arXiv subjects

H. -W. Hammer

Publications and source records attributed to H. -W. Hammer.

At least 37 records · Page 2Linked to original sources

arXiv2019

Neutron transfer reactions in halo effective field theory

Direct reaction experiments provide a powerful tool to probe the structure of neutron-rich nuclei like beryllium-11. We use halo effective field theory to calculate the cross section of the deuteron-induced neutron transfer reaction ${}^{10}\text{Be}(\text{d},\,\text{p}){}^{11}\text{Be}$. The effective theory contains dynamical fields for the beryllium-10 core, the neutron, and the proton. In contrast, the deuteron and the beryllium-11 halo nucleus are generated dynamically from contact interactions using experimental and ab initio input. The reaction amplitude is constructed up to next-to-leading order in an expansion in the ratio of the length scales characterizing the core and the halo. The Coulomb repulsion between core and proton is treated perturbatively. Finally, we compare our results to cross-section data and other calculations.

nucl-th↗

arXiv2019

More on the universal equation for Efimov states

Efimov states are a sequence of shallow three-body bound states that arise when the two-body scattering length is much larger than the range of the interaction. The binding energies of these states are described as a function of the scattering length and one three-body parameter by a transcendental equation involving a universal function of one angular variable. We provide an accurate and convenient parametrization of this function. Moreover, we discuss the effective treatment of range corrections in the universal equation and compare with a strictly perturbative scheme.

cond-mat.quant-gas↗

arXiv2019

Three-body spectrum in a finite volume: the role of cubic symmetry

The three-particle quantization condition is partially diagonalized in the center-of-mass frame by using cubic symmetry on the lattice. To this end, instead of spherical harmonics, the kernel of the Bethe-Salpeter equation for particle-dimer scattering is expanded in the basis functions of different irreducible representations of the octahedral group. Such a projection is of particular importance for the three-body problem in the finite volume due to the occurrence of three-body singularities above breakup. Additionally, we study the numerical solution and properties of such a projected quantization condition in a simple model. It is shown that, for large volumes, these solutions allow for an instructive interpretation of the energy eigenvalues in terms of bound and scattering states.

hep-lat↗

arXiv2018

Signatures of few-body resonances in finite volume

We study systems of bosons and fermions in finite periodic boxes and show how the existence and properties of few-body resonances can be extracted from studying the volume dependence of the calculated energy spectra. Using a plane-wave-based discrete variable representation to conveniently implement periodic boundary conditions, we establish that avoided level crossings occur in the spectra of up to four particles and can be linked to the existence of multi-body resonances. To benchmark our method we use two-body calculations, where resonance properties can be determined with other methods, as well as a three-boson model interaction known to generate a three-boson resonance state. Finding good agreement for these cases, we then predict three-body and four-body resonances for models using a shifted Gaussian potential. Our results establish few-body finite-volume calculations as a new tool to study few-body resonances. In particular, the approach can be used to study few-neutron systems, where such states have been conjectured to exist.

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arXiv2018

Threshold Effects and the Line Shape of the X(3872) in Effective Field Theory

Latest measurements suggest that the X(3872) mass lies less than 200 keV away from the D0-Dbar0* threshold, reenforcing its interpretation as a loosely-bound mesonic molecule. This observation implies that in processes like D0-Dbar0-pi0 production, threshold effects could disguise the actual pole position of the X(3872). We propose a new effective field theory with D0, Dbar0 and pi0 degrees of freedom for the X(3872), considering Galilean invariance to be an exact symmetry. The D0* enters as a D0-pi0 p-wave resonance, allowing for a comprehensive study of the influence of pion interactions on the X(3872) width. We calculate relations between the mass of the X(3872), its width, and its line shape in D0-Dbar0-pi0 production up to next-to-leading order. Our results provide a tool for the extraction of the X(3872) pole position from the experimental data near threshold.

hep-ph↗

arXiv2018

Flow equations for cold Bose gases

We derive flow equations for cold atomic gases with one macroscopically populated energy level. The generator is chosen such that the ground state decouples from all other states in the system as the renormalization group flow progresses. We propose a self-consistent truncation scheme for the flow equations at the level of three-body operators and show how they can be used to calculate the ground state energy of a general $N$-body system. Moreover, we provide a general method to estimate the truncation error in the calculated energies. Finally, we test our scheme by benchmarking to the exactly solvable Lieb-Liniger model and find good agreement for weak and moderate interaction strengths.

