Stable ( ) and (

PHYSICS · Multi-part · Fermi University Physics · Nuclear Physics · Nuclear reactions · Nuclear reactions

The Nucleus Resolved, Ch Neutrons: the reagent with no barrier

Problem

Stable

^{86}\mathrm{Sr}

(

N=48

) and

^{88}\mathrm{Sr}

(

N=50

, a closed neutron shell) both capture neutrons in a stellar neutron flux at

k_BT = 30\,\mathrm{keV}

. Neutron capture on

^{86}\mathrm{Sr}

forms

^{87}\mathrm{Sr}

with neutron separation energy

S_n(^{87}\mathrm{Sr}) = 8.43\,\mathrm{MeV}

; capture on

^{88}\mathrm{Sr}

forms

^{89}\mathrm{Sr}

with

S_n(^{89}\mathrm{Sr}) = 6.36\,\mathrm{MeV}

. Take the level-density parameter of each compound nucleus as

a_{\rm ld} = A/8\,\mathrm{MeV^{-1}}

and the level density as

\rho_{\rm lev}(U) \propto \exp(2\sqrt{a_{\rm ld}U})

. ((a)) State, with a one-sentence reason, which target is predicted to have the larger

30\,\mathrm{keV}

capture cross section. ((b)) Estimate the ratio of the two capture cross sections from the level densities at

S_n