Searcharxiv⌕ Search

arXiv subjects

Daniel R. Phillips

Publications and source records attributed to Daniel R. Phillips.

At least 19 recordsLinked to original sources
arXiv2026

Finite-range EFT for the $E1$ strength distribution of ${}^6$He

Halo effective field theory (Halo EFT) is a powerful tool to describe halo nuclei and predict low-energy observables with quantified uncertainties. However, in the case that there is a leading-order interaction determined by two or more effective-range parameters, such as the $^2P_{3/2}$ $n\alpha$ interaction in $^6$He, the standard implementation in the dimer formalism leads to an energy-dependent interaction. This complicates the construction of a Hilbert space of states, especially beyond the two-body problem. As an alternative, we propose the use of a finite-range formulation of Halo EFT, which avoids these complications. For definiteness, we use separable interactions with Yamaguchi-like form factors, but other choices are possible. We solve for the ${}^6$He bound state in this finite-range EFT up to next-to-leading order (NLO) in the Halo EFT power counting and calculate the ground-state $E1$ strength distribution of $^6$He at this order. The shape of the resulting distribution agrees with that obtained in the dimer formalism of the EFT, but finite-range EFT does not require the use of a non-standard wave function normalization condition. We also calculate the root-mean-square charge radius of $^6$He and find $2.06 \pm 0.35$~fm at LO and $2.00 \pm 0.09$~fm at NLO, in agreement with experimental data. To calculate the full $E1$ strength distribution final-state interactions must be incorporated. We approximate the full-three-body scattering operator first by single M{\o}ller operators and then by products of up to three M{\o}ller operators. The resulting NLO $E1$ strength distribution agrees with the experimental data within theory uncertainties.

nucl-th↗
arXiv2026

A short-range effective theory for single-neutron halo nuclei with a deformed core

We establish a short-range effective theory for deformed s-wave halos. The theory applies to a system in which neutrons are weakly bound to a core nucleus, and that core nucleus also exhibits a low-lying rotational band with a $0^+$ ground state and a first $2_1^+$ excited state. The effective theory then must have both halo degrees of freedom and degrees of freedom associated with rotation of the core. This leads to the particle plus rotor model of Bohr and Mottelson at leading order. We identify the relevant leading-order operators in the Hamiltonian that respect the symmetries of the system and the small parameters which define the effective theory's power counting. We carry out calculations for the $^{11}$Be and $^{17}$C systems in which we compute the low-lying positive-parity states of the core $+$ neutron systems up to the core$(2_1^+)$-neutron threshold. We do this for several different regulator parameters and establish that these energies can be renormalized using the leading-order set of operators. The spectrum is accurately described at leading order in both cases. Decay widths to d-wave core-neutron states have sizable cutoff dependence, but the Asymptotic Normalization Coefficients (ANCs) in $s$-wave channels exhibit regulator dependence of a size consistent with next-to-leading-order effects. We also compute Coulomb breakup observables and compare with experimental data, finding leading-order results in reasonable agreement with data for both ${}^{11}$Be and ${}^{17}$C. The addition of one next-to-leading-order operator renders the ANCs of all s-wave states stable with respect to the regulator. It consequently also removes most of the 30\% variation of the leading-order Coulomb dissociation cross section with the regulator.

