arXiv subjects

Serdar Elhatisari

Publications and source records attributed to Serdar Elhatisari.

54 records · Page 3Linked to original sources

arXiv2021

Hidden spin-isospin exchange symmetry

The strong interactions among nucleons have an approximate spin-isospin exchange symmetry that arises from the properties of quantum chromodynamics in the limit of many colors, $N_c$. However this large-$N_c$ symmetry is well hidden and reveals itself only when averaging over intrinsic spin orientations. Furthermore, the symmetry is obscured unless the momentum resolution scale is close to an optimal scale that we call $Λ_{{\rm large-}N_c}$. We show that the large-$N_c$ derivation requires a momentum resolution scale of $Λ_{{\rm large-}N_c} \sim 500$ MeV. We derive a set of spin-isospin exchange sum rules and discuss implications for the spectrum of $^{30}$P and applications to nuclear forces, nuclear structure calculations, and three-nucleon interactions.

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arXiv2020

Ab initio nuclear thermodynamics

We propose a new Monte Carlo method called the pinhole trace algorithm for {\it ab initio} calculations of the thermodynamics of nuclear systems. For typical simulations of interest, the computational speedup relative to conventional grand-canonical ensemble calculations can be as large as a factor of one thousand. Using a leading-order effective interaction that reproduces the properties of many atomic nuclei and neutron matter to a few percent accuracy, we determine the location of the critical point and the liquid-vapor coexistence line for symmetric nuclear matter with equal numbers of protons and neutrons. We also present the first {\it ab initio} study of the density and temperature dependence of nuclear clustering.

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arXiv2019

Essential elements for nuclear binding

How does nuclear binding emerge from first principles? Our current best understanding of nuclear forces is based on a systematic low-energy expansion called chiral effective field theory. However, recent {\it ab initio} calculations of nuclear structure have found that not all chiral effective field theory interactions give accurate predictions with increasing nuclear density. In this letter we address the reason for this problem and the first steps toward a solution. Using nuclear lattice simulations, we deduce the minimal nuclear interaction that can reproduce the ground state properties of light nuclei, medium-mass nuclei, and neutron matter simultaneously with no more than a few percent error in the energies and charge radii. We find that only four parameters are needed. With these four parameters one can accurately describe neutron matter up to saturation density and the ground state properties of nuclei up to calcium. Given the absence of sign oscillations in these lattice Monte Carlo simulations and the mild scaling of computational effort scaling with nucleon number, this work provides a pathway to high-quality simulations in the future with as many as one or two hundred nucleons.

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arXiv2019

Adiabatic projection method with Euclidean time subspace projection

Euclidean time projection is a powerful tool that uses exponential decay to extract the low-energy information of quantum systems. The adiabatic projection method, which is based on Euclidean time projection, is a procedure for studying scattering and reactions on the lattice. The method constructs the adiabatic Hamiltonian that gives the low-lying energies and wave functions of two-cluster systems. In this paper we seek the answer to the question whether an adiabatic Hamiltonian constructed in a smaller subspace of the two-cluster state space can still provide information on the low-lying spectrum and the corresponding wave functions. We present the results from our investigations on constructing the adiabatic Hamiltonian using Euclidean time projection and extracting details of the low-energy spectrum and wave functions by diagonalizing it. In our analyses we consider systems of fermion-fermion and fermion-dimer interacting via a zero-range attractive potential in one dimension, and fermion-fermion interacting via an attractive Gaussian potential in three dimensions. The results presented here provide a guide for improving the adiabatic projection method and for reducing the computational costs of large-scale calculations of \emph{ab initio} nuclear scattering and reactions using Monte Carlo methods.

