Neutron Widths Research Articles

Distribution of Partial Neutron Widths for Nuclei Close to a Maximum of the Neutron Strength Function

For nuclei near a maximum of the neutron strength function, the secular dependence on energy E of s-wave partial neutron widths differs from the canonical form √E. We derive the universal form of that dependence and show that it is expected to significantly influence the analysis of neutron resonance data.

Anomalous Fluctuations ofs-Wave Reduced Neutron Widths ofPt192,194Resonances

We obtained an unprecedentedly large number of s-wave neutron widths through R-matrix analysis of neutron cross-section measurements on enriched Pt samples. Careful analysis of these data rejects the validity of the Porter-Thomas distribution with a statistical significance of at least 99.997%.

Determination of effective resonance energies for the (n,γ) reactions of 152Sm and 165Ho by using dual monitors

The effective resonance energies E ¯ r for the (n,γ) reactions of 152Sm and 165Ho isotopes were determined by using dual monitors ( 55Mn– 98Mo) due to their favourable resonance properties. The samples were irradiated in an isotropic neutron field obtained from 241Am–Be neutron sources. The induced activities were measured with a high efficient, p-type Ge detector. The necessary correction factors for thermal neutron self-shielding ( G th), resonance neutron self-shielding ( G epi), self absorption ( F s) and true coincidence summing ( F coi) effects for the measured γ-rays were taken into account. Thus, the experimental E ¯ r -values for above (n,γ) reactions are found to be 8.65 ± 1.80 eV for 152Sm and 12.90 ± 2.69 eV for 165Ho isotopes, respectively. The E ¯ r -values for both 152Sm and 165Ho isotopes were also theoretically calculated from the newest resonance data in the literature. Theoretically calculated E ¯ r -values are estimated to be 8.34 eV and 8.53 eV for 152Sm by two different approaches, which are generally, much smaller than that the present experimental value by 1.4–3.6% for 152Sm. In case of 165Ho isotope, the theoretically calculated E ¯ r -value of 8.63 eV from the first approach deviates substantially from the measured value by about 33%, whereas the theoretical E ¯ r -value of 12.95 eV from the second approach agrees very well with our experimentally determined E ¯ r -value. The results show that the present experimental E ¯ r -values for 152Sm and 165Ho isotopes agree with the calculated ones from the second approach within limits of the estimated uncertainty if the recently evaluated resonance data are used. However, it is worth noting that the results for E ¯ r -value calculated from the first approach are not satisfactorily accurate because of neglecting the neutron widths in that approach. Therefore, this study implies that it be regarded to the experimentally determined E ¯ r -value introduced in k 0–NAA method for the determination of any analytical result rather than its theoretical value.

Resonance Parameters and Uncertainties Derived from Epithermal Neutron Capture and Transmission Measurements of Natural Molybdenum

The electron linear accelerator facility at the Rensselaer Polytechnic Institute was used to explore neutron interactions with molybdenum in the energy region from 10 eV to 2 keV. Neutron capture and transmission measurements were performed by the time-of-flight technique. Resonance parameters were extracted from the data using the multilevel R-matrix Bayesian code SAMMY. A table of resonance parameters and their uncertainties is presented. Two transmission measurements were performed at a flight path of 25 m with a 6Li glass scintillation detector. The neutron capture measurements were performed at a flight path of 25 m with a 16-segment sodium iodide multiplicity detector. Nine different thicknesses of elemental molybdenum metal samples ranging from 0.051 mm (0.002 in.) to 6.35 mm (0.250 in.) were measured in either capture or transmission. Reductions in resonance integrals were observed when compared to ENDF/B-VII.0 for six of the seven stable isotopes. The largest reductions were 9% in 97Mo and 11% in 100Mo. The one measured increase in resonance integral relative to ENDF/B-VII.0 occurred in 95Mo, and it was significant (10%). The measured distribution of neutron widths for 95Mo and 97Mo are a better match to a Porter-Thomas distribution than those of ENDF/B-VII.0. Neutron strength functions for 95Mo and 97Mo were measured and compared to ENDF/B-VII.0. The strength of 95Mo and 97Mo are within uncertainties of each other. The measured radiation width distribution for 95Mo and 97Mo are compared to those of ENDF/B-VII.0 and to χ2 distributions. Significant aspects of this analysis are the assignment of radiation widths, the determination of the transmission resolution function, and the propagation of experimental uncertainties into resonance parameter uncertainties.

