Single-particle Degrees Of Freedom Research Articles

Evolution of nuclear structure through isomerism in Fr216

Three new isomers have been identified in the transitional odd-odd $^{216}\mathrm{Fr}$ nucleus. The properties of the $({11}^{+})$ isomer with ${T}_{1/2}$ = 9.6(14) ns are compared with those of the similar isomeric states in neighboring doubly-odd nuclei. The experimental results are compared with predictions of shell-model calculations and a fair agreement is observed between the experimental and calculated excitation energies of the $({11}^{+})$ isomeric state and the states to which it decays. The deviation between the measured and calculated reduced transition probabilities suggests contribution from effects other than the single-particle degrees of freedom in these states. Evidence of two high-spin $[{J}^{\ensuremath{\pi}}>({18}^{+})]$ isomers above 2.2 MeV excitation energy with ${T}_{1/2}=7.8(14)$ and 89(9) ns is also presented. These isomers at high excitation energies reflect a pronounced change in the structure above the previously established level scheme, where moderate quadrupole collectivity and octupole correlations were evident.

Role of Single-Particle Energies in Microscopic Interacting Boson Model Double Beta Decay Calculations

Single-particle level energies form a significant input in nuclear physics calculations where single-particle degrees of freedom are taken into account, including microscopic interacting boson model investigations. The single-particle energies may be treated as input parameters that are fitted to reach an optimal fit to the data. Alternatively, they can be calculated using a mean field potential, or they can be extracted from available experimental data, as is done in the current study. The role of single-particle level energies in the microscopic interacting boson model calculations is discussed with special emphasis on recent double beta decay calculations.

Pairing Dynamics in Low-energy Nuclear Collisions

Superfluidity is a generic feature of various quantum systems at low temperatures and it is in particular important for the description of dynamics of low energy nuclear reactions. The time-dependent density functional theory (TDDFT) is, to date, the only microscopic method which takes into account in a consistent way far from equilibrium dynamics of pairing field and single-particle degrees of freedom. The local version of TDDFT, so called TDSLDA, is particularly useful for the description of nuclear reactions and is well suited for leadership class computers of hybrid (CPU+GPU) architecture. The preliminary results obtained for collisions involving both medium-mass and heavy nuclei at the energies around the Coulomb barrier are presented.

Synergy of nuclear data systematics and proxy-SU(3) in planning future experiments in the superheavies mass region

Spectroscopic information of hard–to–reach superheavy nuclei can be invaluable in understanding the dynamics of nuclear systems at large values of charge and volume. RIB factories of the next generation, such as FAIR, plan to provide heavy ion beams at high energies to facilitate experimental access to these mass regimes. In preparation of future experimental endeavours, a systematic survey of available nuclear data, mainly energies and reduced transition probabilities/lifetimes of short–lived 21+ states in even–even isotopes with Z=82,84,86 was undertaken. The principle motivation is to trace the competition between collective and single-particle degrees of freedom in the mass area just above Pb (Z=82), an area known to exhibit isomerism, octupole degrees of freedom and shape coexistence. Existing data were compared to the theoretical predictions using the analytical, parameter­­–free proxy–SU(3) scheme, for neutron numbers N=96–116. The model was further employed to predict currently unknown values for spectroscopic data in series of Pb, Po and Ra isotopes.

Propagation of statistical uncertainties in covariant density functional theory: Ground state observables and single-particle properties

Statistical errors in ground state observables and single-particle properties of spherical even-even nuclei and their propagation to the limits of nuclear landscape have been investigated in covariant density functional theory (CDFT) for the first time. In this study we consider only covariant energy density functionals with non-linear density dependency. Statistical errors for binding energies and neutron skins significantly increase on approaching two-neutron drip line. On the contrary, such a trend does not exist for statistical errors in charge radii and two-neutron separation energies. The absolute and relative energies of the single-particle states in the vicinity of the Fermi level are characterized by low statistical errors ($\sigma(e_i)\sim 0.1$ MeV). Statistical errors in the predictions of spin-orbit splittings are rather small. Statistical errors in physical observables are substantially smaller than related systematic uncertainties. Thus, at the present level of the development of theory, theoretical uncertainties at nuclear limits are dominated by systematic ones. Statistical errors in the description of physical observables related to the ground state and single-particle degrees of freedom are typically substantially lower in CDFT as compared with Skyrme density functional theory. The correlations between the model parameters are studied in detail. The parametric correlations are especially pronounced for the $g_2$ and $g_3$ parameters which are responsible for the density dependence of the model. The accounting of this fact potentially allows to reduce the number of free parameters of non-linear meson coupling model from six to five.

