Compound nucleus effective moment of inertia has been calculated for several fission reaction systems induced by nucleons, light particles, and heavy ions. Determination of this quantity for these systems is based upon the comparison between the experimental data of the fission fragment angular distributions as well as the prediction of the standard saddle-point statistical model (SSPSM). For the systems, the two cases, namely with and without neutron emission corrections were considered. In these calculations, it is assumed that all the neutrons are emitted before reaching the saddle point.It should be noted that the above method for determining of the effective moment of inertia had not been reported until now and this method is used for the first time to determine compound nucleus effective moment of inertia. Hence, our calculations are of particular importance in obtaining this quantity, and have a significant rule in the field of fission physics. Afterwards, our theoretical results have been compared with the data obtained from the rotational liquid drop model as well as the Sierk model, and satisfactory agreements were found. Finally, we have considered the effective moment of inertia of compound nuclei for the systems that formed similar compound nuclei at similar excitation energies.
The non-perturbative method to compute Adiabatic Time Dependent Hartree Fock Bogoliubov (ATDHFB) collective inertias is extended to the Generator Coordinate Method (GCM) including the case of density dependent forces. The two inertias schemes are computed along the fission path of the $^{234}$U and compared with the perturbative results. We find that the non-perturbative schemes predict very similar collective inertias with a much richer structure than the one predicted by perturbative calculations. Moreover, the non-perturbative inertias show an extraordinary similitude with the exact GCM ine…
Superheavy nuclei produced until now are decaying mainly by $α$ emission and spontaneous fission. Calculated $α$ decay half-lives are in agreement with experimental data within one order of magnitude. The discrepancy between theory and experiment can be as high as ten orders of magnitude for spontaneous fission. We analyze a way to improve the accuracy by using the action integral based on cranking inertia and a potential barrier computed by the macroscopic-microscopic method with a two-center shell model. Illustrations are given for $^{282}$Cn which has a measured fission half-life.
Spontaneous fission barriers, quadrupole inertia, and zero-point quadrupole-energy corrections are calculated for 252,256,258Fm in the framework of the self-consistent Skyrme-Hartree-Fock+BCS theory. Two ways of computing dynamical inertia are employed: the Gaussian Overlap Approximation to the Generator Coordinate Method and cranking ansatz. The Skyrme results are compared with those of the Gogny-Hartree-Fock-Bogolyubov model.
Collective mass tensor derived from the cranking approximation to the adiabatic time-dependent Hartree-Fock-Bogoliubov (ATDHFB) approach is compared with that obtained in the Gaussian Overlap Approximation (GOA) to the generator coordinate method. Illustrative calculations are carried out for one-dimensional quadrupole fission pathways in 256Fm. It is shown that the collective mass exhibits strong variations with the quadrupole collective coordinate. These variations are related to the changes in the intrinsic shell structure. The differences between collective inertia obtained in cranking and…
The spontaneous fission lifetime of 264Fm has been studied within nuclear density functional theory by minimizing the collective action integral for fission in a two-dimensional quadrupole collective space representing elongation and triaxiality. The collective potential and inertia tensor are obtained self-consistently using the Skyrme energy density functional and density-dependent pairing interaction. The resulting spontaneous fission lifetimes are compared with the static result obtained with the minimum-energy pathway. We show that fission pathways strongly depend on assumptions underlyin…
Pre-saddle neutron multiplicity has been calculated for several fission reactions induced by heavy ions and light particles. Experimentally, it is impossible to determine the contribution of neutrons being emitted before the saddle point and those emitted between the saddle and the scission points. Determination of the pre-saddle neutron multiplicity in our research is based on the comparison between the experimental anisotropies and those predicted by the standard saddle-point statistical model. Analysis of the results shows that the pre-saddle neutron multiplicity depends on the fission barr…
