Ab initio alpha–alpha scattering

Abstract

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.

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

“…Hence, a reliable extraction of its parameters is impossible without solving the three-body problem in a finite volume. Furthermore, a rapid advance of lattice nuclear simulations [51][52][53], as well as chiral effective field theories on the lattice [54][55][56][57], provide us with data that can be properly analyzed, if and only if the few-body dynamics in a finite volume is understood. Otherwise, the extraction of reaction rates, elastic and inelastic cross sections, etc.…”

Alpha particle clusters and their condensation in nuclear systems

“…momentum P of the α particle. Neglecting the weak dependence on the asymmetry, for P = 0 the density dependence of the Pauli blocking term W Pauli (n B ) = 4515.9 n B − 100935 n 2 B + 1202538 n 3 B (43) was found in [146]. In particular, the bound state is dissolved and merges with the continuum of scattering states at the Mott density n Mott B = 0.02917 fm −3 .…”

“…So, the shape of the ground state of 12 C is still an open question but a triangular form seems definitely a possibility. state, very accurately with a so-called ab initio lattice QMC approach starting from effective chiral field theory [42,43]. The sign problem has been circumvented exploiting the fact that SU(4) symmetry for the α particles is very well fulfilled.…”

“…Since the distance from the center of the lead core is now denoted by r, we have for r > r cluster the shift of the binding energy of the α-like cluster. Here, the Pauli blocking part has the form W Pauli [n B (r)] given above (43). For r < r cluster , the density of the core nucleus is larger than the Mott density so that no bound state is formed.…”

“…And the intensity of this type of studies does not seem to slow down. For example very recently ab initio studies for cluster states appeared both using the nuclear effective-fieldtheory (EFT) approaches [41,42,43,44] and the symplectic no-core shell model (NCSM) [45,46,47] as we will discuss later in the main text.…”