Nick Connor

Beta decay or β decay represents the disintegration of a parent nucleus to a daughter through the emission of the beta particle. This transition (β^– decay) can be characterized as:

If a nucleus emits a beta particle, it loses an electron (or positron). In this case, the mass number of daughter nucleus remains the same, but daughter nucleus will form different element.

Example of Beta Decay

Free Neutron

A free neutron is a neutron that is not bounded in a nucleus. The free neutron is, unlike a bounded neutron, subject to radioactive beta decay.

It decays into a proton, an electron, and an antineutrino (the antimatter counterpart of the neutrino, a particle with no charge and little or no mass). A free neutron will decay with a half-life of about 611 seconds (10.3 minutes). This decay involves the weak interaction and is associated with a quark transformation (a down quark is converted to an up quark). The decay of the neutron is a good example of the observations which led to the discovery of the neutrino. Because it decays in this manner, the neutron does not exist in nature in its free state, except among other highly energetic particles in cosmic rays. Since free neutrons are electrically neutral, they pass through the electrical fields within atoms without any interaction and they are interacting with matter almost exclusively through relatively rare collisions with atomic nuclei.

It must be noted, a proton cannot  decay in free space. That is, a proton can undergo decay, but only inside a nucleus. It is due to the conservation of baryon number that has been established as a basic principle of physics. This principle provides basis for the stability of the proton. Since the proton is the lightest particle among all baryons, the hypothetical products of its decay would have to be non-baryons.

See also: Stability of Proton

Discovery of Neutrino

The study of beta decay provided the first physical evidence for the existence of the neutrino. The discovery of the neutrino is based on the law of conservation of energy during the process of beta decay.

See also: Discovery of Neutrino

Beta Decay of Tritium

Tritium is a radioactive isotope, bur it emits a very weak form of radiation, a low-energy beta particle that is similar to an electron. It is a pure beta emitter (i.e. beta emitter without an accompanying gamma radiation). The electron’s kinetic energy varies, with an average of 5.7 keV, while the remaining energy is carried off by the nearly undetectable electron antineutrino. Such a very low energy of electron causes, that the electron cannot penetrate the skin or even does not travel very far in air. Beta particles from tritium can penetrate only about 6.0 mm of air.

Tritium decays via negative beta decay into helium-3 with half-life of 12.3 years.

See also:

Beta Decay

Beta decay or β decay represents the disintegration of a parent nucleus to a daughter through the emission of the beta particle. This transition (β^– decay) can be characterized as:

Beta decay is governed by the weak interaction. During beta decay one of two down quarks changes into an up quark by emitting a W^– boson (carries away a negative charge). The W^– boson then decays into a beta particle and an antineutrino. This process is equivalent to the process, in which a neutrino interacts with a neutron.

As can be seen from the figure, the weak interaction changes one flavor of quark into another. Note that, the Standard Model counts six flavours of quarks and six flavours of leptons. The weak interaction is the only process in which a quark can change to another quark, or a lepton to another lepton (flavor change). Neither the strong interaction nor electromagnetic permit flavour changing. This fact is crucial in many decays of nuclear particles. In the fusion process, which, for example, powers the Sun, two protons interact via the weak force to form a deuterium nucleus, which reacts further to generate helium. Without the weak interaction, the diproton would decay back into two hydrogen-1 unbound protons through proton emission. As a result, the sun would not burn without it since the weak interaction causes the transmutation p -> n.

In contrast to alpha decay, neither the beta particle nor its associated neutrino exist within the nucleus prior to beta decay, but are created in the decay process. By this process, unstable atoms obtain a more stable ratio of protons to neutrons. The probability of a nuclide decaying due to beta and other forms of decay is determined by its nuclear binding energy. For either electron or positron emission to be energetically possible, the energy release (see below) or Q value must be positive.

See also:

Beta Decay

Positive Beta Decay – Positron Decay

In positron decay, a proton-rich nucleus emits a positron (positrons are antiparticles of electrons, and have the same mass as electrons but positive electric charge), and thereby reduces the nuclear charge by one unit. In this case, the process can be represented by: An annihilation occurs, when a low-energy positron collides with a low-energy electron.

