Shell-model Interaction Research Articles

Novel nuclear structure aspects of the Oνββ-decay

We explore the influence of the deformation on the nuclear matrix elements of the neutrinoless double beta decay (NME), concluding that the difference in deformation -or more generally in the amount of quadrupole correlations- between parent and grand daughter nuclei quenches strongly the decay. We correlate these differences with the seniority structure of the nuclear wave functions. In this context, we examine the present discrepancies between the NME's obtained in the framework of the Interacting Shell Model and the Quasiparticle RPA. In our view, part of the discrepancy can be due to the limitations of the spherical QRPA in treating nuclei which have strong quadrupole correlations. We surmise that the NME's in a basis of generalized seniority are approximately model independent, i. e. they are "universal".

Collectivity in the light xenon isotopes: A shell model study

The lightest Xenon isotopes are studied in the framework of the Interacting Shell Model (ISM). The valence space comprises all the orbits lying between the magic closures N=Z=50 and N=Z=82. The calculations produce collective deformed structures of triaxial nature that encompass nicely the known experimental data. Predictions are made for the (still unknown) N=Z nucleus 108-Xe. The results are interpreted in terms of the competition between the quadrupole correlations enhanced by the pseudo-SU(3) structure of the positive parity orbits and the pairing correlations brought in by the 0h11/2 orbit. We have studied as well the effect of the excitations from the 100-Sn core on our predictions. We show that the backbending in this region is due to the alignment of two particles in the 0h11/2 orbit. In the N=Z case, one neutron and one proton align to J=11 and T=0. In 110-Xe and 112-Xe the alignment begins in the J=10 T=1 channel and it is dominantly of neutron neutron type. Approaching the band termination the alignment of a neutron and a proton to J=11 and T=0 takes over. In a more academic mood, we have explored the role of the isovector and isoscalar pairing correlations on the structure on the yrast bands of 108-Xe and 110-Xe and examined the role of the isovector and isoscalar pairing condensates in these N~Z nuclei.

Spectral fluctuations and the statistics of electromagnetic transition intensities and electromagnetic moments in [formula omitted] using the framework of the shell model

The fluctuation properties of energy spectrum, electromagnetic transition intensities and electromagnetic moments in Xe 136 nucleus are investigated within the framework of the interacting shell model, using a realistic effective interaction for the N82-model space with a Sn 132 core. The spectral fluctuations (i.e., the nearest-neighbors level spacing distribution and the Δ 3 statistic), the distributions of the electromagnetic transition intensities and of the electromagnetic moments are well described by the Gaussian orthogonal ensemble of random matrices. A clear quantum signature of the breaking of chaoticity (i.e., a transition towards regularity) is observed when the single particle energies are increased.

Shell evolution and nuclear forces

We present a quantitative study of the role played by different components characterizing the nucleon–nucleon interaction in the evolution of the nuclear shell structure. It is based on the spin–tensor decomposition of an effective two-body shell-model interaction and the subsequent study of effective single-particle energy variations in a series of isotopes or isotones. The technique allows to separate unambiguously contributions of the central, vector and tensor components of the realistic effective interaction. We show that while the global variation of the single-particle energies is due to the central component of the effective interaction, the characteristic behavior of spin–orbit partners, noticed recently, is mainly due to its tensor part. Based on the analysis of a well-fitted realistic interaction in the sdpf shell-model space, we analyze in detail the role played by the different terms in the formation and/or disappearance of N=16, N=20 and N=28 shell gaps in neutron-rich nuclei.

Occupancies of individual orbits, and the nuclear matrix element of theGe76neutrinolessββdecay

We discuss the variation of the nuclear matrix element (NME) for the neutrinoless double beta ($0\ensuremath{\nu}\ensuremath{\beta}\ensuremath{\beta}$) decay of $^{76}\mathrm{Ge}$ when the wave functions are constrained to reproduce the experimental occupancies of the two nuclei involved in the transition. In the interacting shell model description the value of the NME is enhanced about 15% compared to previous calculations, whereas in the QRPA the NME's are reduced by 20%--30%. This diminishes the discrepancies between both approaches. In addition, we discuss the effect of the short-range correlations on the NME in light of the recently proposed parametrizations based on a consistent renormalization of the $0\ensuremath{\nu}\ensuremath{\beta}\ensuremath{\beta}$ transition operator.