Background: Microscopic description of spontaneous fission is one of the most challenging subjects in nuclear physics. It is necessary to evaluate the collective potential and the collective inertia along a fission path for a description of quantum tunneling in spontaneous or low-energy fission. In past studies of the fission dynamics based on nuclear energy density functional (EDF) theory, the collective inertia has been evaluated with the cranking approximation, which neglects dynamical residual effects. Purpose: The purpose is to provide a reliable and efficient method to include dynamical …
Exact solution of adiabatic time dependent Hartree-Fock-Bogoliubov inertia for fission
Technische Universität Darmstadt（达姆施塔特工业大学）；GSI Helmholtzzentrum für Schwerionenforschung（GSI亥姆霍兹重离子研究中心）；Helmholtz Forschungsakademie Hessen für FAIR（黑森FAIR亥姆霍兹研究院）；Instituto de Estructura de la Materia, CSIC（CSIC物质结构研究所）；Universidad Autónoma de Madrid（马德里自治大学）；Universidad Politécnica de Madrid（马德里理工大学）
We computed a new set of static fission properties suited for r-process calculations. The potential energy surfaces and collective inertias of 3640 nuclei in the superheavy region are obtained from Self-Consistent Mean-Field calculations using the Barcelona-Catania-Paris-Madrid energy density functional. The fission path is computed as a function of the quadrupole moment by minimizing the potential energy and exploring octupole and hexadecapole deformations. The spontaneous fission lifetimes are evaluated employing different schemes for the collective inertias and vibrational energy correction…
A formalism for semi-adiabatic cranking mass parameters is presented. For the fission process of 234U, the time-dependent pairing equations of motion were used to calculate the excitation energy and to extract values of the cranking inertia. A fission barrier is determined by minimizing the action trajectory in a five dimensional configuration space spanned by elongation, necking, deformations of fragments and mass-asymmetry. The deformation energy is computed in the the frame of the microscopic-macroscopic model. The two center shell model with Woods-Saxon potentials is used in this context. …
We study the role of dynamic pairing correlations in fission dynamics by considering intrinsic Hartree-Fock-Bogoliubov wave functions that are obtained by minimizing the particle number projected energy. For the restricted variational space, the set of self-consistent wave functions with different values of proton and neutron number particle fluctuations are considered. The particle number projected energy is used to define potential energy surface for fission whereas collective inertias are computed within the traditional formulas for the intrinsic states. The results show that the effect of …
Transport properties of nuclear matter from anomalous fission yields
Institut Pluridisciplinaire Hubert Curien, CNRS/IN2P3-UDS（于贝尔·居里多学科研究所）；Institute of Nuclear Physics Polish Academy of Sciences（波兰科学院核物理研究所）；Department of Physics and Astronomy, Chalmers University of Technology（查尔姆斯理工大学物理与天文学系）
The dynamics of induced fission of $^{226}$Th is investigated in a theoretical framework based on the finite-temperature time-dependent generator coordinate method (TDGCM) in the Gaussian overlap approximation (GOA). The thermodynamical collective potential and inertia tensor at temperatures in the interval $T=0 - 1.25$ MeV are calculated using the self-consistent multidimensionally constrained relativistic mean field (MDC-RMF) model, based on the energy density functional DD-PC1. Pairing correlations are treated in the BCS approximation with a separable pairing force of finite range. Constrai…
Low-energy positive and negative parity collective states in the equilibrium minimum, and the dynamics of induced fission of actinide nuclei are investigated in a unified theoretical framework based on the generator coordinate method (GCM) with the Gaussian overlap approximation (GOA). The collective potential and inertia tensor, both at zero and finite temperature, are computed using the self-consistent multidimensionally constrained relativistic mean field (MDC-RMF) model, based on the energy density functional DD-PC1. Pairing correlations are treated in the BCS approximation with a separabl…
Collective inertia is strongly influenced at the level crossing at which quantum system changes diabatically its microscopic configuration. Pairing correlations tend to make the large-amplitude nuclear collective motion more adiabatic by reducing the effect of those configuration changes. Competition between pairing and level crossing is thus expected to have a profound impact on spontaneous fission lifetimes. To elucidate the role of nucleonic pairing on spontaneous fission, we study the dynamic fission trajectories of $^{264}$Fm and $^{240}$Pu using the state-of-the-art self-consistent frame…
