Estimation of the neutron chain-length distribution in subcritical systems using a point Monte Carlo code

A point Monte Carlo code has been developed that simulates the evolution of prompt fission chains in subcritical systems. From this simulation, a numerical estimate of the neutron chain-length distribution as a function of k_eff has been obtained for subcritical systems. We also discuss the importance of the detector efficiency in performing a successful neutron noise measurement in highly subcritical systems.     

Determination of Neutron Multiplication, (II)

The purpose of the present work is to confirm experimentally that the prompt neutron decay constant of fundamental mode, α₀₀₀, satisfies the following two requirements from the concept proposed in Part (I): To be uniquely measurable free from space dependence and detector specification, and to be calculable from the Boltzmann equation. To prove this, a series of pulsed experiments was made at various subcritical states in a reflected graphite-moderated 20% enriched fuel system (SHE).

The experimental results confirmed that α₀₀₀ was obtained as a common and unique value at any point of both core and reflector, determined by separation of spatial harmonics, using bare and Cd-covered BF₃ counters. The state of SHE was changed by attenuating the core, with or without central control rod, and by adding distributed poison to the core and/or to the reflector.

Direct comparison was made between the experimental results and the calculated values from multigroup treatment using P₁ and S₄ approximation. Calculated values of α₀₀₀ for subcritical states with attenuated core, with or without control rod, showed fairly good agreement with the measured values. In addition, the time-dependent spectral changes of the subcritical systems were also investigated in the experiments.     

On the multiplication factor and reactivity definitions for subcritical reactor systems

An analysis is made on the merit of different functions adopted for weighting neutron processes in subcritical nuclear reactor systems, as it appears in expressions of relevant integral quantities, such as reactivity worths, prompt neutron lifetimes, etc. All weight functions may be shown to depend on some sort of explicit or implicit, real or fictitious, system control. Associated with the importance function relevant to the reactor power control, the multiplication factor k_sub and generalized reactivity values ρ_gen are defined. The difference (1-k_sub)/k_sub is shown to be the more appropriate index for generally representing the ADS subcriticality. However, in certain circumstances, when an accidental event is studied in which the criticality condition may be surpassed during the transient, it appears more appropriate to take into account the standard multiplication factor (k_eff) and the reactivity values to which the transient is associated and for the definition of which the standard adjoint flux is adopted.     

Determination of the subcriticality level using the Cf source-detector method

Measurement and monitoring of reactivity in a subcritical state, e.g. during the loading of a power reactor, has a clear safety relevance. The methods currently available for the measurement of k_eff in stationary subcritical conditions should be improved as they refer to the critical state. This is also very important in the framework of ADS (accelerator driven systems) where the measurement of a subcritical level without knowledge of the critical state is looked for. An alternative way to achieve this is by mean of the ²⁵²Cf source-detector method. The method makes use of three detectors inserted in the reactor: two “ordinary” neutron detectors and one ²⁵²Cf source-detector which contains a small amount of ²⁵²Cf that introduces neutrons in the system through spontaneous fission. By observing fissions through the detection system and correlating the signals of the three detectors, the reactivity ρ (and hence the multiplication factor k) can be determined.     

A New Static and Dynamic One-Point Equation and Analytic and Numerical Calculations for a Subcritical System

In this study we derived a new one-point equation based on the balance of fission neutrons. The equation has the same form as the conventional equation using k _eff which represents the neutron balance in the whole core. The variables of the new equation are the number of fission neutrons and delayed neutron precursors, and the coefficients are the multiplication rates of prompt fission neutrons, delayed neutrons and source neutrons. In the conventional equation, the variables are weighted by the adjoint flux; in other words, they are adjusted to the critical state. The variables in the new equation correspond to actual values even in a deep subcritical state; hence, the physical meaning of each term is clear.

The dynamic behavior of a slab core with an external source was analyzed through calculations based on the new equation. Deterministic and probabilistic calculations of the equation were performed for a typical accelerator-driven system in the static state.     