Spectroscopic study of neutron-rich calcium isotopes with a realistic shell-model interaction

We have studied neutron-rich calcium isotopes in terms of the shell model, employing a realistic effective interaction derived from the CD-Bonn nucleon-nucleon potential. The short-range repulsion of the potential is renormalized by way of the ${V}_{\mathrm{low}\ensuremath{-}\mathrm{k}}$ approach. The calculated results are in very good agreement with the available experimental data, thus supporting our predictions for the hitherto unknown spectra of $^{53\ensuremath{-}56}\mathrm{Ca}$ nuclei. In this context, the possible existence of an $N=34$ shell closure is discussed.

Spectroscopy and reduced transition probabilities of negative parity bands up to band termination in 45Ti

The negative parity high spin states in 45Ti have been investigated with the interacting shell model including the full fp shell and the configuration dependent cranked Nilsson–Strutinsky approach. Generally, the shell model has successfully reproduced the energy levels of negative parity bands, especially has a good description of the signature inversion at 17/2−. The reduced electric quadrupole transition probabilities of high spin states are calculated by the two models and compared with the experimental results. Reasonable agreement between theories and experiment are obtained, while the shell model can give more fine structures. The large differences of elctromagnetic moments between the shell model calculation and observation call for more elaborate effective interaction and more active shells.

Survey of Excited State Neutron Spectroscopic Factors forZ=8–28Nuclei

We have extracted 565 neutron spectroscopic factors of sd and fp shell nuclei by systematically analyzing more than 2000 measured (d, p) angular distributions. We are able to compare 125 of the extracted spectroscopic factors to values predicted by large-basis shell-model calculations and evaluate the accuracies of spectroscopic factors predicted by different shell-model interactions in these regions. We find that the spectroscopic factors predicted for most excited states of sd-shell nuclei using the latest USDA or USDB interactions agree with the experimental values. For fp shell nuclei, the inability of the current models to account for the core excitation and fragmentation of the states leads to considerable discrepancies. In particular, the agreement between data and shell-model predictions for Ni isotopes is not better than a factor of 2 using either the GXPF1A or the XT interaction.

0νββnuclear matrix elements and the occupancy of individual orbits

The measured occupancies of valence orbits in 76Ge and 76Se are used as a guideline for modification of the effective mean field energies that results in better description of these quantities. With them, in combination with the self-consistent renormalized quasiparticle random phase approximation (SRQRPA) method that ensures conservation of the mean particle number in the correlated ground state, we show that the resulting 0νββ nuclear matrix element for the 76Ge-->76Se transition is reduced by ~25% compared to the previous QRPA value, and therefore the difference between the present approach and the interacting shell model predictions becomes correspondingly smaller. Analogous modification of the mean field energies for the A=82 system also results in a reduction of 0νββ matrix element for the 82Se-->82Kr transition, making it also closer to the shell model prediction.

Disassembling the nuclear matrix elements of the neutrinoless ββ decay

In this article we analyze the nuclear matrix elements (NME) of the neutrinoless double beta decays ( 0 ν β β ) of the nuclei 48Ca, 76Ge, 82Se, 124Sn, 128Te, 130Te and 136Xe in the framework of the interacting shell model (ISM). We study the relative value of the different contributions to the NME's, such as higher order terms in the nuclear current, finite nuclear size effects and short range correlations, as well as their evolution with the maximum seniority permitted in the wave functions. We discuss also the build-up of the NME's as a function of the distance between the decaying neutrons. We calculate the decays to 0 1 + final states and find that these decays are at least 25 times more suppressed with respect to the ground state to ground state transition.