nucl-th↗
arXiv2026

Two bodies left behind

We consider scenarios in which a shallow bound state undergoes breakup by a probe whose energy is high compared to the binding energy. The first two scenarios, which serve as warm-up exercises, involve a single heavy particle bound to a light particle, analogous to a core nucleus bound to a neutron. We show that in quasi-free kinematics, the leading effect comes from the heavy particle being knocked out by the probe, with corrections suppressed by inverse powers of the probe momentum. This formally justifies extracting neutron form factors from high-energy deuteron breakup in quasi-free kinematics. In Scenario 1, the probe is a local current; in Scenario 2, it is hadron scattering. In Scenarios 3 and 4 we consider, respectively, a local current and hadron scattering, but now on a three-body bound state of a heavy particle and two light particles. Hard knockout of the heavy particle leaves two low-energy particles behind, which can interact with one another. In all four scenarios, we prove that the amplitude is dominated by the nearby on-shell pole of the heavy-particle propagator and derive a closed-form expression for this contribution. When two bodies are left behind, the leading amplitude is the product of the scattering of the two light particles, a dynamical function depending on the probe, and a real function related to the bound-state wavefunction. Thus, quasi-free removal of a core nucleus from a system with halo neutrons provides access to on-shell data on multi-neutron interactions. The resulting amplitudes are relativistic and satisfy unitarity for the remnant subsystem exactly. We also provide complementary non-relativistic derivations. While the derivations are for spinless particles, the generalization to spin is straightforward, since the results depend only on quasi-free knockout kinematics; we make no assumptions about the inter-particle dynamics.

nucl-th↗
arXiv2026

Neglecting correlations leads to misestimated model errors in EFT predictions

Bayesian analyses of the convergence pattern of Effective Field Theories (EFTs) enable estimation of the uncertainty induced by a truncated expansion. When an EFT that has been calibrated to data is used to make a prediction this truncation uncertainty enters the posterior predictive distribution twice: directly from the finite-order calculation of the predicted quantity and indirectly through the posterior probability distributions of the EFT low-energy constants (LECs) determined by the calibration. In this work, we focus on the interplay of these two sources of uncertainty. We do this in the context of a toy EFT that we fit to pseudodata and use to make predictions. Direct EFT truncation uncertainty and LEC uncertainty are correlated in predictions when the predicted quantity is correlated with the observables used to fit the LECs. Here this results in the overall theoretical uncertainty in the EFT prediction being smaller than either the uncertainty induced by the truncation error or that stemming from the LECs alone.

nucl-th↗
arXiv2025

Inferring the breakdown scales of the chiral expansions for $g_A$ and $m_N$

We apply Bayesian inference to the order-by-order chiral perturbation theory ($\chi$PT) expansions for the axial-vector coupling constant $g_A$ and the nucleon mass m_N, and thereby infer the scales at which $\chi$PT breaks down for these two observables. Using a pointwise Bayesian analysis, we find that the inferred breakdown scales are notably different for the two observables. For the chiral expansion of $g_A$, we obtain $251^{+20}_{-50}$ MeV and $211^{+20}_{-30}$ MeV using two distinct sets of low-energy constants, while for the chiral expansion of $m_N$ we infer a significantly larger breakdown scale of $491^{+60}_{-90}$ MeV.

hep-ph↗
arXiv2025

Simultaneous Inference of Effective Range Parameters and EFT Truncation Uncertainty in $^{3}$He-$\alpha$ Scattering

We extend previous halo effective field theory analyses of low-energy elastic scattering of $^{3}$He-$^{4}$He, including the $\frac{7}{2}^{-}$ $f$-wave resonance as an explicit degree of freedom. The presence of this resonance necessitates a changing power counting scheme depending on the kinematic region. Therefore, we construct a theory uncertainty model at the partial wave amplitude level, allowing us to generate a sophisticated theory covariance matrix that captures the way the theory error structure changes as energy increases. We then perform a Bayesian analysis and simultaneously estimate the joint posterior distributions of the effective range theory parameters and the parameters that characterize the effective field theory truncation uncertainty. We compare two different analyses: no $f$-wave interactions for data up to $E_{\text{max}} = 2.6$ MeV, and including $f$-wave interactions for data up to $E_{\text{max}} = 5.5$ MeV. The inferred breakdown scales in each analysis are consistent with previous work. We find that $f$-wave interactions are needed to describe data for $E_{lab} \gtrapprox 3.6$ MeV.

nucl-th↗
arXiv2025

Connecting ground-state properties of ${}^6$Li to each other and to scattering data

