Exotic cluster decay of very heavy nuclei has been studied in the microscopic Super-Asymmetric Fission Model. Relativistic Mean Field model with the force FSU Gold has been employed to obtain the densities of the cluster and the daughter nuclei. The microscopic nuclear interaction DDM3Y1, which has an exponential density dependence, and the Coulomb interaction have been used in the double folding model to obtain the potential between the cluster and the daughter. Half life values have been calculated in the WKB approximation and the spectroscopic factors have been extracted. The latter values are seen to have a simple dependence of the mass of the cluster as has been observed earlier. Predictions have been made for some possible decays.
The effects of relativistic kinematics are studied for nuclear collisions of equal mass nuclei. It is found that the relativistic and non-relativistic elastic scattering amplitudes are nearly indistinguishable, and, hence, the relativistic and non-relativistic differential cross sections become indistinguishable. These results are explained by analyzing the Lippmann-Schwinger equation with the first order optical potential that was employed in the calculation
We have investigated energy levels mirror nuclei of the 17O and 17F in relativistic and non-relativistic shell model. The nuclei 17O and 17F can be modeled as a doubly-magic 17O=n+(N=Z=8) and 17F=p+(N=Z=8), with one additional nucleon (valence) in the ld5/2 level. Then we have selected the quadratic Hellmann potential for interaction between core and single nucleon. Using Parametric Nikiforov-Uvarov method, we have calculated the energy levels and wave function in Dirac and Schrodinger equations for relativistic and non-relativistic, respectively. Finally, we have computed the binding and exci…
By using the scaling method we derive the virial theorem for the relativistic mean field model of nuclei treated in the Thomas-Fermi approach. The Thomas-Fermi solutions statisfy the stability condition against scaling. We apply the formalism to study the excitation energy of the breathing mode in finite nuclei with several relativistic parameter sets of common use.
Density dependent relativistic Hartree-Fock theory has been extended to describe properties of exotic nuclei. The effects of Fock exchange terms and of pi - and rho - meson contributions are discussed. These effects are found to be more important for neutron rich nuclei than for nuclei near the valley of stability.
The identification of pseudospin symmetry as a relativistic symmetry of the Dirac Hamiltonian is used to explain the structure of radial nodes occurring in pseudospin doublets and to illuminate the special status of nodeless intruder states in nuclei.
A relativistic coupled-channels theory for the calculation of dissociation cross sections of halo nuclei is developed. A comparison with non-relativistic models is done for the dissociation of $^{8}$B projectiles. It is shown that neglecting relativistic effects leads to seizable inaccuracies in the extraction of the astrophysical S-factor for the proton+beryllium radiative capture reaction.
We calculate the binding energy and deformation parameter for light nuclei with and without pairing using a deformed relativistic mean field model. The role of BCS-type pairing effect is analyzed for Ne and F isotopes. The calculated odd-even staggering and the deformation parameters argue strongly against the role of pairing in the light nuclei.
Relativistic Mean Field Theory in the rotating frame is used to describe superdeformed nuclei. Nuclear currents and the resulting spatial components of the vector meson fields are fully taken into account. Identical bands in neighboring Rare Earth nuclei are investigated and excellent agreement with recent experimental data is observed.
We review recent developments that show that pseudospin symmetry is an approximate relativistic symmetry of the Dirac Hamiltonian with realistic nuclear mean field potentials.
The hypothesis of a large weak matrix element between single-particle states in heavy nuclei ($\sim 100$ eV) contradicts the results of atomic PNC experiments.
