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[[File:Bosons-Hadrons-Fermions-RGB-png2.png|thumb|331x331px|Bosons form one of the two fundamental classes of [[subatomic particle]], the other being [[fermion]]s. All subatomic particles must be one or the other. A composite particle ([[hadron]]) may fall into either class depending on its composition]]
[[File:Bosons-Hadrons-Fermions-RGB-png2.png|thumb|331x331px|Bosons form one of the two fundamental classes of [[subatomic particle]], the other being [[fermion]]s. All subatomic particles must be one or the other. A composite particle ([[hadron]]) may fall into either class depending on its composition]]


In [[particle physics]], a '''boson''' ({{IPAc-en|ˈ|b|oʊ|z|ɒ|n}}<ref>{{Cite encyclopedia |url=http://www.lexico.com/definition/boson |archive-url=https://web.archive.org/web/20210709191352/https://www.lexico.com/definition/boson |url-status=dead |archive-date=9 July 2021 |title=boson |dictionary=[[Lexico]] UK English Dictionary |publisher=[[Oxford University Press]]}}</ref> {{IPAc-en|ˈ|b|oʊ|s|ɒ|n}}<ref>{{cite book|last=Wells|first=John C.|title=Longman pronunciation dictionary|publisher=Longman|year=1990|isbn=978-0582053830|location=Harlow, England}} entry "Boson"</ref>) is a [[subatomic particle]] whose [[spin quantum number]] has an integer value (0, 1, 2, ...). Bosons form one of the two fundamental classes of subatomic particle, the other being [[fermion]]s, which have odd half-integer spin ({{frac|1|2}}, {{frac|3|2}}, {{frac|5|2}}, ...). Every observed subatomic particle is either a boson or a fermion.
In [[particle physics]], a '''boson''' ({{IPAc-en|ˈ|b|oʊ|z|ɒ|n}}<ref>{{Cite encyclopedia |url=http://www.lexico.com/definition/boson |archive-url=https://web.archive.org/web/20210709191352/https://www.lexico.com/definition/boson |url-status=dead |archive-date=9 July 2021 |title=boson |dictionary=[[Lexico]] UK English Dictionary |publisher=[[Oxford University Press]]}}</ref> {{IPAc-en|ˈ|b|oʊ|s|ɒ|n}}<ref>{{cite book|last=Wells|first=John C.|title=Longman pronunciation dictionary|publisher=Longman|year=1990|isbn=978-0582053830|location=Harlow, England}} entry "Boson"</ref>) is a [[subatomic particle]] whose [[spin quantum number]] has an integer value (0, 1, 2, ...). Bosons form one of the two fundamental classes of subatomic particle, the other being [[fermion]]s, which have odd half-integer spin ({{frac|1|2}}, {{frac|3|2}}, {{frac|5|2}}, ...). Every observed subatomic particle is either a boson or a fermion. [[Paul Dirac]] coined the name ''boson'' to commemorate the contribution of [[Satyendra Nath Bose]], an [[Indian people|Indian]] physicist.


