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Publication date: 3 October 2013
Source:Nuclear Physics A, Volume 915
Author(s): L. Zheng , G.L. Zhang , J.C. Yang , W.W. Qu
The half-lives of cluster decays are calculated using proximity potential model with a new universal function, and compared to the experimentally measured values and the theoretical ones of liquid drop model. The results of the present calculations show reasonable agreement with the experimental data as well as the half-life calculations of liquid drop model. In the present work, it is certified that proximity potential model with the new universal function can be used successfully to calculate the half-lives of cluster decays for heavy nuclei.

Publication date: July 2013
Source:Atomic Data and Nuclear Data Tables, Volume 99, Issue 4
Author(s): M. De Rydt , M. Depuydt , G. Neyens
The current diversity and inconsistency among published quadrupole moments calls for a thorough evaluation of the available data. In this work, a review of the ground-state Q-moments of the oxygen to calcium isotopes is presented, resulting in a revised database of 43 quadrupole moments. For every π (sd) isotope chain, the quadrupole moments are expressed relative to one reference isotope. This common reference rules out the existing arbitrariness and provides a reliable basis for future measurements and theoretical studies. In addition, the evaluated quadrupole-moment values are compared to shell-model calculations, obtained with different effective interactions in the sd and sdpf model spaces and using the standard effective charges e p = 1.3 e and e n = 0.5 e . The discrepancy between theory and experiment, observed for particular isotopes and isotope chains, calls for further fundamental research.

Publication date: November 2012
Source:Atomic Data and Nuclear Data Tables, Volume 98, Issue 6
Author(s): I. Silişteanu , A.I. Budaca
The α-decay is considered from the viewpoint of the many body features of internal nuclear motion and the theory of resonance reactions, as well. The α-half-lives are derived from clustering and scattering amplitudes given by self-consistent nuclear models for the nuclear shell structure and reaction dynamics. Calculations are performed for superheavy nuclei with Z=102–120 using the measured Eα values, microscopic (shell model) or macroscopic (one body) cluster formation amplitudes and resonance scattering amplitudes. Theoretical results for α-half-lives are compared to data and empirical estimates. We prove that the Brown systematics (logTα (s) vs. Zd0.6Qα−1/2, where Qα (MeV) is the effective decay energy, and Zd is the charge number of the daughter nucleus) of current decay data is very useful in the analysis and interpretation of data and prediction of new results. It is shown that by adding even–odd corrections to the calculated α-half-lives, the agreement with experimental data is improved and basic trends in the systematics of data are well reproduced. Spectroscopic information is derived from the ratio of theoretical to experimental results. The accuracy of available experimental half-lives is discussed.

Publication date: January 2013
Source:Atomic Data and Nuclear Data Tables, Volume 99, Issue 1
Author(s): I. Angeli , K.P. Marinova
The present table contains experimental root-mean-square (rms) nuclear charge radii R obtained by combined analysis of two types of experimental data: (i) radii changes determined from optical and, to a lesser extent, Kα X-ray isotope shifts and (ii) absolute radii measured by muonic spectra and electronic scattering experiments. The table combines the results of two working groups, using respectively two different methods of evaluation, published in ADNDT earlier. It presents an updated set of rms charge radii for 909 isotopes of 92 elements from 1H to 96Cm together, when available, with the radii changes from optical isotope shifts. Compared with the last published tables of R-values from 2004 (799 ground states), many new data are added due to progress recently achieved by laser spectroscopy up to early 2011. The radii changes in isotopic chains for He, Li, Be, Ne, Sc, Mn, Y, Nb, Bi have been first obtained in the last years and several isotopic sequences have been recently extended to regions far off stability, (e.g., Ar, Mo, Sn, Te, Pb, Po).

Publication date: 3 October 2013
Source:Nuclear Physics A, Volume 915
Author(s): E. Guliyev , A.A. Kuliev , F. Ertugral
Low-energy magnetic and electric dipole excitations in the even–even isotopes ^176–180Hf have been systematically studied within the rotational, translational and Galilean invariant Quasiparticle Random Phase Approximation (QRPA). The results of the calculations show that most of the states predicted to have magnetic character and the computed M1 strength in these nuclei is less strongly fragmented than in mid-shell isotopes. The results of the calculations are in good agreement with experimental data. The results of the calculations indicate the presence of a few prominent negative parity dipole K=1 states in the energy investigated region. The comparison of the calculations with the available experimental data makes possible the interpretation of the states where parity could not be assigned experimentally.

