# How to excite high spin nuclear state from ground state?

For example, the ground state of a nuclei is $0^+$, and we can excite $1^-$ state with a circular polarized gamma photon, which has a spin angular momentum $1\hbar$. This satisfies the selection rule for E1 (electric dipole) transition.

However, if we want a high spin state, say $2^+$, excited from the ground state, and since we need a photon who carries $2\hbar$ angular momentum to satisfy the angular momentum conservation, what kind of gamma photons is that? I know the decay from $2^+$ to $0^+$ can be an E2 (electric quadruple) transition, but is that quadruple gamma field needed for the same excitation, or we can just use a normal gamma beam?

## 1 Answer

Most high-spin spectroscopy is done on nuclei created in collisions. The volume of phase space for a beam-target or beam-beam collision to be exactly head-on is very small, so in the rest frame of the collision there is always some angular momentum; that angular momentum may be carried after the collision by rapidly-spinning daughter nuclei. A useful homework problem is to take your favorite heavy-nucleus accelerator, make some assumptions about the ratio of the impact parameter to the nuclear radius, and estimate the angular momentum involved in a collision. (The answer at RHIC.)

You can also populate high-spin states in the excited daughter products of decays and fissions.

I'm not aware of any experiment that has produced an ingoing quadrupole gamma ray field; I'm not sure that's a thing.

• Plane waves naturally include all multipole components, with an excitation rate of the order of $(a/\lambda)^\ell$ for a system of size $a$. With optical radiation this is possible (octupole example). Nuclear transitions have a smaller system size, but the wavelength can also be much shorter - at 200 MeV the wavelength is ~1 fm, so as you approach that range quadrupole and higher multipoles become more naturally accessible? – Emilio Pisanty Dec 8 '17 at 23:17
• A lot of Couloumb interaction, particularly for low-level stages. This conference paper iopscience.iop.org/article/10.1088/1742-6596/322/1/012004/pdf contains useful information. – ZeroTheHero Dec 9 '17 at 3:31