Calculated Fission Cross Sections Research Articles

Description of elastic scattering for 7Li-induced reactions on 1p-shell nuclei* *Supported by the National Natural Science Foundation of China (11405099, 11575291, 12065003), the Natural Science Foundation of Shanxi Province, China (202103021224309, 201901D111317). This work is also a part of IAEA Coordinated Research Projects (CRPs) on Recommended Input Parameter Library (RIPL) for Fission Cross Section Calculations (20464)

The experimental data of elastic scattering angular distributions for 9Be, 10B, 11B, 12C, 13C, 15N, and 16O targets from 4.5 to 131.8 MeV and 7Li target from 8.0 to 42.0 MeV are fitted to realize the global phenomenological optical potentials (GPOPs) for the 7Li-induced reactions on 1p-shell nuclei. Thus, the 7Li elastic scattering from the 1p-shell nuclei can be systematically described using the established GPOPs. The elastic scattering angular distributions are also reanalyzed using a microscopic method within the framework of the new version of double folding São Paulo potential (SPP2). To better describe the elastic scattering at backward angles, the contribution of elastic transfer is further estimated by the distorted wave Born approximation (DWBA) method. Based on the obtained GPOPs, the inelastic scattering angular distributions are also obtained through the coupled channels (CC) method for the different excited states.

Implementation of LSD Fission Barrier in Fission Cross Section Calculations

In this paper, the fission cross-sections of Th-232(n, f) and U-238(n, f) have been calculated using the fission barrier parameter obtained from Lublin-Strassbourg Drop Model (LSD) in the statistical model framework. This model has been derived from the modern liquid drop (NLD) by adding a first-order curvature term that depends on the deformation parameter. This term has resulted from the implementation of Leptodermous expansion of nuclear energy. The deformation function involved in LSD formulation is obtained from Funny Hills nuclear shape parameterization. The obtained results would be compared with another result calculated using ETFSI (Extended Thomas Fermi and Strutinsky Integral) method and experimental fission cross-section extracted from ENDF data.

Description of elastic scattering induced by the unstable nuclei 9,10,11,13,14C * *Supported by the National Natural Science Foundation of China (11405099, 11575291, 12065003), Scientific and Technological Innovation Programs of Higher Education Institutions (STIP) in Shanxi of China (2019L0743) and Science Foundation for General in Shanxi of China (201901D111317). This work is also supported by the Open Project of Guangxi Key

The elastic-scattering angular distributions and total reaction cross sections of projectiles were predicted using the obtained and global optical model potentials, respectively. The predictions were analyzed in detail by comparison with the available experimental data. The results indicate that the and global optical model potentials provide a satisfactory description of the elastic scattering data for the reactions induced by the . For the neutron-rich carbon isotope , the elastic scattering can be well described by changing the real part radius parameter of the global optical model potential. Possible physical explanations for the observed differences are further discussed.

Global optical model potential describing 12C-nucleus elastic scattering * *Supported by China National Natural Science Foundation (11405099, 11575291, 12065003), by Scientific and Technological Innovation Programs of Higher Education Institutions (STIP) in Shanxi of China (2019L0743) and by Science Foundation for General in Shanxi of China (201901D111317). This work is also a part of IAEA Coordinated Research Projects (CRPs) on Recommended

We construct a new global optical model potential to describe the elastic scattering of 12C. The experimental data of elastic-scattering angular distributions and total reaction cross sections for targets from 24Mg to 209Bi are considered below 200 MeV within the framework of the optical model. The results calculated using the derived global optical potential are then compared with the existing experimental data. The reliability of the global optical potential is further tested by predicting the elastic scattering data out of the mass and energy ranges, within which the global potential parameters are determined, and reasonable results are also obtained.

Applicability of 9Be global optical potential to description of 8,10,11B elastic scattering * * Supported by the National Natural Science Foundation of China (11405099 and 11575291). This work is also a part of IAEA Coordinated Research Projects (CRPs) on Recommended Input Parameter Library (RIPL) for Fission Cross Section Calculations (20464)

We achieved a set of 9Be global phenomenological optical model potentials by fitting a large experimental dataset of the elastic scattering observable for target mass numbers from 24 to 209. The obtained 9Be global optical model potential was applied to predict elastic-scattering angular distributions and total reaction cross-sections of 8,10,11B projectiles. The predictions are made by performing a detailed analysis comparing with the available experimental data. Furthermore, these elastic scattering observables are also predicted for some lighter targets outside of the given mass number range, and reasonable results are obtained. Possible physical explanations for the observed differences are also discussed.