Electron capture, which is also typical for proton-rich nuclei, competes with positive beta decay, which is more common for lighter nuclei. Electron capture is the primary decay mode for isotopes with insufficient energy (Q < 2 x 511 keV) difference between the isotope and its prospective daughter for the nuclide to decay by emitting a positron. On the other hand, electron capture is always an alternative decay mode for radioactive isotopes that do have sufficient energy to decay by positron emission.

Positron Interactions

The coulomb forces that constitute the major mechanism of energy loss for electrons are present for either positive or negative charge on the particle and constitute the major mechanism of energy loss also for positrons. Whatever the interaction involves a repulsive or attractive force between the incident particle and orbital electron (or atomic nucleus), the impulse and energy transfer for particles of equal mass are about the same. Therefore positrons interact similarly with matter when they are energetic. The track of positrons in material is similar to the track of electrons. Even their specific energy loss and range are about the samefor equal initial energies.

At the end of their path, positrons differ significantly from electrons. When a positron (antimatter particle) comes to rest, it interacts with an electron (matter particle), resulting in the annihilation of the both particles and the complete conversion of their rest mass to pure energy (according to the E=mc² formula) in the form of two oppositely directed 0.511 MeV gamma rays (photons).

See also: Positron Interaction

See also: Shielding of Positrons

See also:

Beta Decay

Negative Beta Decay – Electron Decay.

In electron decay, a neutron-rich nucleus emits a high-energy electron (β^– particle). The electrons are negatively charged almost massless particles Due to the law of conservation of electric charge, the nuclear charge must increase by one unit. In this case, the process can be represented by: 

Beta particles are high-energy, high-speed electrons or positrons emitted by certain types of radioactive nuclei such as potassium-40. The beta particles have greater range of penetration than alpha particles, but still much less than gamma rays. The beta particles emitted are a form of ionizing radiation also known as beta rays.

In a nuclear reactor occurs especially the β− decay, because the common feature of the fission products is an excess of neutrons (see Nuclear Stability). An unstable fission fragment with the excess of neutrons undergoes β− decay, where the neutron is converted into a proton, an electron, and an electron antineutrino. A free neutron also undergo this type of decay. A free neutron will decay with a half-life of about 611 seconds (10.3 minutes) into a proton, an electron, and an antineutrino (the antimatter counterpart of the neutrino, a particle with no charge and little or no mass).

Theory of Beta Decay – Weak Interaction

Beta decay is governed by the weak interaction. During beta decay one of two down quarks changes into an up quark by emitting a W^– boson (carries away a negative charge). The W^– boson then decays into a beta particle and an antineutrino. This process is equivalent to the process, in which a neutrino interacts with a neutron.

As can be seen from the figure, the weak interaction changes one flavor of quark into another. Note that, the Standard Model counts six flavours of quarks and six flavours of leptons. The weak interaction is the only process in which a quark can change to another quark, or a lepton to another lepton (flavor change). Neither the strong interaction nor electromagnetic permit flavour changing. This fact is crucial in many decays of nuclear particles. In the fusion process, which, for example, powers the Sun, two protons interact via the weak force to form a deuterium nucleus, which reacts further to generate helium. Without the weak interaction, the diproton would decay back into two hydrogen-1 unbound protons through proton emission. As a result, the sun would not burn without it since the weak interaction causes the transmutation p -> n.

In contrast to alpha decay, neither the beta particle nor its associated neutrino exist within the nucleus prior to beta decay, but are created in the decay process. By this process, unstable atoms obtain a more stable ratio of protons to neutrons. The probability of a nuclide decaying due to beta and other forms of decay is determined by its nuclear binding energy. For either electron or positron emission to be energetically possible, the energy release (see below) or Q value must be positive.

