We survey odd-even nuclear binding energy staggering using density functional theory with several treatments of the pairing interaction including the BCS, Hartree-Fock-Bogoliubov, and the Hartree-Fock-Bogoliubov with the Lipkin-Nogami approximation. We calculate the second difference of binding energies and compare with 443 measured neutron energy differences in isotope chains and 418 measured proton energy differences in isotone chains. The particle-hole part of the energy functional is taken as the SLy4 Skyrme parametrization and the pairing part of the functional is based on a contact interaction with possible density dependence. An important feature of the data, reproduced by the theory, is the sharp gap quenching at magic numbers. With the strength of the interaction as a free parameter, the theory can reproduce the data to an rms accuracy of about 0.25 MeV. This is slightly better than a single-parameter phenomenological description but slightly poorer than the usual two-parameter phenomenological form C/A^alpha . The following conclusions can be made about the performance of common parametrization of the pairing interaction: (i) there is a weak preference for a surface-peaked neutron-neutron pairing, which might be attributable to many-body effects; (ii) a larger strength is required in the proton pairing channel than in the neutron pairing channel; (iii) pairing strengths adjusted to the well-known spherical isotope chains are too weak to give a good overall fit to the mass differences.
Nuclear shapes and odd-nucleon blockings strongly influence the odd-even differences of nuclear masses. When such effects are taken into account, the determination of the pairing strength is modified resulting in larger pair gaps. The modified pairing strength leads to an improved self-consistent description of moments of inertia and backbending frequencies, with no additional parameters.
The neutron and proton odd-even mass differences are studied with Hartree-Fock+BCS (HFBCS) calculations with Skyrme interactions and an isospin dependent contact pairing interaction, which is recently derived from a microscopic nucleon-nucleon interaction. To this end, we perform HFBCS calculations for even and odd semi-magic Tin and Lead isotopes together with even and odd Z isotones with $N$= 50 and 82. The filling approximation is applied to the last unoccupied particle in odd nuclei. Comparisons with the experimental data show a clear manifestation of the isospin dependent pairing correlat…
The odd-even mass staggering (OES) of nuclei is analyzed in the context of self-consistent mean-field calculations. The procedure developed allows to understand the OES for spherical as well as for deformed nuclei. Comparison with results at the Hartree-Fock level shows the non-perturbative effect on this observable of the inclusion of pairing correlations.
The boson-pair coherent state developed in Part (I) is generalized to the case in which the state is a mixture of even-boson and odd-boson number states. A general framework is shown and its three concrete examples are discussed. Main idea is in the application of the deformed boson scheme presented by the present authors.
An idea of the deformed boson scheme developed by the present authors is applied to the case of boson-pair coherent state. In this state, even and odd boson number difference is stressed and various concrete examples of the boson-pair coherent states are shown. Concerning some of them, mutual relations are investigated in connection to the su(1,1)-algebra. A formulation in terms of the MYT boson mapping is also performed.
First, we briefly outline some aspects of the starting project to design non-empirical energy functionals based on low-momentum vacuum interactions and many-body perturbation theory. Second, we present results obtained within an approximation of such a scheme where the pairing part of the energy density functional is constructed at first order in the nuclear plus Coulomb two-body interaction. We discuss in detail the physics of the odd-even mass staggering and the necessity to compute actual odd-even mass differences to analyze it meaningfully.
A basic idea is proposed for extending the formalism of Part (II) of the series of our paper to the case of the parameter-dependent deformation. It is stressed that, through this extension, the variety of the application increases. Further, an answer for the problem mentioned in Part (II) is presented.
