| 1. |
- Capel, Pierre, et al.
(författare)
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Effective field theory analysis of the Coulomb breakup of the one-neutron halo nucleus 19 C
- 2023
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Ingår i: European Physical Journal A. - 1434-601X .- 1434-6001. ; 59:11
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Tidskriftsartikel (refereegranskat)abstract
- We analyse the Coulomb breakup of 19 C measured at 67A MeV at RIKEN. We use the Coulomb-Corrected Eikonal (CCE) approximation to model the reaction and describe the one-neutron halo nucleus 19 C within Halo Effective Field Theory (Halo EFT). At leading order we obtain a fair reproduction of the measured cross section as a function of energy and angle. The description is insensitive to the choice of optical potential, as long as it accurately represents the size of 18 C. It is also insensitive to the interior of the 19 C wave function. Comparison between theory and experiment thus enables us to infer asymptotic properties of the ground state of 19 C: these data put constraints on the one-neutron separation energy of this nucleus and, for a given binding energy, can be used to extract an asymptotic normalisation coefficient (ANC). These results are confirmed by CCE calculations employing next-to-leading order Halo EFT descriptions of 19 C: at this order the results for the Coulomb breakup cross section are completely insensitive to the choice of the regulator. Accordingly, this reaction can be used to constrain the one-neutron separation energy and ANC of 19 C.
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| 2. |
- Rowlett, Julie, 1978, et al.
(författare)
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Crystallographic Groups, Strictly Tessellating Polytopes, and Analytic Eigenfunctions
- 2021
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Ingår i: American Mathematical Monthly. - : Informa UK Limited. - 1930-0972 .- 0002-9890. ; 128:5, s. 387-406
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Tidskriftsartikel (refereegranskat)abstract
- The mathematics of crystalline structures connects analysis, geometry, algebra, and number theory. The planar crystallographic groups were classified in the late 19th century. One hundred years later, Berard proved that the fundamental domains of all such groups satisfy a very special analytic property: the Dirichlet eigenfunctions for the Laplace eigenvalue equation are all trigonometric functions. In 2008, McCartin proved that in two dimensions, this special analytic property has both an equivalent algebraic formulation, as well as an equivalent geometric formulation. Here we generalize the results of Berard and McCartin to all dimensions. We prove that the following are equivalent: the first Dirichlet eigenfunction for the Laplace eigenvalue equation on a polytope is real analytic, the polytope strictly tessellates space, and the polytope is the fundamental domain of a crystallographic Coxeter group. Moreover, we prove that under any of these equivalent conditions, all of the eigenfunctions are trigonometric functions. To conclude, we connect these topics to the Fuglede and Goldbach conjectures and give a purely geometric formulation of Goldbach's conjecture.
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| 3. |
- Thim, Oliver, 1997, et al.
(författare)
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Bayesian analysis of chiral effective field theory at leading order in a modified Weinberg power counting approach
- 2023
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Ingår i: Physical Review C. - 2469-9993 .- 2469-9985. ; 108:5
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Tidskriftsartikel (refereegranskat)abstract
- We present a Bayesian analysis of renormalization-group invariant nucleon-nucleon interactions at leading order in chiral effective field theory (χEFT) with momentum cutoffs in the range 400–4000 MeV. We use history matching to identify relevant regions in the parameter space of low-energy constants (LECs) and subsequently infer the posterior probability density of their values using Markov chain Monte Carlo. All posteriors are conditioned on experimental data for neutron-proton scattering observables and we estimate the χ EFT truncation error in an uncorrelated limit. We do not detect any significant cutoff dependence in the posterior predictive distributions for two-nucleon observables. For all cutoff values we find a multimodal LEC posterior with an insignificant mode harboring a bound 1S0 state. The 3P0 and 3P2 phase shifts emerging from the Bayesian analysis are less constrained and typically more repulsive compared to the results of a phase shift optimization. We expect that our inference will impact predictions for nuclei. This work demonstrates how to perform inference in the presence of limit-cycle-like behavior and spurious bound states, and lays the foundation for a Bayesian analysis of renormalization-group invariant χEFT interactions beyond leading order.
