← nuclearjs nuclide chart elastic scattering →

ΔE–E telescope

Two silicon detectors in a row. The thin one samples the energy loss, which grows as z²/v²; the thick one stops the particle and takes the rest. Each species falls on its own band.

Detectors (silicon)

ΔE

FWHM

Source

E max

Every species uniform in energy from 0 to E max: the whole band, from particles that stop in ΔE to particles that pass through E.

events

Rendering

To scale along the beam axis: the two silicon thicknesses and the 1 mm ruler. Not to scale: the gap between the detectors, the detector faces, the circuit boards, collimator, chamber and all distances; the hardware is generic, not a particular make. The silicon is drawn see-through so the tracks inside it show. Each track's brightness and width follow the computed dE/dx along it and it stops at the computed range; its speed is slowed for display, in proportion to the true velocity.

Stopping powers: NIST PSTAR and ASTAR for silicon (Berger, Coursey, Zucker, Chang; ICRU Report 49 (1993); NISTIR 4999), ρ = 2.33 g/cm³. d and t from the proton table at the same velocity, S(E) = S_p(E m_p/m); ³He from the α table the same way; ^6,7Li from the α table at the same velocity times the squared ratio of Pierce–Blann mean charges, Phys. Rev. 173, 390 (1968). CSDA range integrated live; for p and α it reproduces the NIST range table to 0.04 % above 0.1 MeV.
Straggling: Bohr variance 4πe⁴z²N_e per unit length, carried through the slowing down to first order (Tschalär, Nucl. Instrum. Methods 61, 141 (1968)). Gaussian throughout: no Landau tail, no dead layers, no pulse-height defect, normal incidence. Each layer is sampled as a Gaussian residual range, which equals the first-order exit-energy Gaussian away from the stopping edge; near the edge an exit-energy Gaussian would be wider than the mean exit energy and the transmitted fraction would jump from 0 to ½ at the CSDA threshold, while the range form passes through it smoothly (½ exactly at the threshold, falling with the range straggling, about 0.9 µm for protons through 50 µm). That edge is still first order: the energies of the few particles that just get through (keV) are not modelled beyond it, and the Bohr width is too large below about 1 MeV/u.
Masses AME2020, levels and α lines ENSDF, via the IAEA LiveChart.

ΔE

target

beam →

1 mm

drag to orbit · scroll to zoom · depth axis to scale, faces and distances not