No-core Shell Model Calculations Research Articles

Charge symmetry breaking in light Λ hypernuclei

Charge symmetry breaking (CSB) is particularly strong in the A = 4 mirror hypernuclei . Recent four-body no-core shell model calculations that confront this CSB by introducing Λ-Σ0 mixing to leading-order chiral effective field theory hyperon-nucleon potentials are reviewed, and a shell-model approach to CSB in p-shell Λ hypernuclei is outlined.

Effective Algorithm for Calculation of Protons and Neutrons Distributions in Atomic Nucleus Shells

This paper presents the protons and neutrons distributions in atomic nucleus shells calculation algorithm which may be used for ab initio no-core nuclear shell model computations. The problem of enumeration of many-particle states is formulated on energetic basis instead of application of the traditional scheme for states classification. The algorithm provides calculations of protons and neutrons occupation restrictions for nuclear shells for an arbitrary number of oscillator quanta. The reported results show that the presented algorithm significantly outperforms the traditional approach and may fit the needs of state-of-the-art no-core shell model calculations of atomic nuclei. DOI: 10.15181/csat.v5i1.1572

Reorientation-effect measurement of the first 2+ state in 12C: Confirmation of oblate deformation

A Coulomb-excitation reorientation-effect measurement using the TIGRESS γ−ray spectrometer at the TRIUMF/ISAC II facility has permitted the determination of the 〈21+‖E2ˆ‖21+〉 diagonal matrix element in 12C from particle−γ coincidence data and state-of-the-art no-core shell model calculations of the nuclear polarizability. The nuclear polarizability for the ground and first-excited (21+) states in 12C have been calculated using chiral NN N4LO500 and NN+3NF350 interactions, which show convergence and agreement with photo-absorption cross-section data. Predictions show a change in the nuclear polarizability with a substantial increase between the ground state and first excited 21+ state at 4.439 MeV. The polarizability of the 21+ state is introduced into the current and previous Coulomb-excitation reorientation-effect analyses of 12C. Spectroscopic quadrupole moments of QS(21+)=+0.053(44) eb and QS(21+)=+0.08(3) eb are determined, respectively, yielding a weighted average of QS(21+)=+0.071(25) eb, in agreement with recent ab initio calculations. The present measurement confirms that the 21+ state of 12C is oblate and emphasizes the important role played by the nuclear polarizability in Coulomb-excitation studies of light nuclei.

Ab initio electromagnetic observables with the in-medium similarity renormalization group

We present the formalism for consistently transforming transition operators within the in-medium similarity renormalization group framework. We implement the operator transformation in both the equations-of-motion and valence-space variants, and present first results for electromagnetic transitions and moments in medium-mass nuclei using consistently-evolved operators, including the induced two-body parts. These results are compared to experimental values, and--where possible--the results of no-core shell model calculations using the same input chiral interaction. We find good agreement between the equations-of-motion and valence space approaches. Magnetic dipole observables are generally in reasonable agreement with experiment, while the more collective electric quadrupole and octupole observables are significantly underpredicted, often by over an order of magnitude, indicating missing physics at the present level of truncation.

AbInitio Description of Open-Shell Nuclei: Merging No-Core Shell Model and In-Medium Similarity Renormalization Group.

We merge two successful abinitio nuclear-structure methods, the no-core shell model (NCSM) and the multireference in-medium similarity renormalization group (IM-SRG) to define a new many-body approach for the comprehensive description of ground and excited states of closed and open-shell nuclei. Building on the key advantages of the two methods-the decoupling of excitations at the many-body level in the IM-SRG and the access to arbitrary nuclei, eigenstates, and observables in the NCSM-their combination enables fully converged no-core calculations for an unprecedented range of nuclei and observables at moderate computational cost. We present applications in the carbon and oxygen isotopic chains, where conventional NCSM calculations are still feasible and provide an important benchmark. The efficiency and rapid convergence of the new approach make it ideally suited for abinitio studies of the complete spectroscopy of nuclei up into the medium-mass regime.

Description of resonant states in the shell model

A technique for describing scattering states within the nuclear shell model is proposed. This technique is applied to scattering of nucleons by $\alpha$ particles based on ab initio No-Core Shell Model calculations of $^5$He and $^5$Li nuclei with JISP16 NN interaction.

