arXiv subjects

Betzalel Bazak

Publications and source records attributed to Betzalel Bazak.

At least 19 recordsLinked to original sources

arXiv2026

Coupled-channel scattering from artificial confinement

Artificial confinement encodes continuum scattering information in discrete, bound-state-like spectra, allowing reaction observables to be extracted with finite-basis or finite-domain methods. We apply this strategy to a two-channel cluster model of $^4$He with open $^3$H+p and $^3$He+n channels. We extract coupled-channel observables from spectra generated by a harmonic-oscillator (HO) trap, a spherical hard wall, and, within a single-partial-wave truncation, a periodic cubic box. The three geometries are formulated in a unified quantization-condition framework and benchmarked against a continuum $R$-matrix calculation. Above the second-channel threshold, several confined levels at a common scattering energy are combined in an overdetermined fit to determine two phase shifts and an inelasticity. Without Coulomb interactions, all three geometries yield consistent results for the $^1S_0$ and $^3P_1$ partial waves. With Coulomb interactions in the charged $^3$H+p channel, the HO and spherical-wall results also agree closely with the continuum reference. A Monte Carlo propagation study shows that spectral uncertainties are amplified near trap-function poles and along poorly conditioned directions associated with the inelasticity and phase-shift difference, whereas the phase-shift sum remains comparatively robust. These results provide a controlled benchmark for confinement-based scattering methods and delineate their strengths and limitations for future few-body and ab initio reaction calculations.

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arXiv2026

Small Clusters of $^4$He Atoms in Finite-Cutoff Effective Field Theory

Small clusters of $^4$He atoms are benchmark systems for universal few-body physics near the unitary limit. We study these systems using a finite-cutoff effective field theory calibrated to low-energy observables from the realistic LM2M2 potential. The chosen two-body cutoff reproduces both the atom--atom scattering length and effective range, while a regulated three-body interaction is adjusted to the trimer and tetramer ground-state energies. We distinguish total binding energies from the one-atom separation energies $S_A^*=B_A^*-B_{A-1}$ of the shallow excited states. Ground-state energies through $A=8$ are reproduced at the few-percent level, but threshold-sensitive observables are less accurate. In particular, the calculated tetramer separation energy is $S_4^*=2.85$~mK, compared with $0.92$--$0.96$~mK in converged LM2M2 calculations, and the atom--trimer scattering length differs substantially from modern LM2M2 benchmarks. For $A\ge5$, the available excited-state benchmarks are sparse and strongly method dependent. Comparison with another soft-core interaction suggests that the discrepancies primarily reflect short-distance physics and higher-order operators omitted from the finite-cutoff Hamiltonian rather than numerical convergence of the stochastic variational calculation. Finite-cutoff EFT therefore provides an efficient description of ground-state systematics, whereas shallow excited states and atom--cluster scattering require a controlled higher-order and cutoff-dependence analysis.

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arXiv2025

Few-Nucleon Systems within Finite-Cutoff Pionless EFT

We investigate pionless effective field theory (\nopieft) with finite-cutoff regularization as a framework for describing few-nucleon systems. This formulation incorporates effective-range effects already at leading order (LO), thereby reaching next-to-leading-order (NLO) accuracy while maintaining computational efficiency. Using correlated-Gaussian stochastic variational methods in a weak harmonic-oscillator trap, together with neutral and Coulomb-modified quantization conditions, we calculate binding energies and low-energy $S$-wave scattering parameters for systems with up to five nucleons. At an optimal cutoff, the computed binding energies of the deuteron, triton, helion, and alpha particle reproduce experimental values at the percent level once a three-body force is included. Scattering parameters for proton--proton, nucleon--deuteron, nucleon--triton, proton--helion, deuteron--deuteron, and nucleon--alpha channels are obtained and found to be consistent with both experimental data and existing NLO \nopieft\ calculations. These results demonstrate that finite-cutoff \nopieft\ offers a robust and predictive framework for few-body nuclear physics.

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arXiv2024

Perturbative application of next-to-leading order pionless EFT for $A\le3$ nuclei in a finite volume

Lattice quantum chromodynamics (LQCD) calculations with physical pion mass would revolutionize nuclear physics by enabling predictions based on the fundamental theory of the strong force. To bridge the gap between finite-volume LQCD results and free-space physical observables, two primary extrapolation methods have been employed so far. The traditional approach relies on the Lüscher formula and its extensions, while a recent alternative employs effective field theories (EFTs) fitted directly to the finite volume data. In this study, we fit pionless EFT with perturbative inclusion of the next-to-leading order to finite-volume energies generated from a phenomenological $NN$ interaction. The theory is then used to extrapolate the finite-volume results into free space as well as to predict new few-body observables. As a benchmark, we also apply the Lüscher formalism directly to the finite-volume data. Through a comprehensive analysis, we explore the characteristics of order-by-order predictions of the pionless EFT fitted within a finite volume, investigate the limitations of the different extrapolation techniques used, and derive recommended box sizes required for reliable predictions.

