Editing Extended periodic table (section)

===End of the periodic table===
The number of physically possible elements is unknown. A low estimate is that the periodic table may end soon after the [[island of stability]],<ref name=EB>{{cite encyclopedia|last1=Seaborg|first1=Glenn T.|url=https://www.britannica.com/EBchecked/topic/603220/transuranium-element|title=transuranium element (chemical element)|encyclopedia=Encyclopædia Britannica|date=c. 2006|access-date=2010-03-16}}</ref> which is expected to center on ''Z''&nbsp;=&nbsp;126, as the extension of the periodic and [[nuclide]] tables is restricted by the proton and the neutron [[Nuclear drip line|drip lines]] and stability toward alpha decay and spontaneous fission.<ref>{{cite journal | first1=S. |last1=Cwiok|first2=P.-H.|last2=Heenen |first3=W.|last3=Nazarewicz |year=2005|title=Shape coexistence and triaxiality in the superheavy nuclei|journal=Nature|volume=433|bibcode = 2005Natur.433..705C |doi = 10.1038/nature03336 | issue=7027 | pmid=15716943 | pages=705–9|s2cid=4368001}}</ref> One calculation by Y. Gambhir ''et al.'', analyzing [[nuclear binding energy]] and stability in various decay channels, suggests a limit to the existence of bound nuclei at ''Z''&nbsp;=&nbsp;146.<ref name=limit146>{{cite journal|last1=Gambhir|first1=Y. K.|last2=Bhagwat|first2=A.|last3=Gupta|first3=M.|title=The highest limiting Z in the extended periodic table|date=2015|journal=Journal of Physics G: Nuclear and Particle Physics|volume=42|issue=12|pages=125105|doi=10.1088/0954-3899/42/12/125105|url= https://www.researchgate.net/publication/284213926|bibcode=2015JPhG...42l5105G}}</ref> Other predictions of an end to the periodic table include ''Z''&nbsp;=&nbsp;128 ([[John Emsley]]) and ''Z''&nbsp;=&nbsp;155 (Albert Khazan).<ref name="emsley"/>

====Elements above the atomic number 137====
It is a "folk legend" among physicists that [[Richard Feynman]] suggested that neutral atoms could not exist for atomic numbers greater than ''Z''&nbsp;=&nbsp;137, on the grounds that the [[Theory of relativity|relativistic]] [[Dirac equation]] predicts that the ground-state energy of the innermost electron in such an atom would be an [[imaginary number]]. Here, the number 137 arises as the inverse of the [[fine-structure constant]]. By this argument, neutral atoms cannot exist beyond atomic number 137, and therefore a periodic table of elements based on electron orbitals breaks down at this point. However, this argument presumes that the atomic nucleus is pointlike. A more accurate calculation must take into account the small, but nonzero, size of the nucleus, which is predicted to push the limit further to ''Z''&nbsp;≈&nbsp;173.<ref name="rsc">{{cite web |url=https://www.chemistryworld.com/opinion/column-the-crucible/3005076.article |title=Would element 137 really spell the end of the periodic table? Philip Ball examines the evidence|author=Philip Ball |date=November 2010 |website=[[Chemistry World]]|publisher=[[Royal Society of Chemistry]] |access-date=2012-09-30}}</ref>

=====Bohr model=====
The [[Bohr model]] exhibits difficulty for atoms with atomic number greater than 137, for the speed of an electron in a [[Atomic orbital|1s electron orbital]], ''v'', is given by

:<math>v = Z \alpha c \approx \frac{Z c}{137.04}</math>

where ''Z'' is the [[atomic number]], and ''α'' is the [[fine-structure constant]], a measure of the strength of electromagnetic interactions.<ref>{{cite book|first1=R. |last1=Eisberg|first2= R.|last2= Resnick|year=1985|title=Quantum Physics of Atoms, Molecules, Solids, Nuclei and Particles|url=https://archive.org/details/quantumphysicsof00eisb |url-access=registration |publisher=[[John Wiley & Sons|Wiley]]|isbn=9780471873730}}</ref> Under this approximation, any element with an atomic number of greater than 137 would require 1s electrons to be traveling faster than ''c'', the [[speed of light]]. Hence, the non-relativistic Bohr model is inaccurate when applied to such an element.