A study on the dependence of nuclear viscosity on temperature

Nuclear viscosity is an irreplaceable ingredient of nuclear fission collective dynamical models. It drives the exchange of energy between the collective variables and the thermal bath of single particle degrees of freedom. Its dependence on the shape and temperature is a matter of controversy. By using systems of intermediate fissility we have demonstrated in a recent study that the viscosity parameters is larger for compact shapes, and decreases for larger deformations of the fissioning system, at variance with the conclusions of the statistical model modified to include empirically viscosity and time scales. In this contribution we propose an experimental scenario to highlight the possible dependence of the viscosity from the temperature.

Collective and single-particle degrees of freedom in rotating nuclei

In 1937, Hermann Jahn and Edward Teller published their research describing a mechanism of symmetry breaking in nonlinear polyatomic molecules resulting in a lifting of orbital degeneracy of an electronic state (Proc. R. Soc. London, Ser. A 1937, 161, 220), yielding insight into molecular structure. The impact of symmetry breaking on the energy and structure of quantum states is not unique to molecules and may be applied to nuclei, involving degenerate nucleon states as opposed to electronic states. Reinhard and Otten showed that the nuclear Jahn–Teller effect provides a mechanism applicable to describe the commonly observed collective quadrupole surface motion (Nucl. Phys. A 1984, 420, 173). To take into account single-particle effects, it is important to properly model the valence nucleons, especially those occupying large angular momenta orbitals near the Fermi level. In this work, a model has been developed in which two valence nucleons of the same kind are coupled to an axially symmetric quadrupole deformed rotor of the D2 symmetry and interact through the nuclear delta force. To test this model, the band of the lowest-energy state at a given spin for 126Ce is reproduced. The resultant wavefunctions are then used to calculate the g factor, reduced electric quadrupole transition probability, and spectroscopic quadrupole moment all as a function of spin. This method lays the groundwork to explore higher order symmetries following the multipole expansion.

Systematic study of multi-quasiparticleK-isomeric bands in tungsten isotopes by the extended projected shell model

Background: The interplay between collective and single-particle degrees of freedom is an important structure aspect to study. The nuclei in theA ≈ 180 mass region are often denoted as good examples to study such problems because these nuclei are known to exhibit many rotational bands based on multi-quasiparticle K isomers. Purpose: A large set of high-quality experimental data on high-K isomeric states in the A ≈ 180 mass region has accumulated. A systematic description of them is a theoretical challenge as it requires a method going beyond the usual mean field with multi-quasiparticle configurations built in the shell-model basis. The K-isomer data provide an ideal testing ground for theoretical models. Method: The recently extended projected shell model (PSM) by the Pfaffian method is employed with a sufficiently large configuration space including up to 10 quasiparticles. The restoration of rotational symmetry which is broken in the deformed mean field is obtained by means of angular-momentum projection. With axial symmetry in the basis deformation, each multi-quasiparticle state, classified by a K quantum number, represents the major component of a rotational K band. Shell-model diagonalization in such a projected basis defines the K mixing, which is the key ingredient of the present method. Results: Quasiparticle structure and rotational properties of high-K isomers in even-even neutron-rich 174−186W isotopes are described. The rotational evolution of the yrast and near-yrast bands is discussed with successive band crossings. Multi-quasiparticle K isomers and associated rotational bands in each W isotope are studied with detailed quasiparticle configurations given. Electromagnetic transition properties are also studied and the calculated B(E2), B(M1), and g-factors are compared with experiment if data exist. Conclusions: Many nuclei of the A ≈ 180 mass region exhibit properties of an axially symmetric shape and K is approximately a good quantum number. For such nuclei, the extended PSM assuming an axially symmetric basis but including K mixing through diagonalization of the two-body Hamiltonian is an appropriate method to study multi-quasiparticle K isomers and K violations in these states. For special examples where one finds highly K-forbidden transitions the present model needs to be further improved.

