Beta Decay Introduction

Beta decay

Introduction

Beta decay is the decay mechanism that affects the largest number of nuclei.

In standard beta decay, or more specifically, beta-minus decay, a nucleus converts a neutron into a proton. The number of neutrons N decreases by one unit, and the number of protons Z increases by one. So the neutron excess decreases by two. Beta decay moves nuclei with too many neutrons closer to the stable range.

Unlike the neutron, the proton has a positive charge, so by itself, converting a neutron into a proton would create charge out of nothing. However, that is not possible as net charge is preserved in nature. In beta decay, the nucleus also emits a negatively charged electron, making the net charge that is created zero as it should.

But there is another problem with that. Now a neutron with spin 1/2 is converted into a proton and an electron, each with spin 1/2. That violates angular momentum conservation. (Regardless of any orbital angular momentum, the net angular momentum would change from half-integer to integer.) In beta decay, the nucleus also emits a second particle of spin 1/2, thus keeping the net angular momentum half- integer. Fermi called that second particle the neutrino, since it was electrically neutral and so small that it was initially impossible to observe. In fact, even at the time of writing, almost a century later, the mass of the neutrino, though known to be nonzero, is too small to measure.

Nowadays the neutrino emitted in beta decay is more accurately identified as the electron antineutrino. An antineutrino is the antiparticle of an ordinary neutrino, just like the positron is the antiparticle of the electron. (Particles and antiparticles are exact opposites in all properties except mass, but including charge, allowing a particle and the corresponding antiparticle to annihilate each other, leaving only pho- tons.)

The reason that an antineutrino is emitted rather than a neutrino is known as conservation of lepton number. Leptons are elementary particles that do not respond to the “strong force,” including electrons and neutrinos. The net lepton number is defined as the number of leptons, minus the number of antilep- tons. It is found that this number is conserved in nature. So when in beta decay the nucleus emits an electron, a lepton, and an antineutrino, an antilepton, the lepton number stays unchanged as it should (like net angular momentum and net charge stay unchanged, as already noted).

The antineutrino does not affect the basics of beta decay, as it has no charge and virtually zero mass. However, the antineutrino does affect the detailed analysis; for one, the antineutrino can come out with a lot of kinetic energy, thus reducing the otherwise expected kinetic energy of the electron.

In beta decay, the new nucleus must be lighter than the original one. Classical mass conservation would say that the reduction in nuclear mass must equal the mass of the emitted electron plus the (neg- ligible) mass of the antineutrino. However, Einstein’s mass-energy relation implies that that is not quite right. Mass is equivalent to energy, and the rest mass reduction of the nucleus must also provide the kinetic energies of the electron and neutrino, as well as the (much smaller) one that the nucleus itself picks up during the decay by recoil. Still, the bottom line is that the nuclear mass reduction must be at least the rest mass of the electron (plus antineutrino). In energy units, it must be at least 0.511 MeV, the rest mass energy of the electron. The first subsection below will graphically examine which nuclei have enough energy to beta decay.

Beta-plus decay is the opposite of beta decay. In beta-plus decay, the nucleus converts a neutron into a proton instead of the other way around. To conserve charge, the nucleus can emit a positron, and with it, an electron neutrino to conserve angular momentum and lepton number.

However, while converting a proton into a neutron, the nucleus has a much easier way to conserve charge. Instead of emitting a positively charged positron, it can absorb a negatively charged electron from the atom it is in. The electron's charge then cancels that of the proton. To preserve angular momentum and lepton number, an electron neutrino is again emitted. This process is called “electron capture” (or also K-capture or L-Capture depending on the electron shell name from which the electron is swiped). Now the nuclear mass reduction does not need to provide the 0.512 MeV rest mass energy of a positron. Instead the nuclear mass can increase up to the 0.512 MeV rest mass energy of the electron that disappears.

So electron capture can occur in circumstances where positron creation is not possible. However, if the nuclear mass reduction is plenty for both electron capture and positron emission, the latter tends to dominate. The reason is the large quantum mechanical uncertainty in position of the low-energy atomic electron. This uncertainty dwarfs the size of the nucleus. It makes it very unlikely for the electron to be found inside the nucleus. A high-energy positron created by the nucleus itself can be created in any state, including high energy ones with short wave lengths.

Also note electron capture is of course not possible if somehow the nucleus has been stripped of all its atomic electrons, like might occur in space.

Electron capture is also called inverse beta decay, because an electron being absorbed by a nucleus is much like a movie of an electron being emitted played backwards in time. But there are some problems with this idea. For one, the time-reversed movie would also have an electron antineutrino going into the nucleus, not an electron neutrino coming out.

Still, absorption of a particle is much like the emission of the corresponding antiparticle, at least as far as conservation laws other than energy are concerned. For example, capture of an electron adds one unit of negative charge, while emission of a positron removes one unit of positive charge. Either way, the nuclear charge becomes one unit more negative. In those terms, the notion of “inverse beta decay” may not be that far out, especially since the neutrino is a minor actor in the first place.