# Physical meaning of the multipolarity of gamma radiation

During my nuclear physics class, we talked about the multipolarity of gamma radiations but without going too much into the details, and I was wondering about the meaning of that, how can the radiation be electric or magnetic ?

• Multipolarity of gamma radiation Commented Mar 18 at 15:50
• @JohnRennie I have already read the wikipedia page but I still don't really understand why we call them electric and magnetic Commented Mar 18 at 15:55

Think of the nucleus as a distribution of charges, which come from the protons, and a distribution of currents, which result from the motion of protons inside the nucleus.

The oscillation of these charges is what causes the emission of electromagnetic radiation from the nucleus. Gamma radiation is electromagnetic radiation after all.

Now, the most basic example of a charge distribution that emits electromagnetic radiation is the electric dipole. Think of two point charges oscillating in the $$z$$-axis with some angular frequency $$\omega$$ for example. The most basic example of a magnetic moment is the one caused by a current in circular motion in the $$xy$$ plane.

From electromagnetism, we know that these distributions can be expanded in a series of multipoles. In nuclear physics, one can use the operator (from Wong):

$$O_{\lambda\mu} = \sum_{i=1}^{A} e(i) r_{i}^{\lambda} Y_{\lambda\mu}^{*}(\theta_{i}, \phi_{i})$$,

where $$e(i)=e$$ for protons and zero for neutrons ($$e = 1.6 \times 10^{-19}$$ C), $$A$$ is the mass number, $$Y_{\lambda\mu}(\theta, \phi)$$ are spherical harmonics, and $$r_{i}$$ is the position vector for each nulceon. This operator can be used to calculate electric transition probabilities and moments.

Similarly, for the magnetic multipole operator (arising from currents):

$$O_{\lambda\mu} = \mu_N \sum_{i=1}^{A} \left\{ \frac{2}{\lambda+1} \left[ g_l(i) \vec{l}(i) + g_s(i) \vec{s}(i) \right] \right\} \cdot \nabla_i \left[ r_{i}^{\lambda} Y_{\lambda\mu}^{*}(\theta_i, \phi_i) \right]$$,

where $$g_l(i) =1$$ for a proton and zero for a neutron, $$g_s(i)=5.586$$ for a proton and $$-3.826$$ for a neutron, $$\mu_N=3.1524512550(15) \times 10^{-8}$$ eV/T, and $$\vec{l}(i)$$, $$\vec{s}(i)$$ are the angular momentum and spin operators respectively.

Using these operators one can calculate electric and magnetic moments, as well as probabilities, and can interpret the nature of the gamma radiation.

To summarize, gamma radiation itself is not intrinsically electric or magnetic but can be understood in terms of electric and magnetic multipole moments arising from the nucleus's charge and current distributions.

The classification into electric and magnetic multipole radiation is a general feature of the multipole expansion of the far field of a radiator, it can even be discussed purely classical. The Wikipedia article on multipole radiation has much more details and explicit formlae for the first few terms for electromagnetic radiation.

The names come about, because the electric multipole radiation is emitted by an ideal electric multipole whose strength oscillates, while the magnetic multipole radiation is emitted by an pulsating ideal magnetic multipole (or a pulsating current). Both kinds of radiation show both electric an magnetic fields (as is required for propagation of electromagnetic fields in the vacuum), but their orientation relative to the axes of the dipole are changed (roughly, the roles of the electric and magnetic field are switched).

• I just mean the structure of far field here – not the emission process. (Although you can construct a classical emitter of higher multipole radiation – just put two dipole emitters of equal strength and in opposite next to each other). Commented Mar 19 at 23:24