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Daniel R. Phillips

Publications and source records attributed to Daniel R. Phillips.

At least 37 records · Page 2Linked to original sources
arXiv2022

Nuclear Forces for Precision Nuclear Physics -- a collection of perspectives

This is a collection of perspective pieces contributed by the participants of the Institute of Nuclear Theory's Program on Nuclear Physics for Precision Nuclear Physics which was held virtually from April 19 to May 7, 2021. The collection represents the reflections of a vibrant and engaged community of researchers on the status of theoretical research in low-energy nuclear physics, the challenges ahead, and new ideas and strategies to make progress in nuclear structure and reaction physics, effective field theory, lattice QCD, quantum information, and quantum computing. The contributed pieces solely reflect the perspectives of the respective authors and do not represent the viewpoints of the Institute for Nuclear theory or the organizers of the program.

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arXiv2021

What hath Weinberg wrought? Reflections on what Weinberg's papers on 'Nuclear Forces from Chiral Lagrangians' did and did not accomplish

I discuss selected legacies of Weinberg's application of chiral Lagrangians to nuclear physics: (1) the use of the chiral expansion to organize the interaction of pions and photons with a nucleus; (2) the much-debated question of why and how the potential derived from a chiral Lagrangian should be inserted in the Schrodinger equation; (3) the emergence of "pionless EFT" as a tool for diagnosing universal correlations that are present in quantum few-body systems of very different sizes, and, perhaps most important of all, (4) an epistemological shift in what is expected of a nuclear-physics calculation.

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arXiv2021

Neutron-neutron scattering length from the $^6$He$(p,pα)nn$ reaction

We propose a novel method to measure the neutron-neutron scattering length using the $^{6}$He$(p,pα)nn$ reaction in inverse kinematics at high energies. The method is based on the final state interaction (FSI) between the neutrons after the sudden knockout of the $α$ particle. We show that the details of the neutron-neutron relative energy distribution allow for a precise extraction of the $s$-wave scattering length. We present the state-of-the-art in regard to the theory of this distribution. The distribution is calculated in two steps. First, we calculate the ground-state wave function of $^6$He as a $αn n$ three-body system. For this purpose we use Halo effective field theory (Halo EFT), which also provides uncertainty estimates for the results. We compare our results at this stage to model calculations done with the computer code FaCE. In a second step we determine the effects of the $nn$ FSI using the $nn$ t-matrix. We compare these FSI results to approximate FSI approaches based on standard FSI enhancement factors. While the final distribution is sensitive to the $nn$ scattering length, it depends only weakly on the effective range. Throughout we emphasize the impact of theoretical uncertainties on the neutron-neutron relative energy distribution, and discuss the extent to which those uncertainties limit the extraction of the neutron-neutron scattering length from the reaction $^{6}$He$(p,pα)nn$.

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arXiv2021

Constrained extrapolation problem and order-dependent mappings

We consider the problem of extrapolating the perturbation series for the dilute Fermi gas in three dimensions to the unitary limit of infinite scattering length and into the BEC region, using the available strong-coupling information to constrain the extrapolation problem. In this constrained extrapolation problem (CEP) the goal is to find classes of approximants that give well converged results already for low perturbative truncation orders. First, we show that standard Padé and Borel methods are too restrictive to give satisfactory results for this CEP. A generalization of Borel extrapolation is given by the so-called Maximum Entropy extrapolation method (MaxEnt). However, we show that MaxEnt requires extensive elaborations to be applicable to the dilute Fermi gas and is thus not practical for the CEP in this case. Instead, we propose order-dependent-mapping extrapolation (ODME) as a simple, practical, and general method for the CEP. We find that the ODME approximants for the ground-state energy of the dilute Fermi gas are robust with respect to changes of the mapping choice and agree with results from quantum Monte Carlo simulations within uncertainties.

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arXiv2020

Scattering Observables from One- and Two-Body Densities: Formalism and Application to $γ\,{}^3$He Scattering

We introduce the transition-density formalism, an efficient and general method for calculating the interaction of external probes with light nuclei. One- and two-body transition densities that encode the nuclear structure of the target are evaluated once and stored. They are then convoluted with an interaction kernel to produce amplitudes, and hence observables. By choosing different kernels, the same densities can be used for any reaction in which a probe interacts perturbatively with the target. The method therefore exploits the factorisation between nuclear structure and interaction kernel that occurs in such processes. We study in detail the convergence in the number of partial waves for matrix elements relevant in elastic Compton scattering on $^3$He. The results are fully consistent with our previous calculations in Chiral Effective Field Theory. But the new approach is markedly more computationally efficient, which facilitates the inclusion of more partial-wave channels in the calculation. We also discuss the usefulness of the transition-density method for other nuclei and reactions. Calculations of elastic Compton scattering on heavier targets like $^4$He are straightforward extensions of this study, since the same interaction kernels are used. And the generality of the formalism means that our $^3$He densities can be used to evaluate any $^3$He elastic-scattering observable with contributions from one- and two-body operators. They are available at https://datapub.fz-juelich.de/anogga.

