J. Rafelski and HE. Rafelski
Abstract
A survey with emphasis on recent results in muon—catalyzed fusion is presented. The objective of this presentation is to elucidate the physical mechanisms and application perspectives.
1. Introduction Table 2 In principle, one ought not to expect that the field of particle Muon—catalyzed hydrogen fusion reactions physics has direct applications, though many indirect benefits to society arise. But the muon, a heavy electron, bridges the ~ 84% 3He (5.4 keV) + 9/ (5.48 MeV) and nuclear worlds, and enormous scale gap between the atomic lp + d —> facilitates spontaneous, Muon-Catalyzed Fusion (MuCF). ~ 16% 3He (0.20 MeV) + ,u (5.29 MeV) Because of this interconnection of atomic and nuclear physics, the detailed understanding of the MuCF cycle of reactions has I s wave p wave proven to be surprisingly rich and subtle. At the origin of the ~ 52% 42% r(1.01 MeV) + p (3.02 MeV) diverse effects is the muonic hydrogen atom, a neutral object d + d —> much like a neutron, capable of entering complex chains of I ~ 48% 58% 3He (0.82 MeV) + n (2.45 MeV) (resonant) reactions at thermal energies. The large mass of the [3+1 4H6 (52 keV) + 7/ (19.76 MeV) muon makes its Bohr radius only 265 fm small when bound to d+t 4H6 (3.56 MeV) + n (14.03 MeV) the mean nuclear separation in the muo— the tritium nucleus, and 111 t+t 4He+n+n (11.33 MeV)I molecular ions dtu is 700 fm (table 1). The energy scale governing the penetration of the Coulomb barrier is of the order of 5 keV. Following a fusion reaction, the muon is mostly set free and is capable of repeating the cycle of muo—atomic and permits at most a few fusions per muon [3], and should not lead molecular processes which lead to the nuclear reaction. to temperature or target-dependent nuclear reaction rates (T = 30-800 K, 0.01—1.5 LHD (liquid hydrogen density) see also table 1). Nonetheless, the report of Aniol et a1. [4] mentions a Table 1 significant temperature dependence of the fusion 5.5 MeV yrate, Parameters governing MuCF reactions and significant dependence of this rate on composition of the target. These results imply that there is a milli—electronvolt Muon mass m,l 206.768 mc structure in the pp + DX or dtt + PX systems (X E P or D), Deuteron mass md 3670.484 me arising perhaps from the near-threshold direct, pseudo-resonant Triton mass mt 5496.922 me reactions [5]. Extremely weakly bound muo—molecular states are (m[ + md — ma ~ mn)('2 l 34.422 me known in the (1l and cit/,1 molecules. Both fusion cycles are hence considerably faster and known to have a strong Muon Bohr radius a‘f,’ 255.928 fm temperature dependence. The latter case is by far the most Liquid hydrogen density (LHD) p0 4.25 X 1022 cm—3 interesting theoretically, experimentally and from a practical Muon decay rate Tl“ A“ 4.552 X 105/3 application point of view among all hydrogen—hydrogen cycles, and is the one emphasized in this survey of recent advances. The main reasons for the particular attention given to the dip case are: The prl reaction (table 2) was the MuCF process first (a) The (1th system possesses a (JV) = (l 1) molecular state considered by Frank in 1947 [1], and it was experimentally believed to be bound by just 596 i 2 meV [6], which can later by Alvarez et al., [2]. Fusion is believed resonate with the second vibrational band of the Dz molecule. discovered l0 years 2] to occur only from the muo—molecule formed by Auger processes (b) The dt nuclear system has a (JTE = (3/2)+) nuclear resonance with a rate of the order of 10934. The small formation rate just 50 keV above the d + t threshold, with a total width of
1?) [99] Gordon and Breach Science Publishers S A Photocopying peimittetl by license only Particle W01|(|,a 2. No l, p 2l428. I99] J Rzll‘elski and H.E Rafelski
70 keV and hence the nuclear d—t reaction is 100 times faster — The y is slowed in the mixture of hydrogen isotopes within than any other involving hydrogen isotopes. < 10"0s to atomic velocities, as can be deduced from the (c) The Q value for the d + t —> a + n reaction is 17.60 MeV, muomc stopplng power. making it one of the most energetic of all hydrogen— — The [,t is captured by one of the hydrogen isotopes (l or r in hydrogen reactions. proportion to their abundance Cd, C[ in a high orbit (n = 14), The last property is important directly and indirectly for primarily by Auger processes. energy yield per muon in MuCF of D + T: the high relative post- — Following the capture in an outer