Some bosons are [[elementary particle]]s occupying a special role in particle physics, distinct from the role of fermions (which are sometimes described as the constituents of "ordinary matter"). Certain elementary bosons (e.g. [[gluon]]s) act as [[force carrier]]s, which give rise to forces between other particles, while one (the [[Higgs boson]]) contributes to the phenomenon of [[mass]]. Other bosons, such as [[meson]]s, are composite particles made up of smaller constituents.
Some bosons are [[elementary particle]]s occupying a special role in particle physics, distinct from the role of fermions (which are sometimes described as the constituents of "ordinary matter"). Certain elementary bosons (e.g. [[gluon]]s) act as [[force carrier]]s, which give rise to forces between other particles, while one (the [[Higgs boson]]) contributes to the phenomenon of [[mass]]. Other bosons, such as [[meson]]s, are composite particles made up of smaller constituents.
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== Name ==
== Name ==
The name ''boson'' was coined by [[Paul Dirac]]<ref>{{cite book|title=Notes on Dirac's lecture ''Developments in Atomic Theory'' at Le Palais de la Découverte, 6&nbsp;December 1945|publisher=UKNATARCHI Dirac Papers|id=BW83/2/257889}}</ref><ref>{{Cite book|last=Farmelo|first=Graham|url=https://books.google.com/books?id=qsodmIGD0fMC&q=farmelo+graham+the+strangest+man|title=The Strangest Man: The Hidden Life of Paul Dirac, Mystic of the Atom|date=2009-08-25|publisher=Basic Books|isbn=9780465019922|pages=331|language=en}}</ref> to commemorate the contribution of [[Satyendra Nath Bose]], an [[Indian people|Indian]] physicist, when he was a reader (later professor) at the [[University of Dhaka]], [[Bengal]] (now in [[Bangladesh]]),<ref name="AP-20120710">{{cite news|last=Daigle|first=Katy|date=10 July 2012|title=India: Enough about Higgs, let's discuss the boson|agency=[[Associated Press]]|url=http://apnews.excite.com/article/20120710/D9VU1DRG0.html|access-date=10 July 2012}}</ref><ref name="NYT-20120919">{{cite news|last=Bal|first=Hartosh Singh|date=19 September 2012|title=The Bose in the Boson|work=[[The New York Times]]|department=Latitude (blog)|url=http://latitude.blogs.nytimes.com/2012/09/19/indians-clamor-for-credit-for-the-bose-in-boson/|url-status=dead|access-date=21 September 2012|archive-url=https://web.archive.org/web/20120922024310/http://latitude.blogs.nytimes.com/2012/09/19/indians-clamor-for-credit-for-the-bose-in-boson/|archive-date=22 September 2012}}</ref> he developed, in conjunction with [[Albert Einstein]], the theory characterising such particles, now known as [[Bose–Einstein statistics]] and [[Bose-Einstein condensate]].<ref>{{cite news|date=4 July 2012|title=Higgs boson: The poetry of subatomic particles|work=BBC News|url=https://www.bbc.co.uk/news/magazine-18708741|access-date=6 July 2012}}</ref>
The name ''boson'' was coined by [[Paul Dirac]]<ref>{{cite book|title=Notes on Dirac's lecture ''Developments in Atomic Theory'' at Le Palais de la Découverte, 6&nbsp;December 1945|publisher=UKNATARCHI Dirac Papers|id=BW83/2/257889}}</ref><ref>{{Cite book|last=Farmelo|first=Graham|url=https://books.google.com/books?id=qsodmIGD0fMC&q=farmelo+graham+the+strangest+man|title=The Strangest Man: The Hidden Life of Paul Dirac, Mystic of the Atom|date=2009-08-25|publisher=Basic Books|isbn=9780465019922|pages=331|language=en}}</ref> to commemorate the contribution of [[Satyendra Nath Bose]], an [[Indian people|Indian]] physicist. When Bose was a reader (later professor) at the [[University of Dhaka]], [[Bengal]] (now in [[Bangladesh]]),<ref name="AP-20120710">{{cite news|last=Daigle|first=Katy|date=10 July 2012|title=India: Enough about Higgs, let's discuss the boson|agency=[[Associated Press]]|url=http://apnews.excite.com/article/20120710/D9VU1DRG0.html|access-date=10 July 2012}}</ref><ref name="NYT-20120919">{{cite news|last=Bal|first=Hartosh Singh|date=19 September 2012|title=The Bose in the Boson|work=[[The New York Times]]|department=Latitude (blog)|url=http://latitude.blogs.nytimes.com/2012/09/19/indians-clamor-for-credit-for-the-bose-in-boson/|url-status=dead|access-date=21 September 2012|archive-url=https://web.archive.org/web/20120922024310/http://latitude.blogs.nytimes.com/2012/09/19/indians-clamor-for-credit-for-the-bose-in-boson/|archive-date=22 September 2012}}</ref> he and [[Albert Einstein]] developed the theory characterising such particles, now known as [[Bose–Einstein statistics]] and [[Bose–Einstein condensate]].<ref>{{cite news|date=4 July 2012|title=Higgs boson: The poetry of subatomic particles|work=BBC News|url=https://www.bbc.co.uk/news/magazine-18708741|access-date=6 July 2012}}</ref>


== Elementary bosons ==
== Elementary bosons ==
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{{See also|List of particles#Bosons}}
{{See also|List of particles#Bosons}}