Subcritical multiplication factor and source efficiency in accelerator-driven system

The subcritical multiplication factor k_s   and the external neutron source efficiency φ^∗${\phi }^{\ast }$ are important parameters in the accelerator-driven system (ADS) performance assessment. The theoretical relation between k_s and the effective multiplication factor k_eff in a subcritical system is discussed in different cases of subcritical system. On the basis of the theoretical background, the dependence of k_s   and φ^∗${\phi }^{\ast }$ on subcriticality, source position, and energy is numerically investigated using a simple thermal subcritical model. For the sake of experimental evaluation of k_s   and φ^∗${\phi }^{\ast }$, the ADS experiments have been carried out in the subcritical systems combined with 14 MeV pulsed neutrons of the Kyoto University Critical Assembly (KUCA). The k_s   and φ^∗${\phi }^{\ast }$ parameters are successfully measured by utilizing the reaction rate distribution obtained by the optical fiber detectors in the subcritical system, within a relative difference of less than 7% and 12% for k_s   and φ^∗${\phi }^{\ast }$, respectively, between measured and calculated values for most studied cases.     

Feynman-Y function for a subcritical assembly with intrinsic spontaneous fissions driven by external pulsed sources

Stochastic neutron transport theory is applied to the derivation of the Feynman-Y function for subcritical assemblies when external pulsed sources are used. We obtain a general relationship between the probability generating functions of the kernel and the source considering the contribution to the detector statistics of both the pulsed source and the intrinsic neutron source. An expansion in α-eigenvalues is derived for the final solution, which permits to take into account the effect of higher harmonics in subcritical systems. In addition, numerical calculations have been done for a proposed model problem to understand the applicability of the method studied.     

Determination of mass attenuation coefficients, effective atomic and electron numbers, mean free paths and kermas for PbO, barite and some boron ores

The total mass attenuation coefficients, μ_m, for PbO, barite, colemanite, tincal and ulexite were determined at 80.1, 302.9, 356.0, 661.7 and 1250.0 keV photon energies by using NaI (Tl) scintillation detector. Effective atomic number, Z_eff, effective electron number, N_eff, total atomic cross-section, σ_t, total electronic cross-section, σ_e, mean free path, mfp, and kerma relative to air were determined experimentally and theoretically. The theoretical mass attenuation coefficients were estimated using mixture rule. The calculated values were compared with the experimental values for all samples.     

Comparison of some lead and non-lead based glass systems, standard shielding concretes and commercial window glasses in terms of shielding parameters in the energy region of 1 keV-100 GeV: A comparative study

The effective atomic numbers, Z_eff of some glass systems with and without Pb have been calculated in the energy region of 1 keV-100 GeV including the K absorption edges of high Z elements present in the glass. Also, these glass systems have been compared with some standard shielding concretes and commercial window glasses in terms of mean free paths and total mass attenuation coefficients in the continuous energy range. Comparisons with experiments were also provided wherever possible for glasses. It has been observed that the glass systems without Pb have higher values of Z_eff than that of Pb based glasses at some high energy regions even if they have lower mean atomic numbers than Pb based glasses. When compared with some standard shielding concretes and commercial window glasses, generally it has been shown that the given glass systems have superior properties than concretes and window glasses with respect to the radiation-shielding properties, thus confirming the availability of using these glasses as substitutes for some shielding concretes and commercial window glasses to improve radiation-shielding properties in the continuous energy region.     

Detected-neutron multiplication factor measured by neutron source multiplication method

An alternative definition of neutron multiplication factor measured by the neutron source multiplication (NSM) method is newly proposed. This newly defined neutron multiplication factor, k_det, is derived on the basis of neutron detection process in a subcritical system with an external neutron source. The definition of k_det is expressed as a ratio of total number of detected fission-neutrons to total number of detected all neutrons. In this paper, a heuristic derivation of k_det is presented, and another interpretation of k_det is explained by using the detector importance function. Based on the idea of k_det, the measurement principle of NSM method is reinterpreted, and the correction factors in the NSM method are clarified. In order to verify our proposed NSM method, numerical analysis of the NSM method is carried out. The numerical results suggest that target neutron multiplication factors of the NSM method can be well estimated even without any corrections by putting a neutron detector where the effective neutron multiplication factor k_eff is well approximated by k_det.     