=====Relativistic Dirac equation=====
[[File:1s negative continuum.svg|thumb|right|540px|Energy eigenvalues for the 1s, 2s, 2p<sub>1/2</sub> and 2p<sub>3/2</sub> shells from solutions of the [[Dirac equation]] (taking into account the finite size of the nucleus) for ''Z''&nbsp;=&nbsp;135–175 (–·–), for the Thomas-Fermi potential (—) and for ''Z''&nbsp;=&nbsp;160–170 with the self-consistent potential (---)<ref name=Fricke/>]]
The [[Theory of relativity|relativistic]] [[Dirac equation]] gives the ground state energy as

:<math>E=\frac{m c^2}{\sqrt{1+\dfrac{Z^2 \alpha^2}{\bigg({n-\left(j+\frac12\right)+\sqrt{\left(j+\frac12\right)^2-Z^ 2\alpha^2}\bigg)}^2}}},</math>

where ''m'' is the rest mass of the electron.<ref>{{cite web |title=Solution of the Dirac Equation for Hydrogen |url=https://quantummechanics.ucsd.edu/ph130a/130_notes/node501.html}}</ref> For ''Z''&nbsp;>&nbsp;137, the wave function of the Dirac ground state is oscillatory, rather than bound, and there is no gap between the positive and negative energy spectra, as in the [[Klein paradox]].<ref>{{cite book|first1=J. D.|last1= Bjorken|first2=S. D.|last2= Drell|year=1964|title=Relativistic Quantum Mechanics|url=https://archive.org/details/relativisticquan0000bjor|url-access=registration|publisher=[[McGraw-Hill]]}}</ref> More accurate calculations taking into account the effects of the finite size of the nucleus indicate that the binding energy first exceeds 2''mc''<sup>2</sup> for ''Z''&nbsp;>&nbsp;''Z''<sub>cr</sub> probably between 168 and 172.<ref name=gamowstates/> For ''Z''&nbsp;>&nbsp;''Z''<sub>cr</sub>, if the innermost orbital (1s) is not filled, the electric field of the nucleus will [[pair production|pull an electron out of the vacuum]], resulting in the spontaneous emission of a [[positron]].<ref>{{cite journal|first1=W. |last1=Greiner|first2= S. |last2=Schramm |year=2008|title=Resource Letter QEDV-1: The QED vacuum |journal=[[American Journal of Physics]] |volume=76 |issue=6|pages=509 |doi=10.1119/1.2820395|bibcode=2008AmJPh..76..509G}}, and references therein</ref><ref>{{cite journal|last1=Wang|first1=Yang|last2=Wong|first2=Dillon|last3=Shytov|first3=Andrey V.|last4=Brar|first4=Victor W.|last5=Choi|first5=Sangkook|last6=Wu|first6=Qiong|last7=Tsai|first7=Hsin-Zon|last8=Regan|first8=William|last9=Zettl|first9=Alex|author9-link=Alex Zettl|last10=Kawakami|first10=Roland K.|last11=Louie|first11=Steven G.|last12=Levitov|first12=Leonid S.|last13=Crommie|first13=Michael F.|title=Observing Atomic Collapse Resonances in Artificial Nuclei on Graphene|journal=Science|date=May 10, 2013|volume=340|issue=6133|pages=734–737|doi=10.1126/science.1234320|arxiv = 1510.02890 |bibcode = 2013Sci...340..734W|pmid=23470728|s2cid=29384402}}</ref> This diving of the 1s subshell into the negative continuum has often been taken to constitute an "end" to the periodic table,<ref name=PT172/><ref name="rsc"/><ref>{{Cite journal|last1=Indelicato|first1=Paul|last2=Bieroń|first2=Jacek|last3=Jönsson|first3=Per|date=2011-06-01|title=Are MCDF calculations 101% correct in the super-heavy elements range?|url=https://dspace.mah.se/handle/2043/12984|journal=Theoretical Chemistry Accounts|language=en|volume=129|issue=3–5|pages=495–505|doi=10.1007/s00214-010-0887-3|issn=1432-881X|hdl=2043/12984|s2cid=54680128|hdl-access=free}}</ref> but in fact it does not impose such a limit, as such resonances can be interpreted as [[Gamow state]]s. Nonetheless, the accurate description of such states in a multi-electron system, needed to extend calculations and the periodic table past ''Z''<sub>cr</sub>&nbsp;≈&nbsp;172, are still open problems.<ref name=gamowstates>{{cite journal |last1=Smits |first1=O. R. |last2=Indelicato |first2=P. |first3=W. |last3=Nazarewicz |first4=M. |last4=Piibeleht |first5=P. |last5=Schwerdtfeger |date=2023 |title=Pushing the limits of the periodic table—A review on atomic relativistic electronic structure theory and calculations for the superheavy elements |url= |journal=Physics Reports |volume=1035 |issue= |pages=1–57 |doi=10.1016/j.physrep.2023.09.004 |access-date=|arxiv=2301.02553 |bibcode=2023PhR..1035....1S }}</ref>

