# Can muons be used to reach the island of stability of superheavy elements?

While reading about the island of stability of superheavy elements[0], experimental approaches and related difficulties[1], an idea has formed in my head. Since I cannot find considerations of such approach in literature or principal physical flaws in it, I’ve decided to ask here.

Disclaimer: Since I’m not a specialist in the field, it’s quite possible that I am simply missing some well known information.

So the question is: Can muons be used for creating new superheavy isotopes near the island of stability?

Some information about contemporary muon beam sources[2], [3].

Consider following variants:

1. The process of muon capture by the nucleus (analog to electron capture, but with muon) becomes the main decay channel for muons in atoms with Z>20.[4], [5]. The resulting nucleus is typically excited to energies in the range of 10–20 MeV[6], because most of the mass energy of the bound muon (-100 MeV) is converted to the kinetic energy of the neutrino. Investigations of muon capture by the nucleus in different materials show, that the fraction of resulting isotopes, which lose excitation without neutron emission is of the order of percent to tens of percent[6], [7]. This suggests that there is hope to use muon capture mechanism for adjusting proton/neutron ratio in desired direction for creating more stable superheavy isotopes. For example, starting from element 117 isotope 294Ts, we can “move” diagonally down-right on p-n diagram https://en.wikipedia.org/wiki/Island_of_stability#/media/File:Island_of_Stability_derived_from_Zagrebaev.svg

Although deexcitation without neutron emission seems unlikely for superheavy nuclei, one-neutron channel (which is the main de-excitation channel) although allows creation of new isotopes (for example 293Lv+µ->292Mc+n).

There are obvious problems: - We don’t know the fraction of neutron-less and single-neutron de-excitation for superheavy isotopes, in best case it will be some percent, and fission will severely decrease the number of surviving nuclei but with facilities like Superheavy Element Factory[8], [9] this might be feasible.

• How to force a single short-living atom to capture a muon. I don’t have expertise to tell if this is very hard or totally impossible for current technology level. But here we can, for example, align muon beam with ions of superheavy elements while they are flying from magnetic separator to detector. In this case, we don't have to hit a single atom in a medium, we have to force a highly ionized isotope to catch a charged muon on an orbital. And it can be in vacuum (though I know that current experiment is gas filled). This seems difficult, but not outright crazy.
1. Yet another approach may be using of muonic hydrogen, deuterium and tritium or, maybe even muonic helium, instead of neutrons for irradiating targets and “jump” over short lifetime isotopes, like 258Fm ("fermium gap")[10]. Like in Muon-catalyzed fusion, hydrogen isotope shielded with muon can be used instead of neutron https://en.wikipedia.org/wiki/Muon-catalyzed_fusion For example we can move from long living 257Fm to long living 260Md by capturing a triton.
• I don’t know how feasible is this, but since using thermonuclear explosives[11] was proposed as a way to “jump” Fermium gap...
1. Maybe by synchronizing ion beam with muon beam, we can create by muon capture a beam of radioactive isotopes “on the fly”.
• I highly doubt if this is possible and intensity of the beam will drop by the orders anyway…

I've asked this question on ResearchGate some time ago, here is a link in case something will turn up there... https://www.researchgate.net/post/Can_muons_be_used_to_reach_the_island_of_stability_of_superheavy_elements

[1] V. Zagrebaev, A. Karpov, and W. Greiner, “Future of superheavy element research: Which nuclei could be synthesized within the next few years?,” J. Phys. Conf. Ser., vol. 420, p. 012001, Mar. 2013, doi: 10.1088/1742-6596/420/1/012001.

[2] S. Cook et al., “Delivering the world’s most intense muon beam,” Phys. Rev. Accel. Beams, vol. 20, no. 3, p. 030101, Mar. 2017, doi: 10.1103/PhysRevAccelBeams.20.030101.

[3] MICE collaboration, “Demonstration of cooling by the Muon Ionization Cooling Experiment,” Nature, vol. 578, no. 7793, pp. 53–59, Feb. 2020, doi: 10.1038/s41586-020-1958-9.

[4] I. H. Hashim et al., “Nuclear Isotope Production by Ordinary Muon Capture Reaction,” Nucl. Instrum. Methods Phys. Res. Sect. Accel. Spectrometers Detect. Assoc. Equip., vol. 963, p. 163749, May 2020, doi: 10.1016/j.nima.2020.163749.

[5] K. Nagamine, Introductory muon science. Cambridge ; New York: Cambridge University Press, 2003.

[6] D. F. Measday, “The nuclear physics of muon capture,” Phys. Rep., vol. 354, no. 4–5, pp. 243–409, Nov. 2001, doi: 10.1016/S0370-1573(01)00012-6.

[7] D. F. Measday, T. J. Stocki, R. Alarcon, P. L. Cole, C. Djalali, and F. Umeres, “Comparison of Muon Capture in Light and in Heavy Nuclei,” in AIP Conference Proceedings, 2007, vol. 947, pp. 253–257, doi: 10.1063/1.2813812.