All observed [[elementary particles]] are either bosons (with integer spin) or [[fermions]] (with odd half-integer spin).<ref name="DarkMatter">{{cite book|author=Carroll, Sean|title=Guidebook|publisher=The Teaching Company|year=2007|isbn=978-1598033502|series=Dark Matter, Dark Energy: The dark side of the universe|at=Part&nbsp;2, p.&nbsp;43|quote=...&nbsp;boson: A force-carrying particle, as opposed to a matter particle (fermion). Bosons can be piled on top of each other without limit. Examples are photons, gluons, gravitons, weak bosons, and the Higgs boson. The spin of a boson is always an integer: 0, 1, 2, and so on&nbsp;...}}</ref> Whereas the elementary particles that make up ordinary matter ([[lepton]]s and [[quark]]s) are fermions, elementary bosons occupy a special role in particle physics. They act either as [[force carrier]]s which give rise to forces between other particles, or in one case give rise to the phenomenon of [[mass]].
All observed [[elementary particles]] are either bosons (with integer spin) or [[fermions]] (with odd half-integer spin).<ref name="DarkMatter">{{cite book|author=Carroll, Sean|title=Guidebook|publisher=The Teaching Company|year=2007|isbn=978-1598033502|series=Dark Matter, Dark Energy: The dark side of the universe|at=Part&nbsp;2, p.&nbsp;43|quote=...&nbsp;boson: A force-carrying particle, as opposed to a matter particle (fermion). Bosons can be piled on top of each other without limit. Examples are photons, gluons, gravitons, weak bosons, and the Higgs boson. The spin of a boson is always an integer: 0, 1, 2, and so on&nbsp;...}}</ref> Whereas the elementary particles that make up ordinary matter ([[lepton]]s and [[quark]]s) are fermions, elementary bosons occupy a special role in particle physics. They act either as [[force carrier]]s which give rise to forces between other particles, or in one case give rise to the phenomenon of [[mass]].


According to the [[Standard Model of Particle Physics]] there are five elementary bosons:
According to the [[Standard Model of Particle Physics]] there are five elementary bosons:
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**{{Subatomic particle|link=yes|Higgs Boson}} [[Higgs boson]] – the particle that contributes to the phenomenon of [[mass]] via the [[Higgs mechanism]]
**{{Subatomic particle|link=yes|Higgs Boson}} [[Higgs boson]] – the particle that contributes to the phenomenon of [[mass]] via the [[Higgs mechanism]]
* Four ''[[vector boson]]s'' (spin = 1) that act as [[force carriers]]. These are the [[gauge boson]]s:
* Four ''[[vector boson]]s'' (spin = 1) that act as [[force carriers]]. These are the [[gauge boson]]s:
**{{Subatomic particle|link=yes|Photon}}   [[Photon]] – the force carrier of the [[electromagnetic field]]
** {{Subatomic particle|link=yes|Photon}}   [[Photon]] – the force carrier of the [[electromagnetic field]]
**{{Subatomic particle|link=yes|Gluon}}   [[Gluon]]s (eight different types) – force carriers that mediate the [[Strong interaction|strong force]]
** {{Subatomic particle|link=yes|Gluon}}   [[Gluon]]s (eight different types) – force carriers that mediate the [[Strong interaction|strong force]]
**{{Subatomic particle|link=yes|Z boson}}   [[W and Z bosons|Neutral weak boson]] – the force carrier that mediates the [[weak interaction|weak force]]
** {{Subatomic particle|link=yes|Z boson}}   [[W and Z bosons|Neutral weak boson]] – the force carrier that mediates the [[weak interaction|weak force]]
**{{Subatomic particle|link=yes|W boson+-}}   [[W and Z bosons|Charged weak boson]]s (two types) – also force carriers that mediate the weak force
** {{Subatomic particle|link=yes|W boson+-}}   [[W and Z bosons|Charged weak boson]]s (two types) – also force carriers that mediate the weak force


A ''second order tensor boson'' (spin = 2) called the [[graviton]] (G) has been hypothesised as the force carrier for [[Gravitational force|gravity]], but so far all attempts to incorporate gravity into the Standard Model have failed.<ref group="lower-alpha">Despite being the carrier of the gravitational force which interacts with mass, the graviton is expected to have no mass.</ref>
* <span class="anchor" id="tensor_boson_anchor"></span> A ''second order tensor boson'' (spin = 2) called the [[graviton]] (G) has been hypothesised as the force carrier for [[Gravitational force|gravity]], but so far all attempts to incorporate gravity into the Standard Model have failed.{{efn|
Despite being the carrier of the gravitational force which interacts with mass, most attempts at [[quantum gravity]] have expected the graviton to have no mass, just like the photon has no electric charge, and the [[W and Z bosons]] have no [[flavour (particle physics)|"flavour"]].
}}