See also:

Beta Decay

There are the following forms of beta decay:

• Negative Beta Decay – Electron Decay. In electron decay, a neutron-rich nucleus emits a high-energy electron (β^– particle). The electrons are negatively charged almost massless particles Due to the law of conservation of electric charge, the nuclear charge must increase by one unit. In this case, the process can be represented by: 
• Positive Beta Decay – Positron Decay. In positron decay, a proton-rich nucleus emits a positron (positrons are antiparticles of electrons, and have the same mass as electrons but positive electric charge), and thereby reduces the nuclear charge by one unit. In this case, the process can be represented by: An annihilation occurs, when a low-energy positron collides with a low-energy electron.
• Inverse Beta Decay – Electron Capture. Electron capture, known also as inverse beta decay is sometimes included as a type of beta decay, because the basic nuclear process, mediated by the weak interaction, is the same. In this process, a proton-rich nucleus can also reduce its nuclear charge by one unit by absorbing an atomic electron. 

The emission of electrons was among the earliest observed decay phenomena. The inverse process, electron capture, was first observed by Luis Alvarez, in vanadium 48. He reported it in a 1937 paper in Physical Review.

In a nuclear reactor occurs especially the β− decay, because the common feature of the fission products is an excess of neutrons (see Nuclear Stability). An unstable fission fragment with the excess of neutrons undergoes β− decay, where the neutron is converted into a proton, an electron, and an electron antineutrino. A free neutron also undergo this type of decay. A free neutron will decay with a half-life of about 611 seconds (10.3 minutes) into a proton, an electron, and an antineutrino (the antimatter counterpart of the neutrino, a particle with no charge and little or no mass).

See also:

Beta Decay

The Auger effect is a process named after the French physicist Pierre Auger, in which electrons with characteristic energies are ejected from atoms in response to a downward transition by another electron in the atom (filling of an inner-shell vacancy of an atom), instead of emitting electromagnetic radiation. These emitted electrons with characteristic energies are known as Auger electrons.

This process is observed as one of the methods of electron rearrangement after electron capture into the nucleus. Since electron capture leaves a vacancy in the electron energy level from which the electron came, the outer electrons of the atom cascade down to fill the lower atomic levels, and one or more characteristic X-rays are usually emitted. Sometimes X-ray may interact with another orbital electron, which may be ejected from the atom. This second ejected electron is called an Auger electron. The probability that an Auger electron will be emitted is called the Auger yield. The Auger yield decreases with atomic number. For zinc (Z=30),  the probabilities of the emission of X-rays from the innermost shell and of the emission of Auger electrons is about equal.

The inner-shell vacancy of an atom may be also produced by by bombardment with high energy electrons or X-rays. This method may be used in Auger electron spectroscopy, which measures the intensity of Auger electrons that result as a function of the Auger electron energy. The Auger electron spectroscopy can be used to determine the identity of the emitting atoms and it is one of the most commonly employed surface analytical techniques for determining the composition of the surface layers of a sample.

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See also:

Electron

Electron capture is a process, in which a parent nucleus captures one of its orbital electrons and emits a neutrino. Electron capture, known also as inverse beta decay is sometimes included as a type of beta decay, because the basic nuclear process, mediated by the weak interaction, is the same. In this process, a proton-rich nucleus can also reduce its nuclear charge by one unit by absorbing an atomic electron.

In this process a parent nucleus may capture one of its orbital electrons and emits a neutrino. The electron is normally captured from an inner shell of an atom (K-shell). This process competes with positive beta decay, which is more common for lighter nuclei. Electron capture is the primary decay mode for isotopes with insufficient energy (Q < 2 x 511 keV) difference between the isotope and its prospective daughter for the nuclide to decay by emitting a positron. On the other hand, electron capture is always an alternative decay mode for radioactive isotopes that do have sufficient energy to decay by positron emission.

The resulting daughter nuclide, if it is in an excited state, then transitions to its ground state usually gamma ray emission, but de-excitation may also take place by internal conversion. Since the process leaves a vacancy in the electron energy level from which the electron came, the outer electrons of the atom cascade down to fill the lower atomic levels, and one or more characteristic X-rays are usually emitted. Sometimes X-ray may interact with another orbital electron, which may be ejected from the atom. This second ejected electron is called an Auger electron.

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EC with X-ray Emission

EC with Auger Effect

Theory of Beta Decay – Weak Interaction

Beta decay is governed by the weak interaction. During beta decay one of two down quarks changes into an up quark by emitting a W^– boson (carries away a negative charge). The W^– boson then decays into a beta particle and an antineutrino. This process is equivalent to the process, in which a neutrino interacts with a neutron.

