Fission Theory Research Articles

Comparing the Parameters of T-odd Asymmetries in Cross Sections of the Ternary Fission of Nuclei by Cold Polarized Neutrons with the Emission of Pre-Scission and Evaporation Third Particles

A comparison is made of two theoretical approaches to describing the coefficients of T-odd asymmetries in the angular distributions of prompt γ-quanta and neutrons evaporated from thermalized fragments of the binary fission of non-oriented target nuclei by cold polarized neutrons, and in angular distributions of pre-scission α particles emitted in the same ternary nuclear fission: the classical approach, which is based on trajectory calculations, and the quantum approach, which is based on quantum fission theory. It is shown that the coefficients for all of the considered nuclei are of a quantum nature and vanish in the classical approach when there is no interference from the fission amplitudes of the different neutron resonances of a compound nucleus. The advantages of the quantum approach versus the classical one are demonstrated.

Diabatic paths through the scission point in nuclear fission

An outstanding problem in the theory of nuclear fission is to understand the Hamiltonian dynamics at the scission point. In this work the fissioning nucleus is modeled in self-consistent mean-field theory as a set of Generator Coordinate (GCM) configurations passing through the scission point. In contrast to previous methods, the configurations are constructed in the Hartree-Fock approximation with axially symmetric mean fields and using the K-partition numbers as additional constraints. The goal of this work is to find paths through the scission point where the overlaps between neighboring configurations are large. A measure of distance along the path is proposed that is insensitive to the division of the path into short segments. For most of the tested K-partitions two shape degrees of freedom are adequate to define smooth paths. However, some of the configurations and candidate paths have sticking points where there are substantial changes in the many-body wave function, especially if quasiparticle excitations are present. The excitation energy deposited in fission fragments arising from thermal excitations in the pre-scission configurations is determined by tracking orbital occupation numbers along the scission paths. This allows us to assess the validity of the well-known scission-point statistical model, in which the scission process is assumed to be fully equilibrated up to the separated fission fragments. The nucleus 236U is taken as a representative example in the calculations.

Vibronic fingerprint of singlet fission in hexacene

Singlet fission has the great potential to overcome the Shockley–Queisser thermodynamic limit and thus promotes solar power conversion efficiency. However, the current limited understandings of detailed singlet fission mechanisms hinder a further improved design of versatile singlet fission materials. In the present study, we combined ultrafast transient infrared spectroscopy with ab initio calculations to elucidate the roles played by the vibrational normal modes in the process of singlet fission for hexacene. Our transient infrared experiments revealed three groups of vibrational modes that are prominent in vibronic coupling upon photoexcitation. Through our computational study, those normal modes with notable Franck-Condon shifts have been classified as ring-twisting modes near 1300.0 cm−1, ring-stretching modes near 1600.0 cm−1, and ring-scissoring modes near 1700.0 cm−1. Experimentally, a ring-stretching mode near 1620.0 cm−1 exhibits a significant blue-shift of 4.0 cm−1 during singlet fission, which reaction rate turns out to be 0.59 ± 0.07 ps. More interestingly, the blue-shifted mode was also identified by our functional mode singlet fission theory as the primary driving mode for singlet fission, suggesting the importance of vibronic coupling when a correlated triplet pair of hexacene is directly converted from its first excited state singlet exciton. Our findings indicate that the ultrafast transient infrared spectroscopy, in conjunction with the nonadiabatic transition theory, is a powerful tool to probe the vibronic fingerprint of singlet fission.

Fission fragment angular anisotropy in neutron-induced fission of U235 measured with a time projection chamber

Fission fragment angular distributions can provide an important constraint on fission theory, improving predictive fission codes, and are a prerequisite for a precise ratio cross section measurement. Available anisotropy data is sparse, especially at neutron energies above 5 MeV. For the first time, a three-dimensional tracking detector is employed to study fragment emission angles and provide a direct measurement of angular anisotropy. The Neutron Induced Fission Fragment Tracking Experiment (NIFFTE) collaboration has deployed the fission time projection chamber (fissionTPC) to measure nuclear data with unprecedented precision. The fission fragment anisotropy of $^{235}$U has been measured over a wide range of incident neutron energies from 180 keV to 200 MeV; a careful study of the systematic uncertainties complement the data.