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arXiv2018

$S$-factor and scattering parameters from ${}^3$He + ${}^4$He $\rightarrow {}^7$Be + $γ$ data

We use the next-to-leading-order (NLO) amplitude in an effective field theory (EFT) for ${}^3$He + ${}^4$He $\rightarrow {}^7$Be + $γ$ to perform the extrapolation of higher-energy data to solar energies. At this order the EFT describes the capture process using an s-wave scattering length and effective range, the asymptotic behavior of $^7$Be and its excited state, and short-distance contributions to the E1 capture amplitude. We use a Bayesian analysis to infer the multi-dimensional posterior of these parameters from capture data below 2 MeV. The total $S$-factor $S(0)= 0.578^{+0.015}_{-0.016}$ keV b at 68% degree of belief. We also find significant constraints on $^3$He-$^4$He scattering parameters.

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arXiv2018

Elastic Compton Scattering from 3He and the Role of the Delta

We report observables for elastic Compton scattering from $^3$He in Chiral Effective Field Theory with an explicit $Δ(1232)$ degree of freedom ($χ$EFT) for energies between 50 and 120 MeV. The $γ\,{}^3$He amplitude is complete at N3LO, $\mathcal{O}(e^2δ^3)$, and in general converges well order by order. It includes the dominant pion-loop and two-body currents, as well as the Delta excitation in the single-nucleon amplitude. Since the cross section is two to three times that for deuterium and the spin of polarised $^3$He is predominantly carried by its constituent neutron, elastic Compton scattering promises information on both the scalar and spin polarisabilities of the neutron. We study in detail the sensitivities of 4 observables to the neutron polarisabilities: the cross section, the beam asymmetry and two double asymmetries resulting from circularly polarised photons and a longitudinally or transversely polarised target. Including the Delta enhances those asymmetries from which neutron spin polarisabilities could be extracted. We also correct previous, erroneous results at N2LO, i.e.~without an explicit Delta, and compare to the same observables on proton, neutron and deuterium targets. An interactive Mathematica notebook of our results is available from hgrie@gwu.edu.

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arXiv2018

Analyzing the Effects of Neutron Polarizabilities in Elastic Compton Scattering off ${}^3$He

Motivated by the fact that a polarized ${}^3$He nucleus behaves as an `effective' neutron target, we examine manifestations of neutron electromagnetic polarizabilities in elastic Compton scattering from the Helium-3 nucleus. We calculate both unpolarized and double-polarization observables using chiral perturbation theory to next-to-leading order (${\mathcal O}(e^2 Q)$) at energies, $ω\leq m_π$, where $m_π$ is the pion mass. Our results show that the unpolarized differential cross section can be used to measure neutron electric and magnetic polarizabilities, while two double-polarization observables are sensitive to different linear combinations of the four neutron spin polarizabilities. [Note added in 2018] The qualitative conclusions and analytic formulae presented in this paper are correct, but several of the numerical results are wrong: see the erratum posted as arXiv:1804.01206 for further details. A full suite of corrected numerical results for cross sections and asymmetries can be found in Margaryan et al., arXiv:1804.00956. They can also be obtained as an interactive Mathematica notebook by emailing hgrie@gwu.edu.

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arXiv2018

Investigating Neutron Polarizabilities through Compton Scattering on $^3$He

We examine manifestations of neutron electromagnetic polarizabilities in coherent Compton scattering from the Helium-3 nucleus. We calculate $γ^3$He elastic scattering observables using chiral perturbation theory to next-to-leading order (${\mathcal O}(e^2 Q)$). We find that the unpolarized differential cross section can be used to measure neutron electric and magnetic polarizabilities, while two double-polarization observables are sensitive to different linear combinations of the four neutron spin polarizabilities. [Note added in 2018] An erratum for this paper has been posted as arXiv:1804.01206. Overall conclusions are unchanged, but quantitative results are affected appreciably.

