Four isotopes on the s-process path are given idealised neutron-capture cross…

PHYSICS · Multi-part · Fermi University Physics · Nuclear Physics · Nuclear astrophysics and applications · Nuclear astrophysics and applications

Stars from the Inside, Ch Thermonuclear energy generation: reaction rates, burning stages and the elements they make

Problem

Four isotopes on the s-process path are given idealised neutron-capture cross sections

\sigma

(in millibarn, at the relevant thermal energy) and relative abundances

N

(arbitrary units). The values are round illustrative numbers, not measurements. Data (isotope, neutron number,

\sigma

N

{}^{88}\mathrm{Sr}

50

5\,\mathrm{mb}

200

;

{}^{96}\mathrm{Zr}

56

50\,\mathrm{mb}

20

;

{}^{140}\mathrm{Ce}

82

20\,\mathrm{mb}

50

;

{}^{150}\mathrm{Sm}

88

100\,\mathrm{mb}

10

. ((a)) Check that these four isotopes obey the steady-flow rule

\sigma_A N_A \approx \text{constant}

, and state the value of that constant. ((b))

{}^{208}\mathrm{Pb}

(

N_{\rm neutrons}=126

) is given, on the same illustrative scale, a cross section

\sigma = 2\,\mathrm{mb}

. Using the same constant, predict its relative abundance, and say why this isotope, together with

{}^{88}\mathrm{Sr}

, sits at an abundance peak.