We study the structural properties of some nuclei in the region of light mass using simple effective interaction in the frame work of microscopic non relativistic Hartree-Fock and relativistic mean field formalism. For the reaction dynamics, well known Glauber model is used with the conjunctions of the densities obtained from these formalism. We observe good agreement of results by both the formalism in comparison to the experimental values. These two different approaches seems to be equally capable to reproduce the ground state properties of nuclei in this region. A careful study of reaction …
Starting with a bare nucleon-nucleon interaction, for the first time the full relativistic Brueckner-Hartree-Fock equations are solved for finite nuclei in a Dirac-Woods-Saxon basis. No free parameters are introduced to calculate the ground-state properties of finite nuclei. The nucleus $^{16}$O is investigated as an example. The resulting ground-state properties, such as binding energy and charge radius, are considerably improved as compared with the non-relativistic Brueckner-Hartree-Fock results and much closer to the experimental data. This opens the door for \emph{ab initio} covariant inv…
The Dirac structure of the nucleon self-energy in asymmetric nuclear matter cannot reliably be deduced from the momentum dependence of the single-particle energies. It is demonstrated that such attempts yield an isospin dependence with even a wrong sign. Relativistic studies of finite nuclei have been based on such studies of asymmetric nuclear matter. The effects of these isospin components on the results for finite nuclei are investigated.
We formulate a general relativistic mean field theory for rotating nuclei starting from the special relativistic $σ- ω$ model Lagrangian. The tetrad formalism is adopted to generalize the model to the accelerated frame.
Shell-model states involving several pseudospin doublets and ``intruder'' levels in nuclei, are combined into larger multiplets. The corresponding single-particle spectrum exhibits a supersymmetric pattern whose origin can be traced to the relativistic pseudospin symmetry of a nuclear mean-field Dirac Hamiltonian with scalar and vector potentials.
Cluster radioactivity is an exotic nuclear decay observed in actinides where a light nucleus is emitted while the remaining heavy mass residue is the doubly magic $^{208}$Pb or a nucleus in its neighborhood. We have investigated this type of decay in heavier nuclei up to Lv $(Z=116)$ within a microscopic theory. It has been found that super asymmetric fission with $^{208}$Pb as heavy fragment may be dominant decay channel in some super heavy nuclei. This reaction is closely related with cluster radioactivity.
Starting from the relativistic form of the Bonn potential as a bare nucleon-nucleon interaction, the full Relativistic Brueckner-Hartree-Fock (RBHF) equations are solved for finite nuclei in a fully self-consistent basis. This provides a relativistic ab initio calculation of the ground state properties of finite nuclei without any free parameters and without three-body forces. The convergence properties for the solutions of these coupled equations are discussed in detail at the example of the nucleus $^{16}$O. The binding energies, radii, and spin-orbit splittings of the doubly magic nuclei $^…
Journal of Combinatorial Theory, Series B, 98(1):173-225, 2008n exotic nuclei are studied in the framework of a fully self-consistent relativistic continuum random phase approximation (RCRPA). In this method the contribution of the continuum spectrum to nuclear excitations is treated exactly by the single particle Green's function. Different from the cases in stable nuclei, there are strong low-energy excitations in neutron-rich nuclei and proton-rich nuclei. The neutron or proton excess pushes the centroid of the strength function to lower energies and increases the fragmentation of the stren…
The DIRHB package consists of three Fortran computer codes for the calculation of the ground-state properties of even-even atomic nuclei using the framework of relativistic self-consistent mean-field models. Each code corresponds to a particular choice of spatial symmetry: the DIRHBS, DIRHBZ and DIRHBT codes are used to calculate nuclei with spherical symmetry, axially symmetric quadrupole deformation, and triaxial quadrupole shapes, respectively. Reflection symmetry is assumed in all three cases. The latest relativistic nuclear energy density functionals are implemented in the codes, thus ena…
Gamow-Teller(GT) resonances in finite nuclei are studied in a fully consistent relativistic random phase approximation (RPA) framework. A relativistic form of the Landau-Migdal contact interaction in the spin-isospin channel is adopted. This choice ensures that the GT excitation energy in nuclear matter is correctly reproduced in the non-relativistic limit. The GT response functions of doubly magic nuclei $^{48}$Ca, $^{90}$Zr and $^{208}$Pb are calculated using the parameter set NL3 and $g_0'$=0.6 . It is found that effects related to Dirac sea states account for a reduction of 6-7 % in the GT…
In this contribution, we present the main relations of the Langevin approach to the description of fission or fusion-fission reactions. The results of Langevin calculations are shown for the mass distributions of fission fragments of super-heavy elements and used for the investigation of memory effects in nuclear fission.