[8] S. Dmitriev, M. Itkis, and Y. Oganessian, “Status and perspectives of the Dubna superheavy element factory,” EPJ Web Conf., vol. 131, p. 08001, 2016, doi: 10.1051/epjconf/201613108001.

[9] Y. T. Oganessian and S. N. Dmitriev, “Synthesis and study of properties of superheavy atoms. Factory of Superheavy Elements,” Russ. Chem. Rev., vol. 85, no. 9, pp. 901–916, Sep. 2016, doi: 10.1070/RCR4607.

[10] V. I. Zagrebaev, A. V. Karpov, I. N. Mishustin, and W. Greiner, “Production of heavy and superheavy neutron-rich nuclei in neutron capture processes,” Phys. Rev. C, vol. 84, no. 4, p. 044617, Oct. 2011, doi: 10.1103/PhysRevC.84.044617.

[11] H. W. Meldner, “Superheavy Element Synthesis,” Phys. Rev. Lett., vol. 28, no. 15, p. 4, 1972.

Maybe you misunderstand about muon capture. The muon replaces the electron in electron capture:

Electron capture (K-electron capture, also K-capture, or L-electron capture, L-capture) is a process in which the proton-rich nucleus of an electrically neutral atom absorbs an inner atomic electron, usually from the K or L electron shells. This process thereby changes a nuclear proton to a neutron and simultaneously causes the emission of an electron neutrino.

Because the mass of the muon would make a radially much smaller orbital than the electron has, it may be not necessary for the muon capture to be in a K shell.

Feynman diagram of the muon capture. A negatively charged muon is captured by a proton. The proton is transformed into a neutron and a muon-neutrino is emitted. The interaction is mediated by a W-boson.

In my opinion, this program of yours:

For example, starting from element 117 isotope 294Ts, we can “move” diagonally down-right on p-n diagram

is not viable, at least not without an accumulation of experimental data on the main decays after a proton is turned into a neutron in the nucleus. How the nucleus will break up into smaller nuclei have to be tabulated in a long program.

The rest of your suggestions are also long shot:

muonic hydrogen, deuterium and tritium or, maybe even muonic helium,

these are of order angstrom and cannot penetrate the order fermi nuclei.

Having a muon in the orbital instead for the electron just means that the probability of capture is higher. The extra energy from the mass of the muon would not help in the formation of the debris nuclei.

The practical use for muon capture is given in the wiki link:

Muon capture is being investigated for practical application in radioactive waste disposal, for example in the artificial transmutation of large quantities of long-lived radioactive waste that have been produced globally by fission reactors. Radioactive waste can be transmuted to stable isotopes following irradiation by an incident muon ($$μ^−$$ ) beam from a compact proton accelerator source.

• Exactly what I misunderstand about muon capture? "Because the mass of the muon would make a radially much smaller orbital than the electron has, it may be not necessary for the muon capture to be in a K shell." Quite so, and irrelevant here, important point is that in heavy atoms muon is mostly captured by the nucleus, not decay. May 10 at 9:58
• Though, rapid transition of muon to 1S state is quite natural, as far as I understand, for example: "Muonic cascade. Once the muon is securely captured by an atom in the target, it cascades down to the 1s level in a time-scale of the order of 10^−13 s which is instantaneously as far as typical counters are concerned. The 4rst part of the cascade is by Auger emission, but around n = 5 muonic X-rays begin to dominate. The details of the cascade depend upon the chemical and physical environment." in [6]. May 10 at 10:01

Muons captured by a nucleus would.essentially convert protons to neutrons, reducing the atomic number of the nucleus. Muons are leptons, and can't directly change the total number of baryons. More protons or neutrons would need to be added to raise the atomic number, then more neutrons, etc. Can't say it's impossible to create superheavy nuclei using a particle beam, except that a pure muon beam won't do it.

• Thanks for catching that; it's fixed now. May 9 at 17:15
• Quite so, the idea is to combine muon capture with existing technique (hot fusion) of creating superheavy elements, not to shoot the target with muon beam only. The problem with creation of the Island of stability isotopes is that beta-stability line deviates to more neutron rich isotopes, so changing n/p ratio of the nucleus is exactly what is needed en.wikipedia.org/wiki/Island_of_stability#/media/… May 10 at 10:16
• Do you see an advantage to subtracting one proton while adding one neutron, rather than "simply" adding a neutron? May 10 at 13:37
• Yes. In experiment we get individual superheavy nuclei flying from target to detector, with half-lives of the order of tens of ms. To hit a single nucleus with neutron seems harder than to make charged ion catch charged muon. For experimental and theoretical review of method, currently used in this field: iopscience.iop.org/article/10.1088/0954-3899/34/4/R01 May 10 at 14:29