Reduced Neutron Widths Research Articles

Convergence behavior of statistical uncertainty in probability table for cross section in unresolved resonance region

ABSTRACT The probability table method is a well-known method for addressing self-shielding effects in the unresolved resonance region. A long computational time is required to generate the table. The effective way to reduce the generation time is the reduction of the number of ladders. The purpose of this study is the estimation of the optimal number of ladders using the statistical uncertainty in the probability table. To this end, the statistical uncertainty quantification method of the probability table was developed and the convergence behavior of the statistical uncertainty was investigated. The product of the probability and the average cross section was considered the target of the statistical uncertainty. The convergence behavior was investigated by using Sr-90, U-235, and U-238 from JENDL-4.0. The calculation results revealed that the convergence rate of the statistical uncertainty was different in each nuclide and it was affected by the average level spacing and the average reduced neutron width. The generation time of the probability table was less than half when the input parameter for the iteration condition was changed from the number of ladders to the tolerance value. The developed method leads to the efficient generation of probability tables and the reduction of processing time.

Spin assignment and statistical properties of neutron resonances from Dy161,163(n,γ) and Er167(n,γ) measured at the DANCE facility

Background: Average resonance spacing ${D}_{0}$ and spin dependence of nuclear level density (NLD) are essential quantities in nuclear physics, especially important for calculations of nuclear reactions and the normalization of NLD models.Purpose: Neutron resonances with different spins in odd-mass targets can form close doublets that are often difficult to resolve. These doublets are not corrected for when accounting for subthreshold resonances during ${D}_{0}$ determination. Moreover, different literature sources disagree on the isotopic assignment of some resonances.Methods: The $\ensuremath{\gamma}$ rays following radiative neutron capture on $^{161,163}\mathrm{Dy}$ and $^{167}\mathrm{Er}$ were measured with the highly segmented $\ensuremath{\gamma}$-ray calorimeter Detector for Advanced Neutron Capture Experiments (DANCE) at the Los Alamos Neutron Science Center. The analysis of spectra using the $\ensuremath{\gamma}$-multiplicity-based spin assignment method allows checking for the presence of the above-mentioned doublets. The calorimetric sensitivity provides unambiguous isotopic assignment.Results: We were able to assign spin to tens of resonances as well as to identify new ones in all three isotopes. Some isotope assignments from the literature were corrected. Detailed analysis of the number of unobserved resonances, assuming that the resonance positions obey predictions of the Gaussian orthogonal ensemble and reduced neutron widths Porter-Thomas fluctuations, allowed determination of ${D}_{0}$ with an uncertainty of a few percent, ${D}_{0}=2.15(5)$, 6.39(24), and 3.86(12) eV for $^{161,163}\mathrm{Dy}$ and $^{167}\mathrm{Er}$, respectively. Thanks to the spin assignment, the spacings for the resonances with the two spins formed in $s$-wave neutron capture, ${D}_{0}^{\ensuremath{-}}$ and ${D}_{0}^{+}$, were determined. Their ratio was compared to different NLD models.Conclusions: Our deduced ${D}_{0}$ for $^{163}\mathrm{Dy}$ is lower than any $^{163}\mathrm{Dy}$ value found in the literature. Good consistency was found with some literature values for $^{161}\mathrm{Dy}$ and $^{167}\mathrm{Er}$. The ratios ${D}_{0}^{\ensuremath{-}}/{D}_{0}^{+}$ are consistent with several models available in the literature, but in a clear contradiction with a few microscopic NLD models.

Neutron width statistics in a realistic resonance-reaction model

A recent experiment on s-wave neutron scattering from $^{192,194,196}$Pt found that the reduced neutron width distributions deviate significantly from the expected Porter-Thomas distribution (PTD), and several explanations have been proposed within the statistical model of compound nucleus reactions. Here, we study the statistics of reduced neutron widths in the reaction $n+ ^{194}$Pt within a model that combines the standard statistical model with a realistic treatment of the neutron channel. We find that, if the correct secular energy dependence of the average neutron widths is used, then the reduced neutron width distribution is in excellent agreement with the PTD for a reasonable range of the neutron-nucleus coupling strength and depth of the neutron channel potential. Within our parameter range, there can be a near-threshold bound or virtual state of the neutron channel potential that modifies the energy dependence of the average width from the $\sqrt{E}$ dependence, commonly assumed in experimental analysis, in agreement with the proposal of H. A. Weidenm\"uller [1]. In these cases, the reduced neutron width distributions extracted using the $\sqrt{E}$ dependence are significantly broader than the PTD. We identify a relatively narrow range of parameters where this effect is significant.