As can be seen from the figure, the weak interaction changes one flavor of quark into another. Note that, the Standard Model counts six flavours of quarks and six flavours of leptons. The weak interaction is the only process in which a quark can change to another quark, or a lepton to another lepton (flavor change). Neither the strong interaction nor electromagnetic permit flavour changing. This fact is crucial in many decays of nuclear particles. In the fusion process, which, for example, powers the Sun, two protons interact via the weak force to form a deuterium nucleus, which reacts further to generate helium. Without the weak interaction, the diproton would decay back into two hydrogen-1 unbound protons through proton emission. As a result, the sun would not burn without it since the weak interaction causes the transmutation p -> n.

In contrast to alpha decay, neither the beta particle nor its associated neutrino exist within the nucleus prior to beta decay, but are created in the decay process. By this process, unstable atoms obtain a more stable ratio of protons to neutrons. The probability of a nuclide decaying due to beta and other forms of decay is determined by its nuclear binding energy. For either electron or positron emission to be energetically possible, the energy release (see below) or Q value must be positive.

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See also:

Radioactive Decay

Beta decay or β decay represents the disintegration of a parent nucleus to a daughter through the emission of the beta particle. This transition (β^– decay) can be characterized as:

If a nucleus emits a beta particle, it loses an electron (or positron). In this case, the mass number of daughter nucleus remains the same, but daughter nucleus will form different element.

Beta particles are high-energy, high-speed electrons or positrons emitted by certain types of radioactive nuclei such as potassium-40. The beta particles have greater range of penetration than alpha particles, but still much less than gamma rays. The beta particles emitted are a form of ionizing radiation also known as beta rays. There are the following forms of beta decay:

• Negative Beta Decay – Electron Decay. In electron decay, a neutron-rich nucleus emits a high-energy electron (β^– particle). The electrons are negatively charged almost massless particles Due to the law of conservation of electric charge, the nuclear charge must increase by one unit. In this case, the process can be represented by: 
• Positive Beta Decay – Positron Decay. In positron decay, a proton-rich nucleus emits a positron (positrons are antiparticles of electrons, and have the same mass as electrons but positive electric charge), and thereby reduces the nuclear charge by one unit. In this case, the process can be represented by: An annihilation occurs, when a low-energy positron collides with a low-energy electron.
• Inverse Beta Decay – Electron Capture. Electron capture, known also as inverse beta decay is sometimes included as a type of beta decay, because the basic nuclear process, mediated by the weak interaction, is the same. In this process, a proton-rich nucleus can also reduce its nuclear charge by one unit by absorbing an atomic electron. 

The emission of electrons was among the earliest observed decay phenomena. The inverse process, electron capture, was first observed by Luis Alvarez, in vanadium 48. He reported it in a 1937 paper in Physical Review.

In a nuclear reactor occurs especially the β− decay, because the common feature of the fission products is an excess of neutrons (see Nuclear Stability). An unstable fission fragment with the excess of neutrons undergoes β− decay, where the neutron is converted into a proton, an electron, and an electron antineutrino. A free neutron also undergo this type of decay. A free neutron will decay with a half-life of about 611 seconds (10.3 minutes) into a proton, an electron, and an antineutrino (the antimatter counterpart of the neutrino, a particle with no charge and little or no mass).

Theory of Beta Decay – Weak Interaction

Beta decay is governed by the weak interaction. During beta decay one of two down quarks changes into an up quark by emitting a W^– boson (carries away a negative charge). The W^– boson then decays into a beta particle and an antineutrino. This process is equivalent to the process, in which a neutrino interacts with a neutron.

As can be seen from the figure, the weak interaction changes one flavor of quark into another. Note that, the Standard Model counts six flavours of quarks and six flavours of leptons. The weak interaction is the only process in which a quark can change to another quark, or a lepton to another lepton (flavor change). Neither the strong interaction nor electromagnetic permit flavour changing. This fact is crucial in many decays of nuclear particles. In the fusion process, which, for example, powers the Sun, two protons interact via the weak force to form a deuterium nucleus, which reacts further to generate helium. Without the weak interaction, the diproton would decay back into two hydrogen-1 unbound protons through proton emission. As a result, the sun would not burn without it since the weak interaction causes the transmutation p -> n.