Publication date: 3 October 2013
Source:Nuclear Physics A, Volume 915
Author(s): Deepika Jain , Raj Kumar , Manoj K. Sharma
The effect of deformation and orientation on barrier height and barrier position is studied using different types of proximity potentials for some 52 colliding nuclei with mass asymmetry parameter in range of 0 to 0.96. Various proximity potentials like Prox 77, Prox 88, Prox 00, Bass 80 and Denisov DP are used to extract barrier characteristics. These potentials cover a wide range of barrier and have different isospin and asymmetry dependence. With the inclusion of deformations, the barrier height and barrier position gets modified along with a significant change in the curvature. In order to study the possible effect of these deformation and orientation dependent proximity potentials, application is made in the framework of Wong formula to O-, Ca- and Ni-based reactions in medium mass region in reference to available data on fusion cross-sections at around and above the Coulomb barrier energies. For ¹⁶O- and ⁴⁸Ca-based reactions, Prox 77 gives better comparison with experimental data as compared to other potentials around the Coulomb barrier energies whereas for ⁶⁴Ni-based reactions Prox 88 seems close to the experimental data. At energies above the Coulomb barrier Bass 80 and Denisov DP compete with each other. Angular dependence of cross-section is also studied. It is observed that deformation and orientation degree of freedom plays a significant role in reaction dynamics.

Publication date: 3 October 2013
Source:Nuclear Physics A, Volume 915
Author(s): Long Zhu , Jun Su , Wen-Jie Xie , Feng-Shou Zhang
The nucleus–nucleus interaction potentials for the fusion reactions ¹⁶O+²⁰⁸Pb, ⁶⁴Ni+⁶⁴Ni, ⁵⁸Ni+⁵⁸Ni and ¹⁶O+¹⁵⁴Sm are extracted from the improved isospin-dependent quantum molecular dynamics model. The shell correction effects are discussed. The negative shell correction energies lower potential barriers of a certain reaction. The incident energy dependence of the potential barrier is investigated for each system. A complex phenomenon of energy dependence is observed. It is also found that incident energy dependence of the barrier radius and barrier height shows opposite behaviors. The Coulomb potential shows weak energy dependence when distance of two colliding nuclei is lower than the touching distance. The isospin effects of the potential barrier are investigated. The orientation effects of the potential barrier is also discussed for the system ¹⁶O+¹⁵⁴Sm. The fusion cross sections that correspond to the equatorial orientation of ¹⁵⁴Sm are very low in sub-barrier region because of the high fusion barriers and the shallow potential pockets.

Author(s): Denis Lacroix, Danilo Gambacurta, and Sakir Ayik

By extending the stochastic mean-field model by including pairing, an approach is proposed for describing the evolution of complex many-body systems in terms of an ensemble of time-dependent Hartree-Fock Bogoliubov trajectories which is determined by incorporating fluctuations in the initial state. ...

[Phys. Rev. C 87, 061302] Published Fri Jun 28, 2013

The fusion cross sections of radioactive $^{134}$Te + $^{40}$Ca were measured at energies above and below the Coulomb barrier. The evaporation residues produced in the reaction were detected in a zero-degree ionization chamber providing high efficiency for inverse kinematics. Both coupled-channel calculations and comparison with similar Sn+Ca systems indicate an increased sub-barrier fusion probability that is correlated with the presence of positive Q-value neutron transfer channels. In comparison, the measured fusion excitation functions of $^{130}$Te + $^{58,64}$Ni, which have positive Q-value neutron transfer channels, were accurately reproduced by coupled-channel calculations including only inelastic excitations. The results demonstrate that the coupling of transfer channels can lead to enhanced sub-barrier fusion but this is not directly correlated with positive Q-value neutron transfer channels in all cases.