orbit: fusion velocity of the fusion products a + n is at the origin of - If the muon is captured by a deuteron, it undergoes the the small muon loss through binding to the produced aparticle. transfer to the heavier tritium isotope. From the atomic dttls ground state, the transfer must compete both with the ddy formation rate and direct in—flight fusion. The 2. The city reaction cycle occasional population of the deuterium ground state Each catalytic cycle contains a number of processes in which, plays an important role in the muon cycle dynamics with some small branching, the muon can be delayed and/or and a significant fraction of the average dt MuCF cycle neutralized. Therefore, it is necessary to understand the cycle time is taken up by the time the muon spends in this history, including small probability alternatives. The main steps state. of the dt cycle (fig. 1) are summarized below, beginning with a - If the muon is captured by the tritium, the muon cascades free muon (all density-dependent rates are scaled to LHD): down to the (rmls state in 10—115.
Representation of the cycle of dry MuCF fusion processes. J Rzni’clski and HE Ral‘elski
— The (tit).S atom (with thermal or epithermal energy) collides value of the branching ratio found in the muon—catalyzed fusion with a D2 or DT molecule and either: reactions carried out at T = 293 K is 1.4 in favour of the 3He - it forms (resonantly) the excited very weakly bound J = l, production (table 2). Most interesting is the result [7] that this v = l dttt, muo-molecule embedded within the host branching ratio drops below unity in MuCF d—d reactions at T = electro—molecule; 70 K. This suggests that s—wave fusion dominates at this - or, there is a direct nuclear reaction from which the muon temperature, the resonant molecular formation rate has decreased emerges generally as a free particle and returns to the enough and other mechanisms leading to the d—d fusion, e.g. the beginning of the cycle. Auger molecular formation or the direct fusion reaction, — In the muo-molecule dt,Lt(11) an Auger transition follows, dominate the dd fusion cycle. primarily to the (JV) = (01) state. This occurs within 10—12s. — Within the next 10—12s the nuclear fusion takes place. Following the fusion, the muon is either free, or sometimes 3. Muon sticking bound to the product a particle. The branching ratio between Muon sticking occurs when the muon following fusion these reactions (initial sticking fraction) is reduced in the becomes bound e.g. in the dry cycle in the oc—particle bound state subsequent slow—down process. The experimentally-observed with quantum numbers ”I. The probability of initial sticking is a sticking fraction for the dt fusion is 0.45%, which may be reaction branching ratio compared to the 12.2% sticking probability for the dd fusion branch reacting into the 3He channel. We will discuss sticking at (00* F(dm—>n+att) (1) length in the following section. 5 F(dt;t——>n+oc+p)+r(dty—>n+au)' Resonant molecular formation occurs when a neutral tit muo— atom enters a hydrogen molecule and binds extremely weakly to The sticking muon has a finite chance of being stripped a deuteron, the muo-molecular binding energy being picked up by during the stopping of the (040+ ion. It is therefore necessary to the (second) vibrational band of the host electro-molecule. The distinguish the initial sticking probability, £02, from the final rate of formation of such resonances is therefore highly sticking, mgr which incorporates the regeneration effects, i.e. temperature-dependent. The understanding of this rate requires a stripping. Sticking is of capital importance to possible practical precise knowledge of the (ll)-state energy including, in applications and therefore perhaps the point of greatest contention particular, QED corrections. That these corrections are relevant is among different research groups. The achievable number of simply seen by noting that energy matching with a precision of fusions per muon, Y. is obtained from the ratio of the cycling rate, the order of milli-electronvolts must be reached given the total AC, to the muon loss rate M. The latter contains aside the rate of binding of the muon of the magnitude 2.7 keV, while the vacuum the muon decay, the rate of muon catalyst poisoning, which is the polarization corrections are of the order of electronvolts. product of the cycling rate, AC, with the probability of muon Furthermore, the spectrum of electro—molecular