An alpha-particle beam of laboratory kinetic energy is incident on a target ( , , )

PHYSICS · Subjective · Fermi University Physics · Quantum Mechanics · Scattering theory · Scattering theory

The Nucleus Resolved, Ch Reactions: four-vectors, amplitudes and partial waves

Problem

An alpha-particle beam of laboratory kinetic energy

T_\alpha = 20.0\,\mathrm{MeV}

is incident on a

^{40}\mathrm{Ca}

target (

m_\alpha = 4.002602\,\mathrm{u}

m(^{40}\mathrm{Ca}) = 39.962591\,\mathrm{u}

1\,\mathrm{u}c^2 = 931.494\,\mathrm{MeV}

). Take the nuclear radius as

R = 1.2\,A^{1/3}\,\mathrm{fm}

for

A=40

. Calculate the centre-of-mass wave number

k

and

kR

, and state the largest partial wave

\ell_{\max}

that contributes appreciably to the reaction.