== Composite bosons ==
== Composite bosons ==
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Composite bosons include:
Composite bosons include:
* All [[meson]]s of every type

* Stable nuclei with even [[mass number]]s such as [[deuterium]], [[helium-4]] (the [[alpha particle]]),<ref>
* All types of [[meson]]
{{cite journal
* Stable nuclei of even [[mass number]] such as [[deuterium]], [[helium-4]] (the [[alpha particle]]),<ref>{{cite journal|last1=Qaim|first1=Syed M.|last2=Spahn|first2=Ingo|last3=Scholten|first3=Bernhard|last4=Neumaier|first4=Bernd|date=June 8, 2016|title=Uses of alpha particles, especially in nuclear reaction studies and medical radionuclide production|url=https://www.degruyter.com/document/doi/10.1515/ract-2015-2566/html|journal=Radiochimica Acta|volume=104|issue=9|page=601|doi=10.1515/ract-2015-2566|access-date=May 22, 2021|s2cid=56100709}}</ref> [[carbon-12]] and [[lead-208]].<ref group="lower-alpha">[[Even and odd atomic nuclei|Even-mass-number nuclides]], which comprise {{frac|153|254}} = ~ 60% of all stable nuclides, are bosons, i.e. they have integer spin. Almost all (148 of the 153) are even-proton, even-neutron (EE) nuclides, which necessarily have spin&nbsp;0 because of pairing. The remaining 5&nbsp;stable bosonic nuclides are odd-proton, odd-neutron stable nuclides (see ''{{section link|Even and odd atomic nuclei#Odd proton, odd neutron}}''); these odd–odd bosons are: {{nuclide|Hydrogen|2|link=yes}}, {{nuclide|Lithium|6|link=yes}},{{nuclide|Boron|10|link=yes}}, {{nuclide|Nitrogen|14|link=yes}} and [[Tantalum-180m|{{nuclide|Tantalum|180|m}}]]). All have nonzero integer spin.</ref>
|last1=Qaim |first1=Syed M. |last2=Spahn |first2=Ingo
|last3=Scholten |first3=Bernhard |last4=Neumaier |first4=Bernd
|date=June 8, 2016
|title=Uses of alpha particles, especially in nuclear reaction studies and medical radionuclide production
|journal=Radiochimica Acta
|volume=104 |issue=9 |page=601
|doi=10.1515/ract-2015-2566 |s2cid=56100709
|url=https://www.degruyter.com/document/doi/10.1515/ract-2015-2566/html
|access-date=May 22, 2021
}}
</ref> [[carbon-12]], [[lead-208]], and many others.<ref group="lower-alpha">
[[Even and odd atomic nuclei|Even-mass-number nuclides]] comprise {{sfrac|&nbsp;153&nbsp;| 254 }} = 60% of all stable nuclides. They are bosons, i.e. they have integer spin, and almost all of them (148 of the 153) are even-proton / even-neutron (EE) nuclides. The EE nuclides necessarily have spin&nbsp;0 because of pairing. The remaining 5&nbsp;stable bosonic nuclides are odd-proton / odd-neutron (OO) stable nuclides (see ''{{section link|Even and odd atomic nuclei#Odd proton, odd neutron}}''). The five odd–odd bosonic nuclides are:
{{div col begin|colwidth=3em}}
: {{nuclide|Hydrogen|2|link=yes}}
: {{nuclide|Lithium|6|link=yes}}
: {{nuclide|Boron|10|link=yes}}
: {{nuclide|Nitrogen|14|link=yes}}
: [[Tantalum-180m|{{nuclide|Tantalum|180|m}}]]
{{div col end}}
Each of the five has integer, nonzero spin.
</ref>


