The r-process path sits where neutron capture and photodisintegration balance,

PHYSICS · Subjective · Fermi University Physics · Nuclear Physics · Nuclear astrophysics and applications · Nuclear astrophysics and applications

The Nucleus Resolved, Ch Stellar burning and the origin of the elements

Problem

(n,\gamma)\rightleftharpoons(\gamma,n)

, giving a neutron separation energy

S_n \approx k_BT\ln\!\left[\frac{2}{N_n\lambda_w^3}\right],\qquad \lambda_w^3=\left(\frac{2\pi\hbar^2}{m_nk_BT}\right)^{3/2},

where

N_n

is the free-neutron number density and

\lambda_w

is the neutron's thermal de Broglie wavelength. At

N_n=10^{23}\,\mathrm{cm^{-3}}

and

k_BT=100\,\mathrm{keV}

this gives

S_n\approx2.6\,\mathrm{MeV}

, putting the

N=82

waiting point at cadmium (

Z=48

). Predict the new value of

S_n

at the same temperature if the neutron density were a hundred times lower,

N_n = 10^{21}\,\mathrm{cm^{-3}}

, and state whether the path moves towards or away from the valley of stability.