cond-mat.quant-gas↗

arXiv2017

Effective field theory description of halo nuclei

Nuclear halos emerge as new degrees of freedom near the neutron and proton driplines. They consist of a core and one or a few nucleons which spend most of their time in the classically-forbidden region outside the range of the interaction. Individual nucleons inside the core are thus unresolved in the halo configuration, and the low-energy effective interactions are short-range forces between the core and the valence nucleons. Similar phenomena occur in clusters of $^4$He atoms, cold atomic gases near a Feshbach resonance, and some exotic hadrons. In these weakly-bound quantum systems universal scaling laws for s-wave binding emerge that are independent of the details of the interaction. Effective field theory (EFT) exposes these correlations and permits the calculation of non-universal corrections to them due to short-distance effects, as well as the extension of these ideas to systems involving the Coulomb interaction and/or binding in higher angular-momentum channels. Halo nuclei exhibit all these features. Halo EFT, the EFT for halo nuclei, has been used to compute the properties of single-neutron, two-neutron, and single-proton halos of s-wave and p-wave type. This review summarizes these results for halo binding energies, radii, Coulomb dissociation, and radiative capture, as well as the connection of these properties to scattering parameters, thereby elucidating the universal correlations between all these observables. We also discuss how Halo EFT's encoding of the long-distance physics of halo nuclei can be used to check and extend ab initio calculations that include detailed modeling of their short-distance dynamics.

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arXiv2017

Analytical approach to the Bose polaron problem in one dimension

We discuss the ground state properties of a one-dimensional bosonic system doped with an impurity (the so-called Bose polaron problem). We introduce a formalism that allows us to calculate analytically the thermodynamic zero-temperature properties of this system with weak and moderate boson-boson interaction strengths for any boson-impurity interaction. Our approach is validated by comparing to exact quantum Monte Carlo calculations. In addition, we test the method in finite size systems using numerical results based upon the similarity renormalization group. We argue that the introduced approach provides a simple analytical tool for studies of strongly interacting impurity problems in one dimension.

cond-mat.quant-gas↗

arXiv2017

Three particle quantization condition in a finite volume: 2. general formalism and the analysis of data

We derive the three-body quantization condition in a finite volume using an effective field theory in the particle-dimer picture. Moreover, we consider the extraction of physical observables from the lattice spectrum using the quantization condition. To illustrate the general framework, we calculate the volume-dependent three-particle spectrum in a simple model both below and above the three-particle threshold. The relation to existing approaches is discussed in detail.

hep-lat↗

arXiv2017

Three-particle quantization condition in a finite volume: 1. The role of the three-particle force

Using non-relativistic effective Lagrangians in the particle-dimer picture, we rederive the expression for the energy shift of a loosely bound three-particle bound state of identical bosons in the unitary limit. The effective field theory formalism allows us to investigate the role of the three-particle force, which has not been taken into account in the earlier treatment of the problem. Moreover, we are able to relax the requirement of the unitary limit of infinite scattering length and demonstrate a smooth transition from the weakly bound three-particle state to a two-particle bound state of a particle and a deeply bound dimer.

hep-lat↗

arXiv2017

Is a Trineutron Resonance Lower in Energy than a Tetraneutron Resonance?

We present quantum Monte Carlo calculations of few-neutron systems confined in external potentials based on local chiral interactions at next-to-next-to-leading order in chiral effective field theory. The energy and radial densities for these systems are calculated in different external Woods-Saxon potentials. We assume that their extrapolation to zero external-potential depth provides a quantitative estimate of three- and four-neutron resonances. The validity of this assumption is demonstrated by benchmarking with an exact diagonalization in the two-body case. We find that the extrapolated trineutron resonance, as well as the energy for shallow well depths, is lower than the tetraneutron resonance energy. This suggests that a three-neutron resonance exists below a four-neutron resonance in nature and is potentially measurable. To confirm that the relative ordering of three- and four-neutron resonances is not an artifact of the external confinement, we test that the odd-even staggering in the helium isotopic chain is reproduced within this approach. Finally, we discuss similarities between our results and ultracold Fermi gases.

