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Background: Spontaneous fission events emit prompt neutrons correlated with one another in emission angle and energy. Purpose: We explore the relationship in energy and angle between correlated prompt neutrons emitted from 252Cf spontaneous fission. Methods: Measurements with the Chi-Nu array provide experimental data for coincident neutrons tagged with a fission chamber signal with 10 degree angular resolution and 1 ns timing resolution for time-of-flight energy calculations. The experimental results are compared to simulations produced by the fission event generators CGMF, FREYA, and MCNPX-POLIMI IPOL(1)=1. Results: We find that the measurements and the simulations all exhibit anisotropic neutron emission, though differences exist between fission event generators. Conclusions: This work shows that the dependence of detected neutron energy on the energy of a neutron detected in coincidence, although weak, is non-negligible, indicating that there may be correlations in energy between two neutrons emitted in the same fission event.

In this work we propose to validate the predictive capabilities of one-dimensional (1D) blood flow models with full three-dimensional (3D) models in the context of patient-specific coronary hemodynamics in hyperemic conditions. Such conditions mimic the state of coronary circulation during the acquisition of the Fractional Flow Reserve (FFR) index. Demonstrating that 1D models accurately reproduce FFR estimates obtained with 3D models has implications in the approach to computationally estimate FFR. To this end, a sample of 20 patients was employed from which 29 3D geometries of arterial trees were constructed, 9 obtained from coronary computed tomography angiography (CCTA) and 20 from intra-vascular ultrasound (IVUS). For each 3D arterial model, a 1D counterpart was generated. The same outflow and inlet pressure boundary conditions were applied to both (3D and 1D) models. In the 1D setting, pressure losses at stenoses and bifurcations were accounted for through specific lumped models. Comparisons between 1D models ($\text{FFR}_{\text{1D}}$) and 3D models ($\text{FFR}_{\text{3D}}$) were performed in terms of predicted $\text{FFR}$ value. Compared to $\text{FFR}_{\text{3D}}$, $\text{FFR}_{\text{1D}}$ resulted with a difference of 0.00$\pm$0.03 and overall predictive capability AUC, Acc, Spe, Sen, PPV and NPV of 0.97, 0.98, 0.90, 0.99, 0.82, and 0.99, with an FFR threshold of 0.8. We conclude that inexpensive $\text{FFR}_{\text{1D}}$ simulations can be reliably used as a surrogate of demanding $\text{FFR}_{\text{3D}}$ computations., Comment: 11 pages, 2 figures, 2 tables, submited to Scientific Reports

We have developed a Hauser-Feshbach fission fragment decay model, HF$^3$D, which can be applied to the statistical decay of more than 500 primary fission fragment pairs (1,000 nuclides) produced by the neutron induced fission of $^{235}$U. The fission fragment yield $Y(A)$ and the total kinetic energy TKE are model inputs, and we estimate them from available experimental data for the $^{235}$U(n$\rm_{th}$,f) system. The model parameters in the statistical decay calculation are adjusted to reproduce some fission observables, such as the neutron emission multiplicity $\overline{\nu}$, its distribution $P(\nu)$, and the mass dependence $\overline\nu(A)$. The calculated fission product yield and isomeric ratio are compared with experimental data. We show that the calculated independent fission product yield $Y_I(A)$ at the thermal energy reproduces the experimental data well, while the calculated isomeric ratios tend to be lower than the Madland-England model prediction. The model is extended to higher incident neutron energies up to the second chance fission threshold. We demonstrate for the first time that most of the isomeric ratios stay constant, although the production of isomeric state itself changes as the incident energy increases.

The $(n,\gamma f)$ process is reviewed in light of modern nuclear reaction calculations in both slow and fast neutron-induced fission reactions on $^{235}$U and $^{239}$Pu. Observed fluctuations of the average prompt fission neutron multiplicity and average total $\gamma$-ray energy below 100 eV incident neutron energy are interpreted in this framework. The surprisingly large contribution of the M1 transitions to the pre-fission $\gamma$-ray spectrum of $^{239}$Pu is explained by the dominant fission probabilities of 0$^+$ and $2^+$ transition states, which can only be accessed from compound nucleus states formed by the interaction of $s$-wave neutrons with the target nucleus in its ground state, and decaying through M1 transitions. The impact of an additional low-lying M1 scissors mode in the photon strength function is analyzed. We review experimental evidence for fission fragment mass and kinetic energy fluctuations in the resonance region and their importance in the interpretation of experimental data on prompt neutron data in this region. Finally, calculations are extended to the fast energy range where $(n,\gamma f)$ corrections can account for up to 3\% of the total fission cross section and about 20\% of the capture cross section., Comment: 14 pages, 19 figures