Distribution of total radiation widths for neutron resonances of Pt isotopes

High quality neutron capture and transmission data were measured on isotopically enriched 192,194,195,196 Pt and natural Pt samples at ORELA. R -matrix analysis of this data revealed resonance parameters for 159, 413, 423, 258, and 11 neutron resonances for neutron energies below 5.0, 16.0, 7.5, 16.0, and 5.0 keV for 192,194,195,196,198 Pt+n, respectively. Earlier analysis of data on reduced neutron widths, Γ0 n , showed that the distributions of Γ0 n for 192,194 Pt deviate significantly from the Porter-Thomas distribution (PTD) predicted by random matrix theory. In this contribution we report on preliminary results of the analysis of distribution of total radiation widths, Γγ , in 192,194,195,196 Pt+n reactions. Comparison of experimental data with predictions made within the nuclear statistical model indicates that standard models of Photon Strength Functions (PSFs) and Nuclear Level Density predict Γγ distributions which are too narrow. We found that satisfactory agreement between experimental and simulated distributions can be obtained only by a strong suppression of the PSFs at low γ -ray energies and/or by violation of the usual assumption that primary transitions from neutron resonances follow the PTD. The shape of PSFs needed for reproduction of our Γγ data also nicely reproduces spectra from several (n,γ ) experiments on the neighbor nuclide 198 Au.

From average parameters to statistical resolved resonances

This paper presents a novel approach using average parameters from statistical models in the continuum to produce statistical resolved resonances in the resonance range. Based on unresolved resonance parameters and the random ladder method, average parameters such as the scattering radius, level spacing, reduced neutron width and the radiative width are used to create resolved resonances from thermal energy up to the first excited level. Using the TALYS reaction code and the CALENDF processing code, the method is tested on ≃2400 isotopes and will be used to produce resolved resonance ranges in the TENDL libraries for reactions missing experimental resolved and unresolved parameters. Additionally, the R-matrix code AVEFIT is used to approximate the resonance structure effects above the first excited level of selected isotopes.

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

I have analyzed reduced neutron widths (${\ensuremath{\Gamma}}_{n}^{0}$) 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 that these widths should follow a ${\ensuremath{\chi}}^{2}$ distribution having one degree of freedom ($\ensuremath{\nu}=1$)---the Porter Thomas distribution (PTD). Careful analysis of the ${\ensuremath{\Gamma}}_{n}^{0}$ values in the NDE rejects the validity of the PTD with a statistical significance of at least 99.97% ($\ensuremath{\nu}=0.801\ifmmode\pm\else\textpm\fi{}0.052$). This striking disagreement with the RMT prediction is most likely due to the inclusion of significant $p$-wave contamination to the supposedly pure $s$-wave NDE. When an energy-dependent threshold is used to remove the $p$-wave contamination, the PTD is still rejected with a statistical significance of at least 98.17% ($\ensuremath{\nu}=1.217\ifmmode\pm\else\textpm\fi{}0.092$). Furthermore, examination of the primary references for the NDE reveals that many resonances in most of the individual data sets were selected using methods derived from RMT. Therefore, using the full NDE data set to test RMT predictions seems highly questionable. These results cast very serious doubt on claims that the NDE represents a striking confirmation of RMT.

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.

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.

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.

