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H. -W. Hammer

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

At least 19 recordsLinked to original sources
arXiv2026

Hadron Physics Opportunities at FAIR

This White Paper outlines a coordinated, decade-spanning programme of hadron and QCD studies anchored at the GSI/FAIR accelerator complex. Profiting from intense deuteron, proton and pion beams coupled with high-rate capable detectors and an international theory effort, the initiative addresses fundamental questions related to the strong interaction featuring confinement and dynamical mass generation. This includes our understanding of hadron-hadron interactions and the composition of hadrons through mapping the baryon and meson spectra, including exotic states, and quantifying hadron structure. This interdisciplinary research connects topics in the fields of nuclear, heavy-ion, and (nuclear) astro (particle) physics, linking, for example, terrestrial data to constraints on neutron star structure. A phased roadmap with SIS100 accelerator start-up and envisaged detector upgrades will yield precision cross sections, transition form factors, in-medium spectral functions, and validated theory inputs. Synergies with external programmes at international accelerator facilities worldwide are anticipated. The programme is expected to deliver decisive advances in our understanding of non-perturbative (strong) QCD and astrophysics, and high-rate detector and data-science technology.

hep-ex↗
arXiv2023

An alternative scheme for pionless EFT: neutron-deuteron scattering in the doublet S-wave

Using the effective-range expansion for the two-body amplitudes may generate spurious sub-threshold poles outside of the convergence range of the expansion. In the infinite volume, the emergence of such poles leads to the breakdown of unitarity in the three-body amplitude. We discuss the extension of our alternative subtraction scheme for including effective range corrections in pionless effective field theory for spinless bosons to nucleons. In particular, we consider the neutron-deuteron system in the doublet S-wave channel explicitly.

nucl-th↗
arXiv2022

Theory of Halo Nuclei

Halo nuclei are characterized by a few weakly bound halo nucleons and a more tightly bound core. This separation of scales can be exploited in a few-body description of halo nuclei, since the detailed structure of the core is not resolved by the halo nucleons. We present an introduction to the effective (field) theory for low-energy properties of halo nuclei. The focus is on halos with S-wave interactions for which universal properties are most pronounced. The special role of the unitary limit is illustrated using the example of multineutron systems and the Efimov effect as a universal binding mechanism for halo nuclei. Connections to ultracold atoms and hadron physics are highlighted and extensions to higher partial waves, Coulomb forces and nuclear reactions are briefly touched upon.

nucl-th↗
arXiv2021

Simulating core excitation in breakup reactions of halo nuclei using an effective three-body force

We extend our previous calculation of the breakup of 11Be using Halo Effective Field Theory and the Dynamical Eikonal Approximation to include an effective 10Be-n-target force. The force is constructed to account for the virtual excitation of 10Be to its low-lying 2+ excited state. In the case of breakup on a 12C target this improves the description of the neutron-energy and angular spectra, especially in the vicinity of the 11Be 5/2+ state. By fine-tuning the range parameters of the three-body force, a reasonable description of data in the region of the 3/2+ 11Be state can also be obtained. This sensitivity to the three-body force's range results from the structure of the overlap integral that governs the 11Be s-to-d-state transitions induced by the three-body force.

nucl-th↗
arXiv2021

Dissecting reaction calculations using Halo EFT and ab initio input

We present a description of the break-up of halo nuclei in peripheral nuclear reactions by coupling a model of the projectile motivated by Halo Effective Field Theory with a fully dynamical treatment of the reaction using the Dynamical Eikonal Approximation. Our description of the halo system reproduces its long-range properties, i.e., binding energy and asymptotic normalization coefficients of bound states and phase shifts of continuum states. As an application we consider the break-up of 11Be in collisions on Pb and C targets. Taking the input for our Halo-EFT-inspired description of 11Be from a recent ab initio calculation of that system yields a good description of the Coulomb-dominated breakup on Pb at energies up to about 2 MeV, with the result essentially independent of the short-distance part of the halo wave function. However, the nuclear dominated break-up on C is more sensitive to short-range physics. The role of spectroscopic factors and possible extensions of our approach to include additional short-range mechanisms are also discussed.

nucl-th↗
arXiv2021

An alternative scheme for effective range corrections in pionless EFT

We discuss an alternative scheme for including effective range corrections in pionless effective field theory. The standard approach treats range terms as perturbative insertions in the T -matrix. In a finite volume this scheme can lead to singular behavior close to the unperturbed energies. We consider an alternative scheme that resums the effective range but expands the spurious pole of the T -matrix created by this resummation. We test this alternative expansion for several model potentials and observe good convergence.