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arXiv2019

Galilean invariance restoration on the lattice

We consider the breaking of Galilean invariance due to different lattice cutoff effects in moving frames and a nonlocal smearing parameter which is used in the construction of the nuclear lattice interaction. The dispersion relation and neutron-proton scattering phase shifts are used to investigate the Galilean invariance breaking effects and ways to restore it. For $S$-wave channels, ${}^1S_0$ and ${}^3S_1$, we present the neutron-proton scattering phase shifts in moving frames calculated using both Lüscher's formula and the spherical wall method, as well as the dispersion relation. For the $P$ and $D$ waves, we present the neutron-proton scattering phase shifts in moving frames calculated using the spherical wall method. We find that the Galilean invariance breaking effects stemming from the lattice artifacts partially cancel those caused by the nonlocal smearing parameter. Due to this cancellation, the Galilean invariance breaking effect is small, and the Galilean invariance can be restored by introducing Galilean invariance restoration operators.

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arXiv2018

Neutron-proton scattering with lattice chiral effective field theory at next-to-next-to-next-to-leading order

We present a new lattice formulation of chiral effective field theory interactions with a simpler decomposition into spin channels. With these interactions the process of fitting to the empirical scattering phase shifts is simplified, and the resulting lattice phase shifts are more accurate than in previous studies. We present results for the neutron-proton system up to next-to-next-to-next-to-leading order for lattice spacings of $1.97$, $1.64$, $1.32$, and $0.99~{\rm fm}$. Our results provide a pathway to $\textit{ab initio}$ lattice calculations of nuclear structure, reactions, and thermodynamics with accurate and systematic control over the chiral nucleon-nucleon force.

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arXiv2018

Lattice calculations for two-component fermion systems with unequal masses: one dimension

We consider systems of two-component fermions with unequal masses and interacting via a short-range attractive potential. We discuss the case where the two-component fermions form a shallow dimer with large scattering length. The three-fermion and four-fermion systems with such properties are universal and charazteried by the two-fermion scattering length $a_{\text{ff}}$ and the ratio of the mass of spin-$\uparrow$ fermion to the mass of spin-$\downarrow$ fermion, $m_{\uparrow}/m_{\downarrow}$. In this study using lattice effective field theory we analyze fermion-dimer and dimer-dimer systems, and calculate the universal fermion-dimer and dimer-dimer scattering lengths for various values of the mass ratio $m_{\uparrow}/m_{\downarrow}$. We find that these universal scattering lengths increase logarithmically with the mass ratio $m_{\uparrow}/m_{\downarrow}$.

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arXiv2018

The Tjon Band in Nuclear Lattice Effective Field Theory

We explore the lattice spacing dependence in Nuclear Lattice Effective Field Theory for few-body systems up to next-to-next-to leading order in chiral effective field theory including all isospin breaking and electromagnetic effects, the complete two-pion-exchange potential and the three-nucleon forces. We calculate phase shifts in the neutron-proton system and proton-proton systems as well as the scattering length in the neutron-neutron system. We then perform a full next-to-next-to-leading order calculation with two-nucleon and three-nucleon forces for the triton and helium-4 and analyse their binding energy correlation. We show how the Tjon band is reached by decreasing the lattice spacing and confirm the continuum observation that a four-body force is not necessary to describe light nuclei.

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arXiv2017

Ab initio calculations of the isotopic dependence of nuclear clustering

Nuclear clustering describes the appearance of structures resembling smaller nuclei such as alpha particles (4He nuclei) within the interior of a larger nucleus. While clustering is important for several well-known examples, much remains to be discovered about the general nature of clustering in nuclei. In this letter we present lattice Monte Carlo calculations based on chiral effective field theory for the ground states of helium, beryllium, carbon, and oxygen isotopes. By computing model-independent measures that probe three- and four-nucleon correlations at short distances, we determine the shape of the alpha clusters and the entanglement of nucleons comprising each alpha cluster with the outside medium. We also introduce a new computational approach called the pinhole algorithm, which solves a long-standing deficiency of auxiliary-field Monte Carlo simulations in computing density correlations relative to the center of mass. We use the pinhole algorithm to determine the proton and neutron density distributions and the geometry of cluster correlations in 12C, 14C, and 16C. The structural similarities among the carbon isotopes suggest that 14C and 16C have excitations analogous to the well-known Hoyle state resonance in 12C.

