Nuclear Ground State Research Articles

Finite- to zero-range relativistic mean-field interactions

We study the relation between the finite-range (meson-exchange) and zero-range (point-coupling) representations of effective nuclear interactions in the relativistic mean-field framework. Starting from the phenomenological interaction DD-ME2 with density-dependent meson-nucleon couplings, we construct a family of point-coupling effective interactions for different values of the strength parameter of the isoscalar-scalar derivative term. In the meson-exchange picture this corresponds to different values of the σ-meson mass. The parameters of the isoscalar-scalar and isovector-vector channels of the point-coupling interactions are adjusted to nuclear matter and ground-state properties of finite nuclei. By comparing results for infinite and semi-infinite nuclear matter, ground-state masses, charge radii, and collective excitations, we discuss constraints on the parameters of phenomenological point-coupling relativistic effective interaction.

Inclusive charged-current neutrino-nucleus reactions calculated with the relativistic quasiparticle random-phase approximation

Inclusive neutrino-nucleus cross sections are calculated using a consistent relativistic mean-field theoretical framework. The weak lepton-hadron interaction is expressed in the standard current-current form, the nuclear ground state is described with the relativistic Hartree-Bogoliubov model, and the relevant transitions to excited nuclear states are calculated in the relativistic quasiparticle random phase approximation. Illustrative test calculations are performed for charged-current neutrino reactions on $^{12}$C, $^{16}$O, $^{56}$Fe, and $^{208}$Pb, and results compared with previous studies and available data. Using the experimental neutrino fluxes, the averaged cross sections are evaluated for nuclei of interest for neutrino detectors. We analyze the total neutrino-nucleus cross sections, and the evolution of the contribution of the different multipole excitations as a function of neutrino energy. The cross sections for reactions of supernova neutrinos on $^{16}$O and $^{208}$Pb target nuclei are analyzed as functions of the temperature and chemical potential.

Single-neutron knockout from intermediate energy beams ofMg30,32: Mapping the transition into the “island of inversion”

The breakdown of the $N=20$ magic number in the so-called island of inversion around $^{32}\mathrm{Mg}$ is well established. Recently developed large-scale shell-model calculations suggest a transitional region between normal- and intruder-dominated nuclear ground states, thus modifying the boundary of the island of inversion. In particular, a dramatic change in single-particle structure is predicted between the ground states of $^{30}\mathrm{Mg}$ and $^{32}\mathrm{Mg}$, with the latter consisting nearly purely of 2p-2h $N=20$ cross-shell configurations. Single-neutron knockout experiments on $^{30,32}\mathrm{Mg}$ projectiles have been performed. We report on a first direct observation of intruder configurations in the ground states of these very neutron-rich nuclei. Spectroscopic factors to low-lying negative-parity states in the knockout residues are deduced and compare well with shell-model predictions.

Neutrino–nucleus reactions with the relativistic quasiparticle RPA

We introduce a novel theoretical framework for the description of weak interaction rates in reactions of leptons with finite nuclei. The weak interaction of leptons with hadrons is expressed in the standard current–current form, the nuclear ground state is described with the relativistic Hartree–Bogoliubov model and the relevant transitions to excited states are calculated in the relativistic quasiparticle random phase approximation. The model is tested for electron– and muon–neutrino reactions on 12C, in a study of cross sections averaged over experimental neutrino fluxes. Using 56Fe as an example, it is shown that at higher neutrino energies the inclusion of spin-dipole transitions, and also excitations of higher multipolarities, is essential for a quantitative description of neutrino–nucleus cross sections.

State-dependent calculation of three-body cluster energy for nuclear matter and the validity of the lowest order constrained variational formalism

It is shown that the method of lowest order constrained variational (LOCV) which is based on the cluster expansion theory is a reliable many-body technique to calculate the nuclear matter equation of state. In this respect, the state dependent correlation functions and the effective interactions which have been produced by the LOCV calculation with the Reid and {delta}-Reid soft core interactions are used to estimate the size of higher order cluster terms such as the effect of three-body cluster energy on the nuclear matter ground state energy. Finally it is shown that the LOCV normalization constraint plays a major role in the convergence of the cluster expansion and the result of LOCV calculation can be as good as more sophisticated approaches which go beyond lowest order.

