Neutron Multiplicity Distributions Research Articles

Prompt neutron emission in 250No spontaneous fission associated with ground and isomeric states decay

Abstract The complete-fusion reaction 204Pb(48Ca,2n)250No was used to study two activities of 250No with distinct half-lives. A total of 1357 events were observed in the SFiNx neutron detection system. The average number of neutrons emitted per spontaneous fission of 250No was determined to be (4.1 ± 0.1). The unusually symmetrical shape of the prompt neutrons multiplicity distribution was restored and presented for the first time. The list of statistical tests was performed to compare the prompt neutron multiplicity distributions associated with the ground state and the K-isomer state decays.

Total kinetic, excitation energy and neutron multiplicity distribution of californium isotopes

The mean total kinetic energy as a function of fission fragments, <TKE>(A), is calculated for neutron-induced fission of 247,249,251,253,255Cf, as well as for spontaneous fission of 248,250,252,254Cf using the scission point model. A comparative analysis is performed between the calculated results and existing experimental data. Investigation into the behavior of <TKE>(A) is conducted, particularly focusing on intermediate and heavy actinides. While nuclear and Coulomb energy evaluations suffice for estimating <TKE> values in light actinides, this approximation proves inadequate for evaluating TKE values for intermediate and heavy actinides. Additionally, an evaluation is made of the total excitation energy as a function of fission fragments, <TXE>(A), concerning spontaneous fission in 247−254Cf. It is found that TXE values sharply increase near the symmetric region across all isotopes and exhibit a gradual increase in heavy fission fragments. Furthermore, an exploration of the total neutron multiplicity as a function of fission fragments, νT(A), is conducted for 252Cf fission using two methods. The νT(A) results obtained through these methods are compared with experimental data, and νT(A) is estimated for unmeasured californium isotopes. The average neutron emission per fission event, ν¯(Ai), is then calculated for spontaneous fission of 251Cf and 253Cf, yielding values of 3.46 and 3.59, respectively.

A method of obtaining the neutron multiplicity distribution online based on the list-mode data acquisition

The obtainment of the neutron multiplicity distribution is the precondition of the neutron coincidence or multiplicity measurement. In related measurements, the calibration of the detector and the optimization of the analysis parameters prefer acquiring the neutron multiplicity distribution through the offline time-correlation analysis of the measured time stamps, while the usual measurement tasks tend to get it online. To meet with the demands of online and offline obtainment of the neutron multiplicity distribution, an online time-correlation analysis method on the basis of list-mode data acquisition technique is proposed in present work. The reliability of the obtained neutron multiplicity distribution is verified through the experiments carried out with a strong and a weak 252Cf neutron sources.

Complete neutron-multiplicity distributions in fast-neutron-induced fission

Complete neutron-multiplicity distributions in fast-neutron-induced fission

Structure of the prompt neutron multiplicity distribution in the spontaneous fission of 256Rf

An experimental study of 256Rf spontaneous fission following the fusion reaction of 50Ti+208Pb was performed using the velocity filter SHELS of the Flerov laboratory at JINR. The average number of neutrons of ν‾=4.30±0.17 and variance of σν2=3.2 from the prompt neutron multiplicity distribution were obtained. The alpha decay branching ratio of bα=0.003−0.003+0.005 and the half-life of T1/2=(6.7±0.2) ms of the isotope were determined. For the first time, our neutron detector system allowed us to extend investigation of the prompt neutron multiplicity study to the superheavy element region.

Neutron and gamma multiplicities calculated in the consistent framework of the Hauser-Feshbach Monte Carlo code FIFRELIN

Monte-Carlo simulations to calculate the number of prompt particles emitted during fission were performed using the Fifrelin code and compared to recent experimental data. We show that we are able to reproduce both the neutron and γ-ray multiplicity distributions as a function of the pre-neutron mass of the fission fragments using a single consistent set of parameters. This result was made possible by using an energy-dependent spin cut-off model, driving the initial total angular momentum of the fission fragments, together with microscopic level densities from the HFB plus combinatorial method. We also discuss, how the initial excitation-energy sharing shapes the TKE-dependent γ-ray multiplicity.

