The low-momentum-transfer expansion of a charge form factor,

PHYSICS · Multi-part · Fermi University Physics · Quantum Mechanics · Nuclear Physics · The nuclear force and nuclear models

The Nucleus Resolved, Ch The deuteron and what two nucleons do to each other

Problem

F(q^2)\approx 1-q^2\langle r^2\rangle/6

, determines a mean square radius, and a purely spherically symmetric (

L=0

) distribution has no preferred axis and so no quadrupole moment; that rule (an

L=0

state has zero electric quadrupole moment) was established for single-particle states. The deuteron,

J^\pi=1^+

, has a measured spectroscopic quadrupole moment

Q_{sp}=+0.286\,\mathrm{fm^2}

. ((a)) Using two-nucleon antisymmetry,

(-1)^{L+S+T}=-1

, and the deuteron's

T=0

(forced by its even

L

and

S=1

through the antisymmetry rule), list every term symbol

^{2S+1}L_J

with

S=1

T=0

that is consistent with

J=1

. ((b)) Explain, using the

L=0\Rightarrow

zero-quadrupole-moment rule, why an admixture beyond the lowest term symbol you found is required by the measured

Q_{sp}

, and identify the operator in the nucleon-nucleon force responsible for connecting the two term symbols while conserving

J

and parity.