In the random-phase-approximation-amended (RPA-amended) Nilsson-Strutinskij method of calculating nuclear binding energies, the conventional shell correction terms derived from the independent-nucleon model and the Bardeen-Cooper-Schrieffer pairing theory are supplemented by a term which accounts for the pair-vibrational correlation energy. This term is derived by means of the RPA from a pairing Hamiltonian which includes a neutron-proton pairing interaction. The method was used previously in studies of the pattern of binding energies of nuclei with approximately equal numbers $N$ and $Z$ of n…
A method to evaluate the particle-phonon coupling (PC) corrections to the single-particle energies in semi-magic nuclei, based on a direct solving the Dyson equation with PC corrected mass operator, is used for finding the odd-even mass difference between 18 even Pb isotopes and their odd-proton neighbors. The Fayans energy density functional (EDF) DF3-a is used which gives rather high accuracy of the predictions for these mass differences already on the mean-field level, with the average deviation from the existing experimental data equal to 0.389 MeV. It is only a bit worse than the correspo…
Two aspects of the problem of evaluating double odd-even mass differences D_2 in semi-magic nuclei are studied related to existence of two components with different properties, a superfluid nuclear subsystem and a non-superfluid one. For the superfluid subsystem, the difference D_2 is approximately equal to 2Δ, the gap Δbeing the solution of the gap equation. For the non-superfluid subsystem, D_2 is found by solving the equation for two-particle Green function for normal systems. Both equations under consideration contain the same effective pairing interaction. For the latter, the semi-microsc…
A method to evaluate the particle-phonon coupling (PC) corrections to the single-particle energies in semi-magic nuclei, based on the direct solution of the Dyson equation with PC corrected mass operator, is presented. It is used for finding the odd-even mass difference between even Pb and Sn isotopes and their odd-proton neighbors. The Fayans energy density functional (EDF) DF3-a is used which gives rather highly accurate predictions for these mass differences already at the mean-field level. In the case of the lead chain, account for the PC corrections induced by the low-laying phonons $2^+_…
We have studied odd-even nuclear mass staggering with the Skyrme-Hartree-Fock-Bogoliubov theory by employing isoscalar and isovector contact pairing interactions. By reproducing the empirical odd-even mass differences of the Sn isotopic chain, the strengths of pairing interactions are determined. The optimal strengths adjusted in this work can give better description of odd-even mass differences than that fitted by reproducing the experimental neutron pairing gap of $^{120}$Sn.
A method is developed to consider the particle-phonon coupling (PC) effects in the problem of finding odd-even double mass differences (DMD) of magic nuclei within the approach starting from the free $NN$-potential. Three PC effects are taken into account, the phonon induced interaction, the renormalization of the "ends" due to the $Z$-factors and the change of the single-particle energies. We use the perturbation theory in $g^2_L$, where $g_L$ is the vertex of the $L$-phonon creation. PC corrections to single-particle energies are found self-consistently with an approximate account for the so…
The neutron and proton odd-even mass differences are systematically studied with Hartree-Fock+BCS (HFBCS) calculations with Skyrme interactions and an isospin dependent contact pairing interaction. The strength of pairing interactions is determined to reproduce empirical odd-even mass differences in a wide region of mass table. By using the optimal parameter, we perform global HF+BCS calculations of nuclei and compare with experimental data. The importance of isospin dependence of the pairing interaction is singled out for odd-even mass differences in medium and heavy isotopes. The proton and …
Recent results of the description of quadrupole moments of odd semi-magic nuclei are briefly reviewed. They are based on the self-consistent theory of finite Fermi systems with account for the phonon-particle coupling (PC) effects. The self-consistent model for describing the PC effects was developed previously for magnetic moments. Account for the non-pole diagrams is an important ingredient of this model. In addition to previously reported results for the odd In and Sb isotopes, which are the proton-odd neighbors of even tin nuclei, we present new results for odd Bi isotopes, the odd neighbo…
The trends with mass number are examined for the odd-even-staggering (OES) in nuclear binding of neutrons and protons through the conventional measures $Δ^{(3)}$. The large differences previously observed between these trends for even and odd values of these measures is found to arise, in part, from the slow variation of binding energies with mass and charge which provides a background contribution. This background is estimated with the liquid-drop model, and accounts for the greater difference found in proton removal relative to neutron removal. The differences which persist after backgrounds…
In order to extract informations on pairing correlations in nuclei from experimental mass differences, the different contributions to odd-even mass differences are investigated within the Skyrme HFB method. In this first paper, the description of odd nuclei within HFB is discussed since it is the key point for the understanding of the above mentioned contributions. To go from an even nucleus to an odd one, the advantage of a two steps process is demonstrated and its physical content is discussed. New results concerning time-reversal symmetry breaking in odd-nuclei are also reported. PACS: 21.1…