Decay widths of highly excited Ra compound nuclei

Excitation functions were obtained for the xn, p xn and αxn decay channels of 216,218,220Ra compound nuclei produced in the reactions 22Ne+ 194,196,198Pt in the excitation energy range of 40–160 MeV. Due to the employment of three platinum isotope targets, the cross section ratios were measured with a high degree of accuracy for evaporation reaction channels resulting in the formation of fixed cold products after the termination of evaporation cascades of a different numbers of stages. Experimental values for the reduced neutron widths of highly excited compound nuclei were obtained from the measured cross section ratios. Evaporation reaction cross sections were well described in the framework of the statistical model taking into account shell effects according to Ignatyuk. Our present, and also earlier, investigations showed that calculations making use of one single set of the model parameters (the scaling factor to the liquid-drop fission barrier of Cohen, Plasil and Swiatecki, C = 0.6–0.7 and the ratio of the level density parameters, a f a v = 1.0 ) reproduces correctly the cross sections of the evaporation reactions in a wide range of compound nuclei extending from Bi to U. Moreover, the measured cross section ratios are exceptionally sensitive to the value of the parameter a f a v , i.e. are very suitable for a high accuracy estimation of this value. By fitting two sets of the experimental data — the absolute cross section values and cross section ratios — we were able to independently estimate the values of two principal parameters of the model, C and a f a y . Our calculations showed that a large part of the pre-fission neutrons is evaporated by hot pre-actinide compound nuclei before they reach the saddle point (50 to 100% of the total number of pre-fission neutrons are pre-saddle).

Retardation of single-particle E1 transitions from the 622 keV broad d-wave neutron resonance in 9Be

Capture gamma rays from the 622 keV d-wave neutron resonance in 9Be with large reduced neutron width have been observed by means of a time-of-flight method, employing an anti-Compton NaI(TI) detector. Partial radiative widths have been derived for the strong primary E1 transition to the 3368 keV (2 +) state in 10Be and also for the weak one to the 5958 keV (2 +) state. Those widths were compared with predictions of the Lane-Mughabghab valence-capture model. As a consequence we found certain evidence to show that the 3368 keV state transition is appreciably hindered. The discrepancy can be removed by using a renormalized neutron effective charge which takes into account the coupling between the d-state neutron single-particle motion and the E1 giant resonance excitation of the target nucleus.

Comparison of the Porter-Thomas distribution with neutron resonance data of even-even nuclei.

The low-energy neutron resonance data of the even-even nuclei $^{152}\mathrm{Sm}$, $^{158}\mathrm{Gd}$, $^{162}\mathrm{Dy}$, $^{166,168}\mathrm{Er}$, $^{182}\mathrm{W}$, $^{232}\mathrm{Th}$, and $^{236,238}\mathrm{U}$ have been examined in order to test the validity of the Porter-Thomas distribution of the reduced neutron widths---a chi-squared distribution with one degree of freedom (v=1). In an attempt to circumvent the ever-present problems of missed or spurious s wave levels as well as extra p wave levels, a maximum likelihood statistic was employed which used only measured widths greater than some minimum value. A Bayes-theory test applied to the data helped to ensure that p wave contamination of the s wave level population was not significant. The error-weighted value of the number of degrees of freedom for the nine nuclei studied, 〈v〉=0.98\ifmmode\pm\else\textpm\fi{}0.10, is consistent with the theoretical expectation of v=1.

Radiative transitions from neutron capture in53Cr resonances

A measurement is described of gamma-ray spectra emitted after neutron capture ins- andp-wave resonances of53Cr, in the range 2–50 keV. The observed decay scheme concerns 38 excited levels of54Cr, with energies up to 5.6 MeV. New information is obtained on the multiplicity of gamma cascades, on the spin and parity of54Cr levels, and on the spin of neutron resonances of53Cr. PartialE1 andM1 radiative widths are obtained for transition energies from 4.1 to 9.7 MeV. The overall energy behaviour ofE1 reduced widths is in rough agreement with a Lorentzian shape, but the average intensity is higher than expected from photo-neutron data. The measured averageE1 strength is =(8.7±±0.8)·10−15, MeV−5. Fluctuations around this average are non-random, showing the existence of an intermediate structure. ReducedE1 widths are strongly correlated with the reduced neutron widths in the whole energy interval. An indication is found for a correlation between reducedE1 widths and spectroscopic factors of54Cr levels. The measured averageM1 strength =(5.9±0.7)·10−9 MeV−3 appears to be energy-independent as in the single-particle model.

Mechanism for electric dipole transitions from the broad p-wave neutron resonance in 24Mg.