We develop a self-consistent description of hot nuclei within the relativistic Thomas--Fermi approximation using the relativistic mean-field model for nuclear interactions. The temperature dependence of the symmetry energy and other physical quantities of a nucleus are calculated by employing the subtraction procedure in order to isolate the nucleus from the surrounding nucleon gas. It is found that the symmetry energy coefficient of finite nuclei is significantly affected by the Coulomb polarization effect. We also examine the dependence of the results on nuclear interactions and make a compa…
Extensive efforts have been made experimentally to reach nuclei in the super heavy mass region of Z = 110 and above with suitable choices of projectile and target nuclei. The cross sections for production of these nuclei are seen to be in the range of a few picobarn or less, and pose great experimental challenges. Theoretically, there have been extensive calculations for highly asymmetric (hot-fusion) and moderately asymmetric (cold-fusion) collisions and only a few theoretical studies are available for near symmetric collisions to estimate the cross sections for production of super-heavy nucl…
In this work we calculate the caloric curve (excitation energy per particle as a function of temperature) for finite nuclei within the non--linear Walecka model for different proton fractions. It is shown that the caloric curve is sensitive to the proton fraction. Freeze-out volume effects in the caloric curve are also studied.
Relativistic Mean Field calculations have been performed for a number of nuclei in mass $A\approx$80 region. Ground state binding energy, charge radius and charge density values have been compared with experiment. Optical potential have been generated folding the nuclear density with the microscopic nuclear interaction DDM3Y. S-factors for low energy ($p,γ$) and ($p,n$) reactions have been calculated and compared with experiment.
The single-particle spectrum of deformed shell-model states in nuclei, is shown to exhibit a supersymmetric pattern. The latter involves deformed pseudospin doublets and intruder levels. The underlying supersymmetry is associated with the relativistic pseudospin symmetry of the nuclear mean-field Dirac Hamiltonian with scalar and vector potentials.
Hartree-Fock calculations with the SKX Skyrme interaction are carried out to obtain alpha-decay Q values for deformed nuclei above $^{208}$Pb assuming axial symmetry. The results for even-even nuclei are compared with experiment and with previous calculations. Predictions are made for alpha-decay Q values and half-lives of even-even super-heavy nuclei. The results are also compared for the recently discovered odd-even chain starting at Z=112 and N=165.
Starting from light to superheavy nuclei, we have calculated the effective surface properties such as the symmetry energy, neutron pressure, and symmetry energy curvature using the coherent density fluctuation model. The isotopic chains of O, Ca, Ni, Zr, Sn, Pb, and Z = 120 are considered in the present analysis, which cover nuclei over the whole nuclear chart. The matter density distributions of these nuclei along with the ground state bulk properties are calculated within the spherically symmetric effective field theory motivated relativistic mean field model by using the recently developed …
A fully consistent relativistic random phase approximation is applied to study the systematic behavior of the isovector giant dipole resonance of nuclei along the $β$-stability line in order to test the effective Lagrangians recently developed. The centroid energies of response functions of the isovector giant dipole resonance for stable nuclei are compared with the corresponding experimental data and the good agreement is obtained. It is found that the effective Lagrangian with an appropriate nuclear symmetry energy, which can well describe the ground state properties of nuclei, could also re…
We study the extremely neutron-rich nuclei for $Z = 17 - 23$, $37 - 40$ and $60 - 64$ regions of the periodic table by using axially deformed relativistic mean field formalism with NL3* parametrization. Based on the analysis of binding energy, two neutron separation energy, quadrupole deformation and root mean square radii, we emphasized the speciality of these considered regions which are recently predicted islands of inversion.
