(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

^{207}\mathrm{Pb}

(

N=125

) forms the compound nucleus

^{208}\mathrm{Pb}

(

N=126

, a closed neutron shell), for which the measured neutron separation energy is

S_n = 7.368\,\mathrm{MeV}

. Capture on

^{208}\mathrm{Pb}

itself forms

^{209}\mathrm{Pb}

(

N=127

, one neutron outside the closed shell), for which

S_n = 3.937\,\mathrm{MeV}

. Using the level-density parameter

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

, and the pairing shift

2\Delta = 24/\sqrt{A}\,\mathrm{MeV}

for the even-even compound nucleus

^{208}\mathrm{Pb}

and

\Delta = 12/\sqrt{A}\,\mathrm{MeV}

for the odd-

A

compound nucleus

^{209}\mathrm{Pb}

, compute the effective excitation energies,

U=S_n-2\Delta

and

U=S_n-\Delta

, for the two nuclei and estimate the ratio

\rho_{\rm lev}(U_{208})/\rho_{\rm lev}(U_{209})

from

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

. State which target,

^{207}\mathrm{Pb}

^{208}\mathrm{Pb}

, has the larger Maxwellian-averaged capture cross section at

k_BT=30\,\mathrm{keV}

, consistent with the measured value of

0.36\,\mathrm{mb}

quoted for

^{208}\mathrm{Pb}

. (b) A worker stands in a thermal-neutron beam of fluence rate

\phi = 1.0\times10^{6}\,\mathrm{cm^{-2}\,s^{-1}}

. The tissue kerma coefficient for thermal neutrons is

k=2.0\times10^{-12}\,\mathrm{Gy\,cm^2}

and the radiation weighting factor for thermal neutrons is

w_R = 2.5

. Assuming charged-particle equilibrium, compute the equivalent dose rate in

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