K-shell absorption jump factors and jump ratios in elements between Tm (Z = 69) and Os (Z = 76) derived from new mass attenuation coefficient measurements

The K-shell absorption jump factors and jump ratios were derived from new mass attenuation coefficients measured using an energy dispersive X-ray fluorescence (EDXRF) spectrometer for Tm, Yb elements being Tm₂O₃, Yb₂O₃ compounds and pure Lu, Hf, Ta, W, Re and Os. The measurements, in the region 56-77 keV, were done in a transmission geometry utilizing the K_α1, K_α2, K_β1 and K_β2 X- rays from different secondary source targets (Yb, Ta, Os, W, Re and Ir, etc.) excited by the 123.6 keV γ-photons from an ⁵⁷Co annular source and detected by an Ultra-LEGe solid state detector with a resolution of 150 eV at 5.9 keV. Experimental results have been compared with theoretically calculated values. The measured values of Tm, Yb, Lu, Hf, Ta, W, Re and Os are reported here for the first time.     

Effects of neutron spectrum and external neutron source on neutron multiplication parameters in accelerator-driven system

The neutron multiplication parameters: neutron multiplication M, subcritical multiplication factor k_s, external source efficiency φ^*, play an important role for numerical assessment and reactor power evaluation of an accelerator-driven system (ADS). Those parameters can be evaluated by using the measured reaction rate distribution in the subcritical system. In this study, the experimental verification of this methodology is performed in various ADS cores; with high-energy (100 MeV) proton–tungsten source in hard and soft neutron spectra cores and 14 MeV D–T neutron source in soft spectrum core. The comparison between measured and calculated multiplication parameters reveals a maximum relative difference in the range of 6.6–13.7% that is attributed to the calculation nuclear libraries uncertainty and accuracy for energies higher than 20 MeV and also dependent on the reaction rate distribution position and count rates. The effects of different core neutron spectra and external neutron sources on the neutron multiplication parameters are discussed.     

Determination of the effective atomic numbers and electron densities for YBaCuO superconductor in the range 59.5-136 keV

The effective atomic numbers and electron densities of YBa₂Cu₃O_7−δ superconductor at 59.5, 65.2, 77.1, 94.6, 122 and 136 keV were calculated by using the measured mass attenuation coefficients. Measurements were made by performing transmission experiments in a well-collimated narrow beam geometry set-up by employing Si(Li) detector with a resolution of 0.16 keV at 5.9 keV. These values are found to be in good agreement with theoretical values calculated based on XCOM data. The observed crystal structure of YBa₂Cu₃O_7−δ superconductor is close to the theoretical structure. Z_eff and N_el experimental values showed good agreement with the theoretical values for calcined and sintered YBa₂Cu₃O_7−δ.     

Contribution of near-edge processes to attenuation of the characteristic X-rays in elements with 48 ≤ Z ≤ 83

Attenuation of the characteristic K X-rays in the ₄₈Cd, ₅₀Sn, ₅₂Te, ₆₄Gd, ₆₅Tb, ₆₆Dy, ₆₈Er, ₇₄Ta, ₇₅Re, ₇₉Au, ₈₂Pb and ₈₃Bi elements have been measured with especial emphasis for the X-ray energies (E_in) in the region of respective K-shell/L_i subshell (i = 1, 2, 3) ionization threshold (B_K/B_Li). The characteristic X-rays were obtained from different fluorescent target elements excited by the X-rays and γ-rays emitted from the ⁵⁵Fe and ²⁴¹Am radioisotopes, respectively. The measurements were performed using an energy-dispersive detection set up involving a low-energy Ge detector. The measured attenuation coefficients for the X-rays with energies away from ionization thresholds of the attenuator element are found to be in good agreement with the available theoretical coefficients, which incorporate contributions of the photoionization, and the Rayleigh and Compton scattering processes. However, the measured attenuation coefficients are found to deviate significantly from the theoretical values for the X-rays with energies in vicinity of B_K/Li. The observed alteration is attributed to the X-ray Absorption Fine Structure (XAFS) for negative B_K/Li − E_in values, and the K-shell/L_i subshell resonant Raman scattering (RRS) process for positive B_K/Li − E_in values. Systematic of the K-shell/L_i subshell RRS contribution to attenuation of the X-rays are discussed in terms of the respective oscillator density and fraction of electrons available in the K-shell/L_i subshell Lorentzian profile of the attenuation element below E_in.     