Applicability of 9Be global optical potential to reactions of 7,10,11,12Be * * Supported by the National Natural Science Foundation of China (11405099, 11575291), this work is also a part of IAEA Coordinated Research Projects (CRPs) on Recommended Input Parameter Library (RIPL) for Fission Cross Section Calculations (20464)

Elastic scattering angular distributions and total reaction cross-sections of 7,10,11,12Be projectiles are predicted by the systematic 9Be global phenomenological optical model potential for target mass numbers ranging from 24 to 209. These predictions provide a detailed analysis by their comparison with the available experimental data. Furthermore, these elastic scattering observables are also predicted for some targets out of the mass number range. The results are in reasonable agreement with the existing experimental data, and they are presented in this study.

Double differential cross sections of light charged particle production for the n+238U reaction**Supported by National Natural Science Foundation of China-NSAF (U1630122), IAEA Coordinated Research Projects (CRPs) on Recommended Input Parameter Library (RIPL) for Fission Cross Section Calculations (20464) and Science Challenge Project (TZ2018005)

Production of light complex particles from the n+238U reaction is analyzed with the exciton model including the improved Iwamoto-Harada pickup mechanism for the preequilibrium process. It is allowed that some of the nucleons forming the complex ejectile come from levels below the Fermi energy, and the intrinsic structure of the emitted particle is taken into account. The equilibrium-state emissions are also considered by using Hauser-Feshbach theory with the width fluctuation correction and the evaporation model. Moreover, all cross sections, angular distributions, energy spectra and double differential cross sections of neutron, proton, deuteron, triton and alpha emissions for the n+238U reaction are consistently calculated and analyzed with nuclear theoretical models in the energy range En ⩽ 150 MeV. ENDF-formatted nuclear data including information about the production of light charged particles are obtained.

MCNP6 updated proton-induced fission cross section calculations at intermediate energies

MCNP6 has been Validated and Verified against intermediate- and high-energy fission cross-section experimental data. Recent improvements contained in CEM03.03F and MCNP6-F to consider precompound emission of heavy clusters up to 28 Mg has necessitated a re-calculation of fission cross sections. With our re-calculation, we find that CEM03.03F, which is used in MCNP6-F, predicts fission cross sections in good agreement with available experimental data for reactions induced by protons on both subactinide and actinide nuclei at incident energies from several tens of MeV to several GeV.

Properties of fission fragments forZ=112−116superheavy nuclei

The dynamical cluster decay model (DCM) is applied to understand the dynamics of $^{48}\mathrm{Ca}+^{238}\mathrm{U},^{244}\mathrm{Pu},^{248}\mathrm{Cm}$ reactions at comparable excitation energies across the barrier. To understand the capture stage of $^{286}112^{*},\phantom{\rule{0.16em}{0ex}}^{292}114^{*}$, and $^{296}116^{*}$ nuclei, the compound nucleus formation probability is calculated. The indication of ${P}_{CN}l1$ in the DCM framework demonstrates the fact that some competing process such as quasifission may occur at the capture stage of the $^{48}\mathrm{Ca}$ induced reactions. To understand this further, the comparative decay analysis of $^{286}112^{*},\phantom{\rule{0.16em}{0ex}}^{292}114^{*}$ and $^{296}116^{*}$, nuclei is carried out using ${\ensuremath{\beta}}_{2i}$ deformations within hot optimum orientation criteria, and the calculated fission cross sections find nice agreement with available data. The fission mass distribution shows a double humped structure where a symmetric peak observed around the Sn region appears to find its genesis in a symmetric quasifission component. On the other hand, the emergence of peaks around Pb in the decay of $Z=112$, 114, and 116 nuclei signify the possible presence of asymmetric quasifission. Higher and broader asymmetric quasifission peaks are observed for $^{296}116^{*}$ and $^{292}114^{*}$ nuclei as compared to $^{286}112^{*}$ nucleus. Beside this, the total kinetic energy (TKE) distribution of the decay fragments is also explored by using different proximity potentials, such as Prox-77, Prox-88, and Prox-00. Prox-88 seems to perform better and the calculated TKE values find relatively better comparison at lower angular momentum states. The possible role of different radii of the decaying nuclei is also exercised to understand the $\overline{\mathrm{TKE}}$ dynamics of $^{48}\mathrm{Ca}+^{238}\mathrm{U},^{244}\mathrm{Pu},^{248}\mathrm{Cm}$ reactions.