Relation of Experimental Features of P-Even, T-Odd Asymmetries in Ternary Nuclear Fission Induced by Cold Polarized Neutrons to Triple and Quintuple Scalar Correlations

In employing the concept of the isotropy of space, the coefficients D of P-even, T-odd asymmetry in the angular distributions of prescission alpha particles emitted as third particles in the ternary fission of nonoriented target nuclei that is induced by polarized cold neutrons are expressed in the lowest orders of perturbation theory in the neutron polarization vector in terms of two P-even scalar coefficients D3 and D5 associated with, respectively, triple and quintuple correlations depending on the unit vectors kα, kLF, and σn, which determine the features of the coefficients being studied. On the basis of the above representation, the experimental values of the coefficients D3 and D5 are determined by using the experimental values of D and the angular distributions of alpha particles emitted in the analogous reaction induced by unpolarized neutrons. The resulting coefficients D3 and D5 are compared with the analogous coefficients found by means of the classical method of trajectory calculations and by means of quantum-mechanical fission theory relying on the concept that it is the rotational mechanism that is responsible for the appearance of the asymmetries being studied. It turns out that the classical method, which disregards the interference between fission amplitudes for different S-wave neutron resonances, leads to an irremovable contradiction between the calculated coefficient D3 and the analogous experimental coefficient for the 233U target nucleus. In the case of employing the quantum-mechanical approach, it is concluded that three-body calculations of the Coriolis interaction—perturbed amplitude of the angular distributions of alpha particles moving in the Coulomb fields of fission fragments are required for the 233U target nucleus.

Decisive Role of Interference Effects in Describing T-Odd Asymmetries in Reactions Induced by Polarized Cold Neutrons

A detailed analysis of T-odd asymmetries in the reactions of true ternary fission of nuclei that involves the emission of prescission alpha particles is performed within quantum-mechanical fission theory. This analysis is based on taking into account the effect of quantum rotation of a fissile compound nucleus formed upon the capture of a polarized cold neutron by an nonoriented target nucleus on angular distributions of both alpha particles and fission fragments. It is shown that the asymmetries in question cannot be described within the approach relying on the use of the classic method of trajectory calculations without taking into account the interference between the fission amplitudes for different neutron resonance states of a fissile compound nucleus that are formed at the initial stage of the reactions being studied.

Alpha particle preformation factor of spherical nuclei for 67 ≤Z ≤91

In this paper, alpha decay half-lives of spherical nuclei in the range [Formula: see text] are studied by considering the Coulomb and proximity potential model (CPPM) and calculating the alpha particle preformation factor. Comparisons are made to existing data in the literature. The half-lives are compared to the experimental values and also with the existing theoretical models, the analytical formula of Royer (R) and also within the modified analytical formula of Royer (MR) and New Akrawy–Poenaru Formula (AKRE) by Akrawy and Poenaru and the semi-empirical model based on fission theory (SemFIS) of Poenaru et al., the Universal Decay Law (UDL) of Qi et al., the Scaling Law of Brown (SLB), the Scaling Law of Horoi et al. (SLH). Compared with the experimental alpha half-lives, it can be found that the half-lives obtained using our formalism is in good agreement with the experimental data.

Super Heavy Elements: On the 150th Anniversary of the Discovery of the Periodic Table of Elements

For more than 23 centuries, from Democritus (460–370 BC) to Dalton (1766–1844), the material world around us was believed to consist of the smallest indivisible particles—atoms, those building blocks of the Universe. A total of just 36 chemical elements—types of atoms known to Dalton, were considered the alphabet of the world creation. The periodic table by D. I. Mendeleev [1] that demonstrated the regularity in the chemical behavior of the 63 elements known by that time showed that the atom (element) is not indivisible, since it has an internal structure that is the basis of this regularity. Indeed, 26 years later J. J. Thomson discovered the smallest negatively charged particles in the atom—the electrons [2], and 14 years later Ernst Rutherford proposed the well-known planetary model of the atom [3] in the form of a nucleus that carries almost the entire mass and all the positive charge, and electrons that move around the nucleus at a large distance. In the earliest theoretical model [4], the atomic nucleus was considered to be a spherical uniformly charged drop of a specific liquid-like substance. On the basis of the liquid-drop model G. Gamov himself developed a theory of alpha-decay, the author of the well-known formula C. F. von Weizsäcker calculated the binding energy of nuclei [5], and N. Bohr and J. A. Wheeler developed their liquid-drop-based theory of nuclear fission [6].

Theoretical calculation and evaluation of n + 240,242,244Pu reactions

The nuclear data of $${\text{n}}\,+\,^{240,242,244}$$ Pu reactions for incident energy below 200 MeV are calculated and evaluated to meet the requirement in the design of an accelerator-driven subcritical system. The optical model is used to calculate the total, nonelastic, shape elastic cross sections, shape elastic scattering angular distributions, and transmission coefficients. The distorted-wave Born approximation is applied to calculate the direct inelastic scatterings to the discrete excited states. The nuclear reaction statistical models and fission theory are applied to describe neutron, proton, deuteron, triton, helium-3, alpha and $$\gamma$$ emissions, and fission consistently. The results thus obtained are compared with experimental data and the evaluated data obtained from ENDF/B-VII.1 and JENDL-4.0.

