Lesson 9 Gamma Ray Decay

Electromagnetic decay There are two types of electromagnetic decay,  -ray emission and internal conversion (IC). In both of these decays  N=  Z=  A=0, with just a lowering of the excitation energy of the nucleus. In  -ray emission, most of the emitted energy appears in the form of a photon. These emitted photons are mono-energetic and have an energy corresponding to almost all of the energy difference between the final and initial state of the system. This is typically depicted as

Electromagnetic decay(cont.)  -rays are the most penetrating nuclear radiation and to attenuate them requires massive shielding. They represent an external radiation hazard. An example of a  -emitter is 60 Co. 60 Co is longer lived nuclide (t 1/2 =5.3 y) that emits  - particles, that populate the excited states of 60 Ni, which emits two  -rays of energy, 1.17 and 1.33 MeV. This nuclide can be created in an “Doomsday machine”, (Dr. Strangelove) with disastrous consequences. The second type of electromagnetic decay is internal conversion. In IC decay, the emitted energy is transferred (radiationlessly) to an orbital electron, ejecting that electron which carries away most of the decay energy.

Isomers, Isomeric Transitions Ordinary electromagnetic transitions take place within s. Occasionally one sees an electromagnetic transition with a lifetime of ns or greater. These transitions are called isomeric transitions (IT) and the originating states are called isomers.

Example of an IT

Energetics of Gamma Decay

Classification of Electromagnetic Decays The initial and final states have a definite angular momentum and parity. The photon carries away a definite amount of angular momentum. Angular momentum and parity must be conserved. Thus where the angular momentum carried away by the photon is

Classification of Electromagnetic Decays (cont.) Multipolarity is a measure of the angular momentum carried away by the photon.

Classification of Electromagnetic Decays (cont.) Transitions are classified as electric or magnetic based on whether the radiation is due to a shift in the charge distribution or a shift in the current distribution. Based upon the type of operator involved in the transition, there are restrictions on the parity change in the transition.

Classification of Electromagnetic Decays (cont.).

Example

Additional points No gamma ray transitions of type 0  0. Possible by IC Can get both electric and magnetic matrix elements contributing to a given decay probability Lowest multipolarity is most favored Electric matrix elements are generally greater than magnetic matrix elements of tthe same multipolarity. E2 and M1 transition rates are similar

Shell model estimates of electromagnetic transition rates Can model the electromagnetic transitions in the shell model as cuased by the change of a single nucleon from one shell model orbital to another. These estimates are referred to as the “Weisskopf single particle estimates” after Victor Weisskopf.

Shell model estimates of electromagnetic transition rates (cont.)

Weisskopf estimates are good within a factor of 10 usually. The Weisskopf estimate is used as unit to express gamma-ray transition rates, i.e., rates are expressed as the (measured rate/Weisskopf rate) or in terms of Weisskopf units (W.u.)

Gamma ray transition rates and the collective model The collective motion of a group of nucleons would be expected to produce a large disturbance in the electromagnetic field of a nucleus, leading to higher probability gamma ray transitions. This primarily affects E2 transition rates which are related to the nuclear quadrupole moment, which is large for deformed nuclei.

Gamma ray transition rates and the collective model(cont.) Within a rotational band

Gamma ray transition rates and the collective model(cont.) Odd A nuclei

Gamma ray transition rates and the collective model(cont.) K conservation Vibrational nuclei --enhanced 2+  2+ transitions

Internal conversion E IC =E transition -E electron binding energy

Internal conversion coefficients, 

Auger effect In internal conversion, create vacancy in electronic shell. This can be filled by an outer electron moving into the vacancy and emitting an X-ray. Sometimes the energy is not released in the form of an X-ray but transferred to another electron, causing it to be emitted, ie, sort of an “atomic internal conversion.” This is called the Auger effect.

Auger effect (cont.) The emitted electrons are called Auger electrons.

Auger effect (cont.) Probability of Auger emission fluorescence yield=fraction of vacancies filled by x-ray emission Auger yield=fraction of vacancies filled by Auger emission

Gamma Ray Angular Correlations The gamma rays emitted from a source are isotropic in direction. There is a way to see something other than isotropic emission and that is to observe two gamma rays that are emitted sequentially by a nucleus. The emission of the first gamma ray polarizes the nucleus, ie, establishes an orientation of the intermediate state.

Consider a 0  1  0 transition

Data Analysis

Mossbauer Effect Emission of a gamma ray causes the nucleus to recoil, with an energy E r =E  2 /2mc 2 Suppose we consider two nuclear states separated by an energy E 0. Then if we shine light on the lower state of energy E 0 + E r, then we can excite the higher state. When the higher state decays, it will emit a gamma ray of energy E 0 - E r, which will not excite another state. We can do two things to change this situation, ie, “clamp” the nuclei in a crystal, making m  m crystal and we can mechanically move one nucleus relative to another.

Voila! This is called recoilless resonant absorption or the Mossbauer effect.

So What? You have created an exquisitely sensitive “instrument”, that can respond to some very small changes, ~10 -6 eV. Use of the “instrument” 1.Measurement of G 2.Chemical studies of the environment of the nucleus

Mossbauer Nuclei