We systematically calculate the spontaneous fission half-lives for heavy and superheavy nuclei between U and Fl isotopes. The spontaneous fission process is studied within the semi-empirical WKB approximation. The potential barrier is obtained using a generalized liquid drop model, taking into account the nuclear proximity, the mass asymmetry, the phenomenological pairing correction, and the microscopic shell correction. Macroscopic inertial-mass function has been employed for the calculation of the fission half-life. The results reproduce rather well the experimental data. Relatively long hal…
We describe the fissioning dynamics of Pu240 from a configuration in the proximity of the outer fission barrier to full scission and the formation of the fragments within an implementation of density functional theory extended to superfluid systems and real-time dynamics. The fission fragments emerge with properties similar to those determined experimentally, while the fission dynamics appears to be quite complex, with many excited shape and pairing modes. The evolution is found to be much slower than previously expected, and the ultimate role of the collective inertia is found to be negligibl…
Microscopic methods and tools to describe nuclear dynamics have considerably been improved in the past few years. They are based on the time-dependent Hartree-Fock (TDHF) theory and its extensions to include pairing correlations and quantum fluctuations. The TDHF theory is the lowest level of approximation of a range of methods to solve the quantum many-body problem, showing its universality to describe many-fermion dynamics at the mean-field level. The range of applications of TDHF to describe realistic systems allowing for detailed comparisons with experiment has considerably increased. For …
The two stages dynamical stochastic model developed earlier for description of fusion-fission reactions is applied to the calculation of mass- and energy-distributions of fission fragments of platinum isotopes in reaction ${\rm ^{36}Ar + ^{142}Nd \to ^{178-x}Pt + xn}$. The first stage of this model is the calculation of the approaching of projectile nucleus to the target nucleus. On the second stage of the model, the evolution of the system formed after the touching of the projectile and target nuclei is considered. The evolution of the system on both stages is described by three-dimensional L…
Semi-analytical expressions are suggested for the temperature dependence of those combinations of transport coefficients which govern the fission process. This is based on experience with numerical calculations within the linear response approach and the locally harmonic approximation. A reduced version of the latter is seen to comply with Kramers' simplified picture of fission. It is argued that for variable inertia his formula has to be generalized, as already required by the need that for overdamped motion the inertia must not appear at all. This situation may already occur above T=2 MeV, w…
The anisotropy in the angular distribution of the fusion-fission and quasifission fragments for the $^{16}$O+$^{238}$U, $^{19}$F+$^{208}$Pb and $^{32}$S+$^{208}$Pb reactions is studied by analyzing the angular momentum distributions of the dinuclear system and compound nucleus which are formed after capture and complete fusion, respectively. The orientation angles of axial symmetry axes of colliding nuclei to the beam direction are taken into account for the calculation of the variance of the projection of the total spin onto the fission axis. It is shown that the deviation of the experimental…
We describe the capture, fusion, fission and evaporation residue formation cross sections of superheavy nuclei within the proposed earlier two stages dynamical model. The approaching of the projectile nucleus to the target nucleus is described in the first stage of the model. On the second stage, the evolution of the system formed after the touching of the projectile and target nuclei is considered. The evolution of the system on both stages is described by Langevin equations. The transport coefficients of these equations are calculated within the microscopic linear response theory. The mutual…
