Fast and accurate evaluation of Wigner 3j, 6j, and 9j symbols using prime factorisation and multi-word integer arithmetic

We present an efficient implementation for the evaluation of Wigner 3j, 6j, and 9j symbols. These represent numerical transformation coefficients that are used in the quantum theory of angular momentum. They can be expressed as sums and square roots of ratios of integers. The integers can be very large due to factorials. We avoid numerical precision loss due to cancellation through the use of multi-word integer arithmetic for exact accumulation of all sums. A fixed relative accuracy is maintained as the limited number of floating-point operations in the final step only incur rounding errors in the least significant bits. Time spent to evaluate large multi-word integers is in turn reduced by using explicit prime factorisation of the ingoing factorials, thereby improving execution speed. Comparison with existing routines shows the efficiency of our approach and we therefore provide a computer code based on this work.Comment: 7 pages, 2 figures. Accepted for publication in SIAM Journal on Scientific Computing (SISC

Analytical approach to electromagnetic processes in loosely bound nuclei: application to 8B

In this paper we develop an analytical model in order to study electromagnetic processes involving loosely bound neutron--rich and proton--rich nuclei. We construct a model wave function, to describe loosely bound few--body systems, having the correct behaviour both at large and small distances. The continuum states are approximated by regular Coulomb functions. As a test case we consider the two--body Coulomb dissociation of 8B and, the inverse, radiative capture reaction. The difference between using a pure two--body model and the results obtained when incorporating many--body effects, is investigated. We conclude that the interpretation of experimental data is highly model dependent and stress the importance of measuring few--body channels.Comment: Accepted for publication in Physics Letters B. Added a comparison with a potential model calculation in Fig.

Analytical E1 strength functions of two-neutron halo nuclei: the 6-He example

An analytical model is developed to study the spectra of electromagnetic dissociation of two-neutron halo nuclei without precise knowledge about initial and final states. Phenomenological three-cluster bound state wave functions, reproducing the most relevant features of these nuclei, are used along with no interaction final states. The 6-He nucleus is considered as a test case, and a good agreement with experimental data concerning the shape of the spectrum and the magnitude of the strength function is found.Comment: 19 pages, 4 figures Accepted for publishing in Nuclear Physics

Fermionization of two-component few-fermion systems in a one-dimensional harmonic trap

The nature of strongly interacting Fermi gases and magnetism is one of the most important and studied topics in condensed-matter physics. Still, there are many open questions. A central issue is under what circumstances strong short-range repulsive interactions are enough to drive magnetic correlations. Recent progress in the field of cold atomic gases allows to address this question in very clean systems where both particle numbers, interactions and dimensionality can be tuned. Here we study fermionic few-body systems in a one dimensional harmonic trap using a new rapidly converging effective-interaction technique, plus a novel analytical approach. This allows us to calculate the properties of a single spin-down atom interacting with a number of spin-up particles, a case of much recent experimental interest. Our findings indicate that, in the strongly interacting limit, spin-up and spin-down particles want to separate in the trap, which we interpret as a microscopic precursor of one-dimensional ferromagnetism in imbalanced systems. Our predictions are directly addressable in current experiments on ultracold atomic few-body systems.Comment: 12 pages, 6 figures, published version including two appendices on our new numerical and analytical approac

Resonance parameters of the first 1/2+ state in 9Be and astrophysical implications

Spectra of the 9Be(e,e') reaction have been measured at the S-DALINAC at an electron energy E_0 = 73 MeV and scattering angles of 93{\deg} and 141{\deg} with high energy resolution up to excitation energies E_x = 8 MeV. The astrophysically relevant resonance parameters of the first excited 1/2+ state of 9Be have been extracted in a one-level approximation of R-matrix theory resulting in a resonance energy E_R = 1.748(6) MeV and width Gamma_R = 274(8) keV in good agreement with the latest 9Be(gamma,n) experiment but with considerably improved uncertainties. However, the reduced B(E1) transition strength deduced from an extrapolation of the (e,e') data to the photon point is a factor of two smaller. Implications of the new results for a possible production of 12C in neutron-rich astrophysical scenarios are discussed.Comment: 8 pages, 7 figures, accepted for publication in Phys. Rev.

Tunneling Theory for Tunable Open Quantum Systems of Ultracold Atoms in One-Dimensional Traps

The creation of tunable open quantum systems is becoming feasible in current experiments with ultracold atoms in low-dimensional traps. In particular, the high degree of experimental control over these systems allows detailed studies of tunneling dynamics, e.g., as a function of the trapping geometry and the interparticle interaction strength. In order to address this exciting opportunity we present a theoretical framework for two-body tunneling based on the rigged Hilbert space formulation. In this approach, bound, resonant and scattering states are included on an equal footing, and we argue that the coupling of all these components is vital for a correct description of the relevant threshold phenomena. In particular, we study the tunneling mechanism for two-body systems in one-dimensional traps and different interaction regimes. We find a strong dominance of sequential tunneling of single particles for repulsive and weakly attractive systems, while there is a signature of correlated pair tunneling in the calculated many-particle flux for strongly attractive interparticle interaction.Comment: To be published in Phys. Rev. A (Rapid Communication

Radiative capture and electromagnetic dissociation involving loosely bound nuclei: the 8^8B example