Author(s): R. T. deSouza, S. Hudan, V. E. Oberacker, and A. S. Umar

Recently measured fusion cross sections for the neutron-rich system ²⁰O+¹²C are compared to dynamic, microscopic calculations using time-dependent density functional theory. The calculations are carried out on a three-dimensional lattice and performed both with and without a constraint on the densit...

[Phys. Rev. C 88, 014602] Published Mon Jul 01, 2013

We explain the low-energy anomaly reported in several experimental studies of the radiative dipole strength functions in medium-mass nuclei. These strength functions at very low gamma-energies correspond to the gamma-transitions between very close nuclear excited states in the quasicontinuum. In terms of the thermal mean-field, the low-energy enhancement of the strength functions in highly-excited compound nuclei is explained by nucleonic transitions from the thermally unblocked single-quasiparticle states to the single-(quasi)particle continuum. This result is obtained within the finite-temperature quasiparticle random phase approximation in the coordinate space with exact treatment of the single-particle continuum and exactly eliminated spurious translational mode. The case of radiative dipole strength functions at the nuclear excitation energies typical for the thermal neutron capture is illustrated for 94-Mo and 144-Nd in comparison to available data.

The isoscalar (IS) and isovector (IV) quadrupole responses of nuclei are systematically investigated using the time-dependent Skyrme Energy Density Functional including pairing in the BCS approximation. Using two different Skyrme functionals, Sly4 and SkM*, respectively 263 and 304 nuclei have been found to be spherical along the nuclear charts. The time-dependent evolution of these nuclei has been systematically performed giving access to their quadrupole responses. It is shown that the mean-energy of the collective high energy state globally reproduces the experimental IS and IV collective energy but fails to reproduce their lifetimes. It is found that the mean collective energy depends rather significantly on the functional used in the mean-field channel. Pairing by competing with parity effects can slightly affect the collective response around magic numbers and induces a reduction of the collective energy compared to the average trend. Low-lying states, that can only be considered if pairing is included, are investigated. While the approach provides a fair estimate of the low lying state energy, it strongly underestimates the transition rate $B(E2)$. Finally, the possibility to access to the density dependence of the symmetry energy through parallel measurements of both the IS- and IV-GQR is discussed.

Author(s): E. B. Balbutsev, I. V. Molodtsova, and P. Schuck

The coupled dynamics of low-lying modes and various giant resonances are studied with the help of the Wigner function moments method on the basis of time-dependent Hartree-Fock equations in the harmonic oscillator model including spin-orbit potential plus quadrupole-quadrupole and spin-spin residual...

[Phys. Rev. C 88, 014306] Published Tue Jul 09, 2013

The electric dipole (E1) response of 208Pb has been precisely determined by measuring Coulomb excitation induced by proton scattering at very forward angles. The electric dipole polarizability, defined as inverse energy-weighted sum rule of the E1 strength, has been extracted as 20.1+-0.6 fm^3. The data can be used to constrain the neutron skin thickness of 208Pb to 0.168(+-0.009)_expt(+-0.013)_theo(+-0.021)_est fm, where the subscript "expt" refers to the experimental uncertainty, "theor" to the theoretical confidence band and "est" to the uncertainty associated with the estimation of the symmetry energy at the saturation density. In addition, a constraint band has been extracted in the plane of the symmetry energy (J) and its slope parameter (L) at the saturation density.

Applying a relatively simple particle-rotor model to odd-odd nuclei, possible presence of multi chiral pair-bands is looked for, where chiral pair-bands are defined not only by near-degeneracy of the levels of two bands but also by almost the same expectation values of squared components of three angular-momenta that define chirality. In the angular-momentum region where two pairs of chiral pair-bands are obtained the possible interband M1/E2 decay from the second-lowest chiral pair-bands to the lowest chiral pair-bands is studied, with the intention of finding how to experimentally identify the multi chiral pair-bands. It is found that up till almost band-head the intraband M1/E2 decay within the second chiral pair-bands is preferred rather than the interband M1/E2 decay to the lowest chiral pair-bands, though the decay possibility depends on the ratio of actual decay energies. It is also found that chiral pair-bands in our model and definition are hardly obtained for $\gamma$ values outside the range $25^{\circ} < \gamma < 35^{\circ}$, although either a near-degeneracy or a constant energy-difference of several hundreds keV between the two levels for a given angular-momentum $I$ in "a pair bands" is sometimes obtained in some limited region of $I$. In the present model calculations the energy difference between chiral pair-bands is always one or two orders of magnitude smaller than a few hundreds keV, and no chiral pair-bands are obtained, which have an almost constant energy difference of the order of a few hundreds keV in a reasonable range of $I$.