We examine the relationship between the Asymptotic Normalization Coefficient (ANC) of $^6$Li and other low-energy observables in the $\alpha$-deuteron system. Our analysis uses a set of calculations carried out within the {\it ab initio} No Core Shell Model with Continuum (NCSMC) using a variety of inter-nucleon interactions and basis sizes, and yielding ${}^6$Li deuteron separation energies between 1.3 and 1.8 MeV [Phys. Rev. Lett. 129, 042503 (2022)]. These NCSMC calculations show that the square of the ANC is strongly correlated with the separation energy over this range. In this work, we investigate the origin of this correlation using the phenomenological $R$-matrix, a single-channel potential and a perturbative approach. We show that this correlation occurs because the depth of the $\alpha$-deuteron central potential changes by only a small relative amount as the separation energy varies. We then investigate if the ANC can be accurately extracted from $\alpha$-deuteron phase shifts in an ideal case in which low-energy data are available and there are no experimental errors. We find that both $R$-matrix and Coulomb-modified effective-range theory (CM-ERE) yield extracted ANCs close to, although not exactly equal to, the true value, provided the extrapolation is constrained by the known position of the bound-state pole and at least three terms are included in the fit function. The $R$-matrix approach converges faster than the CM-ERE as the number of parameters increases and is also more robust against the inclusion of low-energy and high-energy phase shift data. Finally, our study also shows that a naive quantification of uncertainties by comparing different truncations used in both theories is not accurate, and suggests the accuracy of ANCs extracted from phase shift data needs further investigation.

nucl-th↗
arXiv2025

Role of spin-isospin symmetries in nuclear $\beta$-decays

A century ago, Wigner's SU(4) symmetry was introduced to explain the properties of atomic nuclei. Despite recent revived interest, its impact on nuclear structure, transitions, and reactions has not been fully explored. Here, we show that a variety of high-fidelity nuclear interactions predict nuclear states that have $\geq 90$\% probability of being in a single SU(4) irreducible representation. Meanwhile, our analysis of axial current operators in chiral effective field theory ($\chi$EFT) reveals that one-body currents at low momentum transfer act only within SU(4) irreducible representations, while two-body currents connect different representations. These selection rules interfere with the expected convergence pattern of the $\chi$EFT expansion and explain key phenomenological observations, e.g., the unnaturally large two-body corrections to the axial-current matrix elements in eight-body nuclei.

nucl-th↗
arXiv2024

Variational inference of effective range parameters for ${}^3$He-${}^4$He scattering

We use two different methods, Monte Carlo sampling and variational inference (VI), to perform a Bayesian calibration of the effective-range parameters in ${}^3$He-${}^4$He elastic scattering. The parameters are calibrated to data from a recent set of $^{3}$He-${}^4$He elastic scattering differential cross section measurements. Analysis of these data for $E_{\rm lab} \leq 4.3$ MeV yields a unimodal posterior for which both methods obtain the same structure. However, the effective-range expansion amplitude does not account for the $7/2^-$ state of ${}^7$Be so, even after calibration, the description of data at the upper end of this energy range is poor. The data up to $E_{\rm lab}=2.6$ MeV can be well described, but calibration to this lower-energy subset of the data yields a bimodal posterior. After adapting VI to treat such a multi-modal posterior we find good agreement between the VI results and those obtained with parallel-tempered Monte Carlo sampling.