Extended optical model for fission

A comprehensive formalism to calculate fission cross sections based on the extension of the optical model for fission is presented. It can be used for description of nuclear reactions on actinides featuring multi-humped fission barriers with partial absorption in the wells and direct transmission through discrete and continuum fission channels. The formalism describes the gross fluctuations observed in the fission probability due to vibrational resonances, and can be easily implemented in existing statistical reaction model codes. The extended optical model for fission is applied for neutron induced fission cross-section calculations on $^{234,235,238}\mathrm{U}$ and $^{239}\mathrm{Pu}$ targets. A triple-humped fission barrier is used for $^{234,235}\mathrm{U}(n,f)$, while a double-humped fission barrier is used for $^{238}\mathrm{U}(n,f)$ and $^{239}\mathrm{Pu}(n,f)$ reactions as predicted by theoretical barrier calculations. The impact of partial damping of class-II/III states, and of direct transmission through discrete and continuum fission channels, is shown to be critical for a proper description of the measured fission cross sections for $^{234,235,238}\mathrm{U}(n,f)$ reactions. The $^{239}\mathrm{Pu}(n,f)$ reaction can be calculated in the complete damping approximation. Calculated cross sections for $^{235,238}\mathrm{U}(n,f)$ and $^{239}\mathrm{Pu}(n,f)$ reactions agree within 3% with the corresponding cross sections derived within the Neutron Standards least-squares fit of available experimental data. The extended optical model for fission can be used for both theoretical fission studies and nuclear data evaluation.

Fission decay analysis of n-induced reaction using collective clusterization approach

The Dynamical Cluster-decay Model (DCM) is employed for the first time to explore the decay patterns of transactinide Np⁎240 nucleus, formed in n+Np239 reaction. In reference to a recent experimental data, the fission cross-sections are calculated over a wide range of incident energy varying from Elab=0.62–18.75 MeV. For the n-induced reaction, the role of deformations is analyzed by studying the decay paths for spherical as well as the quadrupole (β2i) deformed fragmentation. In addition to this, the effect of orientation degree of freedom is investigated by considering equatorial (compact) and polar (non-compact) configurations. Also, the influence of moment of inertia and hence the centrifugal potential is explored by calculating the cross-sections using sticking (IS) and non-sticking (INS) limits of interaction. Finally, the decay profile of Np⁎240 nucleus is compared with that of U⁎238 formed under similar reaction conditions. For both the nuclei, the DCM calculated fission cross sections show an excellent agreement with the reported experimental data.

Fission dynamics of240Cf*formed in34,36S induced reactions

We have studied the entrance channel effects in the decay of Compound nucleus 240 Cf * formed in 34 S+ 206 Pb and 36 S+ 204 Pb reactions by using energy density dependent nuclear proximity potential in the framework of dynamical cluster-decay model (DCM). At different excitation energies, the fragmentation potential and preformation probability of decaying fragments are almost identical for both the entrance channels, which seem to suggest that decay is independent of its formation and entrance channel excitation energy. It is also observed that, with inclusion of deformation effects upto quadrupole within the optimum orientation approach, the fragmentation path governing potential energy surfaces gets modified significantly. Beside this, the fission mass distribution of Cf* isotopes is also investigated. The calculated fission cross-sections using SIII force for both the channels find nice agreement with the available experimental data for deformed choice of fragments, except at higher energies. In addition to this, the comparative analysis with Blocki based nuclear attraction is also worked out. It is observed that Blocki proximity potential accounts well for the CN decay at all energies whereas the use of EDF based nuclear potential suggests the presence of some non-compound nucleus process (such as quasi-fission (qf)) at higher energies.

