Unitary ambiguity of NN contact interactions and the 3N force

Polarized $pK^-$ scattering in Unitary Baryon Chiral Perturbation Theory

We study $pK^-$ scattering in the energy range from threshold through the $Λ(1520)$ peak in UBChPT, taking into account $\mathcal{O}(q)$ vertices from meson-baryon contact interactions and $s$- and $u$-channel ground-state baryon exchange, $s$- and $u$-channel decuplet- and nonet-baryon exchange and $t$-channel vector-meson exchange, as well as $\mathcal{O}(q^2)$ flavor-breaking vertices. Detailed fits to data are presented, including a substantial body of differential cross-section data with meson momentum $q_\mathrm{lab} > 300$ MeV not considered in previous treatments.

用么正变换方法从手征拉格朗日量计算核力II：双核子系统

Nuclear forces from chiral Lagrangians using the method of unitary transformation II: The two-nucleon system

我们采用文献[1]中导出的手征核子-核子势。[1]研究两核子系统中的束缚态和散射态。在次领先阶，这个势是重整化的一π和二π交换和接触相互作用的总和。在次-主导阶，我们有额外的手征两π介子交换，其低能常数由π-核子散射确定。或者，我们认为Δ（1232）是有效场论中的一个显式自由度。与接触相互作用有关的9个参数可以通过拟合np S波和P波以及实验室能量低于100 MeV的混合参数ε_1来确定。预测的相移和混合参数更高的能量和更高的角动量的能量低于300兆电子伏的大多是很好地描述。S波的描述和现代唯象势一样精确。我们发现一个很好的描述氘核的性质。

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

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 one-body 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…

Pion photoproduction off the proton in a gauge-invariant chiral unitary framework

We investigate pion photoproduction off the proton in a manifestly gauge-invariant chiral unitary extension of chiral perturbation theory. In a first step, we consider meson-baryon scattering taking into account all next-to-leading order contact interactions. The resulting low-energy constants are determined by a fit to s-wave pion-nucleon scattering and the low-energy data for the reaction pi- p --> eta n. To assess the theoretical uncertainty, we perform two different fit strategies. Having determined the low-energy constants, we then analyse the data on the s-wave multipole amplitudes E0+ o…

Ground-state properties of unitary bosons: from clusters to matter

The properties of cold Bose gases at unitarity have been extensively investigated in the last few years both theoretically and experimentally. In this paper we use a family of interactions tuned to two-body unitarity and very weak three-body binding to demonstrate the universal properties of both clusters and matter. We determine the universal properties of finite clusters up to 60 particles and, for the first time, explicitly demonstrate the saturation of energy and density with particle number and compare with bulk properties. At saturation in the bulk we determine the energy, density, two- …

动量相关的核子-核子接触相互作用及其对质子-氘核散射可观测量的影响

Momentum dependent nucleon-nucleon contact interactions and their effect on p-d scattering observables

该研究从相对论核子-核子接触算符的非相对论展开出发，发现两个依赖核子对总动量的低能自由常数，通过幺正变换生成同阶三核子相互作用，结合AV18势的混合方法可拟合低能p-d散射极化可观测量的高精度数据。

Gaussian characterization of the unitary window for $N=3$: bound, scattering and virtual states

The three-body system inside the unitary window is studied for three equal bosons and three equal fermions having $1/2$ spin-isospin symmetry. We perform a gaussian characterization of the window using a gaussian potential to define trajectories for low-energy quantities as binding energies and phase shifts. On top of this trajectories experimental values are placed or, when not available, quantities calculated using realistic potentials that are known to reproduce experimental values. The intention is to show that the gaussian characterization of the window, thought as a contact interaction p…

Giant Resonances based on Unitarily Transformed Two-Nucleon plus Phenomenological Three-Nucleon Interactions

We investigate giant resonances of spherical nuclei on the basis of the Argonne V18 potential after unitary transformation within the Similarity Renormalization Group or the Unitary Correlation Operator Method supplemented by a phenomenological three-body contact interaction. Such Hamiltonians can provide a good description of ground-state energies and radii within Hartree-Fock plus low-order many-body perturbation theory. The standard Random Phase Approximation is applied here to calculate the isoscalar monopole, isovector dipole, and isoscalar quadrupole excitation modes of the 40Ca, 90Zr, a…

Unitary fermions and Luscher's formula on a crystal

We consider the low-energy particle-particle scattering properties in a periodic simple cubic crystal. In particular, we investigate the relation between the two-body scattering length and the energy shift experienced by the lowest-lying unbound state when this is placed in a periodic finite box. We introduce a continuum model for s-wave contact interactions that respects the symmetry of the Brillouin zone in its regularisation and renormalisation procedures, and corresponds to the na{ï}ve continuum limit of the Hubbard model. The energy shifts are found to be identical to those obtained in th…

Comparative study of three-nucleon potentials in nuclear matter

A new generation of local three-body potentials providing an excellent description of the properties of light nuclei, as well as of the neutron-deuteron doublet scattering length, has been recently derived. We have performed a comparative analysis of the equations of state of both pure neutron matter and symmetric nuclear matter obtained using these models of three-nucleon forces. None of the considered potentials simultaneously explains the empirical equilibrium density and binding energy of symmetric nuclear matter. However, two of them provide reasonable values of the saturation density. Th…

非相对论性共形场论与囚禁原子：维里定理与三维态算符对应

On Non-Relativistic Conformal Field Theory and Trapped Atoms: Virial Theorems and the State-Operator Correspondence in Three Dimensions

非相对论费米子接触相互作用的场论可以用来计算简谐势阱中冷原子的少体系统的性质。非相对论性共形场论（NRCFT）的态-算符对应表明，N个简谐囚禁费米子的能量本征值（振子单位）可以由NRCFT中N个费米子算符的标度维数来计算.它们也与自由空间中N体问题的零能量、标度不变解一一对应。我们表明，这两个映射的被困费米子问题的自由空间问题是相关的SL（2，R）代数的共形对称的费米子在酉极限的自同构。这种自同构交换了气体的内部哈密顿量与俘获势，从而提供了一种新的方法来推导维里定理的捕获费米气体在幺正极限。我们还表明，通过计算两个和三个费米子运营商的标度尺寸，并找到与已知的确切结果一致的能级的两个和三个被困费米子在酉极限的状态算子对应可以直接应用在三维空间。