The thermodynamics of pairing phase-transition in nuclei is studied in the canonical ensemble and treating the pairing correlations in a finite-temperature variation after projection BCS approach (FT-VAP). Due to the restoration of particle number conservation, the pairing gap and the specific heat calculated in the FT-VAP approach vary smoothly with the temperature, indicating a gradual transition from the superfluid to the normal phase, as expected in finite systems. We have checked that the predictions of the FT-VAP approach are very accurate when compared to the results obtained by an exact diagonalization of the pairing Hamiltonian. The influence of pairing correlations on specific heat is analysed for the isotopes $^{161,162}$Dy and $^{171,172}$Yb. It is shown that the FT-VAP approach, applied with a level density provided by mean field calculations and supplemented, at high energies, by the level density of the back-shifted Fermi gas model, can approximate reasonably well the main properties of specific heat extracted from experimental data. However, the detailed shape of the calculated specific heat is rather sensitive to the assumption made for the mean field.

A recent proposed method for $\alpha$-decay energies ($Q_\alpha$) [J.M. Dong, W. Zuo, and W. Scheid, Phys. Rev. Lett. \textbf{107}, 012501 (2011)] can reproduce experimental data of superheavy nuclei (SHN) with an $rms$-value of less than 100 keV. However, a sinusoid-like periodic deviation from experiments, which limits the accuracy in predictions, is observed when using different reference nuclei. In this paper, we have further extended this hybrid method, i.e., to predict $Q_\alpha$ of the as-yet-unobserved SHN with the help of known nuclei. It is found that the systematic deviation in previous study is rooted in the nuclear mass model employed. By further analyzing the source of errors, different nuclear mass models are evaluated based on the same procedure.

Background: Neutron-skin thickness is an excellent indicator of isovector properties of atomic nuclei. As such, it correlates strongly with observables in finite nuclei that depend on neutron-to-proton imbalance and the nuclear symmetry energy that characterizes the equation of state of neutron-rich matter. A rich worldwide experimental program involving studies with rare isotopes, parity violating electron scattering, and astronomical observations is devoted to pinning down the isovector sector of nuclear models. Purpose: We assess the theoretical systematic and statistical uncertainties of neutron-skin thickness and relate them to the equation of state of nuclear matter, and in particular to nuclear symmetry energy parameters. Methods: We use the nuclear superfluid Density Functional Theory with several Skyrme energy density functionals and density dependent pairing. To evaluate statistical errors and their budget, we employ the statistical covariance technique. Results: We find that the errors on neutron skin increase with neutron excess. Statistical errors due to uncertain coupling constants of the density functional are found to be larger than systematic errors, the latter not exceeding 0.06 fm in most neutron-rich nuclei across the nuclear landscape. The single major source of uncertainty is the poorly determined slope L of the symmetry energy that parametrizes its density dependence. Conclusions: To provide essential constraints on the symmetry energy of the nuclear energy density functional, next-generation measurements of neutron skins are required to deliver precision better than 0.06 fm.

Author(s): S. Kurth and G. Stefanucci

For molecules weakly coupled to leads the exact linear Kohn-Sham (KS) conductance can be orders of magnitude larger than the true linear conductance due to the lack of dynamical exchange-correlation (xc) corrections. In this work we show how to incorporate dynamical effects in KS transport calculati...

[Phys. Rev. Lett. 111, 030601] Published Fri Jul 19, 2013

The nuclear symmetry energy represents a response to the neutron-proton asymmetry. In this survey we discuss various aspects of symmetry energy in the framework of nuclear density functional theory, considering both non-relativistic and relativistic self-consistent mean-field realizations side-by-side. Key observables pertaining to bulk nucleonic matter and finite nuclei are reviewed. Constraints on the symmetry energy and correlations between observables and symmetry-energy parameters, using statistical covariance analysis, are investigated. Perspectives for future work are outlined in the context of ongoing experimental efforts.