Properties of infrared extrapolations in a harmonic oscillator basis

The success and utility of effective field theory (EFT) in explaining the structure and reactions of few-nucleon systems has prompted the initiation of EFT-inspired extrapolations to larger model spaces in ab initio methods such as the no-core shell model (NCSM). In this contribution, we review and continue our studies of infrared (ir) and ultraviolet (uv) regulators of NCSM calculations in which the input is phenomenological [Formula: see text] and [Formula: see text] interactions fitted to data. We extend our previous findings that an extrapolation in the ir cutoff with the uv cutoff above the intrinsic uv scale of the interaction is quite successful, not only for the eigenstates of the Hamiltonian but also for expectation values of operators, such as [Formula: see text], considered long range. The latter results are obtained with Hamiltonians transformed by the similarity renormalization group (SRG) evolution. On the other hand, a possible extrapolation of ground state energies in the uv cutoff when the ir cutoff is below the intrinsic ir scale is not robust and does not agree with the ir extrapolation of the same data or with independent calculations using other methods.

Jacobi no-core shell model for p-shell nuclei

We introduce an algorithm to obtain coefficients of fractional parentage for light $p$-shell nuclei. The coefficients enable to use Jacobi coordinates in no-core shell model calculations separating off the center-of-mass motion. Fully antisymmetrized basis states are given together with recoupling coefficients that allow one to apply two- and three-nucleon operators. As an example, we study the dependence on the harmonic oscillator frequency of $^3$H, $^4$He, $^6$He, $^6$Li and $^7$Li and extract their binding and excitation energies. The coefficients will be made openly accessible as HDF5 data files.

Open-shell nuclei and excited states from multireference normal-ordered Hamiltonians

We discuss the approximate inclusion of three-nucleon interactions into ab initio nuclear structure calculations using a multi-reference formulation of normal ordering and Wick's theorem. Following the successful application of single-reference normal ordering for the study of ground states of closed-shell nuclei, e.g., in coupled-cluster theory, multi-reference normal ordering opens a path to open-shell nuclei and excited states. Based on different multi-determinantal reference states we benchmark the truncation of the normal-ordered Hamiltonian at the two-body level in no-core shell-model calculations for p-shell nuclei, including 6-Li, 12-C, and 10-B. We find that this multi-reference normal-ordered two-body approximation is able to capture the effects of the 3N interaction with sufficient accuracy, both, for ground-state and excitation energies, at the computational cost of a two-body Hamiltonian. It is robust with respect to the choice of reference states and has a multitude of applications in ab initio nuclear structure calculations of open-shell nuclei and their excitations as well as in nuclear reaction studies.

Lifetime measurements ofC17excited states and three-body and continuum effects

Author(s): Smalley, D; Iwasaki, H; Navratil, P; Roth, R; Langhammer, J; Bader, VM; Bazin, D; Berryman, JS; Campbell, CM; Dohet-Eraly, J; Fallon, P; Gade, A; Langer, C; Lemasson, A; Loelius, C; Macchiavelli, AO; Morse, C; Parker, J; Quaglioni, S; Recchia, F; Stroberg, SR; Weisshaar, D; Whitmore, K; Wimmer, K | Abstract: We studied transition rates for the lowest 1/2+ and 5/2+ excited states of C17 through lifetime measurements with the GRETINA array using the recoil-distance method. The present measurements provide a model-independent determination of transition strengths giving the values of B(M1;1/2+→3/2g.s.+)=1.04-0.12+0.03×10-2μN2 and B(M1;5/2+→3/2g.s.+)=7.12-0.96+1.27×10-2μN2. The quenched M1 transition strength for the 1/2+→3/2g.s.+ transition, with respect to the 5/2+→3/2g.s.+ transition, has been confirmed with greater precision. The current data are compared to importance-truncated no-core shell model calculations addressing effects due to continuum and three-body forces.

Infrared length scale and extrapolations for the no-core shell model

We precisely determine the infrared (IR) length scale of the no-core shell model (NCSM). In the NCSM, the $A$-body Hilbert space is truncated by the total energy, and the IR length can be determined by equating the intrinsic kinetic energy of $A$ nucleons in the NCSM space to that of $A$ nucleons in a $3(A-1)$-dimensional hyper-radial well with a Dirichlet boundary condition for the hyper radius. We demonstrate that this procedure indeed yields a very precise IR length by performing large-scale NCSM calculations for $^{6}$Li. We apply our result and perform accurate IR extrapolations for bound states of $^{4}$He, $^{6}$He, $^{6}$Li, $^{7}$Li. We also attempt to extrapolate NCSM results for $^{10}$B and $^{16}$O with bare interactions from chiral effective field theory over tens of MeV.