Neutron capture gamma rays from the 84-keV ${\mathit{p}}_{3/2}$-wave resonance, 266-keV ${\mathit{p}}_{1/2}$-wave resonance, and 431-keV ${\mathit{p}}_{3/2}$-wave resonance in $^{24}\mathrm{Mg}$ that have large reduced neutron width have been measured with an anti-Compton NaI(Tl) detector, using a time-of-flight technique. Successful extraction of gamma-ray intensities for transitions to low-lying states in $^{25}\mathrm{Mg}$ was performed by an iterative unfolding method, in order to deduce partial radiative widths. Also, we have made an experimental contrivance separating the kernel of the 266-keV broad resonance from that of the 257-keV overlapping narrow resonance. Radiative widths were obtained for the E1 transitions to the ground ((5/${2}^{+}$), 585-keV (1/${2}^{+}$), 975-keV ((3/${2}^{+}$), 1965-keV ((5/${2}^{+}$), 2564-keV (1/${2}^{+}$), and 2801-keV ((3/${2}^{+}$) states, and were compared with theoretical calculations based on the valence capture model that was developed by Lane and Mughabghab. Consequently, we found that in the ${\mathit{p}}_{3/2}$-wave resonance capture the observed and calculated widths for the transitions to the 1/${2}^{+}$ states are in excellent agreement; however, the experimental widths for the transitions to the (5/${2}^{+}$ states are 20--50 % of the theoretical ones. These noteworthy features in the retardation of E1 transition are explained in terms of the renormalized effective charge, which depends on the orbital angular momentum for the single-particle component of final bound states, as a result of the coupling of the single-particle transition with the isovector field generated by the giant dipole resonance. Moreover, the nonadiabatic coupled-channel calculation using a particle-rotator coupling model was carried out for partial radiative widths of the 266-keV ${\mathit{p}}_{1/2}$-wave resonance. The calculations reproduced the observed values satisfactorily.

89Y + n resonances for E = 10–740 keV and intermediate structure

High-resolution neutron total-cross-section measurements on 89Y have been made from a few eV to 1 MeV using the pulsed neutron time-of-flight spectroscopy at ORELA with a neutron burst width of 5 ns and a nominal resolution of 0.025 ns/m at the highest energy. We have analyzed the data from 10–740 keV using a multilevel R-matrix code and obtained the values of resonance parameters ( E 0, J π , g Γ n ). From these results we have obtained the values of average quantities up to about 600 keV: D l = 0 = 4.6 ± 0.3 keV, D l = 1 = 1.35 ± 0.15 keV; S 0 = 0.33 ± 0.045, S 1 = 5.82 ± 0.38, in units of 10 −4 eV − 1 2 . The staircase plots of reduced neutron widths for s- and p-waves and the plots of the Lorentz-weighted strength functions averaged over different energy intervals show an evidence of several doorway states. A least-squares fit to the lorentzian smooth curves provides the best values of Ed (doorway energy) and γ 2d c (escape reduced width of doorway). These values are in qualitative agreement with the theoretical predictions. The experimental ratio of s- to p-wave level spacings was found to be 3.43 ± 0.6. This is in disagreement with the theoretical prediction of 2.06 (for σ = 3.8) and indicates a parity dependence of the level density at high excitation.

Mechanism of s-wave and p-wave neutron resonance capture in light and medium-weight nuclei

Capture gamma-ray spectra of 16O, 28Si and 32S have been measured to investigate the mechanism of neutron capture in s-wave and p-wave resonances with large reduced neutron width. Observed gamma-ray transitions from the 434-keV p3/2-wave resonance of 16O exhibit typical features of valence neutron capture in light nuclei. For the 565-keV and 806-keV p3/2-wave resonances of 28Si, a particle-vibrator coupling model indicates that in these resonance states core excitation is essential to explain the observed partial radiative widths. There is also some possibility of core excitation in the 203-keV p1/2-wave resonance capture in 32S. Moreover, a strong correlation between partial radiative widths and spectroscopic factors of the final states was found for gamma-ray transitions from the 188-keV s-wave resonance of 28Si and the 103-keV s-wave resonance of 32S. A discussion follows on the particle-core coupling scheme in these resonance capture transitions.