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arXiv2023

Five-body calculation of $s$-wave $n$-$^4$He scattering at next-to-leading order pionless effective field theory

We present the first five-body calculations of $s$-wave $n$-$^4$He scattering within leading order and next-to-leading order (NLO) pionless effective field theory. Using an harmonic oscillator trap technique and pionless effective field theory fitted to just six well-established experimental parameters, we predict the $s$-wave $n$-$^4$He phase shifts, scattering length $a^{1/2}_{n ^4\text{He}}(\text{NLO})=2.47(4\ \text{num.})~(17\ \text{theor.})~{\rm fm}$, and effective range $r^{1/2}_{n ^4\text{He}}(\text{NLO})=1.384(3\ \text{num.})~(211\ \text{theor.})~{\rm fm}$ in agreement with experiment. The apparent cutoff independence of our results is used to estimate the theoretical errors coming as an integral part of our final results.

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arXiv2022

Few nucleons scattering in pionless effective field theory

We present a comprehensive theoretical study of low-energy few nucleon scattering for systems with $A\leq 4$. To this end, we utilize pionless effective field theory, which we employ at next-to-leading order. We show that at this level the theory yields accurate predictions for the low-energy scattering parameters in all studied channels. These predictions are on par with the best experimental evaluations and the available theoretical calculations. We confirm the recent observation that a four-body force is needed at next-to-leading-order and find that for nuclear systems it only appears in a single spin-isospin channel.

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arXiv2022

Spectrum of light nuclei in a finite volume

Lattice quantum chromodynamics calculations of multi-baryon systems with physical quark masses would start a new age of ab initio predictions in nuclear physics. Performed on a finite grid, such calculations demand extrapolation of their finite volume numerical results to free-space physical quantities. Such extraction of the physical information can be carried out fitting effective field theories (EFTs) directly to the finite-volume results or utilizing the Lüscher free-space formula or its generalizations for extrapolating the lattice data to infinite volume. To understand better the effect of periodic boundary conditions on the binding energy of few nucleon systems we explore here light nuclei with physical masses in a finite box and in free space. The stochastic variational method is used to solve the few-body systems. Substantial optimizations of the method are introduced to enable efficient calculations in a periodic box. With the optimized code, we perform accurate calculations of light nuclei $A \le 4$ within leading order pionless EFT. Using Lüscher formula for the two-body system, and its generalization for 3- and 4-body systems, we examine the box effect and explore possible limitations of these formulas for the considered nuclear systems.

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arXiv2020

Extrapolating Lattice QCD Results using Effective Field Theory

Lattice simulations are the only viable way to obtain ab-initio Quantum Chromodynamics (QCD) predictions for low energy nuclear physics. These calculations are done, however, in a finite box and therefore extrapolation is needed to get the free space results. Here we use nuclear Effective Field Theory (EFT), designed to provide a low energy description of QCD using baryonic degrees of freedom, to extrapolate the lattice results from finite to infinite volumes. To this end, we fit the EFT to the results calculated with nonphysical high quark masses and solve it with the stochastic variational method in both finite and infinite volumes. Moreover, we perform similar EFT calculations of the physical point and predict the finite-volume effects to be found in future Lattice QCD calculations for atomic nuclei with mass number $A\le4$.

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arXiv2020

Universal Short Range Correlations in Bosonic Helium Clusters

Short-range correlations in bosonic Helium clusters, composed of $^4$He atoms, are studied utilizing the generalized contact formalism. The emergence of universal $n$-body short range correlations is formulated and demonstrated numerically via Monte Carlo simulations. The values of the $n$-particle contacts are evaluated for $n\le5$. In the thermodynamic limit, the two-body contact is extracted from available experimental measurements of the static structure factor of liquid $^4$He at high momenta, and found in a good agreement with the value extracted from our calculations.

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arXiv2020

Efimov physics beyond three particles

Efimov physics originally refers to a system of three particles. Here we review recent theoretical progress seeking for manifestations of Efimov physics in systems composed of more than three particles. Clusters of more than three bosons are tied to each Efimov trimer, but no independent Efimov physics exists there beyond three bosons. The case of a few heavy fermions interacting with a lighter atom is also considered, where the mass ratio of the constituent particles plays a significant role. Following Efimov's study of the (2+1) system, the (3+1) system was shown to have its own critical mass ratio to become Efimovian. We show that the (4+1) system becomes Efimovian at a mass ratio which is smaller than its sub-systems thresholds, giving a pure five-body Efimov effect. The (5+1) and (6+1) systems are also discussed, and we show the absence of 6- and 7-body Efimov physics there.