Electromagnetic processes in loosely bound nuclei are investigated using an analytical model. In particular, electromagnetic dissociation of $^8$B is studied and the results of our analytical model are compared to numerical calculations based on a three-body picture of the $^8$B bound state. The calculation of energy spectra is shown to be strongly model dependent. This is demonstrated by investigating the sensitivity to the rms intercluster distance, the few-body behavior, and the effects of final state interaction. In contrast, the fraction of the energy spectrum which can be attributed to E1 transitions is found to be almost model independent at small relative energies. This finding is of great importance for astrophysical applications as it provides us with a new tool to extract the E1 component from measured energy spectra. An additional, and independent, method is also proposed as it is demonstrated how two sets of experimental data, obtained with different beam energy and/or minimum impact parameter, can be used to extract the E1 component.Comment: Submitted to Phys. Rev. C. 10 pages, 7 figure

Power counting in chiral effective field theory and nuclear binding

Chiral effective field theory ($\chi$EFT), as originally proposed by Weinberg, promises a theoretical connection between low-energy nuclear interactions and quantum chromodynamics (QCD). However, the important property of renormalization-group (RG) invariance is not fulfilled in current implementations and its consequences for predicting atomic nuclei beyond two- and three-nucleon systems has remained unknown. In this work we present a first and systematic study of recent RG-invariant formulations of $\chi$EFT and their predictions for the binding energies and other observables of selected nuclear systems with mass-numbers up to $A =16$. Specifically, we have carried out ab initio no-core shell-model and coupled cluster calculations of the ground-state energy of $^3$H, $^{3,4}$He, $^{6}$Li, and $^{16}$O using several recent power-counting (PC) schemes at leading order (LO) and next-to-leading order (NLO), where the subleading interactions are treated in perturbation theory. Our calculations indicate that RG-invariant and realistic predictions can be obtained for nuclei with mass number $A \leq 4$. We find, however, that $^{16}$O is either unbound with respect to the four $\alpha$-particle threshold, or deformed, or both. Similarly, we find that the $^{6}$Li ground-state resides above the $\alpha$-deuteron separation threshold. These results are in stark contrast with experimental data and point to either necessary fine-tuning of all relevant counterterms, or that current state-of-the-art RG-invariant PC schemes at LO in $\chi$EFT lack necessary diagrams -- such as three-nucleon forces -- to realistically describe nuclei with mass number $A>4$.Comment: 18 pages, 12 figure

Large basis ab initio shell model investigation of 9-Be and 11-Be

We are presenting the first ab initio structure investigation of the loosely bound 11-Be nucleus, together with a study of the lighter isotope 9-Be. The nuclear structure of these isotopes is particularly interesting due to the appearance of a parity-inverted ground state in 11-Be. Our study is performed in the framework of the ab initio no-core shell model. Results obtained using four different, high-precision two-nucleon interactions, in model spaces up to 9\hbar\Omega, are shown. For both nuclei, and all potentials, we reach convergence in the level ordering of positive- and negative-parity spectra separately. Concerning their relative position, the positive-parity states are always too high in excitation energy, but a fast drop with respect to the negative-parity spectrum is observed when the model space is increased. This behavior is most dramatic for 11-Be. In the largest model space we were able to reach, the 1/2+ level has dropped down to become either the first or the second excited state, depending on which interaction we use. We also observe a contrasting behavior in the convergence patterns for different two-nucleon potentials, and argue that a three-nucleon interaction is needed to explain the parity inversion. Furthermore, large-basis calculations of 13-C and 11-B are performed. This allows us to study the systematics of the position of the first unnatural-parity state in the N=7 isotone and the A=11 isobar. The 11-B run in the 9\hbar\Omega model space involves a matrix with dimension exceeding 1.1 x 10^9, and is our largest calculation so far. We present results on binding energies, excitation spectra, level configurations, radii, electromagnetic observables, and 10-Be+n overlap functions.Comment: 17 pages, 12 figures To be published in Phys. Rev. C Resubmitted version. Minor change

Nuclear physics uncertainties in light hypernuclei

The energy levels of light hypernuclei are experimentally accessible observables that contain valuable information about the interaction between hyperons and nucleons. In this work we study strangeness $S = -1$ systems $^{3,4}_\Lambda$H and $^{4,5}_\Lambda$He using the ab initio no-core shell model (NCSM) with realistic interactions obtained from chiral effective field theory ($\chi$EFT). In particular, we quantify the finite precision of theoretical predictions that can be attributed to nuclear physics uncertainties. We study both the convergence of the solution of the many-body problem (method uncertainty) and the regulator- and calibration data-dependence of the nuclear $\chi$EFT Hamiltonian (model uncertainty). For the former, we implement infrared correction formulas and extrapolate finite-space NCSM results to infinite model space. We then use Bayesian parameter estimation to quantify the resulting method uncertainties. For the latter, we employ a family of 42 realistic Hamiltonians and measure the standard deviation of predictions while keeping the leading-order hyperon-nucleon interaction fixed. Following this procedure we find that model uncertainties of ground-state $\Lambda$ separation energies amount to $\sim 20(100)$ keV in $^3_\Lambda$H($^4_\Lambda$H,He) and $\sim 400$ keV in $^5_\Lambda$He. Method uncertainties are comparable in magnitude for the $^4_\Lambda$H,He $1^+$ excited states and $^5_\Lambda$He, which are computed in limited model spaces, but otherwise much smaller. This knowledge of expected theoretical precision is crucial for the use of binding energies of light hypernuclei to infer the elusive hyperon-nucleon interaction.Comment: 16 pages with 8 figure