In contrast to alpha decay, neither the beta particle nor its associated neutrino exist within the nucleus prior to beta decay, but are created in the decay process. By this process, unstable atoms obtain a more stable ratio of protons to neutrons. The probability of a nuclide decaying due to beta and other forms of decay is determined by its nuclear binding energy. For either electron or positron emission to be energetically possible, the energy release (see below) or Q value must be positive.

Example of Beta Decay

Free Neutron

A free neutron is a neutron that is not bounded in a nucleus. The free neutron is, unlike a bounded neutron, subject to radioactive beta decay.

It decays into a proton, an electron, and an antineutrino (the antimatter counterpart of the neutrino, a particle with no charge and little or no mass). A free neutron will decay with a half-life of about 611 seconds (10.3 minutes). This decay involves the weak interaction and is associated with a quark transformation (a down quark is converted to an up quark). The decay of the neutron is a good example of the observations which led to the discovery of the neutrino. Because it decays in this manner, the neutron does not exist in nature in its free state, except among other highly energetic particles in cosmic rays. Since free neutrons are electrically neutral, they pass through the electrical fields within atoms without any interaction and they are interacting with matter almost exclusively through relatively rare collisions with atomic nuclei.

It must be noted, a proton cannot  decay in free space. That is, a proton can undergo decay, but only inside a nucleus. It is due to the conservation of baryon number that has been established as a basic principle of physics. This principle provides basis for the stability of the proton. Since the proton is the lightest particle among all baryons, the hypothetical products of its decay would have to be non-baryons.

See also: Stability of Proton

Energy Spectrum of Beta Decay

In both alpha and gamma decay, the resulting particle (alpha particle or photon) has a narrow energy distribution, since the particle carries the energy from the difference between the initial and final nuclear states. For example, in case of alpha decay, when a parent nucleus breaks down spontaneously to yield a daughter nucleus and an alpha particle, the sum of the mass of the two products does not quite equal the mass of the original nucleus (see Mass Defect). As a result of the law of conservation of energy, this difference appears in the form of the kinetic energy of the alpha particle. Since the same particles appear as products at every breakdown of a particular parent nucleus, the mass-difference should always be the same, and the thermodynamics/what-is-energy-physics/what-is-kinetic-energy/”>kinetic energy of the alpha particles should also always be the same. In other words, the beam of alpha particles should be monoenergetic.

It was expected that the same considerations would hold for a parent nucleus breaking down to a daughter nucleus and a beta particle. Because only the electron and the recoiling daughter nucleus were observed beta decay, the process was initially assumed to be a two body process, very much like alpha decay. It would seem reasonable to suppose that the beta particles would form also a monoenergetic beam.

To demonstrate energetics of two-body beta decay, consider the beta decay in which an electron is emitted and the parent nucleus is at rest, conservation of energy requires:

Since the electron is much lighter particle it was expected that it will carry away most of the released energy, which would have a unique value T_e-.

But the reality was different. The spectrum of beta particles measured by Lise Meitner and Otto Hahn in 1911 and by Jean Danysz in 1913 showed multiple lines on a diffuse background, however. Moreover virtually all of the emitted beta particles have energies below that predicted by energy conservation in two-body decays. The electrons emitted in beta decay have a continuous rather than a discrete spectrumappeared to contradict conservation of energy, under the then-current assumption that beta decay is the simple emission of an electron from a nucleus. When this was first observed, it appeared to threaten the survival of one of the most important conservation laws in physics!

To account for this energy release, Pauli proposed (in 1931) that there was emitted in the decay process another particle, later named by Fermi the neutrino. It was clear, this particle must be highly penetrating and that the conservation of electric charge requires the neutrino to be electrically neutral. This would explain why it was so hard to detect this particle. The term neutrino comes from Italian meaning “little neutral one” and neutrinos are denoted by the Greek letter ν (nu). In the process of beta decay the neutrino carries the missing energy and also in this process the law of conservation of energy remains valid.