Atoms with atomic numbers above ''Z''<sub>cr</sub>&nbsp;≈&nbsp;172 have been termed ''supercritical'' atoms. Supercritical atoms cannot be totally ionised because their 1s subshell would be filled by spontaneous pair creation in which an electron-positron pair is created from the negative continuum, with the electron being bound and the positron escaping. However, the strong field around the atomic nucleus is restricted to a very small region of space, so that the [[Pauli exclusion principle]] forbids further spontaneous pair creation once the subshells that have dived into the negative continuum are filled. Elements 173–184 have been termed ''weakly supercritical'' atoms as for them only the 1s shell has dived into the negative continuum; the 2p<sub>1/2</sub> shell is expected to join around element 185 and the 2s shell around element 245. Experiments have so far not succeeded in detecting spontaneous pair creation from assembling supercritical charges through the collision of heavy nuclei (e.g. colliding lead with uranium to momentarily give an effective ''Z'' of 174; uranium with uranium gives effective ''Z''&nbsp;=&nbsp;184 and uranium with californium gives effective ''Z''&nbsp;=&nbsp;190).<ref>{{cite book|last1=Reinhardt|first1=Joachim|title = Nuclear Physics: Present and Future|pages=195–210|last2=Greiner|first2=Walter|doi=10.1007/978-3-319-10199-6_19|date=2015|chapter=Probing Supercritical Fields with Real and with Artificial Nuclei|isbn=978-3-319-10198-9}}</ref>

Even though passing ''Z''<sub>cr</sub> does not mean elements can no longer exist, the increasing concentration of the 1s density close to the nucleus would likely make these electrons more vulnerable to [[electron capture|''K'' electron capture]] as ''Z''<sub>cr</sub> is approached. For such heavy elements, these 1s electrons would likely spend a significant fraction of time so close to the nucleus that they are actually inside it. This may pose another limit to the periodic table.<ref name=colloq>{{cite journal |title=Colloquium: Superheavy elements: Oganesson and beyond |first1=S. A. |last1=Giuliani |first2=Z. |last2=Matheson |first3=W. |last3=Nazarewicz |first4=E. |last4=Olsen |first5=P.-G. |last5=Reinhard |first6=J. |last6=Sadhukhan |first7=B. |last7=Schtruempf |first8=N. |last8=Schunck |first9=P. |last9=Schwerdtfeger |date=2019 |journal=Reviews of Modern Physics |volume=91 |issue=1 |pages=011001-1–011001-25 |doi=10.1103/RevModPhys.91.011001|bibcode=2019RvMP...91a1001G |s2cid=126906074 |doi-access=free }}</ref>

Because of the factor of ''m'', [[muonic atom]]s become supercritical at a much larger atomic number of around 2200, as [[muon]]s are about 207 times as heavy as electrons.<ref name=gamowstates/>

=====Quark matter=====
{{main|Continent of stability|QCD matter}}
It has also been posited that in the region beyond ''A''&nbsp;>&nbsp;300, an entire "[[continent of stability]]" consisting of a hypothetical phase of stable [[quark matter]], comprising freely flowing [[up quark|up]] and [[down quark|down]] quarks rather than [[quark]]s bound into protons and neutrons, may exist. Such a form of matter is theorized to be a ground state of [[baryonic matter]] with a greater binding energy per [[baryon]] than [[nuclear matter]], favoring the decay of nuclear matter beyond this mass threshold into quark matter. If this state of matter exists, it could possibly be synthesized in the same fusion reactions leading to normal superheavy nuclei, and would be stabilized against fission as a consequence of its stronger binding that is enough to overcome Coulomb repulsion.<ref name="udQM">{{cite journal |last1=Holdom |first1=B. |last2=Ren |first2=J. |last3=Zhang |first3=C. |title=Quark matter may not be strange |date=2018 |journal=Physical Review Letters |volume=120 |issue=1 |pages=222001-1–222001-6 <!-- Deny Citation Bot-->|doi=10.1103/PhysRevLett.120.222001|pmid=29906186 |arxiv=1707.06610 |bibcode=2018PhRvL.120v2001H |s2cid=49216916 }}</ref>

Calculations published in 2020<ref name=udQMnew>{{cite journal |last1=Cheng-Jun |first1=Xia |last2=She-Sheng |first2=Xue |last3=Ren-Xin |first3=Xu |last4=Shan-Gui |first4=Zhou |title=Supercritically charged objects and electron-positron pair creation |doi=10.1103/PhysRevD.101.103031 |journal=Physical Review D |year=2020 |volume=101 |issue=10 |pages=103031|arxiv=2001.03531 |bibcode=2020PhRvD.101j3031X |s2cid=210157134 }}</ref> suggest stability of up-down quark matter (udQM) nuggets against conventional nuclei beyond ''A''&nbsp;~&nbsp;266, and also show that udQM nuggets become supercritical earlier (''Z''<sub>cr</sub>&nbsp;~&nbsp;163, ''A''&nbsp;~&nbsp;609) than conventional nuclei (''Z''<sub>cr</sub>&nbsp;~&nbsp;177, ''A''&nbsp;~&nbsp;480).