A method is developed to consider the particle-phonon coupling (PC) effects in the calculation of the odd-even double mass differences (DMD) in semi-magic nuclei starting from the free $NN$-potential. The PC correction $δΣ^{\rm PC}$ to the mass operator $Σ$ is found in $g_L^2$-approximation, $g_L$ being the vertex of creating the $L$-phonon. The tadpole term of the operator $δΣ^{\rm PC}$ is taken into account. The method is based on a direct, without any use of the perturbation theory, solution of the Dyson equation with the mass operator $Σ(ε){=}Σ_0{+}δΣ^{\rm PC}(ε)$ for finding the single-pa…
We study the isoscalar (T=0) and isovector (T=1) pairing correlations in N=Z nuclei. They are estimated from the double difference of binding energies for odd-odd N=Z nuclei and the odd-even mass difference for the neighboring odd-mass nuclei, respectively. The empirical and BCS calculations based on a T=0 and T=1 pairing model reproduce well the almost degeneracy of the lowest T=0 and T=1 states over a wide range of even-even and odd-odd N=Z nuclei. It is shown that this degeneracy is attributed to competition between the isoscalar and isovector pairing correlations in N=Z nuclei. The calcula…
We have done systematic Hartree-Fock-Bogoliubov calculations in coordinate space on the one-quasi-particle energies and binding energy odd-even staggering (OES) in semi-magic nuclei with the zero-range volume, mixed and surface pairing forces in order to explore the influence of their density dependence. The odd-$N$ isotopes are calculated within the blocking scheme. The strengths for the pairing forces are determined in two schemes by fitting locally to reproduce pairing gap in $^{120}$Sn and globally to all available data on the OES of semi-magic nuclei with $Z\geq8$. In the former calculati…
Neutron rich Ca and Ni nuclei have been studied in spherical Relativistic Mean Field formalism in co-ordinate space. A delta interaction has been has been adopted to treat the pairing correlations for the neutrons. Odd nuclei have been treated in the blocking approximation. The effect of the positive energy continuum and the role of pairing in the stability of nuclei have been investigated using the resonant-BCS (rBCS) approach. In Ca isotopes, N=50 is no longer a magic number while in Ni nuclei, a new magic number emerges at N=70. There is a remarkable difference in the relative positions of …
We examine the general nature of nuclear odd-even mass differences by employing neutron and proton mass relations that emphasize these effects. The most recent mass tables are used. The possibility of a neutron excess dependence of the staggering is examined in detail in separate regions defined by the main nuclear shells, and a clear change in this dependency is found at $Z=50$ for both neutrons and protons. A further separation into odd and even neutron (proton) number produces very accurate local descriptions of the mass differences for each type of nucleons. These odd-even effects are comb…
We calculate P-odd difference of the total cross-sections of the deuteron disintegration by left and right polarized photons. The relative magnitude of this difference in the threshold region is about 10^{-7}. Its experimental measurement would give valuable information on the weak nucleon-nucleon interaction at short distances.
The pseudopotential theory is extended to the Bogoliubov-de Gennes equations to determine the excess energy when one atom is added to the trapped superfluid Fermi system with even number of atoms. Particular attention is paid to systems being at the Feshbach resonance point. The results for relatively small particle numbers are in harmony with the Monte-Carlo calculations, but are also relevant for systems with larger particle numbers. Concerning the additional one quasiparticle state we define and determine two new universal numbers to characterize its widths.
The differences between the experimental and the theoretically calculated binding energies in Relativistic Mean Field (RMF) approach have been calculated for a large number of odd-$Z$ nuclei from $A=47$ to 229. Neutron-proton (n-p) interaction is expected to be the major contributor to this difference. This difference, excluding certain mass regions and taking other effects as well as the odd-even mass difference into account, may be linearly parametrized by the Casten factor, a recognized measure of the n-p interaction in the nucleus. The results follow the same pattern as in the case of even…
Coupled equations for even and odd particle number correlation functions are set up via the equation of motion method. For the even particle number case this leads to self-consistent RPA (SCRPA) equations already known from the literature. From the equations of the odd particle number case the single particle occupation probabilities are obtained in a self-consistent way. This is the essential new procedure of this work. Both, even and odd particle number cases are based on the same correlated vacuum and, thus, are coupled equations. Applications to the Lipkin model and the 1D Hubbard model gi…