nucl-th↗
arXiv2024

Compton Scattering on 4He with Nuclear One- and Two-Body Densities

We present the first \emph{ab initio} calculation of elastic Compton scattering from 4He. It is carried out to $\mathcal{O}(e^2 \delta^3)$ [N3LO] in the $\delta$ expansion of $\chi$EFT. At this order and for this target, the only free parameters are the scalar-isoscalar electric and magnetic dipole polarisabilities of the nucleon. Adopting current values for these yields a parameter-free prediction. This compares favourably with the world data from HI$\gamma$S, Illinois and Lund for photon energies $50\;\mathrm{MeV}\lesssim\omega\lesssim120\;\mathrm{MeV}$ within our theoretical uncertainties of $\pm10\%$. We predict a cross section up to 7 times that for deuterium. As in 3He, this emphasises and tests the key role of meson-exchange currents between np pairs in Compton scattering on light nuclei. We assess the sensitivity of the cross section and beam asymmetry to the nucleon polarisabilities, providing clear guidance to future experiments seeking to further constrain them. The calculation becomes tractable by use of the Transition Density Method. The one- and two-body densities generated from 5 chiral potentials and the AV18$+$UIX potential are available using the python package provided at \url{https://pypi.org/project/nucdens/}.

nucl-th↗
arXiv2023

Effective field theory analysis of the Coulomb breakup of the one-neutron halo nucleus 19C

We analyse the Coulomb breakup of 19C 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 19C within Halo Effective Field Theory (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 18C. It is also insensitive to the interior of the 19C wave function. Comparison between theory and experiment thus enables us to infer asymptotic properties of the ground state of 19C: 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 19C: 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 19C.

nucl-th↗
arXiv2023

Performing Bayesian analyses with AZURE2 using BRICK: an application to the ${}^7$Be system

Phenomenological $R$-matrix has been a standard framework for the evaluation of resolved resonance cross section data in nuclear physics for many years. It is a powerful method for comparing different types of experimental nuclear data and combining the results of many different experimental measurements in order to gain a better estimation of the true underlying cross sections. Yet a practical challenge has always been the estimation of the uncertainty on both the cross sections at the energies of interest and the fit parameters, which can take the form of standard level parameters. Frequentist ($χ^2$-based) estimation has been the norm. In this work, a Markov Chain Monte Carlo sampler, \texttt{emcee}, has been implemented for the $R$-matrix code \texttt{AZURE2}, creating the Bayesian $R$-matrix Inference Code Kit (\texttt{BRICK}). Bayesian uncertainty estimation has then been carried out for a simultaneous $R$-matrix fit of the $^3$He$(α,γ)^7$Be and $^3$He$(α,α)^3$He reactions in order to gain further insight into the fitting of capture and scattering data. Both data sets constrain the values of the bound state $α$-particle asymptotic normalization coefficients in $^7$Be. The analysis highlights the need for low-energy scattering data with well-documented uncertainty information and shows how misleading results can be obtained in its absence.

nucl-th↗
arXiv2023

Universality of $nn$ distributions of $s$-wave $2n$ halos and the unitary limit

We calculate neutron-neutron relative-energy distributions of $s$-wave two-neutron ($2n$) halo nuclei using Halo Effective Field Theory (Halo EFT) at leading order. At this order these systems are described by the $2n$ separation energy, the neutron-core ($nc$) virtual-state energy and the neutron-neutron ($nn$) scattering length. We focus on knockout reactions where the removal of the core is sudden, such that the final-state interactions are dominated by the $nn$ interaction. We consider the neutron relative-energy distribution for the nuclei $^{11}$Li, $^{14}$Be, $^{17}$B, $^{19}$B, and $^{22}$C. We show that the ground-state neutron momentum distributions of all these nuclei stem from a single curve, which can be obtained by taking both the neutron-core and neutron-neutron interaction to the unitary limit. This universal description can be extended to the final distribution measured in experiment by including $nn$ final-state interactions via the approximate technique of enhancement factors. For all the nuclei considered we find good agreement between the full leading-order Halo EFT calculation and the universal prediction obtained in this way. The universality of the ground-state momentum distribution in two-neutron Borromean halos can thus be tested by dividing the experimental results from sudden core knockout by the enhancement factor and comparing to the unitary-limit prediction.

nucl-th↗
arXiv2023

Effective Field Theory for the Bound States and Scattering of a Heavy Charged Particle and a Neutral Atom