As [[Quantum mechanics|quantum particles]], the behaviour of multiple indistinguishable bosons at high densities is described by [[Bose–Einstein statistics]]. One characteristic which becomes important in [[superfluidity]] and other applications of [[Bose–Einstein condensate]]s is that there is no restriction on the number of bosons that may occupy the same [[quantum state]]. As a consequence, when for example a gas of [[helium-4]] atoms is cooled to temperatures very close to [[absolute zero]] and the [[kinetic energy]] of the particles becomes negligible, it condenses into a low-energy state and becomes a [[Superfluid helium-4|superfluid]].
As [[Quantum mechanics|quantum particles]], the behaviour of multiple indistinguishable bosons at high densities is described by [[Bose–Einstein statistics]]. One characteristic which becomes important in [[superfluidity]] and other applications of [[Bose–Einstein condensate]]s is that there is no restriction on the number of bosons that may occupy the same [[quantum state]]. As a consequence, when for example a gas of [[helium-4]] atoms is cooled to temperatures very close to [[absolute zero]] and the [[kinetic energy]] of the particles becomes negligible, it condenses into a low-energy state and becomes a [[Superfluid helium-4|superfluid]].


==Quasiparticles==
== Quasiparticles ==
Certain [[quasiparticle]]s are observed to behave as bosons and to follow [[Bose–Einstein statistics]], including [[Cooper pair]]s, [[plasmon]]s and [[phonon]]s.<ref name="Jr.2004">{{cite book|author1-link=Charles P. Poole|author=Poole, Charles P. Jr.|url=https://books.google.com/books?id=CXwrqM2hU0EC|title=Encyclopedic Dictionary of Condensed Matter Physics|date=11 March 2004|publisher=Academic Press|isbn=978-0-08-054523-3}}</ref>{{rp|130}}
Certain [[quasiparticle]]s are observed to behave as bosons and to follow [[Bose–Einstein statistics]], including [[Cooper pair]]s, [[plasmon]]s and [[phonon]]s.<ref name="Jr.2004">{{cite book|author1-link=|author=Poole, Charles P. Jr.|url=https://books.google.com/books?id=CXwrqM2hU0EC|title=Encyclopedic Dictionary of Condensed Matter Physics|date=11 March 2004|publisher=Academic Press|isbn=978-0-08-054523-3}}</ref>{{rp|130}}


==See also==
== See also ==
*{{annotated link|Anyon}}
* {{annotated link|Anyon}}
*{{annotated link|Bose gas}}
* {{annotated link|Bose gas}}
*{{annotated link|Parastatistics}}
* {{annotated link|Parastatistics}}


== Explanatory notes ==
== Explanatory notes ==

Revision as of 12:02, 3 June 2024

Bosons form one of the two fundamental classes of subatomic particle, the other being fermions. All subatomic particles must be one or the other. A composite particle (hadron) may fall into either class depending on its composition

In particle physics, a boson (/ˈbzɒn/[1] /ˈbsɒn/[2]) is a subatomic particle whose spin quantum number has an integer value (0, 1, 2, ...). Bosons form one of the two fundamental classes of subatomic particle, the other being fermions, which have odd half-integer spin (12, 32, 52, ...). Every observed subatomic particle is either a boson or a fermion. Paul Dirac coined the name boson to commemorate the contribution of Satyendra Nath Bose, an Indian physicist.

Some bosons are elementary particles occupying a special role in particle physics, distinct from the role of fermions (which are sometimes described as the constituents of "ordinary matter"). Certain elementary bosons (e.g. gluons) act as force carriers, which give rise to forces between other particles, while one (the Higgs boson) contributes to the phenomenon of mass. Other bosons, such as mesons, are composite particles made up of smaller constituents.

Outside the realm of particle physics, multiple identical composite bosons (in this context sometimes known as 'bose particles') behave at high densities or low temperatures in a characteristic manner described by Bose–Einstein statistics: for example a gas of helium-4 atoms becomes a superfluid at temperatures close to absolute zero. Similarly, superconductivity arises because some quasiparticles, such as Cooper pairs, behave in the same way.

Name

The name boson was coined by Paul Dirac[3][4] to commemorate the contribution of Satyendra Nath Bose, an Indian physicist. When Bose was a reader (later professor) at the University of Dhaka, Bengal (now in Bangladesh),[5][6] he and Albert Einstein developed the theory characterising such particles, now known as Bose–Einstein statistics and Bose–Einstein condensate.[7]

Elementary bosons

All observed elementary particles are either bosons (with integer spin) or fermions (with odd half-integer spin).[8] Whereas the elementary particles that make up ordinary matter (leptons and quarks) are fermions, elementary bosons occupy a special role in particle physics. They act either as force carriers which give rise to forces between other particles, or in one case give rise to the phenomenon of mass.