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| 4. |
- Thim, Oliver, 1997
(författare)
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Low-Energy Theorems for Neutron–Proton Scattering in χEFT Using a Perturbative Power Counting
- 2024
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Ingår i: Few-Body Systems. - 1432-5411 .- 0177-7963. ; 65:3
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Tidskriftsartikel (refereegranskat)abstract
- Low-energy theorems (LETs) for effective-range parameters in nucleon-nucleon scattering encode properties of the long-range part of the nuclear force. We compute LETs for S-wave neutron–proton scattering using chiral effective field theory with a modified version of Weinberg power counting. Corrections to the leading order amplitude are included in distorted-wave perturbation theory and we incorporate contributions up to the third order in the power counting. We find that LETs in the 1S0 and 3S1 partial waves agree well with empirical effective-range parameters. At the same time, phase shifts up to laboratory scattering energies of about 100 MeV can be reproduced. We show that it is important to consider the pion mass splitting in the one-pion exchange potential in the 1S0 partial wave while the effect is negligible in the 3S1 partial wave. We conclude that pion exchanges, as treated in this power counting, accurately describe the long-range part of the S-wave nuclear interaction.
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| 5. |
- Thim, Oliver, 1997, et al.
(författare)
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Perturbative computations of neutron-proton scattering observables using renormalization-group invariant chiral effective field theory up to N3 LO
- 2024
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Ingår i: Physical Review C. - 2469-9985 .- 2469-9993. ; 109:6
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Tidskriftsartikel (refereegranskat)abstract
- We predict neutron-proton scattering cross sections and polarization observables up to next-to-next-to-next-to-leading order in a renormalization-group invariant description of the strong nucleon-nucleon interaction. Low-energy constants are calibrated to phase shifts, subleading corrections are computed in distorted-wave perturbation theory, and we employ momentum-cutoff values 500 and 2500 MeV. We find a steady order-by-order convergence and realistic descriptions of scattering observables up to a laboratory scattering energy of approximately 100 MeV. We also compare perturbative and nonperturbative calculations for phase shifts and cross sections and quantify how unitarity is gradually restored at higher orders. The perturbative approach offers an important diagnostic tool for any power counting and our results suggest that the breakdown scale in chiral effective field theory might be significantly lower than estimates obtained in nonperturbative calculations.
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| 6. |
- Thim, Oliver, 1997
(författare)
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Renormalization-Group Invariant Formulation of Chiral Effective Field Theory Applied to the Nucleon-Nucleon System
- 2023
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Licentiatavhandling (övrigt vetenskapligt/konstnärligt)abstract
- Chiral effective field theory (χEFT) promises a systematically improvable description of the strong interaction between nucleons consistent with the symmetries of quantum chromodynamics (QCD). A sound power counting (PC) scheme is vital to organize the order-by-order contributions of interaction diagrams to nuclear observables in compliance with renormalization-group (RG) invariance. Numerical values of the low-energy constants (LECs), governing the strengths of pion-nucleon and nucleon-contact diagrams, must be inferred from data and vary with the high-momentum cutoff to remove any dependence on the arbitrary regularization procedure. To date, most χEFT predictions of nuclear systems rely on a PC introduced in the 1990s that does not comply with RG-invariance. One can argue that the lacking RG-invariance makes the connection with QCD muddled and that predictive power is lost. I have developed Bayesian methods for inferring the probability distributions for the numerical values of the LECs at leading order in a recent and RG-invariant PC by Long and Yang. I find that conditioning the inference on neutron-proton (np) scattering observables, rather than scattering phase shifts as is typically done, significantly impacts the results. Furthermore, I use distorted-wave perturbation theory to compute predictions for low-energy np scattering observables up to the fourth chiral order in this PC using point estimates for the LECs. I find a clear order-by-order improvement in the theoretical description of experimental scattering data. This work is an important step towards enabling a Bayesian analysis of low-energy nuclear observables with the aim of assessing whether χEFT, formulated using an RG-invariant PC, accurately predicts the physics of atomic nuclei.
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