Alpha decay and cluster radioactivity of super heavy nuclei 303,304120

The heaviest nuclei produced until now are few isotopes of the oganesson (atomic number Z = 118). We performed calculations of α-decay half-lives using the models AKRA (Akrawy, 2017), ASAF (Analytical Super-Asymmetric Fission, 1980), UNIV (Universal Formula, 2006), and semFIS (Semi-empirical formula based on Fission Theory, 1983). Cluster radioactivity half-lives are calculated with ASAF and UNIV models. The most important result of our calculations shows that 92,94Sr cluster radioactivity of 303,304120 has a branching ratio relative to α-decay of −0.10 and 0.49, respectively. We hope that future measurements will prove that cluster decay may compete with α decay.

Effect of the Wriggling Vibrations of Aligned Nuclei on the Angular Distribution of Fragments from Low-Energy Fissioning

The possibility is investigated of observing deviations in the angular distributions of fragments from the low-energy binary fission of aligned actinide nuclei by resonant neutrons, calculated within the theory of quantum fission with allowance for the wriggling vibrations of fissile nuclei using angular distributions determined with Bohr’s formula. The relative errors of the experimental anisotropy coefficients of these distributions are compared to deviations of the theoretical anisotropy coefficients, calculated with allowance for wriggling vibrations of fissile nuclei, from those calculated using Bohr’s formula. Estimates are obtained on this basis for the wriggling vibration parameters: and for 233U and 235U nuclei, respectively, for which deviations from Bohr’s formula can be detected.

P-Odd Asymmetries in the Angular Distributions of Fragments from the Low-Energy Fission of Nuclei by Polarized Neutrons with Allowance for the Wriggling Vibrations of a Fissile Nucleus

Results are presented from investigating deviations of the coefficients of P-odd asymmetries in the angular distributions of fragments produced by the low-energy fissioning of actinide nuclei by polarized neutrons, calculated using the quantum fission theory with allowance for wriggling vibrations, from the coefficients of these asymmetries described by Bohr’s formula. By comparing relative errors of the experimental measurements of Р-odd asymmetry coefficients and deviations of the theoretical values of asymmetry coefficients, calculated with allowance for the wriggling vibrations of a fissile nucleus, from their values obtained using Bohr’s formula, estimates of wriggling vibration parameters $${{C}_{{\text{w}}}} \leqslant 30$$ and $${{C}_{{\text{w}}}} \leqslant 15$$ are determined for 233U and 235U nuclei, respectively, for which deviations from Bohr’s formula can be detected.

Unified Mechanism behind the Appearance of T-Odd TRI and ROT Asymmetries in Actinide Fission Induced by Cold Polarized Neutrons

Some shortcomings of the approaches that are used to describe T-odd ROT and TRI asymmetries in true ternary fission via reactions involving the emission of prescission alpha particles and which are based on employing the classical method of trajectory calculations are analyzed. These shortcomings are caused by the disregard of the interference between the fission widths of different sJs neutron resonance states formed in the first well of the deformation potential of fissile compound nuclei. It is shown that the method used in some studies to determine T-odd TRI-asymmetries for prescission alpha particles is at odds with basic concepts of the generalizedmodel of the nucleus and approaches to constructing collective (for example, bending) vibrations of a fissile compound nucleus. Quantum-mechanical fission theory is generalized via employing a unified mechanism of formation of T-odd TRI and ROT asymmetries for prescission alpha particles and evaporated photons (neutrons). The proposed mechanism takes correctly into account the effect of quantum rotation of a fissile compound nucleus on the angular distributions of fission fragments and alpha particles for true ternary fission, as well as on the angular distribution of prompt photons (neutrons) emitted by fragments originating from the delayed fission of the aforementioned nuclei.

Nuclear structure dependence of fusion hindrance in heavy element synthesis

The production of the heaviest elements in fusion-evaporation reactions is substantially limited by very low cross sections, as fusion cross sections (including fusion-fission) are greatly reduced by the competing quasifission mechanism. Using the Australian National University Heavy Ion Accelerator Facility and CUBE detector array, fission fragments from the $^{48}\mathrm{Ti}+^{204,208}\mathrm{Pb}$ and $^{50}\mathrm{Ti}+^{206,208}\mathrm{Pb}$ reactions have been measured, with the aim to investigate how the competition between quasifission and fusion-fission evolves with small changes in entrance-channel properties associated mainly with the nuclear structure. Analysis of mass-distribution widths of strongly mass-angle-correlated fission fragments within the framework of the compound-nucleus fission theory demonstrates significant differences in quasifission (and therefore fusion) probabilities among the four reactions. The impact of nuclear structure on fusion highlights the importance of future radioactive beams.

Vibronic exciton theory of singlet fission. III. How vibronic coupling and thermodynamics promote rapid triplet generation in pentacene crystals.