Conservation Laws in Beta Decay

In analyzing nuclear reactions, we apply the many conservation laws. Nuclear reactions are subject to classical conservation laws for charge, momentum, angular momentum, and energy (including rest energies).  Additional conservation laws, not anticipated by classical physics, are:

• Law of Conservation of Lepton Number
• Law of Conservation of Baryon Number
• Law of Conservation of Electric Charge

Certain of these laws are obeyed under all circumstances, others are not. We have accepted conservation of energy and momentum. In all the examples given we assume that the number of protons and the number of neutrons is separately conserved. We shall find circumstances and conditions in which  this rule is not true. Where we are considering non-relativistic nuclear reactions, it is essentially true. However, where we are considering relativistic nuclear energies or those involving the weak interactions, we shall find that these principles must be extended.

Some conservation principles have arisen from theoretical considerations, others are just empirical relationships. Notwithstanding, any reaction not expressly forbidden by the conservation laws will generally occur, if perhaps at a slow rate. This expectation is based on quantum mechanics. Unless the barrier between the initial and final states is infinitely high, there is always a non-zero probability that a system will make the transition between them.

For purposes of analyzing non-relativistic reactions, it is sufficient to note four of the fundamental laws governing these reactions.

1. Conservation of nucleons. The total number of nucleons before and after a reaction are the same.
2. Conservation of charge. The sum of the charges on all the particles before and after a reaction are the same
3. Conservation of momentum. The total momentum of the interacting particles before and after a reaction are the same.
4. Conservation of energy. Energy, including rest mass energy, is conserved in nuclear reactions.

Reference: Lamarsh, John R. Introduction to Nuclear engineering 2nd Edition

Beta Decay – Q-value

In nuclear and particle physics the energetics of nuclear reactions is determined by the Q-value of that reaction. The Q-value of the reaction is defined as the difference between the sum of the rest masses of the initial reactants and the sum of the masses of the final products, in energy units (usually in MeV).

Consider a typical reaction, in which the projectile a and the target A gives place to two products, B and b. This can also be expressed in the notation that we used so far, a + A → B + b, or even in a more compact notation, A(a,b)B.

See also: E=mc2

The Q-value of this reaction is given by:

Q = [ma + mA – (mb + mB)]c²

When describing beta decay (reaction without projectile), the disintegrating nucleus is usually referred to as the parent nucleus and the nucleus remaining after the event as the daughter nucleus. The emission of a beta particle, either an electron, β^–, or a positron, β⁺, changes the atomic number of the nucleus without affecting its mass number. The total rest mass of the daughter nucleus and of the nuclear radiation released in a beta disintegration, m_Daughter + m_Radiation, is always less than that of the parent nucleus, m_parent.

The mass-energy difference,

Q = [m_parent – (m_Daughter + m_Radiation)]c²

appears as the disintegration energy, liberated in the process. For example, the Q-value of typical beta decay is:

In the process of beta decay, either an electron or a positron is emitted. This emission is accompanied by the emission of antineutrino (β- decay) or neutrino (β+ decay), which shares energy and momentum of the decay. The beta emission has a characteristic spectrum. This characteristic spectrum is caused by the fact that either a neutrino or an antineutrino is emitted with emission of beta particle. The shape of this energy curve depends on what fraction of the reaction energy (Q value-the amount of energy released by the reaction) is carried by the massive particle. Beta particles can therefore be emitted with any kinetic energy ranging from 0 to Q. After an alpha or beta decay, the daughter nucleus is often left in an excited energy state. In order to stabilize itself, it subsequently emits high-energy photons, γ-rays.

See also:

Radioactive Decay

Parent Nucleus – Daughter Nucleus

In nuclear physics and physics of nuclear decays, the disintegrating nucleus is usually referred to as the parent nucleus and the nucleus remaining after the event as the daughter nucleus.

Parent Nucleus – Daughter Nucleus in Alpha Decay

For example, the alpha decay represents the disintegration of a parent nucleus to a daughter through the emission of the nucleus of a helium atom. This transition can be characterized as:

As can be seen, the atomic number (as well the mass number) of the daughter nucleus is lower than the atomic number of the parent nucleus.