We present a review of recent applications of the relativistic mean-field theory to the structure of nuclei close to the drip-lines. For systems with extreme isospin values, the relativistic Hartree-Bogoliubov model provides a unified and self-consistent description of mean-field and pairing correlations. The model has been applied in studies of structure phenomena that include: formation of neutron skin and of neutron halos in light nuclei in the mass region above the s-d neutron shell, the strong isospin dependence of the effective spin-orbit interaction and the resulting modification of sur…
A parameter free investigation of the moments of inertia of ground state rotational bands in well deformed rare-earth nuclei is carried out using Cranked Relativistic Hartree-Bogoliubov (CRHB) and non-relativistic Cranked Hartree-Fock-Bogoliubov (CHFB) theories. In CRHB theory, the relativistic fields are determined by the non-linear Lagrangian with the NL1 force and the pairing interaction by the central part of finite range Gogny D1S force. In CHFB theory, the properties in particle-hole and particle-particle channels are defined solely by Gogny D1S forces. Using an approximate particle numb…
The relativistic mean-field effective interaction with density-dependent meson-nucleon couplings DD-ME1 is tested in the calculation of deformed nuclei. Ground-state properties of six isotopic chains ($60\le Z \le 70$) in the region of rare-earth nuclei are calculated by using the relativistic Hartree-Bogoliubov (RHB) model with the DD-ME1 mean-field interaction, and with the Gogny D1S force for the pairing interaction. Results of fully self-consistent RHB calculations for the total binding energies, charge isotope shifts and quadrupole deformation parameters are compared with the available em…
We considered the systematics of $α$-decay (AD) half-life (HL) of super-heavy nuclei versus the decay energy and the total $α$-kinetic energy. We calculated the HL using the experimental Q_{$α$} values. The computed half-lives are compared with the experimental data and also with the existing empirical estimates and are found in good agreement. Also, we obtained $α$-preformation factors from the ratio between theoretical and experimental results for some super heavy nuclei SHN and evaluated the standard deviation. The results indicate the acceptability of the approach.
Total Ordinary Muon Capture (OMC) rates are calculated on the basis of the Quasiparticle Random Phase Approximation for several spherical nuclei from 90^Zr to 208^Pb. It is shown that total OMC rates calculated with the free value of the axial-vector coupling constant g_A agree well with the experimental data for medium-size nuclei and exceed considerably the experimental rates for heavy nuclei. The sensitivity of theoretical OMC rates to the nuclear residual interactions is discussed.
The basic version of the semi-microscopic particle-hole dispersive optical model is implemented to describe main properties of the Gamow-Teller and charge-exchange giant spin-monopole resonances in medium-heavy closed-shell parent nuclei. Calculation results obtained for $^{48}Ca$, $^{90}Zr$, $^{132}Sn$, and $^{208}Pb$ are compared with available experimental data.
We study finite nuclei, at the mean-field level, using the Zimanyi-Moskowski model and one of its variations (the ZM3 model). We calculate energy levels and ground-state properties in nuclei where the mean-field approach is reliable. The role played by the spin-orbit potential in sorting out mean-field model descriptions is emphasized.
Using the relativistic point-coupling model with density functional PC-PK1, the magnetic moments of the nuclei $^{207}$Pb, $^{209}$Pb, $^{207}$Tl and $^{209}$Bi with a $jj$ closed-shell core $^{208}$Pb are studied on the basis of relativistic mean field (RMF) theory. The corresponding time-odd fields, the one-pion exchange currents, and the first- and second-order corrections are taken into account. The present relativistic results reproduce the data well. The relative deviation between theory and experiment for these four nuclei is 6.1% for the relativistic calculations and somewhat smaller t…
We compare the systematics of binding energies computed within the standard and extended versions of the relativistic mean-field (RMF) model and the Skyrme Hartree-Fock (SHF) model. The general trends for the binding energies for super-heavy nuclei are significantly different for these models. The SHF models tend to underbind the superheavy nuclei, while, RMF models show just the opposite trend. The extended RMF model seems to provide remarkable improvements over the results obtained for the standard RMF model.