The Hauser-Feshbach statistical model is applied to the de-excitation of primary fission fragments using input mass yields calculated with macroscopic-microscopic models of the potential energy surface. We test the sensitivity of the prompt fission observables to the input mass yields for two important reactions, $^{235}$U$(n_\mathrm{th},f)$ and $^{239}$Pu$(n_\mathrm{th},f)$, for which good experimental data exist. General traits of the mass yields, such as the location of the peaks and their widths, can impact both the prompt neutron and $\gamma$-ray multiplicities, as well as their spectra. Specifically, we use several mass yields to determine a linear correlation between the calculated prompt neutron multiplicity $\bar{\nu}$ and the average heavy-fragment mass $\langle A_h\rangle$ of the input mass yields $\partial\bar{\nu}/\partial\langle A_h\rangle = \pm 0.1\,n/f/\mathrm{u}$. The mass peak width influences the correlation between the total kinetic energy of the fission fragments and the total number of prompt neutrons emitted $\bar{\nu}_T(\mathrm{TKE})$. Typical biases on prompt particle observables from using calculated mass yields instead of experimental ones are: $\delta \bar{\nu} = 4\%$ for the average prompt neutron multiplicity, $\delta \bar{M}_\gamma = 1\%$ for the average prompt $\gamma$-ray multiplicity, $\delta \bar{\epsilon}_n^\mathrm{LAB} = 1\%$ for the average outgoing neutron energy, $\delta \bar{\epsilon}_\gamma = 1\%$ for the average $\gamma$-ray energy, and $\delta \langle\mathrm{TKE}\rangle = 0.4\%$ for the average total kinetic energy of the fission fragments., Comment: 12 pages, 8 figures, 2 tables

Detailed information on the fission process can be inferred from the observation, modeling and theoretical understanding of prompt fission neutron and $\gamma$-ray~observables. Beyond simple average quantities, the study of distributions and correlations in prompt data, e.g., multiplicity-dependent neutron and \gray~spectra, angular distributions of the emitted particles, $n$-$n$, $n$-$\gamma$, and $\gamma$-$\gamma$~correlations, can place stringent constraints on fission models and parameters that would otherwise be free to be tuned separately to represent individual fission observables. The FREYA~and CGMF~codes have been developed to follow the sequential emissions of prompt neutrons and $\gamma$-rays~from the initial excited fission fragments produced right after scission. Both codes implement Monte Carlo techniques to sample initial fission fragment configurations in mass, charge and kinetic energy and sample probabilities of neutron and $\gamma$~emission at each stage of the decay. This approach naturally leads to using simple but powerful statistical techniques to infer distributions and correlations among many observables and model parameters. The comparison of model calculations with experimental data provides a rich arena for testing various nuclear physics models such as those related to the nuclear structure and level densities of neutron-rich nuclei, the $\gamma$-ray~strength functions of dipole and quadrupole transitions, the mechanism for dividing the excitation energy between the two nascent fragments near scission, and the mechanisms behind the production of angular momentum in the fragments, etc. Beyond the obvious interest from a fundamental physics point of view, such studies are also important for addressing data needs in various nuclear applications. (See text for full abstract.), Comment: 39 pages, 57 figure files, published in Eur. Phys. J. A, reference added this version