Reduced neutron widths in the nuclear data ensemble: Experiment andtheory do not agree

I have analyzed reduced neutron widths (Γ 0 n ) for the subset of 1245 resonances in the nuclear data ensemble (NDE) for which they have been reported. Random matrix theory (RMT) predicts for the Gaussian orthogonal ensemble (GOE) that these widths should follow a χ 2 distribution having one degree of freedom (ν = 1) - the Porter Thomas (PT) distribution. Using the maximum-likelihood (ML) technique, I have determined that the Γ 0 n values in the NDE are best described by a χ 2 distribution having ν = 0.80 ± 0.052, which is 3.8 standard deviations smaller than predicted by RMT. I show that this striking disagreement is most likely due to the inclusion of significant p -wave contamination to the supposedly pure s -wave NDE. Furthermore, when an energy-dependent threshold is used to remove the p -wave contamination, ML analysis yields ν = 1.217 ± 0.092 for the remaining data, still in poor agreement with the RMT prediction for the GOE. These results cast very serious doubt on claims that the NDE represents a striking confirmation of RMT.

Hafnium Resonance Parameter Analysis Using Neutron Capture and Transmission Experiments

The focus of this work is to determine the resonance parameters for stable hafnium isotopes in the 0.005- to 200-eV region, with special emphasis on the overlapping 176Hf and 178Hf resonances near 8 eV. Accurate hafnium cross sections and resonance parameters are needed in order to quantify the effects of hafnium found in zirconium, a metal commonly used in reactors. The accuracy of the cross sections and the corresponding resonance parameters used in current nuclear analysis tools are rapidly becoming the limiting factor in reducing the overall uncertainty on reactor physics calculations.Experiments measuring neutron capture and transmission are routinely performed at the Rensselaer Polytechnic Institute LINAC using the time-of-flight technique. Lithium-6 glass scintillation detectors were used for transmission experiments at flight path lengths of 15 and 25 m, respectively. Capture experiments were performed using a 16-section NaI multiplicity detector at a flight path length of 25 m. These experiments utilized several thicknesses of metallic and isotope-enriched liquid Hf samples. The liquid Hf samples were designed to provide information on the 176Hf and 178Hf contributions to the 8-eV doublet without saturation.Data analyses were performed using the R-matrix Bayesian code SAMMY. A combined capture and transmission data analysis yielded resonance parameters for all hafnium isotopes from 0.005 to 200 eV. Additionally, resonance integrals were calculated, along with errors for each hafnium isotope, using the NJOY and INTER codes. The isotopic resonance integrals calculated were significantly different from previous values. The 176Hf resonance integral, based on this work, is ~73% higher than the ENDF/B-VI value. This is due primarily to the changes to resonance parameters in the 8-eV resonance; the neutron width presented in this work is more than twice that of the previous value. The calculated elemental hafnium resonance integral, however, changed very little.

Neutron capture cross section ofAm241

The neutron capture cross section of $^{241}\mathrm{Am}$ for incident neutrons from 0.02 eV to 320 keV has been measured with the detector for advanced neutron capture experiments (DANCE) at the Los Alamos Neutron Science Center. The thermal neutron capture cross section was determined to be $665\ifmmode\pm\else\textpm\fi{}33$ b. Our result is in good agreement with other recent measurements. Resonance parameters for ${E}_{n}l12$ eV were obtained using an $R$-matrix fit to the measured cross section. The results are compared with values from the ENDF/B-VII.0, Mughabghab, JENDL-3.3, and JEFF-3.1 evaluations. ${\ensuremath{\Gamma}}_{n}$ neutron widths for the first three resonances are systematically larger by 5--15% than the ENDF/B-VII.0 values. The resonance integral above 0.5 eV was determined to be 1553\ifmmode\pm\else\textpm\fi{}7 b. Cross sections in the resolved and unresolved energy regions above 12 eV were calculated using the Hauser-Feshbach theory incorporating the width-fluctuation correction of Moldauer. The calculated results agree well with the measured data, and the extracted averaged resonance parameters in the unresolved resonance region are consistent with those for the resolved resonances.

