# Nuclear density

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{{Short description|Density of the nucleus of an atom}}
{{More citations needed|date=July 2021}}

'''Nuclear density''' is the [density](/source/density) of the nucleons (neutrons and protons) in the [nucleus](/source/atomic_nucleus). For heavy nuclei, it is close to the ''nuclear saturation density'' <math>n_0=0.15\pm0.01</math> [nucleon](/source/nucleon)s/[fm](/source/Femtometer)<sup>3</sup>, which minimizes the energy density of an infinite [nuclear matter](/source/nuclear_matter).<ref name=Horowitz>{{cite journal |last1=Horowitz |first1=C. J. |last2=Piekarewicz |first2=J. |last3=Reed |first3=Brendan |title=Insights into nuclear saturation density from parity-violating electron scattering |url=https://journals.aps.org/prc/abstract/10.1103/PhysRevC.102.044321 |journal=[Phys. Rev. C](/source/Physical_Review) |year=2020 |volume=102 |issue= 4|article-number=044321 |doi=10.1103/PhysRevC.102.044321 |arxiv=2007.07117 |bibcode=2020PhRvC.102d4321H |s2cid=222080305 |access-date=September 7, 2022}}</ref> The ''nuclear saturation mass density'' is thus <math>\rho_0=n_0 m_{\rm u} \approx 2.5\times10^{17}</math> kg/m<sup>3</sup>, where ''m''<sub>u</sub> is the [atomic mass constant](/source/atomic_mass_constant). The descriptive term ''nuclear density'' is also applied to situations where similarly high densities occur, such as within [neutron stars](/source/neutron_stars).

== Evaluation ==
The nuclear density of a typical nucleus can be approximately calculated from the [size of the nucleus](/source/nuclear_size), which itself can be approximated based on the number of protons and neutrons in it. The radius of a typical nucleus, in terms of number of [nucleon](/source/nucleon)s, is
<math>R=A^{1/3}R_0</math>
where <math>A</math> is the [mass number](/source/mass_number) and <math>R_0</math> is 1.25 [fm](/source/femtometre), with typical deviations of up to 0.2&nbsp;fm from this value.{{citation needed|date=September 2022}} The [number density](/source/number_density) of the nucleus is thus:
:<math>n = \frac{A}{{4\over 3} \pi R^3}</math>
The density for any typical nucleus, in terms of mass number, is thus constant, not dependent on ''A'' or ''R'', theoretically:

:<math>n_0^\mathrm{theor} = \frac{A}{{4\over 3} \pi (A^{1/3}R_0)^3} = \frac{3}{4 \pi (1.25\ \mathrm{fm})^3} = 0.122 \ \mathrm{fm}^{-3} = 1.22 \times 10^{44} \ \mathrm{m}^{-3}</math>

The experimentally determined value for the nuclear saturation density is<ref name=Horowitz />

:<math>n_0^\mathrm{exp}=0.15\pm0.01\ \mathrm{fm}^{-3} = (1.5\pm 0.1)\times 10^{44}\ \mathrm{m}^{-3}.</math>

The mass density &rho; is the product of the number density ''n'' by the particle's mass. The calculated mass density, using a [nucleon](/source/nucleon) mass of ''m''<sub>n</sub>=1.67×10<sup>−27</sup> kg, is thus:

:<math>\rho_0^\mathrm{theor}=m_\mathrm{n}\,n_0^\mathrm{theor} \approx 2 \times 10^{17} \ \mathrm{kg} \ \mathrm{m}^{-3}</math> (using the theoretical estimate)

or

:<math>\rho_0^\mathrm{exp}=m_\mathrm{n}\,n_0^\mathrm{exp} \approx 2.5 \times 10^{17} \ \mathrm{kg} \ \mathrm{m}^{-3}</math>  (using the experimental value).

== Applications and extensions ==
The components of an atom and of a nucleus have varying densities. The [proton](/source/proton) is not a fundamental particle, being composed of [quark–gluon matter](/source/Quark%E2%80%93gluon_plasma). Its size is approximately 10<sup>−15</sup> meters and its density 10<sup>18</sup> kg/m<sup>3</sup>. The descriptive term ''nuclear density'' is also applied to situations where similarly high densities occur, such as within [neutron star](/source/neutron_star)s.

Using [deep inelastic scattering](/source/deep_inelastic_scattering), it has been estimated that the "size" of an [electron](/source/electron), if it is not a [point particle](/source/point_particle), must be less than 10<sup>−17</sup> meters.{{citation needed|date=September 2022}} This would correspond to a density of roughly 10<sup>21</sup> kg/m<sup>3</sup>.

There are possibilities for still-higher densities when it comes to [quark matter](/source/quark_matter). In the near future, the highest experimentally measurable densities will likely be limited to [lepton](/source/lepton)s and [quark](/source/quark)s.{{citation needed|date=September 2022}}

==See also==
*{{annotated link|Electron degeneracy pressure}}
*{{annotated link|Nuclear matter}}
*{{annotated link|Quark–gluon plasma}}

==References==
{{Reflist}}

==External links==
*{{cite web |url=https://www.cyberphysics.co.uk/topics/atomic/nucleus.htm |title=The Atomic Nucleus |access-date=2014-11-18}} (derivation of equations and other mathematical descriptions)

Category:Mass density
Category:Atoms

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Adapted from the Wikipedia article [Nuclear density](https://en.wikipedia.org/wiki/Nuclear_density) by Wikipedia contributors ([contributor history](https://en.wikipedia.org/wiki/Nuclear_density?action=history)). Available under [Creative Commons Attribution-ShareAlike 4.0 International](https://creativecommons.org/licenses/by-sa/4.0/). Changes may have been made.