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Ab initio alpha-alpha scattering
Serdar Elhatisari, Dean Lee, Gautam Rupak, Evgeny Epelbaum, Hermann Krebs, Timo A. Lähde, Thomas Luu, Ulf-G. Meißner
TL;DR
Alpha-process scattering remains difficult to calculate from first principles because computational costs grow with projectile size. The paper uses lattice effective field theory and adiabatic projection to compute 4He + 4He phase shifts, finding good agreement with experiment and favorable scaling for heavier alpha processes.
Problem
First-principles calculations of astrophysically important alpha processes remain challenging because computational scaling increases significantly for projectiles with more than a few nucleons.
Method
The study combines lattice effective field theory with adiabatic projection, which uses Euclidean time projection to construct an effective two-cluster Hamiltonian.
Results
The first ab initio 4He + 4He calculation produces S-wave and D-wave phase shifts in good agreement with experimental data.
Takeaways & Limitations
The roughly (A1 + A2)^2 scaling suggests that alpha processes involving heavier nuclei may be accessible with this approach.
Takeaways & Limitations
D-wave results show stronger systematic differences between even and odd Lt projections, which approach the results from opposite sides.
Abstract
from arXiv · showhide
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.
INTRODUCTION
Ab initio calculations for alpha processes remain challenging because computational costs grow sharply with projectile size. This work addresses that challenge with a lattice approach to 4He + 4He scattering and reports agreement with experiment for S-wave and D-wave phase shifts.
- Computational scaling increases significantly when the projectile nucleus contains more than a few nucleons.
- This limits first-principles studies of alpha processes relevant to stellar astrophysics and thermonuclear supernovae.
- The lattice calculation scales roughly as (A1 + A2)^2 for an A1-body + A2-body problem.The authors state that this scaling is mild enough to make first-principles alpha-process calculations possible.
- The study presents the first ab initio calculation of 4He + 4He scattering using lattice effective field theory and adiabatic projection.
- Lattice results agree well with experimental S-wave and D-wave phase shifts.
ADIABATIC PROJECTION METHOD
The adiabatic projection method converts lattice cluster states into an effective two-cluster description for scattering. It begins with separated alpha wave packets, projects them in Euclidean time, and constructs a radial adiabatic Hamiltonian that captures their interaction and polarization.
- The method uses Euclidean time projection, exp(−Hτ), to construct an effective two-cluster Hamiltonian.The underlying microscopic Hamiltonian is H, and practical calculations use discrete time steps.
- Initial two-alpha states are labeled by separation vector R and built from Gaussian wave packets that factorize at large separation.
- Spherical-harmonic projection replaces a large set of three-dimensional separation vectors with angular-momentum channels.The projected states have angular-momentum quantum numbers L and Lz.
- Euclidean evolution dresses the cluster states and automatically incorporates their induced deformation and polarization as they approach.
- Matrix elements of the microscopic Hamiltonian and a norm matrix for nonorthogonal dressed states define the radial adiabatic Hamiltonian.
- At large projection time, the adiabatic Hamiltonian reproduces the low-energy finite-volume spectrum of the microscopic Hamiltonian.For widely separated alpha clusters, it reduces to a two-cluster Hamiltonian with infinite-range interactions such as Coulomb forces.
LATTICE CALCULATIONS AND RESULTS
Lattice effective field theory calculations use projection-based cluster methods to extract alpha-alpha scattering phase shifts. The NNLO results show good agreement with experiment for both S-wave and D-wave scattering, while projection-time dependence introduces systematic effects.
- Lattice method: The calculation combines projection Monte Carlo with auxiliary fields and updates both auxiliary-field configurations and alpha-cluster positions.
- Lattice method: The radial adiabatic Hamiltonian is extended from lattice calculations to a 120 fm box by adding the Coulomb interaction between otherwise non-interacting alpha clusters.
- Phase-shift extraction: Phase shifts are extracted by imposing a hard spherical wall and solving standing-wave modes, with asymptotic radial-wave behavior providing an alternative extraction method.
- S-wave results: S-wave NLO and NNLO phase shifts are quite similar and both agree well with experimental data; error bands reflect variation with projection time steps Lt.
- S-wave results: At NNLO, the calculated 8Be ground state is bound only a small fraction of an MeV from threshold, while even- and odd-Lt results show systematic differences.
- D-wave results: NNLO D-wave phase shifts are in fairly good agreement with experiment, and Coulomb interactions plus higher-order corrections push the 2+ resonance energy upward.
SUMMARY AND OUTLOOK
The study presents the first ab initio 4He + 4He scattering calculation, finding agreement with experiment for S- and D-wave phase shifts and favorable scaling for heavier alpha processes.
- The calculation is the first ab initio treatment of 4He + 4He scattering using lattice effective field theory and adiabatic projection.
- S-wave phase shifts at NNLO are compared with experimental data.
- D-wave phase shifts at NLO and NNLO are compared with experimental data.
- The computational effort for A1-body + A2-body systems scales roughly as (A1 + A2)^2, supporting studies of heavier alpha processes.