The relativistic Hartree approach describing the bound states of both nucleons and anti-nucleons in finite nuclei has been extended to include tensor couplings for the $ω$- and $ρ$-meson. After readjusting the parameters of the model to the properties of spherical nuclei, the effect of tensor-coupling terms rises the spin-orbit force by a factor of 2, while a large effective nucleon mass $m^{*}/M_{N} \approx 0.8$ sustains. The overall nucleon spectra of shell-model states are improved evidently. The predicted anti-nucleon spectra in the vacuum are deepened about 20 -- 30 MeV.
The cranked relativistic mean field (CRMF) theory is applied for the description of superdeformed (SD) rotational bands observed in $^{153}$Ho. The question of the structure of the so-called SD band in $^{154}$Er is also addressed and a brief overview of applications of CRMF theory to the description of rotating nuclei at extreme conditions is presented.
The cranked relativistic Hartree+Bogoliubov theory has been applied for a systematic study of the nuclei around 254No, the heaviest nuclei for which detailed spectroscopic data are available. The deformation, rotational response, pairing correlations, quasi-particle and other properties of these nuclei have been studied with different relativistic mean field (RMF) parametrizations. For the first time, the quasi-particle spectra of odd deformed nuclei have been calculated in a fully self-consistent way within the framework of the RMF theory. The energies of the spherical subshells, from which a…
We present a relativistic model for electroweak pion production from nuclei, focusing on the $Δ$ and the second resonance region. Bound states are derived in the Hartree approximation to the $σ-ω$ Walecka model. Final-state interactions of the outgoing pion and nucleon are described in a factorized way by means of a relativistic extension of the Glauber model. Our formalism allows a detailed study of neutrino pion production through $Q^2$, $W$, energy, angle and out-of-plane distributions.
The equation of state (EOS) of finite nuclei is constructed in the relativistic Thomas-Fermi theory using the non-linear $σ-ω-ρ$ model. The caloric curves are calculated by confining the nuclei in the freeze-out volume taken to be a sphere of size about 4 to 8 times the normal nuclear volume. The results obtained from the relativistic theory are not significantly different from those obtained earlier in a non-relativistic framework. The nature of the EOS and the peaked structure of the specific heat $C_v$ obtained from the caloric curves show clear signals of a liquid-gas phase transition in f…
Recently it has been shown that pseudospin symmetry has its origins in a relativistic symmetry of the Dirac Hamiltonian. Using this symmetry we relate single - nucleon relativistic magnetic moments of states in a pseudospin doublet to the relativistic magnetic dipole transitions between the states in the doublet, and we relate single - nucleon relativistic Gamow - Teller transitions within states in the doublet. We apply these relationships to the Gamow - Teller transitions from $^{39}Ca$ to its mirror nucleus $^{39}K$.
The relativistic mean field theory is applied to study some exotic properties of neutron rich nuclei as recently observed, namely, extension of the drip-line for $F$ nuclei from $^{29}F$ to $^{31}F$ and the appearence of a new shell closure at neutron number N=16. We find $^{31}F$ to be bound against one-neutron dripping but unbound only marginally for two neutron separation. The calculated functional dependence of one-neutron separation energy with neutron number for different values of $T_Z = (N-Z)/2$ signals a new shell closure at N=16 for neutron rich nuclei with $T_Z\ge 3$. This is furthe…
Based on the leading-order covariant pionless effective field theory, a relativistic nuclear Hamiltonian is derived and solved using the variational Monte Carlo approach for $A\le 4$ nuclei by representing the nuclear many-body wave functions with a symmetry-based artificial neural network. It is found that the relativistic effects rescue the renormalizability of the theory, and overcome the energy collapse problem for $^3$H and $^4$He without promoting a repulsive three-nucleon interaction to leading order as in nonrelativistic calculations. Nevertheless, to exactly reproduce the experimental…
A semi-microscopic approach based on both the continum-random-phase-approximation (CRPA) method and a phenomenological treatment of the spreading effect is extended and applied to describe the main properties (particle-hole strength distribution, energy-dependent transition density, partial direct-nucleon-decay branching ratios) of the isoscalar giant dipole, second monopole, and second quadrupole resonances. Abilities of the approach are checked by description of gross properties of the main-tone resonances. Calculation results obtained for the resonances in a few singly- and doubly-closed-sh…
We show that the generators of pseudospin symmetry are the non - relativistic limit of the generators of an SU(2) symmetry which leaves invariant the Dirac Hamiltonian with scalar and vector potentials equal in magnitude but opposite in sign, $V_V = - V_S$. Furthermore, within this framework, we demonstrate that this symmetry may be approximately conserved for realistic scalar and vector potentials.
