an analytical expression has been developed for charge-exchange straggling for ion-polymer combinations, considered in the present study.     

Measurements of Lα, Lβ X-ray production cross sections of Bi by 17-40 keV electron impact

We present results of measurements of L_α, L_β X-ray production cross sections for the element Bi (Z = 83) by 17-40 keV electron impact. The target used in the experiment was prepared by evaporating the element Bi to the thick pure carbon substrate. The effects of multiple scattering of electrons when penetrating the target film, of electrons reflected from the thick pure carbon substrate and of bremsstrahlung photons produced by the impact of incident electrons on the target are corrected by means of Monte Carlo simulation. The experimental data, reported here for the first time in the energy region of 17-40 keV, are compared with the DWBA theory and the PWBA-C-Ex theory. They are in good agreement.     

Measurements of activation cross sections for Lu(n, α)Tm,Lu(n, α)Tm and Lu(n, p)Yb reactions induced by neutrons around 14 MeV

The cross sections for the ¹⁷⁵Lu(n, α)¹⁷²Tm, ¹⁷⁶Lu(n, α)¹⁷³Tm and ¹⁷⁵Lu(n, p)^175m+gYb reactions have been measured in the neutron energy range of 13.5–14.8 MeV using the activation technique. The first data for ¹⁷⁵Lu(n, α)¹⁷²Tm reaction cross sections are presented. In our experiment, the fast neutrons were produced via the ³H(d, n)⁴He reaction on K-400 Neutron Generator at Chinese Academy of Engineering Physics (CAEP). Induced gamma activities were measured by a high-resolution (1.69 keV at 1332 keV for ⁶⁰Co) gamma-ray spectrometer with high-purity germanium (HPGe) detector. Measurements were corrected for gamma-ray attenuations, random coincidence (pile-up), dead time and fluctuation of neutron flux. The neutron fluences were determined by the cross section of ⁹³Nb(n, 2n)^92mNb or ²⁷Al(n, α)²⁴Na reactions. The neutron energy in the measurement was by the cross section ratios of ⁹⁰Zr(n, 2n)^89m+gZr and ⁹³Nb(n, 2n)^92mNb reactions. The results were discussed and compared with experimental data found in the literature and with results of published empirical formulae.     

Void reactivity coefficient benchmark results for a 10 × 10 BWR assembly in the full 0–100% void fraction range

A boiling water reactor SVEA-96+ fresh fuel lattice has been used as the basis for a benchmark study of the void reactivity coefficient at assembly level in the full voidage range. Results have been obtained using the deterministic codes CASMO-4, HELIOS, PHOENIX, BOXER and the probabilistic code MCNP4C, combined for almost all cases with different cross section libraries. A statistical analysis of the results obtained showed that the void reactivity coefficient tends to become less negative beyond 80% void and that the discrepancies between codes tend to increase from less than 15% at voidages lower than 40% to more than 25% at voidages higher than 70%. The void reactivity coefficient results and the corresponding differences between codes were isotopically decomposed to interpret discrepancies. The isotopic decomposition shows that the minimum observed in the void reactivity coefficient between 80% and 90% void is largely due to the decrease in the relative importance of the ¹⁵⁷Gd(n, γ) rate with increasing voidage, and that the fundamental discrepancies between codes or libraries are mainly governed by the different predictions of the ²³⁸U(n, γ) variation with voidage.