Accurate Estimation of Subcriticality Using Indirect Bias Estimation Method, (II)

Subcriticalities were estimated by applying the Indirect Bias Estimation Method to subcritical experiments on a light-water moderated/reflected low-enriched UO₂ lattice cores. Two measurable values, prompt neutron time-decay constant and spatial-decay constant were calculated using MCNP 4A and JENDL-3.2. With these calculation errors, the biases in calculated reactivity were derived from the Indirect Bias Estimation Method. The differences between the calculated and measured spatial-decay constants were more or less at the same extent of experimental errors. These results show that the accuracy of subcriticality estimation of MCNP 4A and JENDL-3.2 ranges within the uncertainty which can be achieved by the exponential experiment. The differences between calculated and measured prompt neutron decay constants derive significant biases in calculated reactivity. The subcriticalities were estimated by using the effective multiplication factors adjusted based on these biases in calculated reactivity.     

Tables of SnNk1k2 and skn for γ-ray perturbed angular correlations with quadrupole interactions

Geometrical coefficients for the interpretation of γ-ray perturbed angular correlations with quadrupole interactions are presented for nuclear spins I ≤ 20. The coefficients S_nN^k₁k₂ for singlecrystal sources with k₁, k₂ = 2, 4 and N = 1, 2, 3, 4, and the coefficients s_kn for polycrystalline sources with k = 1, 2, 3, 4 are tabulated. This work extends previous tables to the higher values of the nuclear spin that are frequently encountered in accelerator experiments that populate high-spin isomeric levels.     

NXcom – A program for calculating attenuation coefficients of fast neutrons and gamma-rays

This work is concerned with a construction and use of NXcom computer program for calculating the removal and attenuation coefficients of transmitted fast neutrons and γ-rays, respectively, through mixtures, composites, concretes and compounds. The program uses only one input data file for neutrons and γ-rays calculations. For γ-ray attenuation, the program predictions were tested by comparing them with the well-known WinXcom program results and an excellent agreement was noticed. Also, it has been used for calculating the values of macroscopic effective removal cross-sections Σ_R (cm⁻¹) for five new published polyamide and anhydride composites designed for shielding mixed neutron and γ-rays. The obtained values for Σ_R using the program and the reported attenuation thicknesses which were based on the Monte Carlo N-Particle (MCNP) code showed the same trend. The NXcom program can be used as a preliminary effective tool for testing the shielding material against fast neutrons and γ-rays.     

Diffusion of tritium in zircaloy-2

The dependency of the tritium diffusion in Zircaloy-2 on the temperature as well as on the oxygen and hydrogen concentration was investigated. From the determined diffusion coefficients the following values for the frequency factor d₀ and the activation energy E_a were obtained: D₀ = (1.04^+0.28_?0.17 ) 10^?3 [cm² · s^?1 ], E_a = -42.1 ± 1.1 [kJ · mol^?1 ]. In the concentration range from 1350 to 11300 ppm oxygen and 15 to 1000 ppm hydrogen no systematic influence of these elements on the tritium diffusion coefficients was observed.     

Dispersion coefficients for interactions between positronium and light atoms with pure Coulomb and screened Coulomb potentials

The Van der Waals two-body dispersion coefficients for interactions between the positronium (Ps) atom and light atoms have been investigated using highly correlated exponential basis functions in the framework of both pure Coulomb and screened Coulomb potentials. The C₆, C₈ and C₁₀ coefficients for Ps-Ps and Ps-H interactions, and the C₆ coefficients for Ps-He interactions for both the screened and unscreened cases, are reported.