The emission of prompt fission $\gamma$ rays within a few nanoseconds to a few microseconds following the scission point is studied in the Hauser-Feshbach formalism applied to the deexcitation of primary excited fission fragments. Neutron and $\gamma$-ray evaporations from fully accelerated fission fragments are calculated in competition at each stage of the decay, and the role of isomers in the fission products, before $\beta$-decay, is analyzed. The time evolution of the average total $\gamma$-ray energy, average total $\gamma$-ray multiplicity, and fragment-specific $\gamma$-ray spectra, is presented in the case of neutron-induced fission reactions of $^{235}$U and $^{239}$Pu, as well as spontaneous fission of $^{252}$Cf. The production of specific isomeric states is calculated and compared to available experimental data. About 7% of all prompt fission $\gamma$ rays are predicted to be emitted between 10 nsec and 5 $\mu$sec following fission, in the case of $^{235}$U and $^{239}$Pu $(n_{\rm th},f)$ reactions, and up to 3% in the case of $^{252}$Cf spontaneous fission. The cumulative average total $\gamma$-ray energy increases by 2 to 5% in the same time interval. Finally, those results are shown to be robust against significant changes in the model input parameters., Comment: 11 pages, 14 figures

Using a random-matrix approach and Monte-Carlo simulations, we generate scattering matrices and cross sections for compound-nucleus reactions. In the absence of direct reactions we compare the average cross sections with the analytic solution given by the Gaussian Orthogonal Ensemble (GOE) triple integral, and with predictions of statistical approaches such as the ones due to Moldauer, to Hofmann, Richert, Tepel, and Weidenm\"{u}ller, and to Kawai, Kerman, and McVoy. We find perfect agreement with the GOE triple integral and display the limits of validity of the latter approaches. We establish a criterion for the width of the energy-averaging interval such that the relative difference between the ensemble-averaged and the energy-averaged scattering matrices lies below a given bound. Direct reactions are simulated in terms of an energy-independent background matrix. In that case, cross sections averaged over the ensemble of Monte-Carlo simulations fully agree with results from the Engelbrecht-Weidenm\"{u}ller transformation. The limits of other approximate approaches are displayed.

We suggest a small set of fission observables to be used as test cases for validation of theoretical calculations. The purpose is to provide common data to facilitate the comparison of different fission theories and models. The proposed observables are chosen from fission barriers, spontaneous fission lifetimes, fission yield characteristics, and fission isomer excitation energies.

At a certain finite neck radius during the descent of a fissioning nucleus from the saddle to the scission point, the attractive nuclear forces can no more withstand the repulsive Coulomb forces producing the neck rupture and the sudden absorption of the neck stubs by the fragments. At that moment, the neutrons, although still characterized by their pre-scission wave functions, find themselves in the newly created potential of their interaction with the separated fragments. Their wave functions become wave packets with components in the continuum. The probability to populate such states gives evidently the emission probability of neutrons at scission. In this way, we have studied scission neutrons for the fissioning nucleus $^{236}$U, using two-dimensional realistic nuclear shapes. Both the emission probability and the distribution of the emission points relative to the fission fragments strongly depend on the quantum numbers of the pre-scission state from which the neutron is emitted. In particular it was found that states with $\Omega \pi$ = 1/2+ dominate the emission. Depending on the assumed pre- and post-scission configurations and on the emission-barrier height, 30 to 50% of the total scission neutrons are emitted from 1/2+ states. Their emission points are concentrated in the region between the newly separated fragments. The upper limit for the total number of neutrons per scission event is predicted to lie between 0.16 and 1.73 (depending on the computational assumptions)., Comment: 31 pages, 16 figures, 2 tables

A dynamical study of the decay of a metastable state by quantum tunneling through an anisotropic, non separable, two-dimensional potential barrier is performed by the numerical solution of the time-dependent Schrodinger equation. Initial quasi- stationary proton states are chosen in the framework of a deformed Woods-Saxon single-particle model. The decay of two sets of states corresponding to true and quasi levels-crossing is studied and the evolution of their decay properties as a function of nuclear deformation is calculated around the crossing point. The results show that the investigation of the proton decay from metastable states in deformed nuclei can unambiguously distinguish between the two types of crossing and determine the structure of the nuclear states involved., Comment: 15 pages, 9 figures, submitted to Phys. Rev. C

Based on a single particle model which describes the time evolution of the wave function during tunneling across a one dimensional potential barrier we study the proton decay of $^{208}$Pb from excited states with non-vanishing angular momentum $\ell$. Several quantities of interest in this process like the decay rate $\lambda$, the period of oscillation $T_{osc}$, the transient time $t_{tr}$, the tunneling time $t_{tun}$ and the average value of the proton packet position $ r_{av} $ are computed and compared with the WKB results., Comment: 12 pages, 4 figures