Mixing single and triple fermions an exact killing operator of the Coupled Cluster Doubles (CCD) wave function with good symmetry was found in \cite{Tohy13}. Using these operators with the equation of motion (EOM) method the so-called self-consistent odd particle number random phase approximation (odd-RPA) was set up. Together with the stationarity condition of the two body density matrix it is shown that the killing conditions allow to reduce the order of correlation functions contained in the matrix elements of the odd-RPA equations to a fully self consistent equation for the single particle…
To assess how anisotropic transverse flow is created in a system out of equilibrium, we compare several kinetic-theoretical models in the few-rescatterings regime. We compare the flow harmonics $v_n$ from three types of transport simulations, with either $2\to 2$ or $2\to 0$ collision kernels and in the former case allowing the particles to rescatter several times or not, and from analytical calculations neglecting the gain term of the Boltzmann equation. We find that the even flow harmonics are similar in all approaches, while the odd ones differ significantly. This suggests that while even $…
The differences between the experimental and Relativistic Mean Field binding energies have been calculated for a large number of even-even nuclei from A=50 to 220. Excluding certain mass regions, the differences, after suitable corrections for particular isotope chains, are found to be proportional to the Casten factor $P$, chosen as a measure of n-p interaction strength in a nucleus. Results for even-$Z$ odd-$N$ nuclei are also seen to follow the same relation, if the odd-even mass difference is taken into account following the semiempirical formula. This indicates that the n-p interaction is…
Odd-even mass differences of well and rigidly deformed nuclei in the rare earth region: A test of a newly proposed fit of average pairing matrix elements
We explore the systematics of odd-even mass staggering with a view to identifying the physical mechanisms responsible. The BCS pairing and mean field contributions have A- and number parity dependencies which can help disentangle the different contributions. This motivates the two-term parametrization c_1 + c_2/A as a theoretically based alternative to the inverse power form traditionally used to fit odd-even mass differences. Assuming that the A-dependence of the BCS pairing is weak, we find that mean-field contributions are dominant below mass number A~40 while BCS pairing dominates in heavi…
We present a systematic analysis of the description of odd nuclei by the Skyrme-Hartree-Fock approach augmented with pairing in BCS approximation and blocking of the odd nucleon. Current and spin densities in the Skyrme functional produce time-odd mean fields (TOMF) for odd nuclei. Their effect on basic properties (binding energies, odd-even staggering, separation energies and spectra) is investigated for the three Skyrme parameterizations SkI3, SLy6, and SV-bas. About 1300 spherical and axially-deformed odd nuclei with 16 < Z < 92 are considered. The calculations demonstrate that the TOMF eff…
Time-odd mean fields (nuclear magnetism) are analyzed in the framework of covariant density functional theory (CDFT). It is shown that they always provide additional binding to the binding energies of odd-mass nuclei. This additional binding only weakly depends on the RMF parametrization reflecting good localization of the properties of time-odd mean fields in CDFT. The underlying microscopic mechanism is discussed in detail. Time-odd mean fields affect odd-even mass differences. However, our analysis suggests that the modifications of the strength of pairing correlations required to compensat…
The anomaly in Coulomb energy differences (CED) between the isospin T=1 states in the odd-odd N=Z nucleus 70Br and the analogue states in its even-even partner 70Se has remained a puzzle. This is a direct manifestation of isospin-symmetry breaking in effective nuclear interactions. Here, we perform large-scale shell-model calculations for nuclei with A=66-78 using the new filter diagonalization method based on the Sakurai-Sugiura algorithm. The calculations reproduce well the experimental CED. The observed negative CED for A=70 are accounted for by the cross-shell neutron excitations from the …
We present a self-consistent theory for odd nuclei with exact blocking and particle number and angular momentum projection. The demanding treatment of the pairing correlations in a variation-after-projection approach as well as the explicit consideration of the triaxial deformation parameters in a projection after variation method, together with the use of the finite-range density-dependent Gogny force, provides an excellent tool for the description of odd-even and even-even nuclei. We apply the theory to the Magnesium isotopic chain and obtain an outstanding description of the ground-state pr…
The odd-even differences in stability peninsula for $106 \leqslant Z \leqslant 112$ region with the deformed relativistic Hartree-Bogoliubov theory in continuum
Accurate estimates of the binding energy of nuclei far from stability that cannot be produced in the laboratory are crucial to our understanding of nuclear processes in astrophysical scenarios. Models based on energy density functionals have shown that they are capable of reproducing all known masses with root-mean-square error better than 800 keV, while retaining a firm microscopic foundation. However, it was recently pointed out in [M. Hukkanen et al., arXiv:2210.10674] that the recent BSkG1 model fails to account for a contribution to the binding energy that is specific to odd-odd nuclei, a…