Spin and Magnetic Moment ofMg33: Evidence for a Negative-Parity Intruder Ground State

We report on the first determination of the nuclear ground-state spin of 33Mg, I=3/2, and its magnetic moment, mu= -0.7456(5) mu(N), by combining laser spectroscopy with nuclear magnetic resonance techniques. These values are inconsistent with an earlier suggested 1 particle-1 hole configuration and provide evidence for a 2 particle-2 hole intruder ground state with negative parity. The results are in agreement with an odd-neutron occupation of the 3/2 [321] Nilsson orbital at a large prolate deformation. The discussion emphasizes the need of further theoretical and experimental investigation of the island of inversion, a region previously thought to be well understood.

Two-Proton Correlations in the Decay ofFe45

The decay of extremely neutron-deficient $^{45}\mathrm{Fe}$ has been studied in detail by means of a novel type of a gaseous detector employing digital imaging to record tracks of charged particles. The two-proton radioactivity channel was clearly identified. For the first time, the angular and energy correlations between two protons emitted from the nuclear ground state were determined, indicating the genuine three-body character of this decay. The half-life of $^{45}\mathrm{Fe}$ was found to be $2.6\ifmmode\pm\else\textpm\fi{}0.2\text{ }\text{ }\mathrm{ms}$ and the observed $2p$ decay branching ratio is $70\ifmmode\pm\else\textpm\fi{}4%$.

Folding model study of the isobaric analog excitation: Isovector density dependence, Lane potential, and nuclear symmetry energy

A consistent folding model analysis of the ($\ensuremath{\Delta}S=0,\ensuremath{\Delta}T=1$) charge exchange $(p,n)$ reaction measured with $^{48}\mathrm{Ca}$, $^{90}\mathrm{Zr}$, $^{120}\mathrm{Sn}$, and $^{208}\mathrm{Pb}$ targets at the proton energies of 35 and 45 MeV is done within a two-channel coupling formalism. The nuclear ground state densities given by the Hartree-Fock-Bogoliubov formalism and the density-dependent CDM3Y6 interaction were used as inputs for the folding calculation of the nucleon optical potential and $(p,n)$ form factor. To have an accurate isospin dependence of the interaction, a complex isovector density dependence of the CDM3Y6 interaction has been carefully calibrated against the microscopic Brueckner-Hartree-Fock calculation by Jeukenne, Lejeune, and Mahaux before being used as folding input. Since the isovector coupling was used to explicitly link the isovector part of the nucleon optical potential to the cross section of the $(p,n)$ reaction exciting the 0${}^{+}$ isobaric analog states in $^{48}\mathrm{Sc}$, $^{90}\mathrm{Nb}$, $^{120}\mathrm{Sb}$, and $^{208}\mathrm{Bi}$, the newly parametrized isovector density dependence could be well tested in the folding model analysis of the $(p,n)$ reaction. The isospin- and density-dependent CDM3Y6 interaction was further used in the Hartree-Fock calculation of asymmetric nuclear matter, and a realistic estimation of the nuclear symmetry energy was made.

Standard and quasideuteron pairing in asymmetric nuclear matter

We study the standard 1 S 0 and the quasideuteron 3 S 1 − 3 D 1 pairing fields in asymmetric nuclear matter, using a Bonn meson-exchange interaction in a Dirac-Hartree-Fock-Bogoliubov approximation. As in earlier calculations, the standard pairing fields fall to zero at densities below saturation, due to relativistic effects. We obtain a quasideuteron field very similar to those found in nonrelativistic calculations at densities below saturation, both in symmetric and asymmetric nuclear matter. This field has the properties of a Bose-Einstein condensate at low densities and those of a BCS condensate at high densities. The quasideuteron pairing field in asymmetric nuclear matter is stable only when accompanied by standard 1 S 0 neutron-neutron and proton-proton pairing fields that are different from the fields obtained when the quasideuteron field is zero. The coupled pairing field configuration is the nuclear matter ground state.

Atomic physics experiments with trapped and cooled highly charged ions

Trapping and cooling techniques have become very important for many fundamental experiments in atomic physics. When applied to highly charged ions confined in Penning traps, these procedures are very effective for testing quantum electrodynamics in extreme electromagnetic fields produced by heavy highly charged ions such as uranium U91+. In addition, fundamental constants or nuclear ground state properties can be determined with high accuracy in these simple systems. Finally, by studying a single trapped radioactive ion, its nuclear decay can be studied in detail by observing the disappearance of the signal of the mother and the appearance of that of the daughter isotope. Such experiments on highly charged ions at extremely low energy will become possible by the HITRAP facility which is currently being built up at GSI. Also the future Facility for Antiproton and Ion Research (FAIR) will be briefly described which is expected to be operational by 2014.

