arXiv subjects

C. Forssén

Publications and source records attributed to C. Forssén.

35 records · Page 2Linked to original sources

arXiv2016

Uncertainty analysis and order-by-order optimization of chiral nuclear interactions

Chiral effective field theory (chiEFT) provides a systematic approach to describe low-energy nuclear forces. Moreover, chiEFT is able to provide well-founded estimates of statistical and systematic uncertainties -- although this unique advantage has not yet been fully exploited. We fill this gap by performing an optimization and statistical analysis of all the low-energy constants (LECs) up to next-to-next-to-leading order. Our optimization protocol corresponds to a simultaneous fit to scattering and bound-state observables in the pion-nucleon, nucleon-nucleon, and few-nucleon sectors, thereby utilizing the full model capabilities of chiEFT. We study the effect on other observables by demonstrating error-propagation methods that can easily be adopted by future works. We employ mathematical optimization and implement automatic differentiation to attain efficient and machine-precise first- and second-order derivatives of the objective function with respect to the LECs. We use power-counting arguments to estimate the systematic uncertainty that is inherent to chiEFT and we construct chiral interactions at different orders with quantified uncertainties. Statistical error propagation is compared with Monte Carlo sampling showing that statistical errors are in general small compared to systematic ones. In conclusion, we find that a simultaneous fit to different sets of data is critical to (i) identify the optimal set of LECs, (ii) capture all relevant correlations, (iii) reduce the statistical uncertainty, and (iv) attain order-by-order convergence in chiEFT. Furthermore, certain systematic uncertainties in the few-nucleon sector are shown to get substantially magnified in the many-body sector; in particlar when varying the cutoff in the chiral potentials. The methodology and results presented in this Paper open a new frontier for uncertainty quantification in ab initio nuclear theory.

nucl-th↗

arXiv2015

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.

physics.comp-ph↗

arXiv2015

Charge, neutron, and weak size of the atomic nucleus

What is the size of the atomic nucleus? This deceivably simple question is difficult to answer. While the electric charge distributions in atomic nuclei were measured accurately already half a century ago, our knowledge of the distribution of neutrons is still deficient. In addition to constraining the size of atomic nuclei, the neutron distribution also impacts the number of nuclei that can exist and the size of neutron stars. We present an ab initio calculation of the neutron distribution of the neutron-rich nucleus $^{48}$Ca. We show that the neutron skin (difference between radii of neutron and proton distributions) is significantly smaller than previously thought. We also make predictions for the electric dipole polarizability and the weak form factor; both quantities are currently targeted by precision measurements. Based on ab initio results for $^{48}$Ca, we provide a constraint on the size of a neutron star.

nucl-th↗

arXiv2015

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.

nucl-th↗

arXiv2015

Accurate nuclear radii and binding energies from a chiral interaction

With the goal of developing predictive ab-initio capability for light and medium-mass nuclei, two-nucleon and three-nucleon forces from chiral effective field theory are optimized simultaneously to low-energy nucleon-nucleon scattering data, as well as binding energies and radii of few-nucleon systems and selected isotopes of carbon and oxygen. Coupled-cluster calculations based on this interaction, named NNLO$_{\rm sat}$, yield accurate binding energies and radii of nuclei up to $^{40}$Ca, and are consistent with the empirical saturation point of symmetric nuclear matter. In addition, the low-lying collective $J^π=3^-$ states in $^{16}$O and $^{40}$Ca are described accurately, while spectra for selected $p$- and $sd$-shell nuclei are in reasonable agreement with experiment.

nucl-th↗

arXiv2015

Strongly interacting few-fermion systems in a trap

Few- and many-fermion systems on the verge of stability, and consisting of strongly interacting particles, appear in many areas of physics. The theoretical modeling of such systems is a very difficult problem. In this work we present a theoretical framework that is based on the rigged Hilbert space formulation. The few-body problem is solved by exact diagonalization using a basis in which bound, resonant, and non-resonant scattering states are included on an equal footing. Current experiments with ultracold atoms offer a fascinating opportunity to study universal properties of few-body systems with a high degree of control over parameters such as the external trap geometry, the number of particles, and even the interaction strength. In particular, particles can be allowed to tunnel out of the trap by applying a magnetic-field gradient that effectively lowers the potential barrier. The result is a tunable open quantum system that allows detailed studies of the tunneling mechanism. In this Contribution we introduce our method and present results for the decay rate of two distinguishable fermions in a one-dimensional trap as a function of the interaction strength. We also study the numerical convergence. Many of these results have been previously published (R. Lundmark, C. Forssén, and J. Rotureau, arXiv: 1412.7175). However, in this Contribution we present several technical and numerical details of our approach for the first time.

