The mass excesses of Be, Be and the neutron are

PHYSICS · Multi-part · Fermi University Physics · Nuclear Physics · Nuclear constituents, size and binding · Nuclear reactions

The Nucleus Resolved, Ch Beams and the edges of the chart: emittance, heavy ions, high spin and the drip lines

Problem

The mass excesses of

^{11}

Be,

^{10}

Be and the neutron are

\Delta(^{11}\mathrm{Be}) = 20.174\,\mathrm{MeV}

\Delta(^{10}\mathrm{Be}) = 12.607\,\mathrm{MeV}

and

\Delta(n) = 8.071\,\mathrm{MeV}

. The ground state of

^{11}

Be places its last neutron in a

2s_{1/2}

(

\ell = 0

) orbital outside a

^{10}

Be core. A group proposes to measure this state by Coulomb-exciting a

^{11}

Be beam on a

^{208}

Pb target. Take

R = 1.3(A_1^{1/3}+A_2^{1/3})\,\mathrm{fm}

for the sum of radii,

\hbar c = 197.327\,\mathrm{MeV\,fm}

e^2/4\pi\epsilon_0 = 1.43996\,\mathrm{MeV\,fm}

and

m_nc^2 = 939.565\,\mathrm{MeV}

. ((a)) Use the mass excesses to find the one-neutron separation energy

S_n

^{11}

Be. ((b)) Using the exponential-tail argument for a low-

\ell

bound neutron outside a core, estimate the rms distance of the tail alone from the

^{10}

Be core. ((c)) Compute the bare Coulomb barrier

B_C

(centre-of-mass frame) for

^{11}

Be on

^{208}

Pb, and the maximum laboratory beam energy that keeps the head-on distance of closest approach at least

5\,\mathrm{fm}

beyond

R

, the condition for pure Coulomb excitation.