Muon Catalyzed Fusion begins in 1947 and still counting...

Muon Catalyzed Fusion of hydrogen isotopes was theoretically supposed in 1947 by F.C.Frank in the UK [Nature 160(1947)525] and in 1948 by A.D.Sakharov in Russia [Report FIAN, M.,(1948)1].
In 1954 Ya.B.Zeldovich [Doklad. Akad. Nauk 95(1954)493] was the first to calculate the rate for the nuclear reaction in ddm muonic molecules showing that it was seven orders of magnitude higher than the muon decay rate and thus could not prevent observation of the predicted phenomenon. In the same paper he pointed out that the major limiting factor could be the rate of formation of muonic deuterium molecules themselves lddm. His first calculations done together with S.S.Gershtein yielded a very small value for the formation rate lddm in liquid deuterium. The predicted value of lddm=0.04x106s-1 [Uspekhi Fiz. Nauk 71(1960)581] seems to be a substantial obstacle for experimental observation of the phenomenon of Muon Catalyzed Fusion.
Yet, Muon Catalyzed Fusion was discovered. As is known, L.W.Alvarez [Phys. Rev. 105(1957)1127] did it quite unexpectedly in Berkeley in 1957. Scanning of pictures taken with a large liquid-deuterium bubble chamber exposed to a beam of K-mesons with a large admixture of muons revealed several events of muon-catalyzed nuclear d+d reaction.
First direct experiments with liquid deuterium bubble chambers carried out by J.G.Fetkovich et al. [Phys. Rev. Lett. 4(1960)570] and J.H.Doede [Phys. Rev. 132(1963)1782] showed that the rate for formation of muonic deuterium molecules was as small as 7x104s-1 and could not ensure even a very short chain of fusion reactions. Those results again reduced interest of many physicists in the problem of Muon Catalyzed Fusion.

V.P. Dzhelepov LARGE
Fig.1. V.P.Dzhelepov the founder of MCF activity in Russia

Fig.2. Muon gives a "gap" in a diffusion chamber.

dm + p = 3He + m (Dubna, 1964)

Unlike others, group in Dubna V.P.Dzhelepov (Fig.1), P.F.Ermolov, V.V.Filchenkov et al. concentrated its effort on studying the process in gaseous (at different temperatures) rather than liquid deuterium. It led to a quite substantial progress. In 1964-77, in the experiments with the diffusion chamber (Fig.2) and after with the high-pressure target and electronics, in Dubna was discovered a new phenomenon of resonant formation of muonic deuterium molecules [Zh. Eksp. teor. Fiz. 50(1966)1235]. It turned out that the rate for formation of ddm molecules sharply increases (Fig.3) in a narrow gas temperature interval 120-380K (dm atom energies) and at 380K it is an order of magnitude higher than the one found by Fetkovich and Doede for liquid hydrogen.
This fact was explained by an estonian theoretician E.A.Vesman [Pisma Zh. Eksp. Teor. Fiz. 5(1967)113], who worked under supervision of S.S.Gershtein in Dubna at that time. As is well known, the essence of their idea (Fig.4) was that on penetrating a D2 molecule a dm atom adds one of the deuterium nuclei and supplies its kinetic energy edmo together with the binding energy eddm11 of the arising ddm complex for excitation of oscillation of the resulting complex dm+D2=[ddm(d2e)]*v.
Resonanse occurs when edmo+ eddm11= DEv. It followed from Vesman's tentative estimations that the binding energy in the ddm molecule must be of the order of 2eV.