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arXiv2019

Removing the Wigner bound in non-perturbative effective field theory

The Wigner bound, setting an upper limit on the scattering effective range, is examined at different orders of contact effective field theory. Using cutoff regulator we show that the bound loosens when higher orders of the theory are considered. For a sharp and a Gaussian regulators, we conjecture an analytic formula for the dependence of the Wigner bound on the theory's order. It follows that the bound vanishes in the limit of infinite order. Using a concrete numerical example we demonstrate that the above surmise still holds after renormalization at finite cutoff. Studying the 3-body system with this example, we have found that limiting the permissible range of cutoffs by the Wigner bound, we avoid the Thomas collapse, and don't need to promote the 3-body force to leading order.

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arXiv2019

Four-Body Scale in Universal Few-Boson Systems

The role of an intrinsic four-body scale in universal few-boson systems is the subject of active debate. We study these systems within the framework of effective field theory. For systems of up to six bosons we establish that no four-body scale appears at leading order (LO). However, we find that at next-to-leading (NLO) order a four-body force is needed to obtain renormalized results for binding energies. With the associated parameter fixed to the binding energy of the four-boson system, this force is shown to renormalize the five- and six-body systems as well. We present an original ansatz for the short-distance limit of the bosonic $A$-body wave function from which we conjecture that new $A$-body scales appear at N$^{A-3}$LO. As a specific example, calculations are presented for clusters of helium atoms. Our results apply more generally to other few-body systems governed by a large scattering length, such as light nuclei and halo states, the low-energy properties of which are independent of the detailed internal structure of the constituents.

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arXiv2018

Stable p-wave resonant two-dimensional Fermi-Bose dimers

We consider two-dimensional weakly-bound heterospecies molecules formed in a Fermi-Bose mixture with attractive Fermi-Bose and repulsive Bose-Bose interactions. Bosonic exchanges lead to an intermolecular attraction, which can be controlled and tuned to a p-wave resonance. Such attractive fermionic molecules can be realized in quasi-two-dimensional ultracold isotopic or heteronuclear mixtures. We show that they are stable with respect to the recombination to deeply-bound molecular states and with respect to the formation of higher-order clusters (trimers, tetramers, etc.)

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arXiv2018

Energy of N two-dimensional bosons with zero-range interactions

We derive an integral equation describing $N$ two-dimensional bosons with zero-range interactions and solve it for the ground state energy $B_N$ by applying a stochastic diffusion Monte Carlo scheme for up to 26 particles. We confirm and go beyond the scaling $B_N\propto 8.567^N$ predicted by Hammer and Son [Phys. Rev. Lett. {\bf 93}, 250408 (2004)] in the large-$N$ limit.

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arXiv2017

Onset of $η$ nuclear binding

Recent studies of $η$ nuclear quasibound states by the Jerusalem-Prague Collaboration are reviewed, focusing on stochastic variational method self consistent calculations of $η$ few-nucleon systems. These calculations suggest that a minimum value Re$\,a_{ηN} \approx 1$ fm (0.7 fm) is needed to bind $η\,^3$He ($η\,^4$He).

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arXiv2017

Mass-imbalanced fermionic mixture in a harmonic trap

The mass-imbalanced fermionic mixture is studied, where $N\le5$ identical fermions interact resonantly with an impurity, a distinguishable atom. The shell structure is explored, and the physics of a dynamic light-impurity is shown to be different from that of the static heavy-impurity case. The energies in a harmonic trap at unitarity are calculated and extrapolated to the zero-range limit. In doing so, the scaling factor of the ground state, as well as of a few excited states, is calculated. In the $2 \le N \le 4$ systems, pure $(N+1)$ Efimov states exist for large enough mass ratio. However, no sign for a six-body Efimov state in the $(5+1)$ system is found in the mass ratio explored, $M/m \le 12$.

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arXiv2017

Five-Body Efimov Effect and Universal Pentamer in Fermionic Mixtures

We show that four heavy fermions interacting resonantly with a lighter atom (4+1 system) become Efimovian at mass ratio 13.279(2), which is smaller than the corresponding 2+1 and 3+1 thresholds. We thus predict the five-body Efimov effect for this system in the regime where any of its subsystem is non- Efimovian. For smaller mass ratios we show the existence and calculate the energy of a universal 4+1 pentamer state, which continues the series of the 2+1 trimer predicted by Kartavtsev and Malykh and 3+1 tetramer discovered by Blume. We also show that the effective-range correction for the light-heavy interaction has a strong effect on all these states and larger effective ranges increase their tendency to bind.

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arXiv2016

Effective Field Theory for Few-Boson Systems

We study universal bosonic few-body systems within the framework of effective field theory at leading order (LO). We calculate binding energies of systems of up to six particles and the atom-dimer scattering length. Convergence to the limit of zero-range two- and three-body interactions is shown, indicating that no additional few-body interactions need to be introduced at LO. Generalizations of the Tjon line are constructed, showing correlations between few-body binding energies and the binding energy of the trimer, for a given dimer energy. As a specific example, we implement our theory for 4He atomic systems, and show that the results are in surprisingly good agreement with those of sophisticated 4He-4He potentials. Potential implications for the convergence of the EFT expansion are discussed.

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