states depends poisoning per cycle, W5, of which the main cycle sticking, (0&1 is sensitively on the isotopic composition of the target hydrogen the dominant contribution: molecule and also on the hyperfine state of the m. The ddit A, 1 1 1 system is quite similar in its behaviour to the dry, but all =_=.dt <—<—d[. (2) processes of interest are 10—100 times less rapid because: (i) the Ag Ao/IIC+CDS +6VVS I’VS COS resonant energy of 2 eV requires high-vibrational excitation and (ii) the dd wave function is symmetric. The try system is also Typical best values are today: Y z 150, 10 E 108s—1, ever present, but it is not a serious competitor in the reaction A, = 2., ><0.006, mgr; 0.004. chain. The fusion of the d and t occurs almost exclusively from the 3.1 Experimental values for the dt sticking probability relative nuclear s-wave states, and it proceeds also practically Most of the US LAMPF (Los Alamos Meson Physics exclusively via a 5He ((3/2)+) nuclear resonance, located 50 keV Facility) dt fusion sticking fraction results were obtained above the d + t threshold. The fusion rate has been computed considering the cycling rate of muons and measuring the rate of from the molecular (Jv) = (00) and (01) states to be of the order muon loss, which is found to be greater than if generated by the of 10125—1. The direct fusion rate from the (11) state is estimated muon decay alone. A somewhat different analysis of kinetics of to be of the order of 1088—1. Fusion in the dd system is somewhat the neutron emission and cycle dynamics was performed at the different due to the symmetry of the relative dd wave function. PSI (Paul Scherrer Institute, Villigen, Switzerland), where the X— The transition rate from the ddu (11) state can only take place if ray muo-atomic transitions from the MuCF cycle have also been accompanied by a spin flip of one of the deuterons. The rate of measured. In a tritium-rich environment this is a very difficult 23 this transition is sufficiently slow (37.3 i 1.5) 106s—l [7], for a p- experiment, as the natural tritium decay generates an X-ray wave fusion to occur directly from the (11) state. Therefore, the background just in the energy window of interest. This issue was .l Rul'clski and H E Rafelski
also taken up at the KEK (National Laboratory for High-Energy the temperature—dependent branching ratio into the small sticking Physics, Tsukuba, Japan) experiment. where an intense magnetic side cycle of direct reactions (sect. 3.3). field was applied to limit the range of the ,8 electrons, and the pulsed—muon beam allowed to enhance the signal—to—noise ratio. 1.0—1_ 'l 'l i l | i ll 'ITI l T ljmli'li All these experiments have yielded sticking significantly below theoretical expectations, though the natural result should have been a greater than anticipated value (allowing for some yet unknown loss mechanisms). These surprising findings stimulated a new series of experiments which are at present in progress. The LAMPF group, in collaboration with the RAL (Rutherford Appleton Laboratory), has developed an apparatus in which coincidence measurements 0.8 _. of a neutron, in conjunction with an a++ or an (040+, can be performed. Apart from the directness of the measurement, the other advantage of this project is that only a minor correction is required to account for stripping of the muon from an (040+ during the passage through the gas target and mylar window, as the muonic ion loses only a fraction of its energy. The LNPI (Leningrad Nuclear Physics Institute) has previously developed a successful direct method to measure sticking in the d—d reaction 0.6 - in a wire ionization chamber. This group, together with the Berkeley—Livermore—PSI group, intends to carry through direct measurement of sticking in a much refined wire ionization chamber. Both the LAMPF and the PSI groups also want to pursue extreme target environments: high density, respectively high (T > 1000 K) and low (T < 3 K) temperature sticking with novel targets. The punch line of these experiments is the very low sticking 0.4llll|||l||||||JJ|| 602.‘ at LHD, close to 0.35% seen at the LAMPF and close to 0.45% seen at the PSI — both results are within error bars of each other. The conventional theoretical value is at ~ 0.62%, which is ~ 1.5 times the experimental value. Similarly the PSI-Munich X-
