Session CF: Few-Body Theory

Deuteron electrodisintegration with variable-resolution Hamiltonians

Renormalization group (RG) methods used to soften Hamiltonians for nuclear many-body calculations change the effective resolution of nuclei. For nucleon knock-out processes, these RG transformations leave cross sections invariant but initial wave functions, interaction currents, and final state interactions are individually altered. We use Deuteron electrodisintegration as a controlled theoretical laboratory for studying how these nuclear structure and reaction components are modified with changes in the resolution of the Hamiltonians. The implications for factorizing structure and reactions will also be discussed.   

Charge symmetry breaking effect for $^3$H and $^3$He within $s$-wave approach

Three-nucleon systems are considered under the assumption that neutrons and protons are to be distinguishable. The configuration space Faddeev equations are used to calculate ground state energies of $^3$H and $^3$He nuclei within $s$-wave approach applying the Malfliet-Tjon MT I-III potential. We modify the potential to define $nn$ and $pp$ singlet components. Numerical evaluation for the charge symmetry breaking energy is done. Results obtained are compared with previous predictions.   

The proton--deuteron scattering length in pionless EFT

We present a fully perturbative calculation of the quartet-channel proton--deuteron scattering length up to next-to-next-to-leading order (NNLO) in pionless effective field theory. In particular, we use a framework that consistently extracts the Coulomb-modified effective range function for a screened Coulomb potential in momentum space and allows for a clear linear extrapolation back to the physical limit without screening. We find a natural convergence pattern as we go to higher orders in the EFT expansion. Our NNLO result of $(10.9\pm0.4)$~fm agrees with older experimental determinations but deviates from more recent results around $14$~fm. As a resolution of this discrepancy, we discuss the scheme dependence of Coulomb subtractions in a three-body system.   

Low energy neutron deuteron scattering to N$^3$LO

\newcommand{\EFT}{EFT$_{\pi \! \! \! /}$}\newcommand{\Lam}{$\Lambda_{\pi \! \! \! /}$}We calculate the next-to-next-to-next-to-leading order (N\textsuperscript{3}LO) $nd$ scattering amplitude in the framework of nonrelativistic pionless effective field theory (\EFT). This theory is only valid when the typical momentum exchange in the scattering is smaller then the mass of the pion. The power counting parameter for \EFT \ is the ratio $\frac{Q}{\Lambda_{\pi \! \! \! /}}$, where $Q$ is the typical momentum exchange in the scattering and \Lam \ is the \EFT \ breakdown scale, \Lam $< m_{\pi}$. The calculation of the amplitude for $nd$ scattering at leading order requires summing an infinite set of diagrams. The first nonzero polarization-dependent observables occur at N\textsuperscript{2}LO. At N\textsuperscript{3}LO new 2-body forces appear, which introduce four new \EFT \ coefficients. These coefficients are fixed by the $^{3}P_{J}$ and $^{1}P_{1}$ phase shifts of NN scattering. We find that these terms have an important impact. The results of this calculation at N\textsuperscript{3}LO will be important for understanding spin polarization observables in $nd$ scattering, in particular the longstanding $A_{y}$ puzzle.   

Configuration space Faddeev equations within the general formalism for studying Nd breakup scattering

Appropriate modifications of the configuration space Faddeev equations have been made to study the three-nucleon system assuming the neutrons and protons to be distinguishable. Breakup amplitudes for n-d and p-d scattering at Elab$=$14.1 MeV are calculated in s-wave approach with the Malfliet-Tjon MT I-III and AV14 potentials. Results obtained for Nd breakup scattering in quartet and doublet spin states are compared with our predictions [1] and those of the Los-Alamos/Iowa group [2]. \\[4pt] [1] V.M. Suslov and B. Vlahovic, Phys. Rev. C69, 044003 (2004)\\[0pt] [2] J.L. Friar, G.L. Payne, W. Gl\"{o}ckle, D. H\"{u}ber, and H. Witala, Phys Rev. C51, 2356 (1995)   

