Nuclear Electromagnetic Moments Electric Multipoles The electric energy

Nuclear Electromagnetic Moments

Electric Multipoles • The electric energy associated with the electric charge distribution in the nucleus is determined by the interaction of the nuclear charge distribution with electric fields.

Parity of Vn goes as (-1)n

QM Analog for the Nucleus • Vn is the multipole operator of order n • is the nuclear wave function • For all fixed-parity states, the contribution from all odd multipole operators is zero!

Electric Multipole Moments • All odd electric multipole moments must vanish for stationary states (e. g. , nuclei, nucleons, etc. ) • Therefore, nuclei must not have – Electric dipole moments (n = 1) – Electric octupole moments (n = 3) – Etc… • Search for electric dipole moment for neutron

Electric Multipole Moments • In more general terms - • All odd electric multipole moments must vanish if the nuclear system is time-reversible - i. e. , if it obeys time reversal symmetry. • Find an electric dipole moment for neutron implies time reversal symmetry violation!

Magnetic Multipole Moments • Classically, a circulating current induces a magnetic dipole moment - • where A is the area enclosed by i. • If i is due to a single charge e moving with velocity v, we get --

Magnetic Multipole Moments • If i is due to a single charge e moving with velocity v, we get --

• In the QM regime, this becomes --

g-factors For the proton For the neutron

g-factors For the electron For the proton For the neutron