We extend the vibronic exciton theory introduced in our previous work to study singlet fission dynamics, in particular addressing recent indications of the importance of vibronic coupling in this process. A microscopic and non-perturbative treatment of electronic and selected vibrational degrees of freedom in combination with Redfield theory allows us to dynamically consider clusters of molecules under conditions close to those in molecular crystals that exhibit fission. Using bulk pentacene as a concrete example, our results identify a number of factors that render fission rapid and effective. Strong coupling to high-frequency Holstein modes generates resonances between the photo-prepared singlet and product triplet states. We furthermore find the large number of triplet combinations associated with bulk periodic systems to be critical to the fission process under such vibronically resonant conditions. In addition, we present results including, in an approximate manner, the effects of Peierls coupling, indicating that this factor can both enhance and suppress fission depending on its interplay with vibronic resonance and thermodynamics.

α decay and cluster radioactivity of nuclei of interest to the synthesis of Z=119 , 120 isotopes

Super-heavy nuclei of interest for the forthcoming synthesis of the isotopes with $Z=119$, 120 are investigated. One of the very interesting latest experiments was performed at the velocity filter SHIP (GSI Darmstadt) trying to produce $^{299}120$ in a fusion reaction $^{248}\mathrm{Cm}(^{54}\mathrm{Cr},3\mathrm{n})^{299}120$. We report calculations of $\ensuremath{\alpha}$-decay half-lives using four models: AKRA (Akrawy), ASAF (analytical superasymmetric fission), UNIV (universal formula), and semFIS (semi-empirical formula based on fission theory). The released energy, $Q$, is calculated using the theoretical model of atomic masses, WS4. For $^{92,94}\mathrm{Sr}$ cluster radioactivity of $^{300,302}120$ we predict a branching ratio relative to $\ensuremath{\alpha}$ decay of $\ensuremath{-}0.10$ and 0.49, respectively, meaning that it is worth trying to detect such kinds of decay modes in competition with $\ensuremath{\alpha}$ decay.

Cluster and alpha decay of superheavy nuclei

We investigated cluster radioactivity and alpha decay of some superheavy nuclei with atomic numbers Z = 119, 120 , which may be produced in the future. Two models are used to calculate the half-lives against cluster radioactivity: ASAF (Analytical Super-Asymmetric Fission) and UNIV (Universal Formula). For $ \alpha$ decay half-lives we are based on four models: ASAF, UNIV, semFIS (semi-empirical formula based on Fission Theory) and AKRA (first author Akrawy). The Q -values are calculated using the theoretical model of atomic masses WS10, which sometimes is called W4.

Fission of SHN and Its Hindrance: Odd Nuclei and Isomers

After shortly analyzing data relevant to fission hindrance of odd-A nuclei and high-$K$ isomers in superheavy (SH) region we point out the inconsistency of current fission theory and propose an approach based on the instanton formalism. A few results of this method, simplified by replacing selfconsistency by elements of the macro-micro model, are given to illustrate its features.

Estimation of the alpha decay of Platinum isotopes using different versions of theoretical formula

The alpha decay half-lives of even–even and even–odd Platinum (Pt) nuclei have been studied within the Coulomb and proximity potential model (CPPM). The present study is restricted to even–even nuclei with [Formula: see text]–198. The results are compared with other calculations such as the Semi-empirical formula (SemFIS) from Poenaru et al. based on fission theory of alpha decay, the Viola–Seaborg (VS), Royer (R) and Brown formulae. Also, the alpha decay half-lives have been calculated using the Scaling law of Brown (SLB), the Universal Decay Law (UDL) of Qi et al., the Scaling Law of Horoi et al. (SLH), and Akrawy–Dorin formula (ADF) of Akrawy and Poenaru, which are the Royer modified formula for alpha decay half-live by adding asymmetry term.

Alpha decay calculations with a new formula

A new semi-empirical formula for calculations of α decay half-lives is presented. It was derived from the Royer relationship by introducing new parameters which are fixed by fit to a set of experimental data. We are using three sets: set A with 130 e–e (even–even), 119 e–o (even–odd), 109 o–e, and 96 o–o, set B with 188 e–e, 147 e–o, 131 o–e and 114 o–o, and set C with 136 e–e, 84 e–o, 76 o–e and 48 o–o alpha emitters. A comparison of results obtained with the new formula (newF) and the following well known relationships: semiempirical relationship based on fission theory (semFIS), analytical superasymmetric fission (ASAF) model and universal formula (UNIV) made in terms of rms standard deviation. We also introduced a weighted mean value of this quantity, allowing us to compare the global properties of a given model. For set B the order of the four models is the following: semFIS, UNIV, newF and ASAF. Nevertheless for even–even alpha emitters, UNIV gives the second best result after semFIS, and for odd–even parents the second is newF. Despite its simplicity in comparison with semFIS, newF, presented in this article, behaves quite well, competing with the other well known relationships.