Effective field theory in the harmonic oscillator basis

Binder, Sven; Ekström, Andreas; Hagen, G.; Papenbrock, T.; Wendt, Kyle

doi:10.1103/physrevc.93.044332

Cited by 74 publications

(164 citation statements)

References 72 publications

Supporting

Mentioning

147

Contrasting

Order By: Relevance

“…A systematic investigation of the role of the many-body forces is an important frontier in low-energy nuclear physics [18]. With all these developments, coupled with on-going efforts towards a reliable quantification of various sources of theoretical uncertainties [19][20][21][22][23][24], nuclear chiral EFT is now entering the precision era [25].…”

Section: Introductionmentioning

confidence: 99%

“…Last but not least, the appearance of the same LEC in the leading 3N force and the short-range part of the 2N weak current opens an exciting possibility to perform nontrivial precision tests of chiral EFT in few-nucleon systems by carrying out a simultaneous calculation of nucleon-deuteron scattering, the binding energy, radius and the precisely known half-life of 3 H and the muon capture rates on 2 H and 3 He, accompanied with a careful analysis of the theoretical uncertainties along the lines of Refs. [21,22].…”

Section: Introductionmentioning

confidence: 99%

“…For the axial current, the diagrams (1-6), (9-15), (19)(20)(21)(22) and (25)(26)(27) give non-vanishing contributions, from which those of graphs (1-5), (9-11), (13), (15) turn out to depend on the unitary phases: …”

mentioning

confidence: 99%

See 2 more Smart Citations

Nuclear axial current operators to fourth order in chiral effective field theory

2017

View full text Add to dashboard Cite

We present the complete derivation of the nuclear axial charge and current operators as well as the pseudoscalar operators to fourth order in the chiral expansion relative to the dominant onebody contribution using the method of unitary transformation. We demonstrate that the unitary ambiguity in the resulting operators can be eliminated by the requirement of renormalizability and by matching of the pion-pole contributions to the nuclear forces. We give expressions for the renormalized single-, two-and three-nucleon contributions to the charge and current operators and pseudoscalar operators including the relevant relativistic corrections. We also verify explicitly the validity of the continuity equation.

show abstract

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Nuclear axial current operators to fourth order in chiral effective field theory

2017

View full text Add to dashboard Cite

show abstract

“…As an interesting aside, the recent works of Binder et al [55] and McElvain and Haxton [56] offer new perspectives on the construction of effective Hamiltonians and choices of basis functions. We focus first on the kinetic energy operator.…”

Section: Single-particle Basis For Infinite Mattermentioning

confidence: 99%

Computational Nuclear Physics and Post Hartree-Fock Methods

Lietz¹,

Novario²,

Jansen³

et al. 2017

An Advanced Course in Computational Nuclear Physics

View full text Add to dashboard Cite

We present a computational approach to infinite nuclear matter employing HartreeFock theory, many-body perturbation theory and coupled cluster theory. These lectures are closely linked with those of chapters 9, 10 and 11 and serve as input for the correlation functions employed in Monte Carlo calculations in chapter 9, the in-medium similarity renormalization group theory of dense fermionic systems of chapter 10 and the Green's function approach in chapter 11. We provide extensive code examples and benchmark calculations, allowing thereby an eventual reader to start writing her/his own codes. We start with an object-oriented serial code and end with discussions on strategies for porting the code to present and planned high-performance computing facilities.

show abstract

“…We also note that fitting the Gamow-Teller matrix element within experimental uncertainties neglects the fact that the calculations are constrained to a particular chiral order, which can be associated with an uncertainty due to the truncation in the chiral expansion (e.g., for recent work, see Refs. [62,63]). This illustrates, in agreement with the main result of this work, that previous works have underestimated the uncertainties when fitting LECs to the triton half-life.…”

Section: Arxiv:161208010v3 [Nucl-th] 24 Apr 2018mentioning

confidence: 99%

Uncertainties in constraining low-energy constants from 3H $ \beta$β decay

Klos¹,

Carbone²,

Hebeler³

et al. 2017

Eur. Phys. J. A

View full text Add to dashboard Cite

We discuss the uncertainties in constraining low-energy constants of chiral effective field theory from 3 H β decay. The half-life is very precisely known, so that the Gamow-Teller matrix element has been used to fit the coupling cD of the axial-vector current to a short-range two-nucleon pair. Because the same coupling also describes the leading one-pion-exchange three-nucleon force, this in principle provides a very constraining fit, uncorrelated with the 3 H binding energy fit used to constrain another low-energy coupling in three-nucleon forces. However, so far such 3 H half-life fits have only been performed at a fixed cutoff value. We show that the cutoff dependence due to the regulators in the axial-vector two-body current can significantly affect the Gamow-Teller matrix elements and consequently also the extracted values for the cD coupling constant. The degree of the cutoff dependence is correlated with the softness of the employed NN interaction. As a result, present three-nucleon forces based on a fit to 3 H β decay underestimate the uncertainty in cD. We explore a range of cD values that is compatible within cutoff variation with the experimental 3 H half-life and estimate the resulting uncertainties for many-body systems by performing calculations of symmetric nuclear matter. Introduction. The development of new and improved nuclear forces within chiral effective field theory (EFT) is currently a very active field of research [1][2][3][4]. In contrast to phenomenological approaches, chiral EFT provides a framework that allows to systematically derive improvable expansions for nucleon-nucleon (NN) and many-body forces as well as electroweak current operators at low energies [5][6][7][8]. Within Weinberg's power counting scheme [9] the contributions to NN forces have been worked out up to fifth order in the chiral expansion [3, 10], whereas three-nucleon (3N) and four-nucleon forces have been developed up to fourth order [11][12][13][14]. Similarly nuclear currents have been derived up to fourth order for axial-vector [15,16] and vector currents [17][18][19][20][21].The contributions to nuclear forces and currents generally depend on low-energy couplings (LECs) that capture the short-distance physics that is not resolved explicitly within the EFT. Therefore, to determine the LECs, fits to data are needed. Up to second (next-to-leading) order there are no contributions from many-body interactions or currents, and the LECs in the NN forces are usually obtained by fits to pion-nucleon and nucleon-nucleon scattering data. At third (next-to-next-to leading) order, N 2 LO, two additional LECs, c D and c E , enter in 3N forces and two-body (2b) currents. While c D enters in both the NN-contact-one-pion exchange 3N force and the

show abstract

Effective field theory in the harmonic oscillator basis

Cited by 74 publications

References 72 publications

Nuclear axial current operators to fourth order in chiral effective field theory

Nuclear axial current operators to fourth order in chiral effective field theory

Computational Nuclear Physics and Post Hartree-Fock Methods

Uncertainties in constraining low-energy constants from 3H $ \beta$β decay

Contact Info

Product

Resources

About