Editing Nuclear density

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

'''Nuclear density''' is the [[density]] of the [[atomic nucleus|nucleus]] of an [[atom]]. For heavy nuclei, it is close to the ''nuclear saturation density'' <math>n_0=0.15\pm0.01</math> [[nucleon]]s/[[Femtometer|fm]]<sup>3</sup>, which minimizes the energy density of an infinite [[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=[[Physical Review|Phys. Rev. C]] |year=2020 |volume=102 |issue= 4|pages=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]]. The descriptive term ''nuclear density'' is also applied to situations where similarly high densities occur, such as within [[neutron stars]].

== Evaluation ==
The nuclear density of a typical nucleus can be approximately calculated from the [[nuclear size|size of the nucleus]], 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]]s, is
<math>R=A^{1/3}R_0</math>
where <math>A</math> is the [[mass number]] and <math>R_0</math> is 1.25 [[femtometre|fm]], with typical deviations of up to 0.2&nbsp;fm from this value.{{citation needed|date=September 2022}} The [[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]] 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]] is not a fundamental particle, being composed of [[Quark–gluon plasma|quark–gluon matter]]. 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]]s.

Using [[deep inelastic scattering]], it has been estimated that the "size" of an [[electron]], if it is not a [[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]]. In the near future, the highest experimentally measurable densities will likely be limited to [[lepton]]s and [[quark]]s.{{citation needed|date=September 2022}}

==See also==
*[[Electron degeneracy pressure]]
*[[Nuclear matter]]
*[[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]]