hep-ph↗
arXiv2021

Nuclear Structure at the Crossroads

Steven Weinberg's seminal papers from 1990-92 initiated the use of effective field theories (EFTs) for nuclei. We summarize progress, priorities, and open questions for nuclear EFT developments based on the 2019 INT program "Nuclear Structure at the Crossroads."

nucl-th↗
arXiv2021

Impurities in a one-dimensional Bose gas: the flow equation approach

A few years ago, flow equations were introduced as a technique for calculating the ground-state energies of cold Bose gases with and without impurities. In this paper, we extend this approach to compute observables other than the energy. As an example, we calculate the densities, and phase fluctuations of one-dimensional Bose gases with one and two impurities. For a single mobile impurity, we use flow equations to validate the mean-field results obtained upon the Lee-Low-Pines transformation. We show that the mean-field approximation is accurate for all values of the boson-impurity interaction strength as long as the phase coherence length is much larger than the healing length of the condensate. For two static impurities, we calculate impurity-impurity interactions induced by the Bose gas. We find that leading order perturbation theory fails when boson-impurity interactions are stronger than boson-boson interactions. The mean-field approximation reproduces the flow equation results for all values of the boson-impurity interaction strength as long as boson-boson interactions are weak.

cond-mat.quant-gas↗
arXiv2020

Lifetime of the hypertriton

We calculate the lifetime of the hypertriton as function of the $Λ$ separation energy $B_Λ$ in an effective field theory with $Λ$ and deuteron degrees of freedom. We also consider the impact of new measurements of the weak decay parameter of the $Λ$. While the sensitivity of the total width to $B_Λ$ is small, the partial widths for decays into individual final states and the experimentally measured ratio $R=Γ_{^3\textrm{He}}/\left(Γ_{^3 \text{He}}+Γ_{pd}\right)$ show a strong dependence. For the standard value $B_Λ=(0.13\pm 0.05)$ MeV, we find $R=0.37\pm 0.05$, which is in good agreement with past experimental studies and theoretical calculations. For the recent STAR value $B_Λ=(0.41\pm0.12\pm0.11)$ MeV, we obtain $R=0.57\pm 0.11$.

nucl-th↗
arXiv2020

Three-Body Hypernuclei in Pionless Effective Field Theory

We calculate the structure of three-body hypernuclei with $S=-1$ using pionless effective field theory at leading order in the isospin $I=0$ and $I=1$ sectors. In both sectors, three-body hypernuclei arise naturally from the Efimov effect and a three-body parameter is required at leading order. We apply our theory to the hypertriton and the hypothetical $Λnn$ bound state and calculate the corresponding scaling factors. Moreover, we discuss constraints on the existence of the $Λnn$ bound state. In particular, we elucidate universal correlations between different observables and provide explicit calculations of wave functions and matter radii.

nucl-th↗
arXiv2020

Nuclear effective field theory: status and perspectives

The nuclear physics landscape has been redesigned as a sequence of effective field theories (EFTs) connected to the Standard Model through symmetries and lattice simulations of Quantum Chromodynamics (QCD). EFTs in this sequence are expansions around different low-energy limits of QCD, each with its own characteristics, scales, and ranges of applicability regarding energy and number of nucleons. We review each of the three main nuclear EFTs -- Chiral, Pionless, Halo/Cluster -- highlighting their similarities, differences, and connections. In doing so, we survey the structural properties and reactions of nuclei that have been derived from the ab initio solution of the few- and many-body problem built upon EFT input.

nucl-th↗
arXiv2019

In-medium bound states of two bosonic impurities in a one-dimensional Fermi gas

We investigate the ground-state energy of a one-dimensional Fermi gas with two bosonic impurities. We consider spinless fermions with no fermion-fermion interactions. The fermion-impurity and impurity-impurity interactions are modelled with Dirac delta functions. First, we study the case where impurity and fermions have equal masses, and the impurity-impurity two-body interaction is identical to the fermion-impurity interaction, such that the system is solvable with the Bethe ansatz. For attractive interactions, we find that the energy of the impurity-impurity subsystem is below the energy of the bound state that exists without the Fermi gas. We interpret this as a manifestation of attractive boson-boson interactions induced by the fermionic medium, and refer to the impurity-impurity subsystem as an in-medium bound state. For repulsive interactions, we find no in-medium bound states. Second, we construct an effective model to describe these interactions, and compare its predictions to the exact solution. We use this effective model to study non-integrable systems with unequal masses and/or potentials. We discuss parameter regimes for which impurity-impurity attraction induced by the Fermi gas can lead to the formation of in-medium bound states made of bosons that repel each other in the absence of the Fermi gas.