cond-mat.quant-gas↗

arXiv2015

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.

cond-mat.quant-gas↗

arXiv2014

Quantum magnetism in strongly interacting one-dimensional spinor Bose systems

Strongly interacting one-dimensional quantum systems often behave in a manner that is distinctly different from their higher-dimensional counterparts. When a particle attempts to move in a one-dimensional environment it will unavoidably have to interact and 'push' other particles in order to execute a pattern of motion, irrespective of whether the particles are fermions or bosons. A present frontier in both theory and experiment are mixed systems of different species and/or particles with multiple internal degrees of freedom. Here we consider trapped two-component bosons with short-range inter-species interactions much larger than their intra-species interactions and show that they have novel energetic and magnetic properties. In the strongly interacting regime, these systems have energies that are fractions of the basic harmonic oscillator trap quantum and have spatially separated ground states with manifestly ferromagnetic wave functions. Furthermore, we predict excited states that have perfect antiferromagnetic ordering. This holds for both balanced and imbalanced systems, and we show that it is a generic feature as one crosses from few- to many-body systems.

cond-mat.quant-gas↗

arXiv2014

Statistical uncertainties of a chiral interaction at next-to-next-to leading order

We have quantified the statistical uncertainties of the low-energy coupling-constants (LECs) of an optimized nucleon-nucleon (NN) interaction from chiral effective field theory ($χ$EFT) at next-to-next-to-leading order (NNLO). In addition, we have propagated the impact of the uncertainties of the LECs to two-nucleon scattering phase shifts, effective range parameters, and deuteron observables.

nucl-th↗

arXiv2014

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.

cond-mat.quant-gas↗

arXiv2013

An optimized chiral nucleon-nucleon interaction at next-to-next-to-leading order

We optimize the nucleon-nucleon interaction from chiral effective field theory at next-to-next- to-leading order. The resulting new chiral force NNLOopt yields χ^2 \approx 1 per degree of freedom for laboratory energies below approximately 125 MeV. In the A = 3, 4 nucleon systems, the contributions of three-nucleon forces are smaller than for previous parametrizations of chiral interactions. We use NNLOopt to study properties of key nuclei and neutron matter, and demonstrate that many aspects of nuclear structure can be understood in terms of this nucleon-nucleon interaction, without explicitly invoking three-nucleon forces.

nucl-th↗

arXiv2011

The Similarity Renormalization Group for Three-Body Interactions in One Dimension

We report on recent progress of the implementation of the similarity renormalization group (SRG) for three-body interactions in a one-dimensional, bosonic model system using the plane wave basis. We discuss our implementation of the flow equations and show results that confirm that results in the three-body sector remain unchanged by the transformation of the Hamiltonian. We also show how the SRG transformation decouples low- from high-momentum nodes in the three-body sector and therefore simplifies the numerical calculation of observables.

nucl-th↗

arXiv2010

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° and 141° 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.

nucl-ex↗

arXiv2009

Effective-interaction approach to the many-boson problem

We show that the convergence behavior of the many-body numerical diagonalization scheme for strongly interacting bosons in a trap can be significantly improved by the Lee-Suzuki method adapted from nuclear physics: One can construct an effective interaction that acts in a space much smaller than the original Hilbert space. In particular for short-ranged forces and strong correlations, the method offers a good estimate of the energy and the excitation spectrum, at a computational cost several orders of magnitude smaller than that required by the standard method.

cond-mat.other↗

arXiv2009

Charge radii and electromagnetic moments of Li and Be isotopes from the ab initio no-core shell model

Recently, charge radii and ground-state electromagnetic moments of Li and Be isotopes were measured precisely. We have performed large-scale ab initio no-core shell model calculations for these isotopes using high-precision nucleon-nucleon potentials. The isotopic trends of our computed charge radii and quadrupole and magnetic-dipole moments are in good agreement with experimental results with the exception of the 11Li charge radius. The magnetic moments are in particular well described, whereas the absolute magnitudes of the quadrupole moments are about 10% too small. The small magnitude of the 6Li quadrupole moment is reproduced, and with the CD-Bonn NN potential, also its correct sign.

nucl-th↗

arXiv2008

Converging sequences in the ab initio no-core shell model

We demonstrate the existence of multiple converging sequences in the ab initio no-core shell model. By examining the underlying theory of effective operators, we expose the physical foundations for the alternative pathways to convergence. This leads us to propose a revised strategy for evaluating effective interactions for $A$-body calculations in restricted model spaces. We suggest that this strategy is particularly useful for applications to nuclear processes in which states of both parities are used simultaneously, such as for transition rates. We demonstrate the utility of our strategy with large-scale calculations in light nuclei.

nucl-th↗

arXiv2003

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

nucl-th↗