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arXiv2017

Universal dimer-dimer scattering in lattice effective field theory

We consider two-component fermions with short-range interactions and large scattering length. This system has universal properties that are realized in several different fields of physics. In the limit of large fermion-fermion scattering length $a_\mathrm{ff}$ and zero-range interaction, all properties of the system scale proportionally with $a_\mathrm{ff}$. For the case with shallow bound dimers, we calculate the dimer-dimer scattering phase shifts using lattice effective field theory. We extract the universal dimer-dimer scattering length $a_\mathrm{dd}/a_\mathrm{ff}=0.618(30)$ and effective range $r_\mathrm{dd}/a_\mathrm{ff}=-0.431(48)$. This result for the effective range is the first calculation with quantified and controlled systematic errors. We also benchmark our methods by computing the fermion-dimer scattering parameters and testing some predictions of conformal scaling of irrelevant operators near the unitarity limit.

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arXiv2016

Nuclear binding near a quantum phase transition

How do protons and neutrons bind to form nuclei? This is the central question of ab initio nuclear structure theory. While the answer may seem as simple as the fact that nuclear forces are attractive, the full story is more complex and interesting. In this work we present numerical evidence from ab initio lattice simulations showing that nature is near a quantum phase transition, a zero-temperature transition driven by quantum fluctuations. Using lattice effective field theory, we perform Monte Carlo simulations for systems with up to twenty nucleons. For even and equal numbers of protons and neutrons, we discover a first-order transition at zero temperature from a Bose-condensed gas of alpha particles (4He nuclei) to a nuclear liquid. Whether one has an alpha-particle gas or nuclear liquid is determined by the strength of the alpha-alpha interactions, and we show that the alpha-alpha interactions depend on the strength and locality of the nucleon-nucleon interactions. This insight should be useful in improving calculations of nuclear structure and important astrophysical reactions involving alpha capture on nuclei. Our findings also provide a tool to probe the structure of alpha cluster states such as the Hoyle state responsible for the production of carbon in red giant stars and point to a connection between nuclear states and the universal physics of bosons at large scattering length.

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arXiv2016

Nucleon-deuteron scattering using the adiabatic projection method

In this paper we discuss the adiabatic projection method, a general framework for scattering and reaction calculations on the lattice. We also introduce several new techniques developed to study nucleus-nucleus scattering and reactions on the lattice. We present technical details of the method for large-scale problems. To estimate the systematic errors of the calculations we consider simple two-particle scattering on the lattice. Then we benchmark the accuracy and efficiency of the numerical methods by applying these to calculate fermion-dimer scattering in lattice effective field theory with and without a long-range Coulomb potential. The fermion-dimer calculations correspond to neutron-deuteron and proton-deuteron scattering in the spin-quartet channel at leading order in the pionless effective field theory.

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arXiv2015

Scattering cluster wave functions on the lattice using the adiabatic projection method

The adiabatic projection method is a general framework for studying scattering and reactions on the lattice. It provides a low-energy effective theory for clusters which becomes exact in the limit of large Euclidean projection time. Previous studies have used the adiabatic projection method to extract scattering phase shifts from finite periodic-box energy levels using Lüschers method. In this paper we demonstrate that scattering observables can be computed directly from asymptotic cluster wave functions. For a variety of examples in one and three spatial dimensions, we extract elastic phase shifts from asymptotic cluster standing waves corresponding to spherical wall boundary conditions. We find that this approach of extracting scattering wave functions from the adiabatic Hamiltonian to be less sensitive to small stochastic and systematic errors as compared with using periodic-box energy levels.

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arXiv2015

Ab initio alpha-alpha scattering

Processes involving alpha particles and alpha-like nuclei comprise a major part of stellar nucleosynthesis and hypothesized mechanisms for thermonuclear supernovae. In an effort towards understanding alpha processes from first principles, we describe in this letter the first ab initio calculation of alpha-alpha scattering. We use lattice effective field theory to describe the low-energy interactions of nucleons and apply a technique called the adiabatic projection method to reduce the eight-body system to an effective two-cluster system. We find good agreement between lattice results and experimental phase shifts for S-wave and D-wave scattering. The computational scaling with particle number suggests that alpha processes involving heavier nuclei are also within reach in the near future.