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arXiv2017

Tetramer Bound States in Heteronuclear Systems

We calculate the universal spectrum of trimer and tetramer states in heteronuclear mixtures of ultracold atoms with different masses in the vicinity of the heavy-light dimer threshold. To extract the energies, we solve the three- and four-body problem for simple two- and three-body potentials tuned to the universal region using the Gaussian expansion method. We focus on the case of one light particle of mass $m$ and two or three heavy bosons of mass $M$ with resonant heavy-light interactions. We find that trimer and tetramer cross into the heavy-light dimer threshold at almost the same point and that as the mass ratio $M/m$ decreases, the distance between the thresholds for trimer and tetramer states becomes smaller. We also comment on the possibility of observing exotic three-body states consisting of a dimer and two atoms in this region and compare with previous work.

cond-mat.quant-gas↗

arXiv2017

Nuclear Physics Around the Unitarity Limit

We argue that many features of the structure of nuclei emerge from a strictly perturbative expansion around the unitarity limit, where the two-nucleon S waves have bound states at zero energy. In this limit, the gross features of states in the nuclear chart are correlated to only one dimensionful parameter, which is related to the breaking of scale invariance to a discrete scaling symmetry and set by the triton binding energy. Observables are moved to their physical values by small, perturbative corrections, much like in descriptions of the fine structure of atomic spectra. We provide evidence in favor of the conjecture that light, and possibly heavier, nuclei are bound weakly enough to be insensitive to the details of the interactions but strongly enough to be insensitive to the exact size of the two-nucleon system.

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arXiv2016

Quantum Monte Carlo calculations of two neutrons in finite volume

Ab initio calculations provide direct access to the properties of pure neutron systems that are challenging to study experimentally. In addition to their importance for fundamental physics, their properties are required as input for effective field theories of the strong interaction. In this work, we perform auxiliary-field diffusion Monte Carlo calculations of the ground and first excited state of two neutrons in a finite box, considering a simple contact potential as well as chiral effective field theory interactions. We compare the results against exact diagonalizations and present a detailed analysis of the finite-volume effects, whose understanding is crucial for determining observables from the calculated energies. Using the Lüscher formula, we extract the low-energy S-wave scattering parameters from ground- and excited-state energies for different box sizes.

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arXiv2016

On the pi pi continuum in the nucleon form factors and the proton radius puzzle

We present an improved determination of the $ππ$ continuum contribution to the isovector spectral functions of the nucleon electromagnetic form factors. Our analysis includes the most up-to-date results for the $ππ\to\bar N N$ partial waves extracted from Roy-Steiner equations, consistent input for the pion vector form factor, and a thorough discussion of isospin-violating effects and uncertainty estimates. As an application, we consider the $ππ$ contribution to the isovector electric and magnetic radii by means of sum rules, which, in combination with the accurately known neutron electric radius, are found to slightly prefer a small proton charge radius.

hep-ph↗

arXiv2016

General aspects of effective field theories and few-body applications

Effective field theory provides a powerful framework to exploit a separation of scales in physical systems. In these lectures, we discuss some general aspects of effective field theories and their application to few-body physics. In particular, we consider an effective field theory for non-relativistic particles with resonant short-range interactions where certain parts of the interaction need to be treated nonperturbatively. As an application, we discuss the so-called pionless effective field theory for low-energy nuclear physics. The extension to include long-range interactions mediated by photon and pion-exchange is also addressed.

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arXiv2016

Lindblad Equation for the Inelastic Loss of Ultracold Atoms

The loss of ultracold trapped atoms due to deeply inelastic reactions has previously been taken into account in effective field theories for low-energy atoms by adding local anti-Hermitian terms to the effective Hamiltonian. Here we show that when multi-atom systems are considered, an additional modification is required in the equation governing the density matrix. We define an effective density matrix by tracing over the states containing high-momentum atoms produced by deeply inelastic reactions. We show that it satisfies a Lindblad equation, with local Lindblad operators determined by the local anti-Hermitian terms in the effective Hamiltonian. We use the Lindblad equation to derive the universal relation for the two-atom inelastic loss rate for fermions with two spin states and the universal relation for the three-atom inelastic loss rate for identical bosons.

cond-mat.quant-gas↗

arXiv2016

Open Effective Field Theories from Deeply Inelastic Reactions

Effective field theories have often been applied to systems with deeply inelastic reactions that produce particles with large momenta outside the domain of validity of the effective theory. The effects of the deeply inelastic reactions have been taken into account in previous work by adding local anti-Hermitian terms to the effective Hamiltonian. Here we show that when multi-particle systems are considered, an additional modification is required in equations governing the density matrix. We define an effective density matrix by tracing over the states containing high-momentum particles, and show that it satisfies a Lindblad equation, with local Lindblad operators determined by the anti-Hermitian terms in the effective Hamiltonian density.

hep-ph↗