Gamow-Teller strengths inNa24using the24Mg(t,3He)reaction at115AMeV

Gamow-Teller transitions from $^{24}\mathrm{Mg}$ to $^{24}\mathrm{Na}$ were studied via the ($t,{}^{3}\mathrm{He}$) reaction at $115A$ MeV using a secondary triton beam produced via fast fragmentation of $150A$ MeV $^{16}\mathrm{O}$ ions. Compared to previous ($t,{}^{3}\mathrm{He}$) experiments at this energy that employed a primary $\ensuremath{\alpha}$ beam, the secondary beam intensity is improved by about a factor of five. Despite the large emittance of the secondary beam, an excitation-energy resolution of $~200$ keV is achieved. A good correspondence is found between the extracted Gamow-Teller strength distribution and those available from other charge-exchange probes. Theoretical calculations using the newly developed USDA and USDB $\mathit{sd}$-shell model interactions reproduce the data well.

D5/2proton hole strength in neutron-richP43: Shell structure and nuclear shapes nearN=28

We report on the use of the one-proton knockout reaction from $^{44}\mathrm{S}$ to determine the location of ${d}_{5/2}$ proton strength in neutron-rich $^{43}\mathrm{P}$. The results are used to test two shell-model frameworks with different pictures of the evolution of single-proton energies along the $N=28$ isotones near the neutron dripline. We observe a concentration of ${d}_{5/2}$ proton hole strength near 1 MeV in excitation energy. This result favors the recent shell-model interaction of Utsuno et al. [Eur. Phys. J. Spec. Top. 150, 187 (2007)] and provides additional evidence for an oblate shape for $^{42}\mathrm{Si}$.

Structure of Neutron-Rich Ar Isotopes BeyondN=28

Results from the gamma-ray spectroscopy of {47,48}Ar exemplifying new limits of sensitivity for characterizing neutron-rich nuclei at energies around the Coulomb barrier are presented. The present results, along with interacting shell model calculations, highlight the role of cross-shell excitations and indicate the presence of a nonaxial deformation in 48Ar.

Effective shell model Hamiltonians from density functional theory: Quadrupolar and pairing correlations

We describe a procedure for mapping a self-consistent mean-field theory (also known as density functional theory) onto a shell-model Hamiltonian that includes quadrupole-quadrupole and monopole pairing interactions in a truncated space. We test our method in the deformed $N=Z \mathit{sd}$-shell nuclei $^{20}\mathrm{Ne}$, $^{24}\mathrm{Mg}$, and $^{36}\mathrm{Ar}$, starting from the Hartree-Fock plus Bardeen-Cooper-Schrieffer (BCS) approximation of the universal $\mathit{sd}$ shell-model interaction. A similar method is then followed using the SLy4 Skyrme energy density functional in the particle-hole channel plus a zero-range density-dependent force in the pairing channel. Based on the ground-state solution of this density functional theory at the Hartree-Fock plus BCS level, an effective shell-model Hamiltonian is constructed. We apply this mapped Hamiltonian to extract quadrupolar and pairing correlation energies beyond the mean-field approximation. The rescaling of the mass quadrupole operator in the truncated shell-model space is found to be almost independent of the coupling strength used in the pairing channel of the underlying mean-field theory.

Determination of theN=16Shell Closure at the Oxygen Drip Line

The neutron unbound ground state of (25)O (Z=8, N=17) was observed for the first time in a proton knockout reaction from a (26)F beam. A single resonance was found in the invariant mass spectrum corresponding to a neutron decay energy of 770_+20(-10) keV with a total width of 172(30) keV. The N=16 shell gap was established to be 4.86(13) MeV by the energy difference between the nu1s(1/2) and nu0d(3/2) orbitals. The neutron separation energies for (25)O agree with the calculations of the universal sd shell model interaction. This interaction incorrectly predicts an (26)O ground state that is bound to two-neutron decay by 1 MeV, leading to a discrepancy between the theoretical calculations and experiment as to the particle stability of (26)O. The observed decay width was found to be on the order of a factor of 2 larger than the calculated single-particle width using a Woods-Saxon potential.

In-beam γ-ray spectroscopy of the neutron-rich nitrogen isotopesN19−22

The structure of N19-22 nuclei was investigated by means of in-beam gamma-ray spectroscopic technique using fragmentation reactions of both stable and radioactive beams. Based on particle-gamma and particle-gamma gamma coincidence data, level schemes are constructed for the neutron-rich nitrogen nuclei. The experimental results are compared with shell model calculations. The strength of the N=14 and Z=8 shell closures and the weakening of the shell model interaction WBT are discussed.