Given a set of collective variables, a method is proposed to obtain the associated conjugated collective momenta and masses starting from a microscopic time-dependent mean-field theory. The construction of pairs of conjugated variables is the first step to bridge microscopic and macroscopic approaches. The method is versatile and can be applied to study a large class of nuclear processes. An illustration is given here with the fission of $^{258}$Fm. Using the quadrupole moment and eventually higher-order multipole moments, the associated collective masses are estimated along the microscopic me…
The role of dynamical pairing in induced fission dynamics is investigated using the time-dependent generator coordinate method in the Gaussian overlap approximation, based on the microscopic framework of nuclear energy density functionals. A calculation of fragment charge yields for induced fission of $^{228}$Th is performed in a three-dimensional space of collective coordinates that, in addition to the axial quadrupole and octupole intrinsic deformations of the nuclear density, also includes an isoscalar pairing degree of freedom. It is shown that the inclusion of dynamical pairing has a pron…
The decimal logarithm of spontaneous fission half-life of the superheavy nucleus $^{286}$Fl experimentally determined is $\log_{10} T_f^{exp} (s) = -0.632$. We present a method to calculate the half-life based on the cranking inertia and the deformation energy, functions of two independent surface coordinates, using the best asymmetric two center shell model. In the first stage we study the statics. At a given mass asymmetry up to about $η=0.5$ the potential barrier has a two hump shape, but for larger $η$ it has only one hump. The touching point deformation energy versus mass asymmetry shows …
In highly dissipative collisions between heavy ions, the optimal conditions to investigate different de-excitation channels of hot nuclei such as evaporation, fission or multifragmentation are well known. One crucial issue remains the excitation energy region where fission gives way to multifragmentation. In this paper, the onset of multi-fragment exit channels is investigated in terms of sequential fission. For the first time, the dynamical approach based on solving Langevin transport equations in multidimensional collective coordinate space is used to follow the de-excitation of highly excit…
In peripheral high-energy heavy-ion collisions only parts of colliding nuclei interact leading to the production of a fireball. The remnants of such nuclei are called spectators. We estimated the excitation energy as a function of impact parameter. Their excitation energy is of the order of 100 MeV. The dynamical evolution of hot nuclei is described by solving a set of Langevin equations in four-dimensional collective coordinate space. The range of nuclear masses and excitation energies suits very well to ability of our model. Thus for the first time we investigate dynamically the fission and …
We report on Hartree-Fock-Bogoliubov (HFB) calculations of the ground-state rotationnal band of the heavy nucleus $^{254}$No recently observed experimentally. The calculated quadrupole deformation is consistent with the experimental value of $β=0.27$ and is almost constant over the whole band. We also reproduce fairly well the excitation spectra and moments of inertia of this isotope up to the maximal experimentally observed state of spin 20. The rather high stability of this nucleus against fission is illustrated by the deformation energy curve providing very high fission barriers at zero spi…
A model of electromagnetic interaction of relativistic heavy ions which makes it possible to calculate the inclusive and exclusive characteristics of such interactions is presented. The multistep model includes (1) the single and double virtual photon absorption by a nucleus, (2) intranuclear cascades of produced hadrons and (3) statistical decay of excited residual nuclei described by evaporation, fission and multifragmentation mechanisms. Components of the model were verified by comparison of calculation results with experimental data obtained with monoenergetic photons and heavy ions at KEK…
Rotational bands of $^{252, 253, 254}$No and the fission barriers of $^{254}$No at spin 0$\hbar$ and 20$\hbar$ are calculated with the Hartree-Fock-Bogolyubov theory and the Lipkin-Nogami approximate particle number projection. The SLy4 Skyrme force is used in the particle-hole channel. A zero-range force with and without density-dependence is used in the particle-particle channel. The experimental ground state deformation (${\cal{Q}}_{20}$ = 32.8 b) is reproduced as well as the increase of the dynamical moment of inertia with frequency both for $^{252}$No and $^{254}$No. The rotational band o…