Calculation of β-decay rates in a relativistic model with momentum-dependent self-energies

The relativistic proton-neutron quasiparticle random phase approximation (PN-RQRPA) is applied in the calculation of \ensuremath{\beta}-decay half-lives of neutron-rich nuclei in the $Z\ensuremath{\approx}28$ and $Z\ensuremath{\approx}50$ regions. The study is based on the relativistic Hartree-Bogoliubov calculation of nuclear ground states, using effective Lagrangians with density-dependent meson-nucleon couplings, and also extended by the inclusion of couplings between the isoscalar meson fields and the derivatives of the nucleon fields. This leads to a linear momentum dependence of the scalar and vector nucleon self-energies. The residual QRPA interaction in the particle-hole channel includes the $\ensuremath{\pi}+\ensuremath{\rho}$ exchange plus a Landau-Migdal term. The finite-range Gogny interaction is employed in the $T=1$ pairing channel, and the model also includes a proton-neutron particle-particle interaction. The results are compared with available data, and it is shown that an extension of the standard relativistic mean-field framework to include momentum-dependent nucleon self-energies naturally leads to an enhancement of the effective (Landau) nucleon mass, and thus to an improved PN-QRPA description of ${\ensuremath{\beta}}^{\ensuremath{-}}$-decay rates.

APPLICATION OF SUPPORT VECTOR MACHINES TO GLOBAL PREDICTION OF NUCLEAR PROPERTIES

Advances in statistical learning theory present the opportunity to develop statistical models of quantum many-body systems exhibiting remarkable predictive power. The potential of such "theory-thin" approaches is illustrated with the application of Support Vector Machines (SVMs) to global prediction of nuclear properties as functions of proton and neutron numbers Z and N across the nuclidic chart. Based on the principle of structural-risk minimization, SVMs learn from examples in the existing database of a given property Y, automatically and optimally identify a set of "support vectors" corresponding to representative nuclei in the training set, and approximate the mapping (Z, N) → Y in terms of these nuclei. Results are reported for nuclear masses, beta-decay lifetimes, and spins/parities of nuclear ground states. These results indicate that SVM models can match or even surpass the predictive performance of the best conventional "theory-thick" global models based on nuclear phenomenology.

Particle number projection in the macroscopic–microscopic approach

We perform nuclear ground-state pairing calculations with the monopole pairing interaction. The particle number fluctuations are taken into account by the particle number projection method, with variation after projection. The pairing-correction energies obtained in this approach are compared to the BCS-model results. We discuss extensively how to properly incorporate different pairing models in global macroscopic–microscopic nuclear mass calculations. A method to calculate the smoothly changing part of the particle number projected energy is developed based on the Strutinsky procedure, making it possible to extract a pairing-shell energy. The behavior of the different pairing models is investigated in detail in the nuclei 164Er and 165Tm. Calculations are then performed along the β-stability line and for several isotope and isotone chains from the proton drip-line to the neutron drip-line. The single-particle energy levels used are obtained from two different single-particle potentials: the folded-Yukawa and the modified-harmonic oscillator potentials. The pairing calculations in the two potentials differ slightly in the fine-structure but the overall results are very similar. When comparing the particle number projected model and the BCS model it is found that the pairing-shell energy is quite insensitive to which microscopic pairing model is used.

Underground search for the decay ofTa180m

Tantalum-180m is a very rare primordial isotope and is not in its nuclear ground state. The radioactivity of Ta180m has not yet been observed. Previous attempts to measure the half-life of Ta180m have been performed using various detectors located above ground. In this work a 606 g Ta disk of natural isotopic composition was measured for 170 d in the 225 m deep underground laboratory HADES. The new lower bound for the half-life is 1.7×1016 y for electron capture decay and 1.2×1016 y for Beta- decay. This gives a total lower bound for the half-life of 7.1×1015 y, which is a factor of 6 higher than the previous lower bound.

