Editing Alpha decay (section)

== Mechanism ==

The [[nuclear force]] holding an atomic nucleus together is very strong, in general much stronger than the repulsive [[electromagnetic force]]s between the protons. However, the nuclear force is also short-range, dropping quickly in strength beyond about 3 [[femtometers]], while the electromagnetic force has an unlimited range. The strength of the attractive nuclear force keeping a nucleus together is thus proportional to the number of the nucleons, but the total disruptive electromagnetic force of proton-proton repulsion trying to break the nucleus apart is roughly proportional to the square of its atomic number. A nucleus with 210 or more nucleons is so large that the [[strong nuclear force]] holding it together can just barely counterbalance the electromagnetic repulsion between the protons it contains. Alpha decay occurs in such nuclei as a means of increasing stability by reducing size.<ref name=beiser>
{{cite book
  |title=Concepts of Modern Physics
  |url=http://phy240.ahepl.org/Concepts_of_Modern_Physics_by_Beiser.pdf
  |year=2003
  |publisher=McGraw-Hill
  |isbn=0-07-244848-2
  |chapter=Chapter 12: Nuclear Transformations
  |pages=432–434
  |edition=6th
  |author1=Arthur Beiser
  |access-date=2016-07-03
  |archive-url=https://web.archive.org/web/20161004204701/http://phy240.ahepl.org/Concepts_of_Modern_Physics_by_Beiser.pdf
  |archive-date=2016-10-04
  |url-status=dead
  }}</ref>

One curiosity is why alpha particles, helium nuclei, should be preferentially emitted as opposed to other particles like a single [[proton emission|proton]] or [[neutron emission|neutron]] or [[cluster decay|other atomic nuclei]].<ref group="note">These other decay modes, while possible, are extremely rare compared to alpha decay.</ref> Part of the reason is the high [[binding energy]] of the alpha particle, which means that its mass is less than the sum of the masses of two free protons and two free neutrons. This increases the disintegration energy. Computing the total disintegration energy given by the [[Mass–energy equivalence|equation]]
<math display="block">E_{di} = (m_\text{i} - m_\text{f} - m_\text{p})c^2,</math>
where {{math|''m''<sub>i</sub>}} is the initial mass of the nucleus, {{math|''m''<sub>f</sub>}} is the mass of the nucleus after particle emission, and {{math|''m''<sub>p</sub>}} is the mass of the emitted (alpha-)particle, one finds that in certain cases it is positive and so alpha particle emission is possible, whereas other decay modes would require energy to be added. For example, performing the calculation for [[uranium-232]] shows that alpha particle emission releases 5.4&nbsp;MeV of energy, while a single proton emission would ''require'' 6.1&nbsp;MeV. Most of the disintegration energy becomes the [[kinetic energy]] of the alpha particle, although to fulfill [[conservation of momentum]], part of the energy goes to the recoil of the nucleus itself (see [[atomic recoil]]). However, since the mass numbers of most alpha-emitting radioisotopes exceed 210, far greater than the mass number of the alpha particle (4), the fraction of the energy going to the recoil of the nucleus is generally quite small, less than 2%.<ref name="beiser" /> Nevertheless, the recoil energy (on the scale of keV) is still much larger than the strength of chemical bonds (on the scale of eV), so the daughter nuclide will break away from the chemical environment the parent was in. The energies and ratios of the alpha particles can be used to identify the radioactive parent via [[Alpha-particle spectroscopy|alpha spectrometry]].

These disintegration energies, however, are substantially smaller than the repulsive [[potential barrier]] created by the interplay between the strong nuclear and the electromagnetic force, which prevents the alpha particle from escaping. The energy needed to bring an alpha particle from infinity to a point near the nucleus just outside the range of the nuclear force's influence is generally in the range of about 25&nbsp;MeV. An alpha particle within the nucleus can be thought of as being inside a potential barrier whose walls are 25&nbsp;MeV above the potential at infinity. However, decay alpha particles only have energies of around 4 to 9&nbsp;MeV above the potential at infinity, far less than the energy needed to overcome the barrier and escape.