Ab initioeffective interactions forsd-shell valence nucleons

We perform \textit{ab initio} no-core shell-model calculations for $A=18$ and $19$ nuclei in a $4\hbar\Omega$, or $N_{\rm max}=4$, model space by using the effective JISP16 and chiral N3LO nucleon-nucleon potentials and transform the many-body effective Hamiltonians into the $0\hbar\Omega$ model space to construct the $A$-body effective Hamiltonians in the $sd$-shell. We separate the $A$-body effective Hamiltonians with $A=18$ and $A=19$ into inert core, one-, and two-body components. Then, we use these core, one-, and two-body components to perform standard shell-model calculations for the $A=18$ and $A=19$ systems with valence nucleons restricted to the $sd$ shell. Finally, we compare the standard shell-model results in the $0\hbar\Omega$ model space with the exact no-core shell model results in the $4\hbar\Omega$ model space for the $A=18$ and $A=19$ systems and find good agreement.

No-core Monte Carlo shell model calculations with unitary correlation operator method and similarity renormalization group**Supported by Fundamental Research Funds for the Central Universities (JUSRP1035), National Natural Science Foundation of China (11305077)

The unitary correlation operator method (UCOM) and the similarity renormalization group theory (SRG) are compared and discussed in the framework of the no-core Monte Carlo shell model (MCSM) calculations for 3H and 4He. The treatment of spurious center-of-mass motion by Lawson's prescription is performed in the MCSM calculations. These results with both transformed interactions show good suppression of spurious center-of-mass motion with proper Lawson's prescription parameter βc.m. values. The UCOM potentials obtain faster convergence of total energy for the ground state than that of SRG potentials in the MCSM calculations, which differs from the cases in the no-core shell model calculations (NCSM). These differences are discussed and analyzed in terms of the truncation scheme in the MCSM and NCSM, as well as the properties of the potentials of SRG and UCOM.

Spin-orbit decomposition ofab initionuclear wave functions

Although the modern shell-model picture of atomic nuclei is built from single-particle orbits with good total angular momentum $j$, leading to $j$-$j$ coupling, phenomenological models suggested decades ago that for $0p$-shell nuclides a simpler picture can be realized via coupling of total spin $S$ and total orbital angular momentum $L$. I revisit this idea with large-basis, no-core shell model (NCSM) calculations using modern \textit{ab initio} two-body interactions, and dissect the resulting wavefunctions into their component $L$- and $S$-components. Remarkably, there is broad agreement with calculations using the phenomenological Cohen-Kurath forces, despite a gap of nearly fifty years and six orders of magnitude in basis dimensions. I suggest $L$-$S$ may be a useful tool for analyzing \textit{ab initio} wavefunctions of light nuclei, for example in the case of rotational bands.

Continuum and three-nucleon force effects onBe9energy levels

We extend the recently proposed ab initio no-core shell model with continuum to include three-nucleon (3N) interactions beyond the few-body domain. The extended approach allows for the assessment of effects of continuum degrees of freedom as well as of the 3N force in ab initio calculations of structure and reaction observables of p- and lower-sd-shell nuclei. As first application we concentrate on energy levels of the 9Be system for which all excited states lie above the n-8Be threshold. For all energy levels, the inclusion of the continuum significantly improves the agreement with experiment, which was an issue in standard no-core shell model calculations. Furthermore, we find the proper treatment of the continuum indispensable for reliable statements about the quality of the adopted 3N interaction from chiral effective field theory. In particular, we find the 1/2+ resonance energy, which is of astrophysical interest, in good agreement with experiment.

