Multipolarity of gamma radiation

Transitions between excited states (or excited states and the ground state) of a nuclide lead to the emission of gamma quanta. These can be classified according to their multipolarity . There are two types: electrical and magnetic multipole radiation (both are electromagnetic radiation ).

Electric dipole radiation. The dipole lies in the plane of the drawing, points vertically upwards and oscillates at about 1 Hz. The color shows the strength of the field that migrates outwards. The magnetic field lines are perpendicular to the plane of the drawing.

Electric dipole, quadrupole , octupole radiation (generally: 2 ^ℓ -polar radiation) are also called E1, E2, E3 radiation (generally: E: radiation).

Analogously, magnetic dipole, quadrupole, octupole: (generally 2 ^ℓ (in general: Mℓ radiation) as M1, M2, M3 Polstrahlung -Polstrahlung) referred to (see also: Hertzian dipole ).

There is no monopole radiation ( ). ${\ displaystyle \ ell = 0}$

In quantum mechanics , the angular momentum is quantized. The different multipole fields have different values of angular momentum: Eℓ radiation has angular momentum in units of ; analogously, Mℓ radiation has an angular momentum in units of . The law of conservation of angular momentum leads to selection rules , i. H. to rules which multipole radiation can take place in concrete transitions or not. ${\ displaystyle \ ell}$ ${\ displaystyle \ hbar}$ ${\ displaystyle \ ell}$ ${\ displaystyle \ hbar}$

A simple classic comparison: consider the image of the oscillating electric dipole. It creates outwardly migrating electric and magnetic field lines, which are coupled by Maxwell's equations . This system of field lines is then that of E1 radiation. Similar considerations apply to oscillating electrical or magnetic high-order multipole fields.

On the other hand, it is plausible that the multipolarity of the radiation can be inferred from the angular distribution of the emitted radiation.

Quantum numbers and selection rules for multipole radiation

Simplified decay scheme of ⁶⁰ Co, specifying the angular momentum and parities

The quantum state of a nuclide is described by its energy above the ground state, by its angular momentum and by its parity , i.e. i.e., through its behavior in the event of spatial reflection ( positive + or negative -). Since the spin of a nucleon is 1/2 and the orbital angular momentum is an integer, it can be an integer or half-integer (in units of ). ${\ displaystyle J}$ ${\ displaystyle J}$ ${\ displaystyle \ hbar}$

Electric and magnetic multipole radiation of the same order , d. H. Dipole or quadrupole radiation have the same orbital angular momentum (in units of ) but different parity. The following relationships apply to : ${\ displaystyle \ ell}$ ${\ displaystyle \ ell}$ ${\ displaystyle \ hbar}$ ${\ displaystyle \ ell> 0}$

Electric multipole radiation: parity Here the electric field has parity and the magnetic field . ${\ displaystyle {} = + (- 1) ^ {\ ell}}$
${\ displaystyle - (- 1) ^ {\ ell}}$ ${\ displaystyle + (- 1) ^ {\ ell}}$
Magnetic multipole radiation: parity Here the electric field has parity and the magnetic field . ${\ displaystyle {} = - (- 1) ^ {\ ell}}$
${\ displaystyle + (- 1) ^ {\ ell}}$ ${\ displaystyle - (- 1) ^ {\ ell}}$

The term “ electrical multipole radiation” is appropriate because the main part of this radiation is generated by the charge density in the source; the “ magnetic multipole radiation”, on the other hand, is mainly based on the current density in the source.

An example: in the simplified decay scheme of ⁶⁰ Co above, the angular momentum and parities of the various states are given (plus means positive parity, minus means negative parity). Consider the 1.33 MeV transition to the ground state. It must obviously have an angular momentum of 2 without changing the parity. So it's an E2 junction. The 1.17 MeV transition requires a somewhat more complicated consideration: the transition from to could emit all angular momenta between 2 and 6. In practice, however, the smallest values are most likely; it is therefore also a quadrupole transition, namely E2, since the parity remains unchanged. ${\ displaystyle J = 4}$ ${\ displaystyle J = 2}$

Individual evidence

↑ ^a ^b ^c ^d J.M. Blatt, VF Weisskopf: Theoretical Nuclear Physics . Springer, New York 1979.

[B&W-1] J.M. Blatt, VF Weisskopf: Theoretical Nuclear Physics . Springer, New York 1979.