Neutron decay width of one-particle resonant levels in deformed nuclei

The neutron partial decay width of one-particle resonant levels that are the bandhead states in odd-$N$ deformed nuclei is estimated in the formalism with a real-energy variable, using the width of one-particle resonance calculated in terms of eigenphase. It is shown that because of the presence of various ($\ensuremath{\ell}j$) components in a given one-particle resonant level of deformed nuclei, the neutron decay width can be quite different from the one obtained from assuming a spherically symmetric nuclear shape. As a numerical example, the formalism is applied to the case of the nucleus ${}_{4}^{13}$Be${}_{9}$, which lies outside the neutron drip line by 100--200 keV. Considering that the core of the nucleus consisting of four protons and eight neutrons is most likely prolately deformed, we point out the possibility that two lowest lying levels have ${I}^{\ensuremath{\pi}}=1/{2}^{+}$ for the $N=9$ nucleus, and the higher lying one may have a neutron decay width that is much narrower than the one expected for an ${s}_{1/2}$ level at the same resonance energy. The structure of some ${\ensuremath{\Omega}}^{\ensuremath{\pi}}=1/{2}^{+}$ one-particle resonant levels, which are smoothly connected to weakly bound one-particle levels as the potential strength becomes stronger, is also analyzed using the present formalism.

Spin measurements forSm147+nresonances: Further evidence for nonstatistical effects

We have determined the spins $J$ of resonances in the $^{147}\mathrm{Sm}$($n,\ensuremath{\gamma}$) reaction by measuring multiplicities of $\ensuremath{\gamma}$-ray cascades following neutron capture. Using this technique, we were able to determine $J$ values for all but 14 of the 141 known resonances below ${E}_{n}=1$ keV, including 41 firm $J$ assignments for resonances whose spins previously were either unknown or tentative. These new spin assignments, together with previously determined resonance parameters, allowed us to extract level spacings (${D}_{0,3}=11.76\ifmmode\pm\else\textpm\fi{}0.93$ and ${D}_{0,4}=11.21\ifmmode\pm\else\textpm\fi{}0.85$ eV) and neutron strength functions (${10}^{4}{S}_{0,3}=4.70\ifmmode\pm\else\textpm\fi{}0.91$ and ${10}^{4}{S}_{0,4}=4.93\ifmmode\pm\else\textpm\fi{}0.92$) for $J=3$ and 4 resonances, respectively. Furthermore, cumulative numbers of resonances and cumulative reduced neutron widths as functions of resonance energy indicate that very few resonances of either spin have been missed below ${E}_{n}=700$ eV. This conclusion is strengthened by the facts that, over this energy range, Wigner distributions calculated using these ${D}_{0}$ values agree with the measured nearest-neighbor level spacings to within the experimental uncertainties, and that the ${\ensuremath{\Delta}}_{3}$ values calculated from the data also agree with the expected values. Because a nonstatistical effect recently was reported near ${E}_{n}=350$ eV from an analysis of $^{147}\mathrm{Sm}$($n,\ensuremath{\alpha}$) data, we divided the data into two regions; $0<{E}_{n}<350$ eV and $350<{E}_{n}<700$ eV. Using neutron widths from a previous measurement (corrected for new unresolved doublets identified in this work) and published techniques for correcting for missed resonances and for testing whether data are consistent with a Porter-Thomas distribution, we found that the ${\ensuremath{\Gamma}}_{n}^{0}$ distribution for resonances below 350 eV is consistent with the expected Porter-Thomas distribution. However, we found that ${\ensuremath{\Gamma}}_{n}^{0}$ data in the $350<{E}_{n}<700$ eV region are inconsistent with a Porter-Thomas distribution, but in good agreement with a ${\ensuremath{\chi}}^{2}$ distribution having $\ensuremath{\nu}\ensuremath{\geqslant}2$ We discuss possible explanations for these observed nonstatistical effects and their possible relation to similar effects previously observed in other nuclides.

Neutron Capture and Total Cross-Section Measurements and Resonance Parameters of Gadolinium

Neutron capture and transmission measurements were performed by the time-of-flight technique at the Rensselaer Polytechnic Institute linac facility using metallic and liquid Gd samples. The liquid samples were isotopically enriched in either 155Gd or 157Gd. The capture measurements were made at the 25-m flight station with a multiplicity-type capture detector, and the transmission measurements were performed at 15- and 25-m flight stations with 6Li glass scintillation detectors. The multilevel R-matrix Bayesian code SAMMY was used to extract resonance parameters.Among the significant findings are the following. The neutron width of the largest resonance in Gd, at 0.032 eV in 157Gd, has been measured to be (9 ± 1)% smaller than that given in ENDF/B-VI updated through release 8. The thermal (2200 m/s) capture cross section of 157Gd has been measured to be 11% smaller than that calculated from ENDF. The other major thermal resonance, at 0.025 eV in 155Gd, did not display a significant deviation from the thermal capture cross section given by ENDF.In the epithermal region, the analysis provided here represents the most extensive to date. Twenty-eight new resonances are proposed, and other resonances previously identified in the literature have been revisited. The assignment of resonances within regions of complicated structure incorporated the observations of other researchers, particularly on the six occasions where ENDF resonances are recommended to be removed. The poor match of the ENDF parameters to the current data is significant, and substantial improvement to the understanding of gadolinium cross sections is presented, particularly above 180 eV where the ENDF resolved region for 155Gd ends.