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arXiv2018

Comprehensive Study of Observables in Compton Scattering on the Nucleon

We present an analysis of $13$ observables in Compton scattering on the proton. Cross sections, asymmetries with polarised beam and/or targets, and polarisation-transfer observables are investigated for energies up to the $Δ(1232)$ resonance to determine their sensitivity to the proton's dipole scalar and spin polarisabilities. The Chiral Effective Field Theory Compton amplitude we use is complete at N$^4$LO, $\mathcal{O(}e^2δ^4)$, for photon energies $ω\sim m_π$, and so has an accuracy of a few per cent there. At photon energies in the resonance region it is complete at NLO, $\mathcal{O}(e^2δ^0)$, and so its accuracy there is about $20$\%. We find that for energies from pion-production threshold to about $250\;\mathrm{MeV}$, multiple asymmetries have significant sensitivity to presently ill-determined combinations of proton spin polarisabilities. We also argue that the broad outcomes of this analysis will be replicated in complementary theoretical approaches, e.g., dispersion relations. Finally, we show that below the pion-production threshold, $6$ observables suffice to reconstruct the Compton amplitude, and above it $11$ are required. Although not necessary for polarisability extractions, this opens the possibility to perform "complete" Compton-scattering experiments. An interactive Mathematica notebook, including results for the neutron, is available from judith.mcgovern@manchester.ac.uk .

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arXiv2017

The reactions $ππ\rightarrowππ$ and $γγ\rightarrowππ$ in $χ$PT with an isosinglet scalar resonance

The lowest-lying resonance in the QCD spectrum is the $0^{++}$ isoscalar $σ$ meson, also known as the $f_0(500)$. We augment SU(2) chiral perturbation theory ($χ$PT) by including the $σ$ meson as an additional explicit degree of freedom, as proposed by Soto, Talavera, and Tarrús and others. In this effective field theory, denoted $χ$PT$_S$, the $σ$ meson's well-established mass and decay width are not sufficient to properly renormalize its self energy. At $\mathcal{O}(p^4)$ another low-energy constant appears in the dressed $σ$-meson propagator; we adjust it so that the isoscalar pion-pion scattering length is also reproduced. We compare the resulting amplitudes for the $ππ\rightarrowππ$ and $γγ\rightarrowππ$ reactions to data from threshold through the energies at which the $σ$-meson resonance affects observables. The leading-order (LO) $ππ$ amplitude reproduces the $σ$-meson pole position, the isoscalar $ππ$ scattering lengths and $ππ$ scattering and $γγ\rightarrow ππ$ data up to $\sqrt{s} \approx 0.5$ GeV. It also yields a $γγ\rightarrowππ$ amplitude that obeys the Ward identity. The value obtained for the $π^0$ polarizability is, however, only slightly larger than that obtained in standard $χ$PT.

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arXiv2017

Models, measurements, and effective field theory: proton capture on Beryllium-7 at next-to-leading order

We employ an effective field theory (EFT) that exploits the separation of scales in the p-wave halo nucleus $^8\mathrm{B}$ to describe the process $^7\mathrm{Be}(p,γ)^8\mathrm{B}$ up to a center-of-mass energy of 500 keV. The calculation, for which we develop the lagrangian and power counting, is carried out up to next-to-leading order (NLO) in the EFT expansion. The power counting we adopt implies that Coulomb interactions must be included to all orders in $α_{\rm em}$. We do this via EFT Feynman diagrams computed in time-ordered perturbation theory, and so recover existing quantum-mechanical technology such as the two-potential formalism for the treatment of the Coulomb-nuclear interference. Meanwhile the strong interactions and the E1 operator are dealt with via EFT expansions in powers of momenta, with a breakdown scale set by the size of the ${}^7$Be core, $Λ\approx 70$ MeV. Up to NLO the relevant physics in the different channels that enter the radiative capture reaction is encoded in ten different EFT couplings. The result is a model-independent parametrization for the reaction amplitude in the energy regime of interest. To show the connection to previous results we fix the EFT couplings using results from a number of potential model and microscopic calculations in the literature. Each of these models corresponds to a particular point in the space of EFTs. The EFT structure therefore provides a very general way to quantify the model uncertainty in calculations of $^7\mathrm{Be}(p,γ)^8\mathrm{B}$. We also demonstrate that the only N$^2$LO corrections in $^7\mathrm{Be}(p,γ)^8\mathrm{B}$ come from an inelasticity that is practically of N$^3$LO size in the energy range of interest, and so the truncation error in our calculation is effectively N$^3$LO. We also discuss the relation of our extrapolated $S(0)$ to the previous standard evaluation.