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arXiv2014

Fermion-dimer scattering using an impurity lattice Monte Carlo approach and the adiabatic projection method

We present lattice Monte Carlo calculations of fermion-dimer scattering in the limit of zero-range interactions using the adiabatic projection method. The adiabatic projection method uses a set of initial cluster states and Euclidean time projection to give a systematically improvable description of the low-lying scattering cluster states in a finite volume. We use Lüscher's finite-volume relations to determine the s-wave, p-wave, and d-wave phase shifts. For comparison, we also compute exact lattice results using Lanczos iteration and continuum results using the Skorniakov-Ter-Martirosian equation. For our Monte Carlo calculations we use a new lattice algorithm called impurity lattice Monte Carlo. This algorithm can be viewed as a hybrid technique which incorporates elements of both worldline and auxiliary-field Monte Carlo simulations.

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arXiv2014

Low Energy Continuum and Lattice Effective Field Theories

In the first part of the thesis we consider the constraints of causality and unitarity for particles interacting via strictly finite-range interactions. We generalize Wigner's causality bound to the case of non-vanishing partial-wave mixing. Specifically we analyze the system of the low-energy interactions between protons and neutrons. We also analyze low-energy scattering for systems with arbitrary short-range interactions plus an attractive $1/r^α$ tail for $α\geq2$. In particular, we focus on the case of $α=6$ and we derive the constraints of causality and unitarity also for these systems and find that the van der Waals length scale dominates over parameters characterizing the short-distance physics of the interaction. This separation of scales suggests a separate universality class for physics characterizing interactions with an attractive $1/r^{6}$ tail. We argue that a similar universality class exists for any attractive potential $1/r^α$ for $α\geq2$. In the second part of the thesis we present lattice Monte Carlo calculations of fermion-dimer scattering in the limit of zero-range interactions using the adiabatic projection method. The adiabatic projection method uses a set of initial cluster states and Euclidean time projection to give a systematically improvable description of the low-lying scattering cluster states in a finite volume. We use Lüscher's finite-volume relations to determine the $s$-wave, $p$-wave, and $d$-wave phase shifts. For comparison, we also compute exact lattice results using Lanczos iteration and continuum results using the Skorniakov-Ter-Martirosian equation. For our Monte Carlo calculations we use a new lattice algorithm called impurity lattice Monte Carlo. This algorithm can be viewed as a hybrid technique which incorporates elements of both worldline and auxiliary-field Monte Carlo simulations.

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arXiv2013

Causality, universality, and effective field theory for van der Waals interactions

We analyze low-energy scattering for arbitrary short-range interactions plus an attractive 1/r^6 tail. We derive the constraints of causality and unitarity and find that the van der Waals length scale dominates over parameters characterizing the short-distance physics of the interaction. This separation of scales suggests a separate universality class for physics characterizing interactions with an attractive 1/r^6 tail. We argue that a similar universality class exists for any attractive potential 1/r^{alpha} for alpha >= 2. We also discuss the extension to multi-channel systems near a magnetic Feshbach resonance. We discuss the implications for effective field theory with attractive singular power law tails.

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arXiv2012

Causality bounds for neutron-proton scattering

We consider the constraints of causality and unitarity for the low-energy interactions of protons and neutrons. We derive a general theorem that non-vanishing partial-wave mixing cannot be reproduced with zero-range interactions without violating causality or unitarity. We define and calculate interaction length scales which we call the causal range and the Cauchy-Schwarz range for all spin channels up to J = 3. For some channels we find that these length scales are as large as 5 fm. We investigate the origin of these large lengths and discuss their significance for the choice of momentum cutoff scales in effective field theory and universality in many-body Fermi systems.

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