By 1928, George Gamow (and independently by Ronald Gurney and Edward Condon) had solved the theory of alpha decay via quantum tunneling. They assumed that the alpha particle and the daughter nucleus exist within the parent nucleus prior to its dissociation, namely the decay of quasistationary states (QS).  A quasistationary state is defined as a long-lived state that eventually decays. Initially, the alpha cluster oscillates in the potential of the daughter nucleus, with the Coulomb potential preventing their separation. The alpha particle is trapped in a potential well by the nucleus. Classically, it is forbidden to escape, but according to the (then) newly discovered principles of quantum mechanics, it has a tiny (but non-zero) probability of “tunneling” through the barrier and appearing on the other side to escape the nucleus. Using the tunneling mechanism, Gamow, Condon and Gurney calculated the penetrability of the tunneling α particle through the Coulomb barrier, finding the lifetimes of some α emitting nuclei.

Parent Nucleus – Daughter Nucleus in Beta Decay

If a nucleus emits a beta particle, it loses an electron (or positron). In this case, the mass number of daughter nucleus remains the same, but daughter nucleus will form different element. This transition can be characterized as:

Parent Nucleus – Daughter Nucleus in Gamma Decay

In nuclear physics and nuclear chemistry, the various species of atoms whose nuclei contain particular numbers of protons and neutrons are called nuclides. Nuclides are also characterized by its nuclear energy states (e.g. metastable nuclide ^242mAm). Nuclides with equal proton number and equal mass number (thus making them by definition the same isotope) but different energy states are known as isomers. We usually indicate isomers with a superscript m. As a result, in the gamma decay parent and daughter nuclei have equal proton number and equal mass number, but differ in their energy states. This transition can be characterized as:

See also:

Atomic Nucleus

Alpha decay (or α-decay and also alpha radioactivity) represents the disintegration of a parent nucleus to a daughter through the emission of the nucleus of a helium atom. This transition can be characterized as:

Alpha decay is a quantum tunneling process. In order to be emitted, the alpha particle must penetrate a potential barrier. This is similar to cluster decay, in which an atomic nucleus emits a small “cluster” of neutrons and protons (e.g. ¹²C).

The height of the Coulomb barrier for nuclei of A « 200 is about 20-25 MeV. The alpha particles emitted in nuclear decay have typical energies of about 5 MeV. On the one hand an incoming 5 MeV alpha particle is scattered from a heavy nucleus and it cannot penetrate the Coulomb barrier and get sufficiently close to the nucleus to interact via the strong force. On the other hand, a 5 MeV alpha particle bound in a nuclear potential well is able to tunnel that same Coulomb barrier.

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Alpha Decay – Q-value

In nuclear and particle physics the energetics of nuclear reactions is determined by the Q-value of that reaction. The Q-value of the reaction is defined as the difference between the sum of the rest masses of the initial reactants and the sum of the masses of the final products, in energy units (usually in MeV).

Consider a typical reaction, in which the projectile a and the target A gives place to two products, B and b. This can also be expressed in the notation that we used so far, a + A → B + b, or even in a more compact notation, A(a,b)B.

See also: E=mc2

The Q-value of this reaction is given by:

Q = [ma + mA – (mb + mB)]c²

When describing alpha decay (a reaction without projectile), the disintegrating nucleus is usually referred to as the parent nucleus and the nucleus remaining after the event as the daughter nucleus. The total rest mass of the daughter nucleus and of the nuclear radiation released in an alpha disintegration, m_Daughter + m_Radiation, is always less than that of the parent nucleus, m_parent. The mass-energy difference,

Q = [m_parent – (m_Daughter + m_Radiation)]c²

appears as the disintegration energy, liberated in the process. For example, the Q-value of typical alpha decay is:

The disintegration energy of about 5 MeV is typical kinetic energy of alpha particle. In order to fulfill the law of conservation of momentum, most of the disintegration energy must appear as the kinetic energy of alpha particle. After an alpha or beta decay, the daughter nucleus is often left in an excited energy state. In order to stabilize itself, it subsequently emits high-energy photons, γ-rays.

See also:

Alpha Decay