Triaxial shape fluctuations and quasiparticle excitations in heavy nuclei

The deformation parameters beta and gamma together with the two-quasiparticle excitations are taken into account, for the first time, as coordinates within a symmetry conserving (angular momentum and particle number) generator coordinate method. The simultaneous consideration of collective as well as single particle degrees of freedom allows us to describe soft and rigid nuclei as well as the transition region in between. We apply the new theory to the study of the spectra and transition probabilities of the 156-172Er isotopes with a Pairing plus Quadrupole residual interaction. Good agreement with the experimental results is obtained for most of the observables studied and with the same quality for the very soft and the strongly deformed nuclei.

Neutron drip line: Single-particle degrees of freedom and pairing properties as sources of theoretical uncertainties

The sources of theoretical uncertainties in the prediction of the two-neutron drip line are analyzed in the framework of covariant density functional theory. We concentrate on single-particle and pairing properties as potential sources of these uncertainties. The major source of these uncertainties can be traced back to the differences in the underlying single-particle structure of the various covariant energy density functionals (CEDF). It is found that the uncertainties in the description of single-particle energies at the two-neutron drip line are dominated by those existing already in known nuclei. Only approximately one third of these uncertainties are due to the uncertainties in the isovector channel of CEDF's. Thus, improving the CEDF description of single-particle energies in known nuclei will also reduce the uncertainties in the prediction of the position of two-neutron drip line. The predictions of pairing properties in neutron rich nuclei depend on the CEDF. Although pairing properties affect moderately the position of the two-neutron drip line they represent only a secondary source for the uncertainties in the definition of the position of the two-neutron drip line.

Dissipation dynamics and spin-orbit force in time-dependent Hartree-Fock theory

We investigate the one-body dissipation dynamics in heavy-ion collisions of $^{16}\mathrm{O}+^{16}\mathrm{O}$ using a fully three-dimensional time-dependent Hartree-Fock (TDHF) theory with the modern Skyrme energy functional and without any symmetry restrictions. The energy dissipation is revealed to decrease in deep-inelastic collisions of the light systems as the bombarding energy increases owing to the competition between collective motion and single-particle degrees of freedom. The role of spin-orbit force is given particular emphasis in deep-inelastic collisions. The spin-orbit force causes a significant enhancement of the dissipation. The time-even coupling of spin-orbit force plays a dominant role at low energies, while the influence of time-odd terms is notable at high energies. About 40--65% of the total dissipation depending on the different parameter sets is predicted to arise from the spin-orbit force. The theoretical fusion cross section has a reasonably good agreement with the experimental data, considering that no free parameters are adjusted to reaction dynamics in the TDHF approach.

Effect of tensor force on dissipation dynamics in time-dependent Hartree-Fock theory

The role of tensor force on the collision dynamics of 16O+16O is investigated in the framework of a fully three-dimensional time-dependent Hartree-Fock theory. The calculations are performed with modern Skyrme energy functional plus tensor terms. Particular attention is given on the analysis of dissipation dynamics in heavy-ion collisions. The energy dissipation is found to decrease as an initial bombarding energy increases in deep-inelastic collisions for all the Skyrme parameter sets studied here because of the competition between the collective motion and the single-particle degrees of freedom. We reveal that the tensor forces may either enhance or reduce the energy dissipation depending on the different parameter sets. The fusion cross section without tensor force overestimates the experimental value by about 25%, while the calculation with tensor force T11 has good agreement with experimental cross section.

Low-lying bands with different quadrupole deformation in155Dy

To investigate the interplay between collective and single particle degrees of freedom in odd nuclei, Recoil distance Doppler-shift and Doppler-shift attenuation lifetime measurements were carried out for levels in 155Dy in coincidence detection of gamma-rays. 26 lifetimes were determined using the Differential decay curve method. Particle plus triaxial rotor model (PTRM) calculations were performed to compare the experimental level scheme and transition strengths with theoretical ones in order to get information on the quadrupole deformation (є,γ) of the bands. As a result, different quadrupole deformations for the one-quasineutron bands at low and medium spins are deduced.