Author(s): B. P. Kay, J. P. Schiffer, and S. J. Freeman

Cross sections for proton knockout observed in (e,e^′p) reactions are apparently quenched by a factor of ∼0.5, an effect attributed to short-range correlations between nucleons. Here we demonstrate that such quenching is not restricted to proton knockout, but a more general phenomenon associated with...

[Phys. Rev. Lett. 111, 042502] Published Wed Jul 24, 2013

We present new formulae for the matrix elements of one-body and two-body physical operators in compact forms, which are applicable to arbitrary Hartree-Fock-Bogoliubov wave functions, including those for multi-quasiparticle excitations. The test calculations show that our formulae may substantially accelerate the process of symmetry restoration when applied to the heavy nuclear system.

A completely microscopic beyond mean-field approach has been elaborated to overcome some intrinsic limitations of self-consistent mean-field schemes applied to nuclear systems, such as the incapability to produce some properties of single-particle states (e.g. spectroscopic factors), as well as of collective states (e.g. their damping width and their gamma decay to the ground state or to low lying states). Since commonly used effective interactions are fitted at the mean-field level, one should aim at refitting them including the desired beyond mean-field contributions in the refitting procedure. If zero-range interactions are used, divergences arise. We present some steps towards the refitting of Skyrme interactions, for its application in finite nuclei.

Author(s): Kazuyuki Sekizawa and Kazuhiro Yabana

Multinucleon transfer processes in heavy-ion reactions at energies slightly above the Coulomb barrier are investigated in a fully microscopic framework of the time-dependent Hartree-Fock (TDHF) theory. Transfer probabilities are calculated from the TDHF wave function after collision using the projec...

[Phys. Rev. C 88, 014614] Published Tue Jul 30, 2013

Giant resonances encapsulate the dynamic response of the nuclear ground state to external perturbations. As such, they offer a unique view of the nucleus that is often not accessible otherwise. Although interesting in their own right, giant resonances are also enormously valuable in providing stringent constraints on the equation of state of asymmetric matter. We this view in mind, we focus on two modes of excitation that are essential in reaching this goal: the isoscalar giant monopole resonance (GMR) and the isovector giant dipole resonance (GDR). GMR energies in heavy nuclei are sensitive to the symmetry energy because they probe the incompressibility of neutron-rich matter. Unfortunately, access to the symmetry energy is hindered by the relatively low neutron-proton asymmetry of stable nuclei. Thus, the measurement of GMR energies in exotic nuclei is strongly encouraged. In the case of the GDR, we find the electric dipole polarizability of paramount importance. Indeed, the electric dipole polarizability appears as one of two laboratory observables -- with the neutron-skin thickness being the other -- that are highly sensitive to the density dependence of the symmetry energy. Finally, we identify the softness of skin and the nature of the pygmy resonance as important unsolved problems in nuclear structure.

\item[Background] For cranked mean-field calculations with arbitrarily oriented rotational frequency vector $\boldsymbol{\omega}$ in the intrinsic frame, one has to employ constraints on average values of the quadrupole-moment tensor, so as to keep the nucleus in the principal-axis reference frame. Kerman and Onishi [Nucl. Phys. A {\bf 361}, 179 (1981)] have shown that the Lagrangian multipliers that correspond to the required constraints are proportional to $\boldsymbol{\omega} \times \boldsymbol{J}$, where $\boldsymbol{J}$ is the average angular momentum vector.

\item[Purpose] We study the validity and consequences of the Kerman-Onishi conditions in the context of self-consistent tilted-axis-cranking (TAC) mean-field calculations.

\item[Methods] We perform a two-dimensional self-consistent calculations (with and without pairing) utilizing the symmetry-unrestricted solver {\sc hfodd}. At each tilting angle, we compare the calculated values of quadrupole-moment-tensor Lagrangian multipliers and $\boldsymbol{\omega} \times \boldsymbol{J}$.

