(a) Capture of a neutron on ( ) forms the compound nucleus ( , a closed neutron…

PHYSICS · Subjective · Fermi University Physics · Nuclear Physics · Radiation interactions, detection and dosimetry · Nuclear reactions

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

Problem

(a) Capture of a neutron on

^{87}\mathrm{Sr}

(

N=49

) forms the compound nucleus

^{88}\mathrm{Sr}

(

N=50

, a closed neutron shell), while capture on

^{88}\mathrm{Sr}

(

N=50

) forms

^{89}\mathrm{Sr}

(

N=51

, one neutron outside the closed shell). Using the level-density parameter

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

and the effective excitation energies (separation energy less pairing correction)

U_1 = 10.0\,\mathrm{MeV}

for

^{88}\mathrm{Sr}

and

U_2 = 5.0\,\mathrm{MeV}

for

^{89}\mathrm{Sr}

, estimate the ratio

\rho_{\rm lev}(U_1)/\rho_{\rm lev}(U_2)

from

\rho_{\rm lev}(U)\propto U^{-5/4}\exp(2\sqrt{a_{\rm ld}U})

, and state which target,

^{87}\mathrm{Sr}

^{88}\mathrm{Sr}

, has the larger Maxwellian-averaged capture cross section at

k_BT=30\,\mathrm{keV}

. (b) A shielded neutron detector near a reactor records a fluence rate of

2\,\mathrm{MeV}

neutrons of

\phi = 5.0\times10^{4}\,\mathrm{cm^{-2}\,s^{-1}}

. The tissue kerma coefficient at this energy is

k = 8.0\times10^{-12}\,\mathrm{Gy\,cm^2}

, and the radiation weighting factor there is

w_R = 15

. Assuming charged-particle equilibrium, so that the absorbed dose rate equals the kerma rate, compute the equivalent dose rate in

\mathrm{mSv\,h^{-1}}