The time-dependent density functional theory (TDDFT) provides a unified description of the structure and reaction. The linear approximation leads to the random-phase approximation (RPA) which is capable of describing a variety of collective motion in a harmonic regime. Beyond the linear regime, we present applications of the TDDFT to nuclear fusion and fission reaction. In particular, the extraction of the internuclear potential and the inertial mass parameter is performed using two different methods. A fusion hindrance mechanism for heavy systems is investigated from the microscopic point of …
The hot rotating nuclei could be formed in the complete and incomplete fusion reaction of two heavy ions. At low bombarding energies the reaction goes via compound nucleus formation and subsequent evaporation of charged particles, neutrons and $γ$-rays. However, with increasing the energy of the projectile, the emission of particles during the equilibration process becomes more and more probable. This effect can be estimated by the Heavy-Ion Phase-Space Exploration (HIPSE) code which describes the production of clusters of various size from nucleons initially in the target or projectile. This …
The induced-activity investigations in off-line analysis performed in different experiments, concerning pre-actinide and actinide nuclei, are here presented and discussed. Generalized expressions for the determination of independent yields/cross sections of radioactive nuclei, formed in the targets, are derived and analysed. The fragment mass distribution from U-238, Th-232 and Ta-181 photofission at the bremsstrahlung end-point energies of 50 and 3500 MeV, and from Am-241, U-238 and Np-237 fission induced by 660-MeV protons, are scrutinized from the point of view of the multimodal fission app…
The cranked relativistic Hartree-Bogoliubov (CRHB) theory has been applied for a systematic study of pairing and rotational properties of actinides and light superheavy nuclei. Pairing correlations are taken into account by the Brink-Booker part of finite range Gogny D1S force. For the first time in the covariant density functional theory (CDFT) framework the pairing properties are studied via the quantities (such as three-point $Δ^{(3)}$ indicators) related to odd-even mass staggerings. The investigation of the moments of inertia at low spin and the $Δ^{(3)}$ indicators shows the need for an …
The mass, radius and crustal fraction of moment of inertia in neutron stars are calculated using $β$-equilibrated nuclear matter obtained from Skyrme effective interaction. The transition density, pressure and proton fraction at the inner edge separating the liquid core from the solid crust of the neutron stars are determined from the thermodynamic stability conditions using the KDE0v1 set. The neutron star masses obtained by solving the Tolman-Oppenheimer-Volkoff equations using neutron star matter obtained from this set is able to describe highly massive compact stars $\sim$2$M_{\odot}$. The…
We study nuclear reactions induced by virtual photons associated with Lorentz-boosted Coulomb fields of ultrarelativistic heavy ions. Evaporation, fission and multifragmentation mechanisms are included in a new RELDIS code, which describes the deexcitation of residual nuclei formed after single and double photon absorption in peripheral heavy-ion collisions. Partial cross sections for different dissociation channels, including the multiple neutron emission ones, are calculated and compared with data when available. Rapidity and transverse momentum distributions of nucleons, nuclear fragments a…
The 119-126Sn nuclei have been produced as fission fragments in two reactions induced by heavy ions: 12C+238U at 90 MeV bombarding energy, 18O+208Pb at 85 MeV. Their level schemes have been built from gamma rays detected using the Euroball array. High-spin states located above the long-lived isomeric states of the even- and odd-A 120-126Sn nuclei have been identified. Moreover isomeric states lying around 4.5 MeV have been established in 120,122,124,126Sn from the delayed coincidences between the fission fragment detector SAPhIR and the Euroball array. The states located above 3-MeV excitation…
The 124-131Te nuclei have been produced as fission fragments in two fusion reactions induced by heavy-ions (12C + 238U at 90 MeV bombarding energy and 18O + 208Pb at 85 MeV) and studied with the Euroball array. Their high-spin level schemes have been extended to higher excitation energy from the triple gamma-ray coincidence data. The gamma-gamma angular correlations have been analyzed in order to assign spin and parity values to many observed states. Moreover the half-lives of isomeric states have been measured from the delayed coincidences between the fission-fragment detector SAPhIR and Euro…