cond-mat.quant-gas↗
arXiv2019

Universal physics of bound states of a few charged particles

We study few-body bound states of charged particles subject to attractive zero-range/short-range plus repulsive Coulomb interparticle forces. The characteristic length scales of the system at zero energy are set by the Coulomb length scale $D$ and the Coulomb-modified effective range $r_{\mathrm{eff}}$. We study shallow bound states of charged particles with $D\gg r_{\mathrm{eff}}$ and show that these systems obey universal scaling laws different from neutral particles. An accurate description of these states requires both the Coulomb-modified scattering length and the effective range unless the Coulomb interaction is very weak ($D\to \infty$). Our findings are relevant for bound states whose spatial extent is significantly larger than the range of the attractive potential. These states enjoy universality -- their character is independent of the shape of the short-range potential.

nucl-th↗
arXiv2019

Electric structure of shallow D-wave states in Halo EFT

We compute the electric form factors of one-neutron halo nuclei with shallow D-wave states up to next-to-leading order and the E2 transition from the S-wave to the D-wave state up to leading order in Halo Effective Field Theory (Halo EFT). The relevant degrees of freedom are the core and the halo neutron. The EFT expansion is carried out in powers of $R_{core}/R_{halo}$, where $R_{core}$ and $R_{halo}$ denote the length scales of the core and the halo, respectively. We propose a power counting scenario for weakly-bound states in one-neutron Halo EFT and discuss its implications for higher partial waves in terms of universality. The scenario is applied to the $\frac{5}{2}^+$ first excited state and the $\frac{1}{2}^+$ ground state of $^{15}\text{C}$. We obtain several universal correlations between electric observables and use data for the E2 transition $\frac{5}{2}^+\to \frac{1}{2}^+$ together with ab initio results from the No-Core Shell Model to predict the quadrupole moment.

nucl-th↗
arXiv2019

Momentum-space probability density of ${}^6$He in Halo Effective Field Theory

We compute the momentum-space probability density of ${}^6$He at leading order in Halo EFT. In this framework, the ${}^6$He nucleus is treated as a three-body problem with a ${}^4$He core ($c$) and two valence neutrons ($n$). This requires the $nn$ and $nc$ t-matrices as well as a $cnn$ force as input in the Faddeev equations. Since the $nc$ t-matrix corresponds to an energy-dependent potential, we consider the consequent modifications to the standard normalization and orthogonality conditions. We find that these are small for momenta within the domain of validity of Halo EFT. In this regime, the ${}^6$He probability density is regulator independent, provided the cutoff is significantly above the EFT breakdown scale.

nucl-th↗
arXiv2019

Energy shift of the three-particle system in a finite volume

Using the three-particle quantization condition recently obtained in the particle-dimer framework, the finite-volume energy shift of the two lowest three-particle scattering states is derived up to and including order $L^{-6}$. Furthermore, assuming that a stable dimer exists in the infinite volume, the shift for the lowest particle-dimer scattering state is obtained up to and including order $L^{-3}$. The result for the lowest three-particle state agrees with the results from the literature, and the result for the lowest particle-dimer state reproduces the one obtained by using the Luescher equation.

hep-lat↗
arXiv2019

Efimov universality with Coulomb interaction

The universal properties of charged particles are modified by the presence of a long-range Coulomb interaction. We investigate the modification of Efimov universality as a function of the Coulomb strength using the Gaussian expansion method. The resonant short-range interaction is described by Gaussian potentials to which a Coulomb potential is added. We calculate binding energies and root mean square radii for the three- and four-body systems of charged particles and present our results in a generalised Efimov plot. We find that universal features can still be discerned for weak Coulomb interaction, but break down for strong Coulomb interaction. The root-mean-square radius plateaus at increasingly smaller values for strong Coulomb interaction and the probablity distributions of the states become more concentrated inside the Coulomb barrier. As an example, we apply our universal model to nuclei with an alpha-cluster substructure. Our results point to strong non-universal contributions in that sector.

nucl-th↗