We present a model which describes the properties of odd-even nuclei with one nucleon more, or less, with respect to the magic number. In addition to the effects related to the unpaired nucleon, we consider those produced by the excitation of the closed shell core. By using a single particle basis generated with Hartree-Fock calculations, we describe the polarization of the doubly magic-core with Random Phase Approximation collective wave functions. In every step of the calculation, and for all the nuclei considered, we use the same finite-range nucleon-nucleon interaction. We apply our model …
The basis space in the triaxial projected shell model (TPSM) approach is generalized for odd-odd nuclei to include two-neutron and two-proton configurations on the basic one-neutron coupled to one-proton quasiparticle state. The generalization allows to investigate odd-odd nuclei beyond the band crossing region and as a first application of this development, high-spin band structures recently observed in odd-odd $^{194-200}$Tl isotopes are investigated. In some of these isotopes, the doublet band structures observed after the band crossing have been conjectured to arise from the spontaneous br…
The odd-even mass staggering in nuclei is analyzed in the context of self-consistent mean-field calculations, for spherical as well as for deformed nuclei. For these nuclei, the respective merits of the energy differences $Δ^{(3)}$ and $Δ^{(5)}$ to extract both the pairing gap and the time-reversal symmetry breaking effect at the same time are extensively discussed. The usual mass formula $Δ^{(3)}$, is shown to contain additional mean-field contributions when realistic pairing is used in the calculation. A simple tool is proposed in order to remove time-reversal symmetry breaking effects from …
Two types of average neutron-proton interaction formulas are compared: In the first type, neutron-proton interactions for even-even and odd-$A$ nuclei extracted from experimental binding energies show a smooth behavior as a function of mass number $A$ and are dominated by the contribution from the symmetry energy. Whereas in the second type large systematic staggering is seen between even-$A$ and odd-$A$ nuclei. This deviation is understood in term of the additional neutron-proton interaction in odd-odd nuclei relative to the neighboring even-even and odd-$A$ systems. We explore three possible…
Beta-decay properties of proton-rich odd-A and even-even Krypton isotopes are studied in the framework of a deformed selfconsistent Hartree-Fock calculation with density-dependent Skyrme forces, including pairing correlations between like nucleons in BCS approximation. Residual spin-isospin interactions are consistently included in the particle-hole and particle-particle channels and treated in Quasiparticle Random Phase Approximation. The similarities and differences in the treatment of even-even and odd-A nuclei are stressed. Comparison to available experimental information is done for Gamow…
A simple model based on the group SO(5) suggests that both the like-particle and neutron-proton components of isovector pairing correlations in odd-A nuclei are Pauli blocked. The same effect emerges from Monte Carlo Shell-model calculations of proton-rich nuclei in the full fp shell. There are small differences between the two models in their representation of the effects of an odd nucleon on the competition between like-particle and neutron-proton pairing, but they can be understood and reduced by using a two-level version of the SO(5) model. On the other hand, in odd-odd nuclei with N not e…
Approximate analytical formulas for the self-consistent renormalization of P,T-odd and P-odd weak nuclear potentials by the residual nucleon-nucleon strong interaction are derived. The contact spin-flip nucleon-nucleon interaction reduces the constant of the P,T-odd potential 1.5 times for the proton and 1.8 times for the neutron. Renormalization of the P-odd potential is caused by the velocity dependent spin-flip component of the strong interaction. In the standard variant of $π+ ρ$-exchange, the conventional strength values lead to anomalous enhancement of the P-odd potential. Moreover, the …
We present an approach for the calculation of odd-nuclei with exact self-consistent blocking and particle number and angular momentum projection with the finite range density dependent Gogny force. As an application we calculate the nucleus $^{31}$Mg at the border of the $N=20$ inversion island. We evaluate the ground state properties, the excited states and the transition probabilities. In general we obtain a good description of the measured observables.
The orthosymplectic extension of the Interacting Vector Boson Model (IVBM) is used for the simultaneous description of the spectra of different families of neighboring heavy nuclei. The structure of even-even nuclei is used as a core on which the collective excitations of the neighboring odd-mass and odd-odd nuclei are built on. Hence, the spectra of the odd-mass and odd-odd nuclei arise as a result of the consequent and self-consistent coupling of the fermion degrees of freedom of the odd particles, specified by the fermion sector $SO^{F}(2Ω)\subset OSp(2Ω/12,R)$, to the boson core which stat…
In these proceedings, we report first results for particle-number and angular-momentum projection of self-consistently blocked triaxial one-quasiparticle HFB states for the description of odd-A nuclei in the context of regularized multi-reference energy density functionals, using the entire model space of occupied single-particle states. The SIII parameterization of the Skyrme energy functional and a volume-type pairing interaction are used.