A structural comparison of supercooled water and intermediate density amorphous ices

New data are presented on neutron diffraction in ultrapure bulk supercooled heavy water measured down to 262 K. The data are analysed in terms of the trends observed in the first sharp diffraction peak (FSDP) parameters, the feature which dominates the measured neutron spectra. The neutron FSDP position, height and width are compared to literature data for supercooled water, water under pressure and to the same parameters obtained for recently discovered intermediate density amorphous ices. It is found that the FSDP parameters in supercooled water and the amorphous ices generally exhibit a similar behaviour, suggesting a new structural regime may occur in deeply supercooled water below Q 0 ∼ 1.83 Å−1 (T ∼ 251 K) associated with increased intermediate range ordering. It is argued that this structural regime may be linked to a similar trend in the density which appears when the density is plotted as a function of FSDP position. A detailed comparison of the neutron and X-ray structure factors for supercooled water and intermediate density amorphous ices with the same FSDP positions is also made. The diffraction data show that although the overall general structures are qualitatively very similar, the amorphous ice correlations are considerably sharper and extend to much higher radial distances.

R-matrix analysis of the 3He(n, p)3H and 7Be(n, p)7Li reactions

We apply the R-matrix formalism to the 3He(n, p)3H and 7Be(n, p)7Li reactions, which play an important role in the big-bang nucleosynthesis. The cross sections are analysed along with the 4He and 8Be spectra near threshold. Neutron and proton widths of high-energy states are determined. A statistical analysis of the uncertainties provide fairly low error bars (typically 2% at the 1σ confidence level) on the reaction rates.

147Sm(n, α) Cross Section Measurements from 3 eV to 500 keV: Resonance Neutrons

The cross section of the 147Sm(n, α) reaction was measured from 3 eV to 500 keV at ORELA in the frame of an ORNL – FLNP collaboration. Total α-particle widths of 104 resolved neutron resonances with spin Jπ = 3- or Jπ=4- were measured in the energy interval 3 eV - 700 eV. A statistical analysis of α-particle widths of the resonances was carried out for each spin state. Deviations of the α-width distributions from statistical theory are discussed. A detailed discussion is devoted to a specific resonance (or doublet) at E0 = 184 eV having an unusual α-particle spectrum and unusually large α-particle and neutron widths.

The Neutron Total Cross Section of 129I below 1 keV

Although the isotope 129I is known to be an important fission product of conventional nuclear power plants, only few measurements describe its properties in the resonance region 1,)2,)3 mainly because of sample procurement and handling problems. In order to improve nuclear data for nuclear waste transmutation purposes, time-of-flight measurements (TOF) of the total cross section of 129I have been performed in the energy range from 0.14eV up to 100keV at the white neutron source GELINA of the Institute of Reference Materials and Measurements (IRMM) in Geel, Belgium.The neutron resonance shape fitting program REFIT 4) was used to determine the energy E0, the radiative width Γγ and the neutron width Γn of the resonances.

Neutron Data Measurements for Waste Transmutation at Gelina

During the last decade there has been a growing interest in Partitioning and Transmutation technologies as a means of strongly reducing the long-term radiotoxic inventory of nuclear waste. Main emphasis has been placed on the burning of minor actinides (MA) and of long-lived fission products (LLFP). In order to contribute building a sound data base for the neutron induced reactions of the concerned isotopes, a collaboration has been started in 1995 between the Service de Physique Nuclaire of CEA France and the Institute for Reference Materials and Measurements of Geel, Belgium. In the frame of this co-operation, a mixed group of scientists carries out measurements and analysis of neutron capture and transmission cross sections at the GELINAtime-of-flight facility of the IRMM. An important preparatory activity is also the procurement of such radioactive isotopes and the production of gram-quantity samples, a work that is also carried out at the IRMM, Geel. The isotopes investigated so far are 99Tc, 129I and 237Np. Work on 99Tc, which is considered the most offending LLFP, is practically completed: a total of 659 resonances have been analyzed up to 10 keV neutron energy making use of both capture and transmission data. Spin has also been assigned to 51 s-wave levels. Quantities such as the average level spacing, the average capture width and the strength function for s- and p-wave levels have been derived from such a large sample of resonances. Average capture and transmission cross sections have also been determined in the unresolved region from 10 to 150 keV. The analysis of 237Np transmission data has allowed to determine the neutron widths, and at low energy also the capture widths, of some 570 resonances below 500 eV and preliminary data up to 1 keV are available. Preliminary results of 129I transmission measurements below 1 keV energy are presented at this conference in a separate contribution. 1)