Reconstruction of neutron multiplicity distributions from low-order statistical information

A point-kinetic methodology for rapid and accurate computation of neutron multiplicity distributions in fixed time intervals is demonstrated. The approach uses an optimal combination of low-order count probabilities and low-order statistical moments, both of which are inexpensively computed from a backward Master equation, to reconstruct distributions valid for all count numbers. For high count numbers a generalized Laguerre polynomial representation is shown to accurately reconstruct the multiplicity distribution from five or fewer statistical moments when the zero-count probability is negligible. For intermediate count numbers and when the zero-count probability is significant, maximum information entropy reconstruction constrained by low-order moments and low-order count probabilities reproduces the overall count distribution very accurately. Numerical results for count number distributions and reconstruction accuracy as a function of number of constraints, relative to a system state-updating stochastic simulation MC algorithm (SSA), are presented to demonstrate the efficacy of this approach.

A Stochastic Transport Model for the Cumulative Number of Fissions and Deposited Fission Energy

The stochastic theory of neutron transport is extended to describe the cumulative distribution of fission numbers and deposited fission energy in a subvolume of a multiplying assembly. Solutions for the probability distributions are obtained using analytical approximations and Monte Carlo simulation in lumped geometry and in symmetric homogeneous and heterogeneous spheres. The results show the development of a power-law tail in the steady-state fission number and deposited energy distributions when the medium is critical, independent of the fission neutron multiplicity distribution and domain heterogeneity. In contrast, the asymptotic decay is faster than exponential in subcritical media due to rapid chain extinction and in supercritical media due to the increasing probability of chain divergence. A formal asymptotic analysis of the problem in lumped geometry with an arbitrary fission neutron multiplicity confirms the existence of power-law tails at critical.

Evidence for competing bi-faceted compound nucleus fission modes in 232Th(α,f) reaction

Relative isotopic yield distributions have been extracted for nine correlated fission fragment pairs following a detailed analysis of prompt γ−γ coincidence events from 232Th(α,f) reaction at Elab = 30 MeV. Simultaneously, the charge and mass yield distributions of the even-even fission fragments have been obtained from the measured relative isotopic yields. The onset of a triple-hump structure is seen in the extracted charge as well as mass yield distributions of the fragments. The results are consistent with the two-mode fission hypothesis of compound nucleus and in good agreement with the theoretical predictions, based on relevant fission models. The detailed results provide experimental evidence for the presence of two distinct compound nucleus fission modes, where the asymmetric and symmetric fission components are 83% and 17%, respectively. An average neutron multiplicity value of 4.60 ± 0.09 has been obtained, and the extracted neutron multiplicity distribution pattern corroborates the observed features of the multifaceted fission modes. Comparing the measured yield distributions following the 232Th(α,f) surrogate reaction, which produces 236U⁎ at an excitation energy of 21.5 MeV, with that of the direct reaction of 14 MeV neutron induced fission of 235U, an increase of about 11% in the yield of the symmetric component has been observed.

Transport Calculation of the Multiplicity Moments for Cylinders

In a previous paper by Pázsit and Pál [“Multiplicity Theory Beyond the Point Model,” Ann. Nucl. Energy, Vol. 154 (2021)], a general transport theory calculation of the factorial moments of the number of neutrons emitted spontaneously from a sample was elaborated. In contrast to the original derivations by Hage and Cifarelli [“On the Factorial Moments of the Neutron Multiplicity Distribution of Fission Cascades,” Nucl. Instrum. Meth. Phys. Res. A, Vol. 236 (1985)] and Böhnel [“The Effect of Multiplication on the Quantitative Determination of Spontaneously Fissioning Isotopes by Neutron Correlation Analysis,” Nucl. Sci. Eng., Vol. 90 (1985)], also referred to as the point model, in the transport model the spatial and angular dependence of the internal fission chain is taken into account with a one-speed transport theory treatment. Quantitative results were given for a spherical item, and the bias of the point model regarding the estimation of the fission rate as compared to the more exact space-dependent model was estimated as a function of the size of the sphere and the factor. In the present paper the formalism and the quantitative work are extended to the treatment of items with cylindrical shapes, which are more relevant in many practical applications. Results are presented for both square cylinders () and for tall () and flat () cylinders. This way the differences between the cylinder and the sphere on one hand and those between the various cylinder shapes on the other hand can be estimated. The results show that the bias depends on the geometry of the cylinder quite moderately, but similarly to the case of the sphere, the bias of the point model is quite significant for larger item sizes and values, and it is nonconservative (underestimates the fissile mass) as well.

Simultaneous description of charge, mass, total kinetic energy, and neutron multiplicity distributions in fission of Th and U isotopes

For fissioning isotopes of thorium and uranium, the simultaneous description of the charge, mass, total kinetic energy, and neutron multiplicity distributions of fission fragments is presented within the improved scission-point model. Correlations between all these observables are analyzed. The influence of the transition from symmetric to asymmetric fission mode on the shape of neutron multiplicity distribution is studied.