Halo Effective Field Theory of 6He

Halo nuclei exhibit separation of scales and are therefore amenable to an Effective Field Theory (EFT) description. In Halo EFT, $^6$He can be thought of as a tight $^4$He $(\alpha)$ core surrounded by two loosely bound neutrons ($n$), hence it constitutes an effective Borromean three-body system. The valence neutrons of $^6$He interact with the $\alpha$-core predominantly through a $p$-wave $(^2P_{3/2})$ resonance while the two neutrons are in the relative resonant $^1S_0$ partial wave. The leading order (LO) Halo EFT calculations using momentum-space Faddeev equations pertinent to such a treatment of bound $^6$He were carried out by Ji et al. in Phys.\ Rev.\ C {\bf 90}, 044004 (2014). As an extension to that work, we are investigating $^6$He up to NLO within Halo EFT. In this talk, I will demonstrate how the NLO piece of the $^1S_0$ $nn$ dimer propagator, the NLO piece of the $^2P_{3/2}$ $n\alpha$ dimer propagator and the contact $n\alpha$ vertex in the $^2S_{1/2}$ channel enter the NLO amplitude for the $nn\alpha$ system. I will discuss the divergences and renormalization at this order and show results for the Faddeev components.   

Ab initio NCSMC for three-cluster systems and application to 6He

The \emph{Ab initio} no-core shell model/resonating group method (NCSM/RGM) introduced in Ref. [1] is a technique able to describe both structure and reactions in light nuclear systems. This approach combines a microscopic cluster technique with the use of realistic inter-nucleon interactions and a consistent microscopic description of the nucleon clusters. In Refs.[2,3], we introduced the treatment of three-body cluster dynamics, making the approach suitable for the investigation of systems presenting such structure and presented results for $^6$He within a $^4$He(g.s.)+$n$+$n$ basis. In this work, we go a step further and include short-range correlations by means of the no-core shell model with continuum (NCSMC), which couples the NCSM/RGM continuous cluster basis with the A-body NCSM discrete basis. We find that these correlations play an important role in the structure of the $^6$He ground state and 2$^+_1$ resonance. We will present results for $^6$He ground and continuum states as well as initial results for the $^5$H unbound nucleus within a $^3$H+$n$+$n$ basis. [1] S. Quaglioni and P. Navr\'atil, PRL 101, 092501 (2008). [2] S. Quaglioni, C. Romero-Redondo, P. Navr\'atil, PRC 88, 034320 (2013). [3] CRR, S. Quaglioni, P. Navr\'atil and G. Hupin. PRL 113, 032503 (2014)   

Quantifying truncation errors in effective field theory

Bayesian procedures designed to quantify truncation errors in perturbative calculations of QCD observables are adapted to expansions in effective field theory (EFT). In the Bayesian approach, such truncation errors are derived from degree-of-belief (DOB) intervals for EFT predictions. Computation of these intervals requires specification of prior probability distributions (``priors'') for the expansion coefficients. By encoding expectations about the naturalness of these coefficients, this framework provides a statistical interpretation of the standard EFT procedure where truncation errors are estimated using the order-by-order convergence of the expansion. It also permits exploration of the ways in which such error bars are, and are not, sensitive to assumptions about EFT-coefficient naturalness. We demonstrate the calculation of Bayesian DOB intervals for the EFT truncation error in some representative cases and explore several methods by which the convergence properties of the EFT for a set of observables may be used to check the statistical consistency of the EFT expansion parameter.   

Bayesian parameter estimation for effective field theories

We present a procedure based on Bayesian statistics for effective field theory (EFT) parameter estimation from experimental or lattice data. The extraction of low-energy constants (LECs) is guided by physical principles such as naturalness in a quantifiable way and various sources of uncertainty are included by the specification of Bayesian priors. Special issues for EFT parameter estimation are demonstrated using representative model problems, and a set of diagnostics is developed to isolate and resolve these issues. We apply the framework to the extraction of the LECs of the nucleon mass expansion in SU(2) chiral perturbation theory from synthetic lattice data.