MCNP6 Fission Cross Section Calculations at Intermediate and High Energies

MCNP6 has been Validated and Verified (V&V) against intermediate- and high-energy fission-cross-section experimental data. An error in the calculation of fission cross sections of 181Ta and a few nearby target nuclei by the CEM03.03 event generator in MCNP6 and al “bug” in the calculation of fission cross sections with the GENXS option of MCNP6 while using the LAQGSM03.03 event generator were detected during our V&V work. After fixing both problems, we find that MCNP6 using CEM03.03 and LAQGSM03.03 calculates fission cross sections in good agreement with available experimental data for reactions induced by nucleons, pions, and photons on both subactinide and actinide nuclei at incident energies from several tens of MeV to about 1 TeV.

DeterminingPa234(n,f) cross sections using the surrogate method

The fission decay probabilities of the $^{235}\mathrm{Pa}$ and $^{236}\mathrm{U}$ compound nuclei produced in a single experiment in $^{232}\mathrm{Th}$($^{7}\mathrm{Li}$, $\ensuremath{\alpha}f$)$^{235}\mathrm{Pa}$ and $^{232}\mathrm{Th}$($^{7}\mathrm{Li}$, $tf$)$^{236}\mathrm{U}$ transfer induced fission reaction channels, have been measured at ${E}_{\mathrm{lab}}=39.5$ MeV in the excitation energy range of 14--20 MeV. The $^{234}\mathrm{Pa}$(n, f) cross sections are then deduced from the measured fission decay probability ratios of $^{235}\mathrm{Pa}$ and $^{236}\mathrm{U}$ compound systems in the equivalent neutron energy range of 8--14 MeV within the framework of the hybrid surrogate ratio method, considering the well-measured $^{235}\mathrm{U}$(n, f) cross sections as the reference. The experimental data on $^{234}\mathrm{Pa}$(n, f) cross sections have been compared with the calculated fission cross sections using empire-3.1 code with the fission barrier height values obtained from barrier formula (BF) as well as ripl-3 [24]. The present experimental results are found to be in very good agreement with the empire-3.1 predictions for the fission barrier heights predicted by the BF.

Cross sections and barriers for nuclear fission induced by high-energy nucleons

The cross sections for the fission of 232Th, 235,238U, 237Np, and 239Pu target nuclei that was induced by 20- to 1000-MeV neutrons and protons were calculated. The respective calculations were based on the multiconfiguration-fission (MCFx) model, which was used to describe three basic stages of the interaction of high-energy nucleons with nuclei: direct processes (intranuclear cascade), equilibration of the emerging compound system, and the decay of the compound nucleus (statistical model). Fission barriers were calculated within the microscopic approach for isotopic chains formed by 15 to 20 nuclei of the required elements. The calculated fission cross sections were compared with available experimental data. It was shown that the input data set and the theoretical model used made it possible to predict satisfactorily cross section for nuclear fission induced by 20- to 1000-MeV nucleons.

Towards Predictions of Fission Probabilities for Astrophysics Applications

Abstract In almost all the evaluations of the neutron-induced fission cross section for nuclei involved in nuclear applications, a double- humped fission barrier described by two independent inverted parabolas is considered. In addition, the continuum transition states are described by a simple Fermi-gas type nuclear level density expression for which the formulation as well as the parametrization remain highly uncertain. For these reasons, these approaches can be considered as having a rather poor predictive power and are not recommended for applications requiring a proper description of fission for nuclei far from stability, such as nuclear astrophysics. Hartree-Fock-Bolgolyubov (HFB) calculation are now available and can provide all the nuclear ingredients required to describe the fission path from the equilibrium deformation up to the nuclear scission point. The aim of this contribution is to apply the basic features of the optical model for fission, using the full microscopic information obtained from HFB models to calculate neutron- induced fission cross sections on selected actinide nuclei. This approach includes not only the details of the energy surface along the fission path, but also the estimate of the nuclear level density derived within the combinatorial approach on the basis of the same HFB single-particle properties, in particular at the fission saddle points. The sensitivity of the calculated fission cross sections to different model approximations is illustrated and the predictive power of such a microscopic approach tested. It is also shown that the various inputs can be tuned to reproduce at best experimental data in one unique coherent framework, so that in a close future it should become possible to make, on the basis of such models, accurate fission cross-section calculations and the corresponding estimates for nuclei, energy ranges or reaction channels for which no data exist. Finally, the same model is applied to the calculation of the fission probabilities, including β-delayed fission, spontaneous fission and neutron-induced fission, for all nuclei potentially produced by the r-process nucleosynthesis. Nucleosynthesis calculations resulting from the decompression of neutron star matter are performed and the sensitivity of the abundance calculation with respect to nuclear fission uncertainties (including fission probabilities and fission fragment distributions) is studied.