Fig.3. Rate for formation of muonic deuterium molecules vs. temperature

Fig.4. Resonant formation of ddm molecules

Dubna theoreticians L.I.Ponomarev, I.V.Puzynin and their colleagues [Zh. Eksp. Teor. Fiz. 74(1978)849] managed to work out a procedure to calculate the binding energy of a three-body system with Coulomb interaction. They were the first to find the energy of the weakly bound state in the ddm molecule. It turned out to be -1.96eV.
Relying on successful calculations for ddm molecules, L.I.Ponomarev and his colleagues extended the idea of resonant molecule formation to dtm molecules and predicted the existence of a similar weakly bound level in the dtm molecule as well. Their calculations 1977-78 showed that this level does exist, its energy being only -0.63eV.
Yet, since the tm + D2 system changes to the oscillating state of the [dtm(d2e)]*v=2 instead of [ddm(d2e)]*v=7 as in case with deuterium, it followed from the calculations that the formation rate for dtm molecule ldtm is 1x108s-1 exceeding lddm by a factor of 100. This very intriguing result made Dubna experimentalists (V.M.Bystritsky, V.P.Dzhelepov, V.G.Zinov, V.V.Filchenkov et al.) quickly produce necessary equipment and develop a new measurement technique. It should be stressed that Dubna original technique for studying the muon catalyzed fusion dt reaction turned out to be very efficient and virtually became a classical one, later used by some other groups.
In the experiments with the dt mixture carried out in early summer 1979 Dubna group established for the first time that the dtm formation rate exceeds 108s-1 being almost hundred time as high as that for ddm molecules. The rate for the isotope exchange
(dm) + t = (tm) +d was also found to be high ldt=(2.9+/-0.4)x108s-1. Those experimental data agreed well with theoretical predictions and, considering the calculated value of the coefficient of muon sticking to 4He (ws=0.6%), showed that each muon can initiate on the average about 100 dt fusion reactions within muon lifetime tm=2.2ms.

Dubna results excited the scientific community, renewed interest in Muon Catalyzed Fusion, and initiated extensive experimental and theoretical investigations of this problem by a lot of nuclear centers in the USA, Switzerland, Russia, Japan, Canada, UK, etc. (Fig.5).

LARGE Phasotron
Fig.5. Experimental data for Muon Catalyzed Fusion parameters (V.P.Dzhelepov, Hyp.Int. 101/102(1996)xiii.)

Fig.6. Muon Catalyzed Fusion in Dubna was studied in the building of Phasotron

It is so happened that immediately after accomplishment of the experiments yhat resulted in determination of two most important MCF constants ldtm and ldt our worn 680MeV synchrocyclotron was shut down for conversion at the end of 1979 and Dubna group stoped its investigations for several years. The new accelerator Phasotron (Fig.6) in Dubna became available for physics program in 1985.
The high efficiency of the MCF dt reaction discovered in Dubna stimulated physicists at LAMPF, PSI, PNPI, KEK, TRIUMF and they start widespread investigation of the problem. As a result, in 1981-82 active methodical research and production of experimental setups began. By the end of 1982 the Los Alamos group made deuterium-tritium targets operational at a pressure 1000-3000bar in the temperature range 13-600K and associated equipment to record neutrons from muon catalyzed dt and dd reactions [A.J.Caffrey et al., MCF 1(1987)53]. In 1983 an original high pressure 100bar ionization chamber for recording charged particles from the same reactions [D.V.Balin et al., MCF 2(1988)241] was built in Gatchina, and so on.
Equipment created by different groups in 1983-93 allowed a great deal of very important and widely known results. The first were the LAMPF data obtained by S.Jones-J.Bradbury's group. Using non-equilibrium D2+T2 mixture with a high tritium content (up to 70%) they succeeded in determining ldtm and ldt in 1983. Later (in 1986) they also measured the mean number Nc of the reactions catalyzed by one muon during its lifetime. Among more recent development of interesting lines in the experimental investigation one should mention the study of spin effects in resonant formation of muonic deuterium molecules ddm. The first experiments were carried out in 1987 by W.Breunlich et al. [J.Zmeskal et al., MCF 1(1987)109] at the PSI accelerator. They studied dependence lddm(T) for each of the dm atomic HFS states (spin F=1/2 and F=3/2)(fig.7). The experiments were carried out at a low gas density f=0.02-0.04 of the liquid hydrogen density (1LHD=4.25x1022nucl/cm3). In the same figure there are Dubna 1991 data for f=1 [V.P.Dzhelepov et al., Zh. Eksp. Teor. Fiz. 101(1992)1105].

Fig.7. Temperature dependence of rates for ddm formation from different spin states of the dm atom: open circles - at D2 density f=0.02-0.04 (Vienna-PSI); filled circles - at D2 density f=1 (Dubna)

Fig.8. Temperature dependence of rates for ddm formation from different spin states of the dm atom: triangle - solid D2 f=1.4 (TRIUMF); filled circles - solid and liquid D2 at density f=0.8-1.4 (Dubna)

Further development of experimental technique made possible measurements of spin effects in solid deuterium. For this purpose the solid hydrogen film target technology in TRIUMF and the solid deuterium target in Dubna were created. Two different groups TRIUMF and Dubna using different experimental technique came simultaniously to the same result. It appeared that in solid deuterium the formation rate of muonic deuterium in the HFS state F=3/2 is no temperature dependent (Fig.8). This phenomenon still needs proper theoretical and experimental efforts.