Struct ScatteringTable 

pub struct ScatteringTable { /* private fields */ }

Precomputed centre-of-mass scattering angle theta(eps, beta).

The table stores y = ln tan(theta/2) on a grid uniform in ln eps and ln beta, and interpolates bilinearly in those coordinates. y is close to linear in ln beta at both ends (tan(theta/2) ~ 1/beta as beta -> 0, and theta ~ beta^-k for large beta), which is what makes bilinear interpolation accurate. Since d theta = sin(theta) dy, an error dy in the table value is at most dy radians in theta.

The angle depends on (eps, beta) and on the screening function only; Z1, Z2 and the screening length enter through the reduced variables. The table keeps its Potential so one table serves one (Z1, Z2, potential) pair and converts to and from SI. It is built once and shared read-only (&ScatteringTable is Sync).

Error bound

At build time the interpolation error against direct quadrature is measured at cell centres (where bilinear interpolation error peaks) on a deterministic subset of cells. ScatteringTable::max_abs_error is the largest absolute error in theta seen (radians) and ScatteringTable::max_rel_error the largest relative error where theta > 1e-6. These are empirical bounds from sampling, not proofs.

Outside the grid: beta >= beta_max returns 0.0; beta < beta_min is clamped to beta_min; eps outside [eps_min, eps_max] returns None.

Implementations

impl ScatteringTable

pub fn build(potential: &Potential, spec: &TableSpec) -> Self

Build a table by direct quadrature. Serial and deterministic.

pub fn potential(&self) -> &Potential

The potential this table was built for.

pub fn spec(&self) -> &TableSpec

The grid specification.

pub fn max_abs_error(&self) -> f64

Largest absolute theta error (radians) found against quadrature at sampled cell centres.

pub fn max_rel_error(&self) -> f64

Largest relative theta error found at sampled cell centres where theta > 1e-6.

pub fn theta(&self, eps: f64, beta: f64) -> Option<f64>

Interpolated centre-of-mass angle (radians), or None if eps is out of the tabulated range.

pub fn half_angle_tan(&self, eps: f64, beta: f64) -> Option<f64>

Interpolated tan(theta / 2) (the stored quantity is its logarithm), or None if eps is out of the tabulated range; 0.0 for beta >= beta_max. ScatteringTable::theta is 2 atan of this.

The collision code needs sin and cos of theta / 2 (energy transfer, lab angles), which follow from the tangent by algebra, so it avoids the atan here and the trigonometric calls that would undo it.

pub fn shape(&self) -> (usize, usize)

Number of grid points in (eps, beta).

Trait Implementations

impl Clone for ScatteringTable

fn clone(&self) -> ScatteringTable

Returns a duplicate of the value.

fn clone_from(&mut self, source: &Self)

Performs copy-assignment from source.

impl Debug for ScatteringTable

fn fmt(&self, f: &mut Formatter<'_>) -> Result

Formats the value using the given formatter.