Proton-neutron (p-n) interactions and its various aspects in $N\approx Z$ nuclei of $g_{9/2}$- and $f_{7/2}$ subshell are studied using a schematic model interaction with four force parameters proposed recently. It is shown that the model interaction well reproduces observed physical quantities: the double differences of binding energies, symmetry energy, Wigner energy, odd-even mass difference and separation energy, which testifies the reliability of the model interaction and its p-n interactions. First of all, the double differences of binding energies are used for probing the p-n interactio…
The binding energies of even-even and odd-odd N=Z nuclei are compared. After correcting for the symmetry energy we find that the lowest T=1 state in odd-odd N=Z nuclei is as bound as the ground state in the neighboring even-even nucleus, thus providing evidence for isovector np pairing. However, T=0 states in odd-odd N=Z nuclei are several MeV less bound than the even-even ground states. We associate this difference with a pair gap and conclude that there is no evidence for an isoscalar pairing condensate in N=Z nuclei.
The self-consistent model, developed previously to describe phonon coupling (PC) effects in magnetic moments of odd magic and semi-magic nuclei, is extended to quadrupole moments. It is based on the theory of finite Fermi systems with the use of the perturbation theory in $g_L^2$, where $g_L$ is the vertex creating the $L$-phonon. Accounting for the phonon tadpole diagrams is an important ingredient of this model. The calculation scheme is based on the Fayans energy density functional DF3-a and does not contain any adjusted parameters. The odd In and Sb isotopes are considered, which are the p…
The self-consistent Theory of Finite Fermi Systems based on the Energy Density Functional by Fayans et al. with the set DF3-a of parameters fixed previously is used to calculate three kinds of quadrupole moments. At first, we examined systematically quadrupole moments of odd neighbors of semi-magic lead and tin isotopes and $N=50,N=82$ isotones. Second, we found quadrupole moments of the first $2^+$ states in the same two chains of isotopes. Finally, we evaluated quadrupole moments of odd-odd nuclei neighboring to double magic ones. Reasonable agreement with available experimental data has bee…
We develop a novel theoretical method for calculating spectroscopic properties of those nuclei with odd number of nucleons, that is based on the nuclear density functional theory and the particle-boson coupling scheme. Self-consistent mean-field calculation based on the DFT is performed to provide microscopic inputs to build the Hamiltonian of the interacting boson-fermion systems, which gives excitation spectra and transition rates of odd-mass nuclei. The method is successfully applied to identify the quantum shape phase transitions and the role of octupole correlations in odd-mass nuclei, an…
Spectroscopic properties that characterize shape phase transitions in neutron-rich odd-A Zr isotopes are investigated using the framework of nuclear density functional theory and particle-core coupling. The interacting-boson Hamiltonian of the even-even core nuclei, and the single-particle energies and occupation probabilities of the unpaired neutron are completely determined by deformation constrained self-consistent mean-field calculations based on the relativistic Hartree-Bogoliubov model with a choice of a universal energy density functional and pairing interaction. The triaxial $(β,γ)$ de…
Systematic odd-even binding energy differences in finite metallic particles are usually attributed to mean-field orbital energy effects or to a coherent pairing interaction. We show analytically and numerically that a purely random two-body Hamiltonian can also give rise to an odd-even staggering. We explore the characteristics of this chaotic mechanism and discuss distinguishing features with respect to the other causes of staggering. In particular, randomness-induced staggering is found to be a smooth function of particle number, and the mechanism is seen to be largely insensitive to the pre…
We present a method to calculate spectroscopic properties of odd-odd nuclei within the framework of the Interacting Boson-Fermion-Fermion Model based on the Gogny energy density functional. The $(β,γ)$-deformation energy surface of the even-even (boson-)core nucleus, spherical single-particle energies and occupation probabilities of the odd neutron and odd proton, are provided by the constrained self-consistent mean-field calculation within the Hartree-Fock-Bogoliubov method with the Gogny-D1M functional. These quantities are used as a microscopic input to fix most of the parameters of the IBF…
The Coulomb effects hypothesis is used to interpret even-odd effects of maximum total kinetic energy as a function of mass and charge of fragments from thermal neutron induced fission of 235U. Assuming spherical fragments at scission, the Coulomb interaction energy between fragments (C_sph) is higher than the Q-value, the available energy. Therefore at scission the fragments must be deformed, so that the Coulomb interaction energy does not exceed the Q-value. The fact that the even-odd effects in the maximum total kinetic energy as a function of the charge and mass, respectively, are lower tha…