Relativistic mean-field model and random-phase approximation with vacuum polarization

The collective multipole excitations are studied in the framework of relativistic random-phase approximation with the vacuum polarization. First, we show for the nuclear ground state that the leading order of derivative expansion of the effective action arising from the vacuum correction agrees with the exact calculation using the Green function method very well. The derivative expansion makes us easy to perform a fully self-consistent calculation, even for the random-phase approximation. A remarkable effect of the inclusion of the vacuum polarization is the increase of the effective mass meff/mN ~ 0.9, which gives, for all multipole modes, smaller energy-weighted sum rule values than those of the typical relativistic model. Also, the large effective mass constrained by the vacuum polarization can give an excellent agreement with experimental data on the excitation energy for the isoscalar quadrupole resonances. It is shown, further, that the change of the shell structure due to the vacuum polarization plays an important role in the dipole compression modes.

Global Calculations of Ground-State Axial Shape Asymmetry of Nuclei

Important insight into the symmetry properties of the nuclear ground-state (gs) shape is obtained from the characteristics of low-lying collective energy-level spectra. In the 1950s, experimental and theoretical studies showed that in the gs many nuclei are spheroidal in shape rather than spherical. Later, a hexadecapole component of the gs shape was identified. In the 1970-1995 time frame, a consensus that reflection symmetry of the gs shape was broken for some nuclei emerged. Here we present the first calculation across the nuclear chart of axial symmetry breaking in the nuclear gs. We show that we fulfill a necessary condition: Where we calculate axial symmetry breaking, characteristic gamma bands are observed experimentally. Moreover, we find that, for those nuclei where axial asymmetry is found, a systematic deviation between calculated and measured masses is removed.

GIANT RESONANCES AND ASYMMETRY ENERGY

A microscopic analysis of the asymmetry energy is performed through the investigation of nuclear giant resonances in the relativistic approach. Nuclear ground state properties are calculated in an extended relativistic mean-field theory plus BCS method, where the contribution of the resonant continuum to pairing correlations is properly treated. The nuclear giant resonances are investigated in the relativistic random phase approximation (RRPA) or quasi-particle RRPA. Special emphases are paid to the correlation between the giant dipole resonance or pygmy resonance and the density dependence of the asymmetry energy.

Resonance ionization spectroscopy of bismuth at the IGISOL facility

A programme of research has commenced at the IGISOL facility, Jyvaskyla, combining the technique of resonance ionization spectroscopy with the development of the highly selective laser ion source trap (LIST). The first element of interest is bismuth, which contains three isomers of multi-quasiparticle states in near-spherical nuclei, namely 207Bi (21/2+, 182 μs), 204Bi (10−, 13 ms) and 204Bi (17+, 1.07 ms). A measurement of the optical isomer shift provides a direct comparison of the mean-square charge radii between the isomer and the nuclear ground state. Due to the short isomer lifetimes the spectroscopy will be done either within the ion guide or in a sextupole ion beam guide (SPIG), located after the ion guide and used in the development of the LIST. A mixed dye-Ti: Sapphire laser ionization scheme has been successfully tested for bismuth and first off-line results have been obtained.

An upper limit of ground-state energy fluctuations in nuclear masses

Shell model calculations are employed to estimate an upper limit of statistical fluctuations in the nuclear ground-state energies. In order to mimic the presence of quantum chaos associated with neutron resonances at energies between 6 and 10 MeV, calculations include random interactions in the upper shells. The upper bound for the energy fluctuations at mid-shell is shown to have the form σ(A)≈20 A−1.34 MeV. This estimate is consistent with the mass errors found in large-shell model calculations along the N=126 line, and with local mass error estimated using the Garvey–Kelson relations, all being smaller than 100 keV. It agrees in both size and functional form with the fluctuations deduced independently from second-order perturbation theory.

Hartree-Fock and many body perturbation theory with correlated realisticNNinteractions

We employ correlated realistic nucleon-nucleon interactions for the description of nuclear ground states throughout the nuclear chart within the Hartree-Fock approximation. The crucial short-range central and tensor correlations, which are induced by the realistic interaction and cannot be described by the Hartree-Fock many-body state itself, are included explicitly by a state-independent unitary transformation in the framework of the unitary correlation operator method (UCOM). Using the correlated realistic interaction ${V}_{\mathrm{UCOM}}$ resulting from the Argonne V18 potential, bound nuclei are already obtained on the Hartree-Fock level. However, the binding energies are smaller than the experimental values because long-range correlations have not been accounted for. Their inclusion by means of many-body perturbation theory leads to a remarkable agreement with experimental binding energies over the whole mass range from $^{4}\mathrm{He}$ to $^{208}\mathrm{Pb}$, even far off the valley of stability. The observed perturbative character of the residual long-range correlations and the apparently small net effect of three-body forces provides promising perspectives for a unified nuclear structure description.