Microscopic approaches to nuclear structure: Configuration interaction

The configuration interaction (CI) approach to solving the nuclear many-body problem, also known as the interacting shell model, has proven to be powerful tool in understanding the structure of nuclei. The principal criticism of past applications of the shell model is the reliance on empirical tuning to interaction matrix elements. If an accurate description of nuclei far from the valley of stability, where little or no data is available, a more fundamental approach is needed. This starts with recent ab initio approaches with effective interactions in the no-core shell model (NCSM). Using effective-field theory for guidance, fully ab initio descriptions of nuclei up to 16O with QCD based NN, NNN, and NNNN interactions will be possible within the next five years. An important task is then to determine how to use these NCSM results to develop effective interactions to describe heavier nuclei without the need to resort to an empirical retuning with every model space. Thus, it is likely that more traditional CI applications utilizing direct diagonalization and more fundamental interactions will be applicable to nuclei with perhaps up to one hundred constituents. But, these direct diagonalization CI applications will always be computationally limited due to the rapid increase in the number of configurations with particle number. Very recently, the shifted-contour method has been applied to the Auxiliary-field Monte Carlo approach to the Shell Model (AFMCSM), and preliminary applications exhibit a remarkable taming of the notorious sign problem. If the mitigation of the sign problem holds true, the AFMCSM will offer a method to compute quantum correlations to mean-field applications for just about all nuclei; giving exact results for CI model spaces that can approach 1020-25. In these lectures, I will discuss modern applications of CI to the nuclear many-body problem that have the potential to guide nuclear structure theory into the next decade.

Influence of Pairing on the Nuclear Matrix Elements of the NeutrinolessββDecays

We study in this Letter the neutrinoless double beta decay nuclear matrix elements (NME's) in the framework of the interacting shell model. We analyze them in terms of the total angular momentum of the decaying neutron pair and as a function of the seniority truncations in the nuclear wave functions. This point of view turns out to be very adequate to gauge the accuracy of the NME's predicted by different nuclear models. In addition, it gives back the protagonist role in this process to the pairing interaction, the one which is responsible for the very existence of double beta decay emitters. We show that low seniority approximations, comparable to those implicit in the quasiparticle RPA in a spherical basis, tend to overestimate the NME's in several decays.

Ab InitioStudy ofCa40with an Importance-Truncated No-Core Shell Model

We propose an importance truncation scheme for no-core shell model or configuration interaction approaches, which enables converged calculations for nuclei well beyond the p shell. It is based on an a priori measure for the importance of individual basis states constructed by means of many-body perturbation theory. Only the physically relevant states of the no-core model space are considered, which leads to a dramatic reduction of the basis dimension. We analyze the validity and efficiency of this truncation scheme using different realistic nucleon-nucleon interactions and compare to conventional no-core shell model calculations for 4He and 16O. Then, we present first converged calculations for the ground state of 40Ca within no-core model spaces including up to 16 PlanckOmega excitations using realistic low-momentum interactions. The scheme is universal and can be easily applied to other quantum many-body problems.

Global properties of fp-shell interactions in many-nucleon systems

Spectral distribution theory, which can be used to compare microscopic interactions over a broad range of nuclei, is applied in an analysis of two modern effective interactions based on the realistic CD-Bonn potential for 0 ℏ Ω no-core shell model calculations in the fp shell, as well as in a comparison of these with the realistic shell-model GXPF1 interaction. In particular, we explore the ability of these interaction to account for the development of isovector pairing correlations and collective rotational motion in the fp shell. Our findings expose the similarities of these two-body interactions, especially as this relates to their pairing and rotational characteristics. Further, the GXPF1 interaction is used to determine the strength parameter of a quadrupole term that can be used to augment an isovector-pairing model interaction with Sp ( 4 ) dynamical symmetry, which in turn is shown to yield reasonable agreement with the low-lying energy spectra of 58Ni and 58Cu.