Reconstruction of Spontaneous Fission Neutron Multiplicity Distribution Spectra by the Statistical Regularization Method

Reconstruction of Spontaneous Fission Neutron Multiplicity Distribution Spectra by the Statistical Regularization Method

Neutral-current background induced by atmospheric neutrinos at large liquid-scintillator detectors. II. Methodology for in situ measurements

Future large liquid-scintillator (LS) detectors are competitive with and complementary to the water-Cherenkov detectors on the searches for diffuse supernova neutrino background and nucleon decay. In a companion paper, we have performed a systematic calculation of the neutral-current (NC) background induced by atmospheric neutrino interactions on $^{12}\mathrm{C}$ nuclei in LS detectors, which are expected to be crucially important for the experimental searches for the diffuse supernova neutrino background and nucleon decay. In this paper, we perform a systematic study on the measurement of the NC background and evaluate the associated uncertainties. We first exploit the characteristics of the NC background, in particular, the multiplicities of neutrons and pions, and the possible association with unstable residual nuclei. It turns out that the neutron multiplicity distribution is very powerful to discriminate among different models. Then, we develop a maximum-likelihood method to allow an in situ measurement of the NC interactions with a triple-coincidence signature. Finally, a data-driven approach is proposed to evaluate the uncertainty of the NC background in the search for the diffuse supernova neutrino background. We conclude that future large LS experiments like the Jiangmen Underground Neutrino Observatory will be able to make a unique contribution to the worldwide dataset to improve the prediction of atmospheric neutrino NC interactions on $^{12}\mathrm{C}$.

Slow-neutron production as a probe of hadron formation in high-energy γ*A reactions

Deep Inelastic Scattering (DIS) experiments at the planned Electron-Ion Collider will be affected by details of the hadron formation inside the nuclear volume. Besides semi-inclusive particle production experiments decays of the target nucleus via emission of neutrons provide an additional opportunity to probe this domain. This paper reports on the hybrid dynamical+statistical calculations of low-energy neutron production in muon- and virtual photon-induced collisions with nuclei. We confirm the conclusion that the E665 data on neutron production in $\mu^-$ + Pb DIS at 470 GeV indicate a strong suppression of the final state interaction for hadrons with momenta above $\sim 1$ GeV/c. Ultraperipheral heavy-ion collisions at the Large Hadron Collider (LHC) and the Relativistic Heavy Ion Collider (RHIC) can be used to test this suppression. The calculations of the neutron multiplicity distributions and $p_t$-spectra in photon - nucleus collisions at the energies accessible at the LHC and RHIC are presented for several models of hadron formation. We argue that studies of neutron production in ultraperipheral heavy ion collisions open a new window on the small-$x$ dynamics and hadron component of the photon wave function.

Prompt neutron multiplicity distributions inferred from γ -ray and fission fragment energy measurements

We propose a novel method to extract the prompt neutron multiplicity distribution, $P(\nu)$, in fission reactions based on correlations between prompt neutrons, $\gamma$ rays, and fragment kinetic energy arising from energy conservation. In this approach, only event-by-event measurements of the total $\gamma$-ray energy released as a function of the total kinetic energy (TKE) of the fission fragments are performed, and no neutron detection is required. Using the $\texttt{CGMF}$ fission event generator, we illustrate the method and explore the accuracy of extracting the neutron multiplicity distribution when taking into account the energy resolution and calibration of the energy measurements. We find that a TKE resolution of under 2 MeV produces reasonably accurate results, independent of typical $\gamma$-ray energy measurement resolution.

Study of Very Forward Neutrons with the CMS Zero Degree Calorimeter

Forward neutrons are studied in proton-lead collisions at the CMS experiment at the CERN LHC. They provide information on the centrality and event plane of collisions and provide an opportunity to study nuclear breakup. At the CMS experiment they are detected by the Zero Degree Calorimeters (ZDCs) in the | η | &gt; 8.5 pseudorapidity range. The ZDCs are quartz fiber Cherenkov calorimeters using tungsten as absorber. Test beam data and events with a single spectator neutron are used for the calibration of these detectors. A Fourier-based method is used correct for the effect of multiple pPb collisions. The corrected ZDC energy distribution is used to calculate centrality percentiles and unfold the neutron multiplicity distribution.