Structure of unbound states in 29Si from neutron resonance spectroscopy of 28Si + n.

Resonance structure in the $^{28}+\mathrm{n}$ system has been investigated by performing neutron total cross section and capture \ensuremath{\gamma}-ray measurements. A detailed analysis of resonance parameters was carried out up to a neutron energy of 2.75 MeV. Level densities were determined for s- and p-wave resonances, as well as neutron strength functions and partial radiative widths. The neutron strengths are compared with existing model calculations. The neutron width of at least one T=(3/2 level has been determined, providing a measure of isobaric spin mixing. Whereas other workers previously reported a strong correlation between the reduced neutron widths (${\ensuremath{\Gamma}}_{\mathrm{n}{}^{l}}$) and total radiative widths, we observe no significant correlation between ${\ensuremath{\Gamma}}_{\mathrm{n}{}^{l}}$ and the partial radiative widths for ground state transitions. We conclude that radiative capture in $^{28}+\mathrm{n}$ does not proceed via a simple valence mechanism, but must involve several competing doorway states. The observed M1 strength in $^{29}\mathrm{Si}$ is lower than that reported for $^{28}\mathrm{Si}$ from inelastic electron scattering, suggesting either a considerable fragmentation or a significant reduction due to the presence of the additional neutron.

Particle-vibrator coupling model calculation of partial radiative widths for [formula omitted] wave neutron resonance on 28Si

A particle-vibrator coupling model was applied to the calculation of partial radiative widths for the 28 Si p 3 2 wave neutron resonance with large reduced neutron width. The calculation assumed a neutron excitation coupled to one-phonon vibrational states of the 28Si nucleus and neglected the continuum nature of the resonance state wave function in the nuclear external region. The model wave functions were generated from a coupled-channel Schrödinger equation so as to reproduce the observed neutron escape width, neutron binding energies, and spectroscopic factors. Excellent agreement was achieved between the observed and calculated partial radiative widths for the transitions from the 565 keV resonance to the low-lying states of 29Si. As a result, it was confirmed that the core excitation is quite essential to explain the observed partial radiative widths. We emphasize that this resonance can be interpreted as a particle-vibrator doorway state common to the neutron and gamma-ray emission channels, and that a dominant component of the doorway-state wave function belongs to the configuration in which a single quasibound 1 d 3 2 neutron is coupled to the 3 − vibrational state of the 28Si nucleus.

Calculation of resonance reduced neutron widths by semiclassical description

A semiclassical description of the excited composite nucleus, obtained after resonance capture of a neutron is proposed and applied to calculations of reduced neutron width. Results of calculations are compared with experimental data. The proposed description can reasonably explain the gross structure in dependence of the average reduced neutron width on neutron number.

Structure of 19O from measurement and R-matrix analysis of σ(θ) for 18O(n, n) 18O and 18O(n, n′) 18O ∗(1.98 MeV)

Differential cross sections for neutrons elastically scattered from 18O and inelastically scattered to the first excited state 18O ∗ (1.98 MeV) have been measured at forty-two incident energies for 5.0 < E n < 7.5 MeV corresponding to excitation energies in 19O of 8.7 to 11.1 MeV. The cross sections were measured at eleven laboratory angles per energy from 20° to 160° and show considerable resonance structure. These new elastic and inelastic 1.98 MeV level data have been analyzed together with previously published cross sections for 0 < E n < 2.5 MeV using a multilevel-multichannel R-matrix program to determine J, π, E λ and γ λc for states in 19O. The new assignments are compared to previous work where possible. Several previous assignments for resonances in the 0 < E n < 2.5 MeV region were verified, and disagreements over the J π assignments for several levels in this region have been resolved. A total of fourteen new J π assignments were made in the 5 < E n < 7.5 MeV region. An attempt was made to identify T = 3 2 analog states in 19F for the newly assigned levels in 19O. On the basis of spin, parity, excitation energy and a comparison of reduced neutron widths in 19O with reduced proton widths in 19F, six previously-identified T = 3 2 analogs were verified and eight new T = 3 2 analogs were tentatively assigned. Comparisons with existing theoretical work are discussed.