Decay of the213,217Fr*systems formed in19F + 194,198Pt reactions atEc.m.=80–94 MeV

The dynamical cluster-decay model (DCM) is used to study the odd-mass nuclear systems ${}^{213}$Fr${}^{*}$ (with $N=126$) and ${}^{217}$Fr${}^{*}$ (with $N=130$) formed in ${}^{19}$F + ${}^{194,198}$Pt reactions. The measured anomaly in fission anisotropy for ${}^{213}$Fr${}^{*}$ in this reaction is said to be due to either the possible role of the magic $N=126$ shell of the compound nucleus (CN) or the presence of a noncompound nucleus component, such as quasifission, in the fission cross section. Our calculations are made within the DCM for the fragments having quadrupole (${\ensuremath{\beta}}_{2}$) deformations with orientations of compact, hot configurations, compared with spherical as well as ${\ensuremath{\beta}}_{2}$--${\ensuremath{\beta}}_{4}$ deformed considerations. For quadrupole deformed fragments (with ``optimal'' orientations), the calculated fission cross-sections (as well as the evaporation residue cross-sections) match the data nearly exactly, without invoking a significant contribution from quasifission. The calculated fission mass distribution for the two systems is quite similar for either of the spherical, ${\ensuremath{\beta}}_{2}$-alone deformed, and ${\ensuremath{\beta}}_{2}$--${\ensuremath{\beta}}_{4}$ deformed choices of fragments. A small hump or shoulder is seen in fragment preformation yields for the deformed case (${\ensuremath{\beta}}_{2}$ or ${\ensuremath{\beta}}_{2}$--${\ensuremath{\beta}}_{4}$) in both the systems due to a deformed closed shell around ${Z}_{2}=36$ and a spherical magic shell around ${Z}_{1}=50$, which for ${}^{213}$Fr${}^{*}$ ($N=126$) decay is somewhat more pronounced as compared to ${}^{217}$Fr${}^{*}$ ($N=130$). Note that the magic shell of the CN proton/neutron number plays no role in DCM.

Cascade-exciton model analysis of level density parameter dependence in proton induced fission cross sections of some sub-actinide nuclei

Fission cross sections strongly depend on the ratio of the level density parameter in fission to neutron emission, af/an. In this work, a cascade-exciton model implemented in the code CEM95 has been used to observe this effect for proton induced fission cross sections of tungsten, lead and bismuth. The method was employed using different level density parameter ratios for each fission cross section calculation. The calculated fission cross sections are compared with the available experimental data in the literature. It has been observed that a change of the ratio of the level density parameter, af/an, is necessary with the incident energy of the proton, to best estimate the fission cross sections in CEM95.

Fission Cross section Calculations of Actinides with EMPIRE Code

Fission Cross section Calculations of Actinides with EMPIRE Code

Towards Improved Evaluation of Neutron-Induced Fission Cross Section

Mean-field calculations can nowadays provide all the nuclear ingredients required to describe the fission path from the equilibrium deformation up to the nuclear scission point. The information obtained from microscopic mean-field models has been included in reaction codes to improve the predictions of neutron-induced fission cross section. The nuclear inputs concern not only the details of the energy surface along the fission path, but also the coherent estimate of the nuclear level density derived within the combinatorial approach on the basis of the same single-particle properties, in particular at the fission saddle points. The predictive power of such a microscopic approach is tested. It is also shown that the various inputs can be tuned to reproduce at best experimental data in one unique coherent framework, so that it is now possible to make reliable and accurate fission cross-section calculations on the basis of microscopic models, but also to use such approaches to estimate the corresponding modeling uncertainties for nuclei, energy ranges or reaction channels for which no data exist.