Genetic algorithm for nuclear data evaluation applied to subcritical neutron multiplication inference benchmark experiments

An optimization algorithm has been developed for the first time for application to International Criticality Safety Benchmark Evaluation Project (ICSBEP) subcritical neutron multiplication inference benchmark experiments. The optimization algorithm is a genetic algorithm for nuclear data evaluation adjustments, specifically applied to subcritical benchmark measurements. The algorithm has been tested and yields improvement in (C-E)/E values of subcritical benchmark observables of interest. In this work, the genetic algorithm is applied to improvement of fission neutron multiplicity distribution parameters using several subcritical neutron multiplication inference benchmarks; specifically a series of reflected 4.5 kg α-phase spherical plutonium benchmarks. The algorithm results suggest changing the mean (ν¯) and standard deviation (σ) of the number of neutrons emitted by 240Pu in spontaneous fission from 2.1510 to 2.1460 and from 1.1510 to 1.1395, respectively. In addition, the standard deviation of the number of neutrons emitted by 239Pu in induced fission should remain unchanged at 1.1400. These changes are all within 1 standard deviation.

Sensitivity of neutron observables to the model input in simulations of 252Cf(sf)

Within the framework of $\mathtt{FREYA}$ event-by-event fission simulations, we study the sensitivity of various neutron observables to the input yield function $Y(A,Z,\mathrm{TKE})$ on which the fission event sampling is based. We first perform a statistical analysis of the available fission data in order to determine the distribution of possible yield functions $Y(A,Z,\mathrm{TKE})$ and we then construct a sample of 15 000 such yield functions. For each of these, $\mathtt{FREYA}$ is used to generate one million fission events, leading to a corresponding ensemble of fission observables, including the neutron multiplicity distribution and its factorial moments, the neutron energy spectrum, and the neutron-neutron angular correlation. This procedure allows us to study the sensitivity of those neutron observables to the uncertainty in the experimental data. Particular attention is given to the pronounced anticorrelation between the mean neutron multiplicity $\overline{\ensuremath{\nu}}$ and the mean total fragment kinetic energy $\overline{\mathrm{TKE}}$. Because the former observable is very well determined experimentally, it is possible to exploit that inherent anticorrelation to derive a significantly stricter tolerance on $\overline{\mathrm{TKE}}$. In addition, we study the sensitivity to the various $\mathtt{FREYA}$ parameters and we introduce a method for determining a $A$-dependent $x$ parameter, $x(A)$, based on the measured $A$-dependent neutron multiplicity, $\overline{\ensuremath{\nu}}(A)$.

Expansion of the surrogate method to measure the prompt fission neutron multiplicity for Pu241

Fission neutron multiplicity data are imperative for nuclear models that support criticality safety, nuclear nonproliferation, and stockpile stewardship. This work presents the first experimental measurement to determine the average neutron multiplicity ($\overline{\ensuremath{\nu}}$) and the neutron multiplicity distribution using a surrogate reaction. $^{241}\mathrm{Pu}$ has a short half-life of 14.3 yr. To circumvent experimental difficulties, inelastic scattering of 53.96-MeV $\ensuremath{\alpha}$ particles on $^{242}\mathrm{Pu}$ served as a surrogate for $^{241}\mathrm{Pu}(n,f)$. The present text reports and discusses the average neutron multiplicity, in addition to the neutron multiplicity moments and distribution for equivalent neutron energies up to 20 MeV. The $\overline{\ensuremath{\nu}}$ measured in this experiment agrees with previous measurements until 12 MeV, where discrepancies arise due to preequilibrium neutron emission.

In-depth evaluation of 252Cf absolute calibration by passive neutron correlation counting method

252Cf neutron sources are particularly convenient, and therefore widely used, to characterize and calibrate many kinds of neutron detectors for both scientific and technological applications. An emerging interest is the use of 252Cf to calibrate neutron correlation counters for the verification and assay of Pu-items as part of the international effort to safeguard nuclear materials. Passive neutron correlation counting (PNCC) methods, combined with knowledge of the fission neutron multiplicity distribution, can be used as an absolute technique to determine the neutron emission rate of 252Cf sources. This means that common equipment used by the safeguards community can, in principle, be used to self-certify, to high accuracy, the strength of physically small 252Cf sealed sources for use in calibration. This is the first step in using 252Cf in place of extensive Pu reference materials for experimental calibration by the safeguards community. The theoretical foundation is already clear but the present work presents the first systematic attempt at demonstrating the practical utility of the concept across a variety of typical instruments. We compare four emission rate estimators for four detector configurations on a common source previously certified by the MnSO4-bath technique. We find that the estimator based on the singles to doubles rate ratio provides consistent and precise results across all of the instruments and that these agree with the MnSO4-bath technique within combined uncertainties. This success suggests that the absolute PNCC method could become a technically defensible and commonly used, method capable of sub 1% accuracy for routine calibration work.