Editing Beta decay (section)

===Bound-state β{{sup|−}} decay===
A very small minority of free neutron decays (about four per million) are "two-body decays": the proton, electron and antineutrino are produced, but the electron fails to gain the 13.6 eV energy necessary to escape the proton, and therefore simply remains bound to it, as a neutral [[hydrogen atom]].<ref>[http://www.physi.uni-heidelberg.de/Publications/ckm_byrne.pdf An Overview Of Neutron Decay] {{Webarchive|url=https://web.archive.org/web/20170919055418/http://www.physi.uni-heidelberg.de/Publications/ckm_byrne.pdf |date=2017-09-19 }} J. Byrne in Quark-Mixing, CKM Unitarity (H. Abele and D. Mund, 2002), see p.XV</ref> In this type of beta decay, in essence all of the neutron [[decay energy]] is carried off by the antineutrino.

For fully ionized atoms (bare nuclei), it is possible in likewise manner for electrons to fail to escape the atom, and to be emitted from the nucleus into low-lying atomic bound states (orbitals). This cannot occur for neutral atoms with low-lying bound states which are already filled by electrons.

Bound-state β{{sup|−}} decays were predicted by [[Raymond Daudel|Daudel]], Jean, and Lecoin in 1947,<ref>{{cite journal| last1=Daudel | first1=Raymond | first2=Maurice | last2=Jean | first3=Marcel | last3=Lecoin | year=1947 | title=Sur la possibilité d'existence d'un type particulier de radioactivité phénomène de création e | journal=J. Phys. Radium | volume=8 | issue=8 | pages=238–243 | doi=10.1051/jphysrad:0194700808023800| url=https://hal.archives-ouvertes.fr/jpa-00234057/document }}</ref> and the phenomenon in fully ionized atoms was first observed for [[isotopes of dysprosium|{{sup|163}}Dy{{sup|66+}}]] in 1992 by Jung et al. of the [[GSI Helmholtz Centre for Heavy Ion Research|Darmstadt Heavy-Ion Research Center]]. Though neutral {{sup|163}}Dy is stable, fully ionized {{sup|163}}Dy{{sup|66+}} undergoes β{{sup|−}} decay into the K and L shells with a half-life of 47 days.<ref>{{cite journal
 |last1=Jung |first1=M.
 |display-authors=etal
 |year=1992
 |title=First observation of bound-state β<sup>&minus;</sup> decay
 |journal=[[Physical Review Letters]]
 |volume=69 |issue=15 |pages=2164–2167
 |bibcode=1992PhRvL..69.2164J
 |doi=10.1103/PhysRevLett.69.2164
 |pmid=10046415
}}</ref> The resulting nucleus – [[isotopes of holmium|{{sup|163}}Ho{{sup|66+}}]] – is stable only in this almost fully ionized state and will decay via [[electron capture]] into {{sup|163}}Dy in the neutral state. Likewise, while being stable in the neutral state, the fully ionized [[Isotopes of thallium|{{sup|205}}Tl{{sup|81+}}]] undergoes bound-state β{{sup|−}} decay to [[isotopes of lead|{{sup|205}}Pb{{sup|81+}}]] with a half-life of {{val|291|33|27|}} days.<ref>{{cite web|url=http://www.ca.infn.it/~oldeman/resneu/p1522_1.pdf |title=Bound-state beta decay of highly ionized atoms|access-date=June 9, 2013 |url-status=dead |archive-url=https://web.archive.org/web/20131029205727/http://www.ca.infn.it/~oldeman/resneu/p1522_1.pdf |archive-date=October 29, 2013 }}</ref><ref>{{cite journal |last1=Bai |first1=M. |last2=Blaum |first2=K. |last3=Boev |first3=B. |last4=Bosch |first4=F. |last5=Brandau |first5=C. |last6=Cvetković |first6=V. |last7=Dickel |first7=T. |last8=Dillmann |first8=I. |last9=Dmytriiev |first9=D. |last10=Faestermann |first10=T. |last11=Forstner |first11=O. |last12=Franczak |first12=B. |last13=Geissel |first13=H. |last14=Gernhäuser |first14=R. |last15=Glorius |first15=J. |last16=Griffin |first16=C. J. |last17=Gumberidze |first17=A. |last18=Haettner |first18=E. |last19=Hillenbrand |first19=P.-M. |last20=Kienle |first20=P. |last21=Korten |first21=W. |last22=Kozhuharov |first22=Ch. |last23=Kuzminchuk |first23=N. |last24=Langanke |first24=K. |last25=Litvinov |first25=S. |last26=Menz |first26=E. |last27=Morgenroth |first27=T. |last28=Nociforo |first28=C. |last29=Nolden |first29=F. |last30=Pavićević |first30=M. K. |last31=Petridis |first31=N. |last32=Popp |first32=U. |last33=Purushothaman |first33=S. |last34=Reifarth |first34=R. |last35=Sanjari |first35=M. S. |last36=Scheidenberger |first36=C. |last37=Spillmann |first37=U. |last38=Steck |first38=M. |last39=Stöhlker |first39=Th. |last40=Tanaka |first40=Y. K. |last41=Trassinelli |first41=M. |last42=Trotsenko |first42=S. |last43=Varga |first43=L. |last44=Wang |first44=M. |last45=Weick |first45=H. |last46=Woods |first46=P. J. |last47=Yamaguchi |first47=T. |last48=Zhang |first48=Y. H. |last49=Zhao |first49=J. |last50=Zuber |first50=K. |title=Bound-State Beta Decay of {{sup|205}}Tl{{sup|81+}} Ions and the LOREX Project |collaboration=E121 Collaboration and LOREX Collaboration |journal=Physical Review Letters |date=2 December 2024 |volume=133 |issue=23 |pages=232701 |publisher=American Physical Society |doi=10.1103/PhysRevLett.133.232701 |url=https://link.aps.org/doi/10.1103/PhysRevLett.133.232701|arxiv=2501.06029 }}</ref> The half-lives of neutral {{sup|163}}Ho and {{sup|205}}Pb are respectively 4570 years and {{val|1.73|e=7}} years. In addition, it is estimated that β{{sup|−}} decay is energetically impossible for natural atoms but theoretically possible when fully ionized also for <sup>193</sup>Ir, <sup>194</sup>Au, <sup>202</sup>Tl, <sup>215</sup>At, <sup>243</sup>Am, and <sup>246</sup>Bk.<ref name="bs-prediction">{{cite journal |last1=Liu |first1=Shuo |last2=Gao |first2=Chao |last3=Xu |first3=Chang |date=2021 |title=Investigation of bound state β<sup>−</sup> decay half-lives of bare atoms |url= |journal=Physical Review C |volume=104 |issue=2 |pages=024304 |doi=10.1103/PhysRevC.104.024304 |bibcode=2021PhRvC.104b4304L |access-date=}}</ref>