Neutron resonance spectroscopy of104Pd,105Pd,and110Pd

We have measured neutron resonances in the palladium isotopes 104, 105, and 110 for neutron energies from 1 to 2100 eV. Many new p-wave resonances have been observed. Their neutron widths and, in several cases, the radiative widths were measured. The average level spacings and the s-wave and p-wave neutron strength functions were determined. The time-of-flight method was used for both neutron total cross section measurements and total $(n,\ensuremath{\gamma})$ reaction yield measurements at the pulsed spallation neutron source of Los Alamos Neutron Science Center. Well established resonance spectroscopy for these isotopes is essential for the analysis of parity violation data that were recently measured in palladium.

The5H Nucleus in a Microscopic Cluster Model

The 5 H nucleus is investigated in the Generator Coordinate Method, using 3 H+n+n three-cluster wave functions. The 5 H energy is found to be E 3 MeV with respect to the 3 H+n+n threshold, and the neutron width is F n 1- 2 MeV or Γ n 1- 4 MeV, according to the nucleon-nucleon interaction.

Resonance neutron capture in 60Ni below 450 keV

High-resolution neutron capture cross-section measurements on 60Ni have been performed at the Geel Linear Accelerator in the energy range from 1 to 450 keV. An experimentally determined weighting function, obtained by a total energy detection set-up, has been applied to the measured capture spectra. The parameters of 275 resonances have been determined in a recent reanalysis using the FANAC R-matrix shape fitting code. Accurate values of the maxwellian-averaged capture cross section for stellar temperatures ranging from kT=5 to 100 keV, corresponding to different scenarios of s-process stellar nucleosynthesis, have been calculated. The distributions of partial radiative widths for s- and p-wave resonances have been derived. A correlation of 0.64 between capture and reduced neutron widths is compatible with the presence of nonstatistical effects in the capture of 60Ni.

Minimizing the statistical error of resonance parameters and cross-sections derived from transmission measurements

Total neutron cross-sections are usually measured by a transmission experiment. In this experiment the transmission through a sample is measured by taking the ratio of the background corrected counts measured with and without the sample in the beam. This procedure can be optimized to reduce the statistical error in the measured cross-section. The objective is to find the optimal sample thickness and time split between the open beam, sample and background measurements. An optimization procedure for constant cross-section measurement is derived and extended to the area under the total cross-section curve of an isolated resonance. The minimization of the statistical error in the measured area also minimizes the statistical error in the inferred neutron width. Comparison of the analytical expression developed in this paper and resonance parameters obtained from the SAMMY (Updated users's guide for SAMMY: Multilevel R-Matrix fits to neutron data using Bays’ equation, version m2, ORNTL/TM/-9179/R4) code is shown. The comparison was done with both simulated data and data from transmission experiments that were previously done at RPI. It is shown that the analytical expression can be used as a design tool for optimizing transmission experiments. This will consequently result in more accurate measurements of resonance parameters and can shorten the time required to reach a given accuracy.

Microscopic cluster study of the5Hnucleus

The ${}^{5}\mathrm{H}$ nucleus is investigated in the generator coordinate method, using ${}^{3}\mathrm{H}+n+n$ three-cluster wave functions. The model is tested with the ${}^{3}\mathrm{H}+n$ and ${}^{3}\mathrm{He}+p$ properties which agree fairly well with the experimental data. The ${}^{5}\mathrm{H}$ energy is found to be $E\ensuremath{\approx}3 \mathrm{MeV}$ with respect to the ${}^{3}\mathrm{H}+n+n$ threshold, and the neutron width is ${\ensuremath{\Gamma}}_{n}\ensuremath{\approx}1--2 \mathrm{MeV}$ or ${\ensuremath{\Gamma}}_{n}\ensuremath{\approx}1--4 \mathrm{MeV},$ according to the nucleon-nucleon interaction. We therefore suggest that the ${}^{5}\mathrm{H}$ lifetime should be larger than the ${}^{4}\mathrm{H}$ lifetime $({\ensuremath{\Gamma}}_{n}\ensuremath{\approx}5--6 \mathrm{MeV}).$