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arXiv2017

Three-nucleon bound states and the Wigner-SU(4) limit

We examine the extent to which the properties of three-nucleon bound states are well-reproduced in the limit that nuclear forces satisfy Wigner's SU(4) (spin-isospin) symmetry. To do this we compute the charge radii up to next-to-leading order (NLO) in an effective field theory (EFT) that is an expansion in powers of $R/a$, with $R$ the range of the nuclear force and $a$ the nucleon-nucleon ($N\!N$) scattering lengths. In the Wigner-SU(4) limit, the triton and Helium-3 point charge radii are equal. At NLO in the range expansion both are $1.66$ fm. Adding the first-order corrections due to the breaking of Wigner symmetry in the $N\!N$ scattering lengths gives a ${}^3\mathrm{H}$ point charge radius of $1.58$ fm, which is remarkably close to the experimental number, $1.5978\pm0.040$ fm (Angeli and Marinova in At Data Nucl Data Tables 99:69-95, 2013). For the ${}^3\mathrm{He}$ point charge radius we find $1.70$ fm, about 4% away from the experimental value of $1.77527\pm0.0054$ fm (Angeli and Marinova 2013). We also examine the Faddeev components that enter the tri-nucleon wave function and find that an expansion of them in powers of the symmetry-breaking parameter converges rapidly. Wigner's SU(4) symmetry is thus a useful starting point for understanding tri-nucleon bound-state properties.

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arXiv2016

Nucleon Polarisabilities at and Beyond Physical Pion Masses

We examine the results of Chiral Effective Field Theory ($χ$EFT) for the scalar- and spin-dipole polarisabilities of the proton and neutron, both for the physical pion mass and as a function of $m_π$. This provides chiral extrapolations for lattice-QCD polarisability computations. We include both the leading and sub-leading effects of the nucleon's pion cloud, as well as the leading ones of the $Δ(1232)$ resonance and its pion cloud. The analytic results are complete at N$^2$LO in the $δ$-counting for pion masses close to the physical value, and at leading order for pion masses similar to the Delta-nucleon mass splitting. In order to quantify the truncation error of our predictions and fits as $68$\% degree-of-belief intervals, we use a Bayesian procedure recently adapted to EFT expansions. At the physical point, our predictions for the spin polarisabilities are, within respective errors, in good agreement with alternative extractions using experiments and dispersion-relation theory. At larger pion masses we find that the chiral expansion of all polarisabilities becomes intrinsically unreliable as $m_π$ approaches about $300\;$MeV---as has already been seen in other observables. $χ$EFT also predicts a substantial isospin splitting above the physical point for both the electric and magnetic scalar polarisabilities; and we speculate on the impact this has on the stability of nucleons. Our results agree very well with emerging lattice computations in the realm where $χ$EFT converges. Curiously, for the central values of some of our predictions, this agreement persists to much higher pion masses. We speculate on whether this might be more than a fortuitous coincidence.

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arXiv2016

Time-reversal-invariance-violating nucleon-nucleon potential in the 1/N_c expansion

We apply the large-$N_c$ expansion to the time-reversal-invariance-violating (TV) nucleon-nucleon potential. The operator structures contributing to next-to-next-to-leading order in the large-$N_c$ counting are constructed. For the TV and parity-violating case we find a single operator structure at leading order. The TV but parity-conserving potential contains two leading-order terms, which however are suppressed by 1/$N_c$ compared to the parity-violating potential. Comparison with phenomenological potentials, including the chiral EFT potential in the TV parity-violating case, leads to large-$N_c$ scaling relations for TV meson-nucleon and nucleon-nucleon couplings.

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arXiv2015

Universal Relations for Range Corrections to Efimov Features

In a three-body system of identical bosons interacting through a large S-wave scattering length $a$, there are several sets of Efimov features related by discrete scale invariance. Effective field theory was recently used to derive universal relations between these Efimov features that include the first-order correction due to a nonzero effective range $r_s$. We reveal a simple pattern in these range corrections that had not been previously identified. The pattern is explained by the renormalization group for the effective field theory, which implies that the Efimov three-body parameter runs logarithmically with the momentum scale at a rate proportional to $r_s/a$. The running Efimov parameter also explains the empirical observation that range corrections can be largely taken into account by shifting the Efimov parameter by an adjustable parameter divided by a. The accuracy of universal relations that include first-order range corrections is verified by comparing with various theoretical calculations using models with nonzero range.

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