We show the system of a heavy charged particle and a neutral atom can be described by a low-energy effective field theory where the attractive $1/r^4$ induced dipole potential determines the long-distance/low-energy wave functions. The $1/r^4$ interaction is renormalized by a contact interaction at leading order. Derivative corrections to that contact interaction give rise to higher-order terms. We show that this ``Induced-dipole EFT'' (ID-EFT) reproduces the $π^+$-hydrogen phase shifts of a more microscopic potential, the Temkin-Lamkin potential, over a wide range of energies. Already at leading order it also describes the highest-lying excited bound states of the pionic-hydrogen ion. Lower-lying bound states receive substantial corrections at next-to-leading order, with the size of the correction proportional to their distance from the scattering threshold. Our next-to-leading order calculation shows that the three highest-lying bound states of the Temkin-Lamkin potential are well-described in ID-EFT.

nucl-th↗
arXiv2022

Long Range Plan: Dense matter theory for heavy-ion collisions and neutron stars

Since the release of the 2015 Long Range Plan in Nuclear Physics, major events have occurred that reshaped our understanding of quantum chromodynamics (QCD) and nuclear matter at large densities, in and out of equilibrium. The US nuclear community has an opportunity to capitalize on advances in astrophysical observations and nuclear experiments and engage in an interdisciplinary effort in the theory of dense baryonic matter that connects low- and high-energy nuclear physics, astrophysics, gravitational waves physics, and data science

nucl-th↗
arXiv2022

Final-state interactions and spin structure in $E1$ breakup of $^11$Li in Halo EFT

We calculate the $E1$ breakup of the $2n$ halo nucleus $^{11}$Li in Halo Effective Field Theory (Halo EFT) at leading order. In Halo EFT, $^{11}$Li is treated as a three-body system of a $^{9}$Li core and two neutrons. We present a detailed investigation of final-state interactions (FSI) in the neutron-neutron $(nn)$ and neutron-core $(nc)$ channels. We employ Moller operators to formulate an expansion scheme that satisfies the non-energy-weighted cluster sum rule and successively includes higher-order terms in the multiple-scattering series for the FSI. Computing the $E1$ strength up to third order in this scheme, we observe apparent convergence and good agreement with experiment. The neutron-neutron FSI is by far the most important contribution and largely determines the maximum value of the $E1$ distribution. However, inclusion of $nc$ FSI does shift the peak position to slightly lower energies. Moreover, we investigate the sensitivity of the $E1$ response to the spin structure of the neutron-${}^9$Li interaction. We contrast results for an interaction that is the same in the spin-1 and spin-2 channels with one that is only operative in the spin-2 channel, and find that good agreement with experimental data is only obtained if the interaction is present in both spin channels. The latter case is shown to be equivalent to a calculation in which the spin of $^9$Li is neglected.

nucl-th↗
arXiv2022

Effective Field Theory analysis of ${}^3$He-$α$ scattering data

We treat low-energy $^3$He-$α$ elastic scattering in an Effective Field Theory (EFT) that exploits the separation of scales in this reaction. We compute the amplitude up to Next-to-Next-to-Leading Order (NNLO), developing a hierarchy of the effective-range parameters that contribute at various orders. We use the resulting formalism to analyze data for recent measurements at center-of-mass energies of 0.38-3.12 MeV using the SONIK gas target at TRIUMF as well as older data in this energy regime. We employ a likelihood function that incorporates the theoretical uncertainty due to truncation of the EFT and use Markov Chain Monte Carlo sampling to obtain the resulting posterior probability distribution. We find that the inclusion of a small amount of data on the analysing power $A_y$ is crucial to determine the sign of the p-wave splitting in such an analysis. The combination of $A_y$ and SONIK data constrains all effective-range parameters up to $O(p^4)$ in both s- and p-waves quite well. The ANCs and s-wave scattering length are consistent with a recent EFT analysis of the capture reaction ${}^3$He($α$,$γ$)${}^7$Be.

nucl-th↗