Transfer Reaction Studies with Spectrometers

The revival of transfer reaction studies benefited from the construction of the new generation large solid angle spectrometers, coupled to large γ arrays. The recent results of γ-particle coincident measurements in Ca+Zr and Ar+Pb reactions demonstrate a strong interplay between single-particle and collective degrees of freedom that is pertinent to the reaction dynamics. The development of collectivity has been followed in odd Ar isotopes populated in the Ar+Pb reaction through the excitation of the 11/2− states, understood as the coupling of single particle degrees of freedom to nuclear vibration quanta. Pair transfer modes is another important degree of freedom which is presently being studied with Prisma in inverse kinematics at energies far below the Coulomb barrier. First results from the Zr+Ca reaction elucidate the role played by nucleon–nucleon correlation.

TIDAL WAVES – A NON-ADIABATIC MICROSCOPIC DESCRIPTION OF THE YRAST STATES IN NEAR-SPHERICAL NUCLEI

The yrast states of nuclei that are spherical or weakly deformed in their ground states are described as quadrupole waves running over the nuclear surface, which we call "tidal waves". The energies and E 2 transition probabilities of the yrast states in nuclides with Z= 44, 46, 48 and N= 56, 58,…, 66 are calculated by means of the cranking model in a microscopic way. The nonlinear response of the nucleonic orbitals results in a strong coupling between shape and single particle degrees of freedom.

10.1007/s11450-008-2005-8

A method is proposed for quantitatively describing the preequilibrium decay of deformed nuclei with allowance for the interplay of collective and single-particle degrees of freedom. This approach makes it possible to take consistently into account the structure of a deformed nucleus in determining observables. The assumption according to which the integrated rate of single-particle transitions is constant and which is used in analytically solving the arising equations is found to have a limited range of validity. It is shown that the behavior of a relaxing system depends greatly on this rate.

Pygmy dipole resonance in nuclei

A brief survey of the state of the modern microscopic theory of the so-called pygmy dipole resonance in nuclei is given—in particular, some unresolved problems are listed. It is emphasized that, in order to explain the pygmy dipole resonance, it is necessary but not sufficient to take into account the coupling of single-particle degrees of freedom to photon degrees of freedom. The results of the calculations performed for the first time for the isovector pygmy dipole resonance and the isovector electric giant dipole resonance in 124Sn within a self-consistent approach involving, in addition to the standard quasiparticle random-phase approximation, a single-particle continuum and quasiparticle-phonon coupling of single-particle degrees of freedom to phonon degrees of freedom are presented. The results are found to be in satisfactory agreement with experimental data. The calculation of the isoscalar strength function in the energy region of the pygmy dipole resonance revealed that the nuclear-structure mechanism does not provide the isoscalar-strength suppression observed at energies in excess of 7 MeV in (α, α′γ) reactions; therefore, this suppression may stem from the reaction mechanism.

Investigation into theB(E2)anomaly inNd144using Coulomb excitation

The ratio of $B(E2)$ strengths between the lowest lying members of the ground state band in $^{144}\mathrm{Nd}$, ${B}_{4/2}=B(E2;{4}_{1}^{+}\ensuremath{\rightarrow}{2}_{1}^{+})/B(E2;{2}_{1}^{+}\ensuremath{\rightarrow}{0}_{1}^{+})$, which is used to quantify collectivity in nonmagic nuclei, has been remeasured by means of Coulomb excitation. Ambiguities in literature values for this ratio have been resolved. The results are discussed in terms of the interplay of collective and single-particle degrees of freedom, and in the context of the formation of collective structures in the $A=140$ mass region, and more generally near (sub)shell closures. In addition, the ${B}_{4/2}$ ratio of $^{148}\mathrm{Sm}$ has been remeasured, and the quadrupole moment of the ${4}_{1}^{+}$ state is found to be on the order of $1 e b$.

Preequilibrium-decay model with allowance for excitation-energy dissipation

A method is proposed for quantitatively describing the preequilibrium decay of deformed nuclei with allowance for the interplay of collective and single-particle degrees of freedom. This approach makes it possible to take consistently into account the structure of a deformed nucleus in determining observables. The assumption according to which the integrated rate of single-particle transitions is constant and which is used in analytically solving the arising equations is found to have a limited range of validity. It is shown that the behavior of a relaxing system depends greatly on this rate.

Superheavy nuclei : self-consistency effects and single-particle degrees of freedom(International Workshop on Nuclear Structure-New Pictures in the Extended Isospin Space(NS07)-)

Superheavy nuclei : self-consistency effects and single-particle degrees of freedom(International Workshop on Nuclear Structure-New Pictures in the Extended Isospin Space(NS07)-)