Comparison between shell model and self-consistent mean field calculations for ground charge density distributions and elastic form factors of 12C and 16O nuclei

The ground charge density distributions, elastic form factors and root mean square radii for 12C and 16O nuclei in 1p-shell nuclei are calculated in shell model using core plus valence and no-core–shell model calculations. The single-particle wave functions of harmonic-oscillators potential are used. For such potential, two harmonic-oscillators size parameters are used: one for neutron and the other for proton. Calculations are compared with the results of self-consistent mean field using SKX Skyrme parameterization and experimental data. The calculated charge density distributions in shell model for 12C and 16O nuclei show good agreement with experimental data. The calculated charge form factors at low q in shell model for 12C and 16O show good agreement with experimental data. At high q, the result for 16O shows no prediction for the position of second diffraction minimum. In general, it is found that enlarging the model space in shell model leads to suppress slightly the behavior of density distribution around central region and also the behavior of form factor at high q, which is good to approach experimental data. On the other side, such increase in model space leads to increase the calculated root mean square radii, which is the same behaviour of the results of Hartree–Fock calculations. The calculated charge form factors in Hartree–Fock calculations show the existence of many diffraction minima, which do not agree with experimental data in contrary to shell model, which predicts less diffraction minima.

Alternative similarity renormalization group generators in nuclear structure calculations

The similarity renormalization group (SRG) has been successfully applied to soften interactions for ab initio nuclear calculations. In almost all practical applications in nuclear physics, an SRG generator with the kinetic energy operator is used. With this choice, a fast convergence of many-body calculations can be achieved, but at the same time substantial three-body interactions are induced even if one starts from a purely two-nucleon (NN) Hamiltonian. Three-nucleon (3N) interactions can be handled by modern many-body methods. However, it has been observed that when including initial chiral 3N forces in the Hamiltonian, the SRG transformations induce a non-negligible four-nucleon interaction that cannot be currently included in the calculations for technical reasons. Consequently, it is essential to investigate alternative SRG generators that might suppress the induction of many-body forces while at the same time might preserve the good convergence. In this work we test two alternative generators with operators of block structure in the harmonic oscillator basis. In the no-core shell model calculations for 3H, 4He and 6Li with chiral NN force, we demonstrate that their performances appear quite promising.

Collective Modes in Light Nuclei from First Principles

Results for ab initio no-core shell model calculations in a symmetry-adapted SU(3)-based coupling scheme demonstrate that collective modes in light nuclei emerge from first principles. The low-lying states of 6Li, 8Be, and 6He are shown to exhibit orderly patterns that favor spatial configurations with strong quadrupole deformation and complementary low intrinsic spin values, a picture that is consistent with the nuclear symplectic model. The results also suggest a pragmatic path forward to accommodate deformation-driven collective features in ab initio analyses when they dominate the nuclear landscape.

Symmetry-adapted ab initio no-core shell model calculations for 12C

Symmetry-adapted no-core shell-model calculations reveal dominant symmetry patterns in the structure of light nuclei, independent of whether the system Hamiltonian is phenomenological in nature or derived from realistic interactions. We show results of large-scale nuclear structure computations based on the ab initio symmetry-adapted no-core shell model that use only a fraction of the model space. In addition, the symmetry patterns unveiled in these results are employed to explore ultra-large model spaces for 12C. The outcome suggests a possible path forward for realizing collective theories that target correlated highly-deformed and alpha-cluster structures in terms of microscopic degrees of freedom that build forward from the nucleon-nucleon interaction itself.

Clusters and halos in light nuclei

The fermionic molecular dynamics approach uses Gaussian wave packets as single-particle basis states. Many-body basis states are Slater determinants projected on parity, angular momentum and total linear momentum. The wave-packet basis is very flexible – FMD contains harmonic oscillator shell model and Brink-type cluster states as special cases. The parameters of the wave packets are obtained by variation. A realistic effective interaction derived from the Argonne V18 interaction by means of the unitary correlation operator method is employed. We discuss the fully microscopic calculation of the 3He(α, γ)7Be capture reaction within the FMD approach. The model space contains frozen cluster configurations at large distances and polarized configurations in the interaction region. The polarized configurations are essential for a successful description of the 7Be bound state properties and for the S- and D-wave scattering states. The calculated cross section agrees well with recent measurements regarding both the absolute normalization and the energy dependence. We also discuss the structure of the cluster states, including the famous Hoyle state, in 12C. From the two-body densities we conclude that the Hoyle state has a spatially extended triangular α-cluster structure, whereas the third 0+ state features a chain-like obtuse triangle structure. We also calculate the NħΩ decomposition of our wave functions to illuminate the challenges of no-core shell model calculations for these cluster states.