\item[Results] We show that in self-consistent calculations, the Kerman-Onishi conditions are obeyed with high precision. Small deviations seen in the calculations with pairing can be attributed to the truncation of the quasiparticle spectrum. We also provide results of systematic TAC calculations for triaxial strongly deformed bands in $^{160}$Yb.

\item[Conclusions] For non-stationary TAC solutions, Kerman-Onishi conditions link the non-zero values of the angle between rotational-frequency and angular-momentum vectors to the constraints on off-diagonal components of the quadrupole-moment tensor. To stabilize the convergence of self-consistent iterations, such constraints have to be taken into account. Only then one can determine the Routhian surfaces as functions of the tilting angles.

We develop a new framework of the self-consistent deformed proton-neutron quasiparticle-random-phase approximation (pnQRPA), formulated in the Hartree-Fock-Bogoliubov (HFB) single-quasiparticle basis. The same Skyrme force is used in both the HFB and pnQRPA calculations except in the proton-neutron particle-particle channel, where an S=1 contact force is employed. Numerical application is performed for Gamow-Teller (GT) strength distributions and $\beta$-decay rates in the deformed neutron-rich Zr isotopes located around the path of the rapid-neutron-capture process nucleosynthesis. It is found that the GT strength distributions are fragmented due to deformation. Furthermore we find that the momentum-dependent terms in the particle-hole residual interaction leads to a stronger collectivity of the GT giant resonance. The T=0 pairing enhances the low-lying strengths cooperatively with the T=1 pairing correlation, which shortens the $\beta$-decay half lives by at most an order of magnitude. The new calculation scheme reproduces well the observed isotopic dependence of the $\beta$-decay half lives of deformed $^{100-110}$Zr isotopes.

Author(s): S. Goriely, N. Chamel, and J. M. Pearson

Our family of three Hartree-Fock-Bogoliubov (HFB) mass models, labeled BSk19, BSk20, and BSk21, is here extended by (a) refitting to the 2012 Atomic Mass Evaluation (AME), and (b) varying the symmetry coefficient J. Five new models, labeled BSk22 to BSk26, along with their mass tables, HFB-22 to HFB...

[Phys. Rev. C 88, 024308] Published Wed Aug 07, 2013

The pseudospin symmetry (PSS) has been studied extensively for bound states. Recently we justified rigorously that the PSS in single particle resonant states is exactly conserved when the attractive scalar and repulsive vector potentials of the Dirac Hamiltonian have the same magnitude but opposite sign [PRL 109, 072501 (2012)]. To understand more deeply the PSS, we focus on several issues related to the exact conservation and breaking mechanism of the PSS in single particle resonances. In particular, we are interested in how the energy and width splittings of PS partners depend on the depth of the scalar and vector potentials. We investigate the asymptotic behaviors of radial Dirac wave functions. Spherical square well potentials are employed in which the PSS breaking part in the Jost function can be well isolated. By examining the zeros of Jost functions corresponding to small components of the radial Dirac wave functions, general properties of the PSS are analyzed. By examining the Jost function, the occurrence of intruder orbitals is explained and it is possible to trace continuously the PSS partners from the PSS limit to the case with a finite potential depth. The dependence of the PSS in resonances as well as in bound states on the potential depth is investigated systematically. We find a threshold effect in the energy splitting and an anomaly in the width splitting of pseudospin partners when the depth of the single particle potential varies from zero to a finite value. The conservation and the breaking of the PSS in resonant states and bound states share some similar properties. The appearance of intruder states can be explained by examining the zeros of Jost functions. Origins of the threshold effect in the energy splitting and the anomaly in the width splitting of PS partners, together with many other problems, are still open and should be further investigated.

We present results of calculations based on the Skyrme energy density functional including the arbitrary mixing between protons and neutrons. In this framework, single-particle states are superpositions of proton and neutron components and the energy density functional is fully invariant with respect to three-dimensional rotations in the isospin space. The isospin of the system is controlled by means of the isocranking method, which carries over the standard cranking approach to the isospin space. We show numerical results of the isocranking calculations performed for isobaric analogue states in the A=14 and $A=40-56$ nuclei. We also present such results obtained for high-isospin states in $^{48}$Cr, with constraints on the isospin implemented by using the augmented Lagrange method.