According to the Standard Model of Particle Physics there are five elementary bosons:

  • A second order tensor boson (spin = 2) called the graviton (G) has been hypothesised as the force carrier for gravity, but so far all attempts to incorporate gravity into the Standard Model have failed.[a]

Composite bosons

Composite particles (such as hadrons, nuclei, and atoms) can be bosons or fermions depending on their constituents. Since bosons have integer spin and fermions odd half-integer spin, any composite particle made up of an even number of fermions is a boson.

Composite bosons include:

As quantum particles, the behaviour of multiple indistinguishable bosons at high densities is described by Bose–Einstein statistics. One characteristic which becomes important in superfluidity and other applications of Bose–Einstein condensates is that there is no restriction on the number of bosons that may occupy the same quantum state. As a consequence, when for example a gas of helium-4 atoms is cooled to temperatures very close to absolute zero and the kinetic energy of the particles becomes negligible, it condenses into a low-energy state and becomes a superfluid.

Quasiparticles

Certain quasiparticles are observed to behave as bosons and to follow Bose–Einstein statistics, including Cooper pairs, plasmons and phonons.[10]: 130 

See also

  • Anyon – Type of two-dimensional quasiparticle
  • Bose gas – State of matter of many bosons
  • Parastatistics – Notion in statistical mechanics

Explanatory notes

  1. ^ Despite being the carrier of the gravitational force which interacts with mass, most attempts at quantum gravity have expected the graviton to have no mass, just like the photon has no electric charge, and the W and Z bosons have no "flavour".
  2. ^ Even-mass-number nuclides comprise  153 / 254 = 60% of all stable nuclides. They are bosons, i.e. they have integer spin, and almost all of them (148 of the 153) are even-proton / even-neutron (EE) nuclides. The EE nuclides necessarily have spin 0 because of pairing. The remaining 5 stable bosonic nuclides are odd-proton / odd-neutron (OO) stable nuclides (see Even and odd atomic nuclei § Odd proton, odd neutron). The five odd–odd bosonic nuclides are:

    Each of the five has integer, nonzero spin.

References

  1. ^ "boson". Lexico UK English Dictionary. Oxford University Press. Archived from the original on 9 July 2021.
  2. ^ Wells, John C. (1990). Longman pronunciation dictionary. Harlow, England: Longman. ISBN 978-0582053830. entry "Boson"
  3. ^ Notes on Dirac's lecture Developments in Atomic Theory at Le Palais de la Découverte, 6 December 1945. UKNATARCHI Dirac Papers. BW83/2/257889.
  4. ^ Farmelo, Graham (25 August 2009). The Strangest Man: The Hidden Life of Paul Dirac, Mystic of the Atom. Basic Books. p. 331. ISBN 9780465019922.
  5. ^ Daigle, Katy (10 July 2012). "India: Enough about Higgs, let's discuss the boson". Associated Press. Retrieved 10 July 2012.
  6. ^ Bal, Hartosh Singh (19 September 2012). "The Bose in the Boson". Latitude (blog). The New York Times. Archived from the original on 22 September 2012. Retrieved 21 September 2012.
  7. ^ "Higgs boson: The poetry of subatomic particles". BBC News. 4 July 2012. Retrieved 6 July 2012.
  8. ^ Carroll, Sean (2007). Guidebook. Dark Matter, Dark Energy: The dark side of the universe. The Teaching Company. Part 2, p. 43. ISBN 978-1598033502. ... boson: A force-carrying particle, as opposed to a matter particle (fermion). Bosons can be piled on top of each other without limit. Examples are photons, gluons, gravitons, weak bosons, and the Higgs boson. The spin of a boson is always an integer: 0, 1, 2, and so on ...
  9. ^ Qaim, Syed M.; Spahn, Ingo; Scholten, Bernhard; Neumaier, Bernd (8 June 2016). "Uses of alpha particles, especially in nuclear reaction studies and medical radionuclide production". Radiochimica Acta. 104 (9): 601. doi:10.1515/ract-2015-2566. S2CID 56100709. Retrieved 22 May 2021.
  10. ^ Poole, Charles P. Jr. (11 March 2004). Encyclopedic Dictionary of Condensed Matter Physics. Academic Press. ISBN 978-0-08-054523-3.