The analysis of quasiparticle spectra in heaviest $A\sim 250$ nuclei with spectroscopic data provides an additional constraint for the choice of effective interaction for the description of superheavy nuclei. It strongly suggest that only the parametrizations of the relativistic mean field Lagrangian which predict Z=120 and N=172 as shell closures are reliable for superheavy nuclei. The influence of the central depression in the density distribution of spherical superheavy nuclei on the shell structure is studied. Large central depression produces large shell gaps at Z=120 and N=172. The shell…
The correlated basis function theory is applied to the study of medium-heavy doubly closed shell nuclei with different wave functions for protons and neutrons and in the jj coupling scheme. State dependent correlations including tensor correlations are used. Realistic two-body interactions of Argonne and Urbana type, together with three-body interactions have been used to calculate ground state energies and density distributions of the 12C, 16O, 40Ca, 48Ca and 208Pb nuclei.
Exotic cluster decay of very heavy nuclei is studied using the microscopic nuclear potentials obtained by folding density dependent M3Y effective interaction with the densities of the cluster and the daughter nuclei. The microscopic nuclear potential, Coulomb interaction and the centrifugal barrier arising out of spin-parity conservation are used to obtain the potential between the cluster and the daughter nuclei. Half life values are calculated in the WKB framework and the preformation factors are extracted. The latter values are seen to have only a very weak dependence on the mass of the emi…
We construct a scaling function $f(ψ^{\prime})$ for inclusive electron scattering from nuclei within the Coherent Density Fluctuation Model (CDFM). The latter is a natural extension to finite nuclei of the Relativistic Fermi Gas (RFG) model within which the scaling variable $ψ^{\prime}$ was introduced by Donnelly and collaborators. The calculations show that the high-momentum components of the nucleon momentum distribution in the CDFM and their similarity for different nuclei lead to quantitative description of the superscaling in nuclei. The results are in good agreement with the experimental…
As the experimental data from kaonic atoms and $K^{-}N$ scatterings imply that the $K^{-}$-nucleon interaction is strongly attractive at saturation density, there is a possibility to form $K^{-}$-nuclear bound states or kaonic nuclei. In this work, we investigate the ground-state properties of the light kaonic nuclei with the relativistic mean field theory. It is found that the strong attraction between $K^{-}$ and nucleons reshapes the scalar and vector meson fields, leading to the remarkable enhancement of the nuclear density in the interior of light kaonic nuclei and the manifest shift of t…
The shell corrections and shell gaps in nuclei are systematically studied with the latest Weizsäcker-Skyrme (WS4) mass model. We find that most of asymmetric nuclei with (sub)-shell closures locate along the shell stability line (SSL), $N=1.37Z+13.5$, which might be due to a strong correlation between neutrons and protons near Fermi surface. The double magicity of nuclei $^{46}$Si and $^{78}$Ni is predicted according to the corresponding shell gaps, shell corrections and nuclear deformations. The unmeasured super-heavy nuclei $^{296}$118 and $^{298}$120, with relatively large shell gaps and sh…
