Conventions and the clean-room position
Units
The library works in SI internally. At the input and output boundary the
units are in the key names: energies in eV (_ev), lengths in nm (_nm),
angles in degrees (_deg), densities in g/cm³. Electronic stopping cross
sections are reported per target atom, in the customary
eV·10⁻¹⁵ cm² (to_ev_1e15_cm2 converts from J m²).
Throughout the manual \( Z_1, M_1 \) are the atomic number and mass of the moving particle, \( Z_2, M_2 \) those of the target atom, \( E \) the laboratory kinetic energy, \( N \) the atom density, \( a_0 \) the Bohr radius, \( v_0 = \alpha c \) the Bohr velocity, and \( e^2 \) stands for \( e^2 / 4\pi\varepsilon_0 \). Physical constants are CODATA 2022 (Mohr et al. 2025).
Reduced variables
The collision models use the reduced variables of Lindhard, Scharff and Schiøtt (1963). With a screening length \( a \) (see Screening lengths):
\[ x = \frac{r}{a}, \qquad \beta = \frac{b}{a}, \qquad \varepsilon = \frac{a\, E_\mathrm{cm}}{Z_1 Z_2 e^2}, \qquad E_\mathrm{cm} = E \frac{M_2}{M_1 + M_2}, \]
with \( r \) the separation and \( b \) the impact parameter. In these variables the scattering angle depends only on \( (\varepsilon, \beta) \) and on the screening function.
Determinism
Every model is a pure function of its arguments. Random numbers come from a counter-based stream (ChaCha8) keyed on the run seed and the index of the primary history, so a run gives the same bits on one thread or many. A model page that introduces randomness says which draws it makes and in which order.
The clean-room position
lindhard implements published physics from the papers. It does not use the
code or the data of closed or copyleft programs (the tiers are set out in
CONTRIBUTING.md). In particular:
- No SRIM stopping tables, and nothing interpolated or fitted from one, and no ICRU stopping tables. Electronic stopping is computed from closed-form models; tabulated stopping enters only as a user-supplied table that carries its own provenance, and is never committed with SRIM- or ICRU-derived numbers.
- No ZBL stopping tables. The ZBL universal screening function (eight published coefficients) and the ZBL reduced nuclear stopping fit are used; the electronic stopping coefficient sets of the same book are not.
- Terms whose only published coefficients are tabulated (the Barkas term, shell corrections, multi-oscillator density-effect parameters, Chu and Yang-O’Connor-Wang straggling) are declined, and the declines are listed in Validity ranges and declined terms.
Every coefficient that enters the code as a number has a row in
docs/data-provenance.md
saying where it comes from and how far it has been verified. Where a value
has only been checked against a secondary source, its page says so.
How a model page is laid out
Each page has the same sections: what the model is, the equations, the
assumptions, the validity range, how to select it (the TOML key and the Rust
type), its verification status, and its references. New models start from
the template book/src/models/_template.md in the repository.
References
- J. Lindhard, M. Scharff, H. E. Schiøtt, Mat. Fys. Medd. Dan. Vid. Selsk. 33 (14) (1963).
- P. J. Mohr, D. B. Newell, B. N. Taylor, E. Tiesinga, Rev. Mod. Phys. 97, 025002 (2025), doi:10.1103/RevModPhys.97.025002 (CODATA 2022).
- D. J. Bernstein, ChaCha, a variant of Salsa20 (2008); J. K. Salmon, M. A. Moraes, R. O. Dror, D. E. Shaw, Proc. SC’11 (2011) (counter-based random streams).