=== Quantum tunneling ===
Quantum mechanics, however, allows the alpha particle to escape via quantum tunneling. The quantum tunneling theory of alpha decay, independently developed by George Gamow<ref>
{{cite journal
 |author=G. Gamow
 |year=1928
 |title=Zur Quantentheorie des Atomkernes (On the quantum theory of the atomic nucleus)
 |journal=[[Zeitschrift für Physik]]
 |volume=51
 |issue=3
 |pages=204–212
 |doi=10.1007/BF01343196
 |bibcode = 1928ZPhy...51..204G |s2cid=120684789
 }}</ref> and by [[Ronald Wilfred Gurney]] and [[Edward Condon]] in 1928,<ref name="gurney-Condon">
{{cite journal
 |author=Ronald W. Gurney & Edw. U. Condon
 |year=1928
 |title=Wave Mechanics and Radioactive Disintegration
 |journal=[[Nature (journal)|Nature]]
 |volume=122
 |issue=3073
 |page=439
 |doi=10.1038/122439a0
 |bibcode = 1928Natur.122..439G |doi-access=free
 }}</ref> was hailed as a very striking confirmation of quantum theory. Essentially, the alpha particle escapes from the nucleus not by acquiring enough energy to pass over the wall confining it, but by tunneling through the wall. Gurney and Condon made the following observation in their paper on it:
<blockquote>It has hitherto been necessary to postulate some special arbitrary 'instability' of the nucleus, but in the following note, it is pointed out that disintegration is a natural consequence of the laws of quantum mechanics without any special hypothesis... Much has been written of the explosive violence with which the α-particle is hurled from its place in the nucleus. But from the process pictured above, one would rather say that the α-particle almost slips away unnoticed.<ref name="gurney-Condon"/></blockquote>

The theory supposes that the alpha particle can be considered an independent particle within a nucleus, that is in constant motion but held within the nucleus by strong interaction. At each collision with the repulsive potential barrier of the electromagnetic force, there is a small non-zero probability that it will tunnel its way out. An alpha particle with a speed of 1.5×10<sup>7</sup>&nbsp;m/s within a nuclear diameter of approximately 10<sup>−14</sup>&nbsp;m will collide with the barrier more than 10<sup>21</sup> times per second. However, if the probability of escape at each collision is very small, the half-life of the radioisotope will be very long, since it is the time required for the total probability of escape to reach 50%. As an extreme example, the half-life of the isotope [[bismuth-209]] is {{val|2.01|e=19|u=years}}.

The isotopes in [[beta-decay stable isobars]] that are also stable with regards to [[double beta decay]] with [[mass number]] ''A''&nbsp;=&nbsp;5, ''A''&nbsp;=&nbsp;8, 143&nbsp;≤&nbsp;''A''&nbsp;≤&nbsp;155, 160&nbsp;≤&nbsp;''A''&nbsp;≤&nbsp;162, and ''A''&nbsp;≥&nbsp;165 are theorized to undergo alpha decay. All other mass numbers ([[isobar (nuclide)|isobar]]s) have exactly one theoretically [[stable nuclide]]. Those with mass 5 decay to helium-4 and a [[proton]] or a [[neutron]], and those with mass 8 decay to two helium-4 nuclei; their half-lives ([[helium-5]], [[lithium-5]], and [[beryllium-8]]) are very short, unlike the half-lives for all other such nuclides with ''A''&nbsp;≤&nbsp;209, which are very long. (Such nuclides with ''A''&nbsp;≤&nbsp;209 are [[primordial nuclide]]s except <sup>146</sup>Sm.)<ref name=bellidecay>{{cite journal |last1=Belli |first1=P. |last2=Bernabei |first2=R. |last3=Danevich |first3=F. A. |last4=Incicchitti |first4=A. |last5=Tretyak |first5=V. I. |display-authors=3 |title=Experimental searches for rare alpha and beta decays |journal=European Physical Journal A |date=2019 |volume=55 |issue=8 |pages=140–1–140–7 |doi=10.1140/epja/i2019-12823-2 |issn=1434-601X |arxiv=1908.11458 |bibcode=2019EPJA...55..140B|s2cid=201664098 }}</ref>

Working out the details of the theory leads to an equation relating the half-life of a radioisotope to the decay energy of its alpha particles, a theoretical derivation of the empirical [[Geiger–Nuttall law]].