Another possibility is that a fully ionized atom undergoes greatly accelerated β decay, as observed for [[Isotopes of rhenium|{{sup|187}}Re]] by Bosch et al., also at Darmstadt. Neutral {{sup|187}}Re does undergo β{{sup|−}} decay, with half-life {{val|4.12|e=10}} years,{{NUBASE2020|ref}} but for fully ionized {{sup|187}}Re{{sup|75+}} this is shortened to only 32.9 years. This is because {{sup|187}}Re{{sup|75+}} is energetically allowed to undergo β{{sup|−}} decay to the first-excited state in {{sup|187}}Os{{sup|75+}}, a process energetically disallowed for natural {{sup|187}}Re.<ref>{{cite journal
 |last1=Bosch |first1=F.
 |display-authors=etal
 |year=1996
 |title=Observation of bound-state beta minus decay of fully ionized {{sup|187}}Re: {{sup|187}}Re–{{sup|187}}Os Cosmochronometry
 |journal=[[Physical Review Letters]]
 |volume=77 |issue=26 |pages=5190–5193
 |bibcode=1996PhRvL..77.5190B
 |doi=10.1103/PhysRevLett.77.5190
 |pmid=10062738
}}
<br />"Note also, that the decay of bare <sup>187</sup>Re is dominated by the nonunique transition to the first excited state of <sup>187</sup>Os, since the decay to the ground state has a much smaller matrix element."</ref> Similarly, neutral [[Plutonium-241|{{sup|241}}Pu]] undergoes β{{sup|−}} decay with a half-life of 14.3 years, but in its fully ionized state the beta-decay half-life of {{sup|241}}Pu{{sup|94+}} decreases to 4.2 days.<ref>{{cite journal |last1=Takahashi |first1=K. |last2=Boyd |first2=R. N. |last3=Mathews |first3=G. J. |last4=Yokoi |first4=K. |title=Bound-state beta decay of highly ionized atoms |journal=Physical Review C |date=1 October 1987 |volume=36 |issue=4 |pages=1522–1528 |doi=10.1103/PhysRevC.36.1522 |pmid=9954244 |bibcode=1987PhRvC..36.1522T |url=https://www.researchgate.net/publication/13335547}}</ref> For comparison, the variation of decay rates of other nuclear processes due to chemical environment is [[radioactive decay#Changing rates|less than 1%]]. Moreover, current mass determinations cannot decisively determine whether {{sup|222}}Rn is energetically possible to undergo β{{sup|−}} decay (the decay energy given in AME2020 is (−6 ± 8) keV),{{AME2020 II|ref}}<ref>{{cite journal |last1=Belli |first1=P. |last2=Bernabei |first2=R. |last3=Cappella |first3=C. |last4=Caracciolo |first4=V. |last5=Cerulli |first5=R. |last6=Danevich |first6=F.A. |last7=Di Marco |first7=A. |last8=Incicchitti |first8=A. |last9=Poda |first9=D.V. |last10=Polischuk |first10=O.G. |last11=Tretyak |first11=V.I. |title=Investigation of rare nuclear decays with BaF<sub>2</sub> crystal scintillator contaminated by radium |date=2014 |journal=European Physical Journal A |volume=50 |issue=9 |pages=134–143 |doi=10.1140/epja/i2014-14134-6 |arxiv=1407.5844|bibcode=2014EPJA...50..134B |s2cid=118513731 }}</ref> but in either case it is predicted that β{{sup|−}} will be greatly accelerated for fully ionized {{sup|222}}Rn{{sup|86+}}.<ref name="bs-prediction" />