We present an alternative organizational scheme for developing effective theories of 2- and 3-body systems that is systematic, accurate, and efficient with controlled errors. To illustrate our approach we consider the bound state and scattering properties of the 2- and 3-nucleon systems. Our approach combines the computational benefits of using separable potentials with the improved convergence properties of potentials evolved with a renormalization group procedure. Long ago Harms showed that any potential can be expanded in a series of separable terms, but this fact is only useful if the expansion can be truncated at low order. The separable expansion provides an attractive organizational scheme that incorporates the two body bound state in the leading term while allowing for systematic corrections thereafter. We show that when applied to a renormalization group-evolved potential, the separable expansion converges rapidly, with accurate results for both 2- and 3-body scattering processes using only two separable terms.
In the paper the covariant kernel of the nucleon-nucleon interaction of particles with scalar propagators is analyzed. The Bethe-Salpeter equation for the T matrix is considered in the rank- one separable kernel. The parameters of the kernel for the specific partial-wave channels explicitly connect with the observables { low energy scattering parameters and phase shifts, deuteron binding energy. Covariant separable kernels forthe partial-wave channels with total angular momentum J = 0 (1S0, 3P0) and J = 1 (3S1 -3D1, 1P1, 3P1) are constructed.
In the paper the so-called modified Yamaguchi function for the Bethe-Salpeter equation with a separable kernel is discussed. The type of the functions is defined by the analytic stucture of the hadron current with breakup - the reactions with interacting nucleon-nucleon pair in the final state (electro-, photo-, and nucleon-disintegration of the deuteron).
Elastic electron-helium-3 scattering is studied in the relativistic impulse approximation. The amplitudes for the three-nucleon system are obtained by solving the relativistic generalization of the Faddeev equations with a separable rank-one kernel of the nucleon-nucleon interaction. The contribution of partial-wave states with nonzero orbital moment of a nucleon pair is investigated. The static approximation and additional relativistic corrections for the 3He charge form factor are calculated for the momentum transfer squared up to 100 fm^-2. The contribution of the 3D1 partial-wave state and…
One important ingredient for many applications of nuclear physics to astrophysics, nuclear energy, and stockpile stewardship are cross sections for reactions of neutrons with rare isotopes. Since direct measurements are often not feasible, indirect methods, e.g. (d,p) reactions, should be used. Those (d,p) reactions may be viewed as three-body reactions and described with Faddeev techniques. Faddeev equations in momentum space have a long tradition of utilizing separable interactions in order to arrive at sets of coupled integral equations in one variable. Optical potentials representing the e…
We study radiative capture reactions using quasi-separable potentials. This procedure allows an easier treatment of non-local effects that can be extended to three-body problems. Using this technique, we calculate the neutron and proton radiative capture cross sections on $^{12}$C. The results obtained are shown to be in good agreement with the available experimental data.
Separable form of low-momentum realistic NN interaction
从核子-核子相互作用的实际模型导出的低动量相互作用$V_{\text{low-k}}$以可分离的形式给出。这种可分离力由接触相互作用支持，以实现对称核物质的饱和性质。在可分形式的$V_{\text{low-k}}$和接触项的两种不同参数化下，研究了核物质和有限核的体性质。讨论了Hartree-Fock计算中可分离力相对于原始相互作用$V_{\text{low-k}}$的精度。对于2 fm $^{-1}$的截止参数$Λ$，通过秩2可分离力的表示产生足够的精度，而对于较大的截止参数需要较高的秩。所得到的可分离力以简单的方式被参数化，以允许在其他原子核结构计算中容易地应用。
Background: Separable interactions have a long history in nuclear physics. In the last few years, separable expansions have been used to represent the optical potential between a nucleon (proton or neutron) and a target. Purpose: We explore the non-local properties of these separable optical potentials as well as their convergence behavior. Method: For a couple of cases, we use the generalized Ersnt-Shakin-Thaler scheme to generate separable interactions starting from local optical potentials. We study the variation of the interaction with energy range and rank. Results: We find that, overall …
For the coefficients of the amplitude a set of simultaneous equations is derived in momentum space. By the auxiliary conditions they are equivalent to nonrelativistic equations and suitable for the investigation of two-nucleon system.
We construct a folding potential between the $α$ and $Λ$ particles based on underlying nucleon-nucleon and hyperon-nucleon interactions. Starting from a phenomenological $Λ$-N potential and a Gaussian form of the $α$-particle wave function we obtain for the built $α$-$Λ$ interaction a bound $^5_Λ$He state with the binding energy (3.10 MeV), which is consistent with recent experimental data $3.12 \pm 0.02$ MeV. When in turn an exact solution of the four-body Faddeev-Yakubovsky equation for the $α$-particle calculated with the CDBonn, Nijmegen or Argonne V18 realistic nucleon-nucleon potential i…
The properties of nuclear matter are studied using state-of-the-art nucleon-nucleon forces up to fifth order in chiral effective field theory. The equations of state of symmetric nuclear matter and pure neutron matter are calculated in the framework of the Brueckner-Hartree-Fock theory. We discuss in detail the convergence pattern of the chiral expansion and the regulator dependence of the calculated equations of state and provide an estimation of the truncation uncertainty. For all employed values of the regulator, the fifth-order chiral two-nucleon potential is found to generate nuclear satu…
Recently, a relativistic chiral nucleon-nucleon interaction is formulated up to leading order which provides a good description of the phase shifts of $J\leq1$ partial waves [Chin. Phys. C 42 (2018) 014103]. Nevertheless, a separable regulator function that is not manifestily covariant was used in solving the relativistic scattering equation. In the present work, we first propose a covariant and separable form factor to regularize the kernel potential and then apply it to study the simplest but most challenging $^1S_0$ channel which features several low-energy scales. In addition to being self…
We employ a variety of ab initio methods including Faddeev-Yakubovsky equations, No-Core Configuration Interaction Approach, Coupled-Cluster Theory and In-Medium Similarity Renormalization Group to perform a comprehensive analysis of the nucleon-deuteron elastic and breakup reactions and selected properties of light and medium-mass nuclei up to 48Ca using the recently constructed semilocal coordinate-space regularized chiral nucleon-nucleon potentials. We compare the results with those based on selected phenomenological and chiral EFT two-nucleon potentials, discuss the convergence pattern of …
We present and discuss predictions for a cross section of bulk and single-particle properties in symmetric nuclear matter based on recent high-quality nucleon-nucleon potentials at N3LO and including all subleading three-nucleon forces. We begin with the equation of state and its saturation properties and proceed to the single-nucleon potential. We also explore short-range correlations as seen through the defect function. The various predictions which we present have a common foundation in an internally consistent ab initio approach.
We compare the subtractive renormalization and the Wilsonian renormalization group approaches in the context of an effective field theory for the two-nucleon system. Based on an exactly solvable model of contact interactions, we observe that the standard Wilsonian renormalization group approach with a single cutoff parameter does not cover the whole space spanned by the renormalization scale parameters of the subtractive formalism. In particular, renormalization schemes corresponding to Weinberg's power counting in the case of an unnaturally large scattering length are beyond the region covere…