ray data [10] are a factor of 1.5 lower than was theoretically Temperature dependence of the initial sticking fraction. The error bars in the expected (end of next subsection). Furthermore, while there is experimental values include uncertainties in the regeneration factor R [5]. only a slight density dependence arising from the stripping, there is a pronounced trend (within the error bars) for an increase of sticking with decreasing density in the LAMPF data, their result 3.2 The theory of sticking may be seen to disagree with the PSI data. However, the density Assuming that the nuclear interaction can be accounted for as dependence in the LAMPF data could also be related to the fact a perturbation (an issue which has often been questioned), the [5] that the high-density points were obtained by changing the branching ratio of the reaction is temperature in the liquid DT phase. A further disagreement at densities below LHD between the LAMPF and the PSI may be 0 _ ZnZiOMH ”LINE-Pr (3) traced to differences between the groups in applied corrections, s — . 2 . 2 ’ required in the DT environment due to a certain small number of 2n2i
the initial population of the excited states or from the excitation of the ground state during the ot particle slow—down process. In 0 | 3 * —ikl W030) why: Id rgolé,(r)c 1/2 - (4) either case the radiative transitions occur in competition to the 1 (id3rlll/(I‘,0)|2 l l other density-driven Coulomb processes and hence their observed intensity provides key supplementary information about sticking. where the tl—t distance R = 0 in eq. (4) really means ~ 3—7 fm, The X-ray yield per muon fusion is easily obtained from the the range of the nuclear (l—t interaction. This expression was used time-dependent populations of the excited states of the 041+ ion early on with the Born—Oppenheimer three—body wave function which is found during the calculation of the muon regeneration. [3] which was, for some time, considered as an approximation in There is little that can be done theoretically to make the yield of the sense that the muon had to be captured instantly as fusion X—rays independent of the regeneration probability and hence occurred. Such an approximation scheme would be utterly invalid these two quantities are closely related [8].The reduction of the as can be easily seen in computing the Wigner function phase— (in principle unknown) stopping power of the au+ ion which space distribution of muons after the fusion and studying its leads to greater re—activation and hence smaller final sticking, evolution with time in a Monte Carlo approach [9], if eq. (4) had enhances the yield of muonic X-rays emitted after fusion. This not been the exact quantuum mechanical result. Jackson [3] found observation precludes any ad [106 manipulation of the stopping (1)2 ~ 1.2 for the initial three—body muo-molecular helium—like power of the (040+ ion with the goal of reducing the final wave function in the Born—Oppenheimer adiabatic approximation sticking, as the result is a very similar proportional enhancement at the moment of nuclear contact. At the present moment, three— of the theoretical X—ray yield which is already 1.5 times greater body non-adiabatic wave functions lead to a somewhat smaller than the experiment [10], while the sticking, as we saw, is about a value a)? = 0.89%. The R-matrix approaches, incorporating the factor 1.5 smaller. Thus, there are two discreponcier limiting the change of the muon—fusion amplitude due to nuclear forces, understanding of the MuCF potential for applications. increase this value to a)? = 0.92%, which is today viewed as the A complication arises from the fact that with and without best conventional value for the total initial sticking probability sticking, the 05 particle and the muon travel, after the nuclear [6]. reaction, very close to each other on the atomic scale The initial sticking is reduced even at arbitrarily low density (1 A/200 = 500 fm) and their mutual interaction with matter of the target by 30% due to the stripping of bound muons from during their slow-down is difficult to understand at the level of the energetic (0410+. With a sticking muon, the kinematics of the precision required, viz. 0.1%. There is the possibility to capture nuclear reaction is slightly altered. The (0510+ ion possesses an these convoy muons, initially in relative continuum states to the initial velocity: van = 5.837 a.u., corresponding to an energy of a particle. It is the final-state Coulomb interaction of the negative 3.48 MeV. The time required to bring the (040+ to rest in liquid muon with the outgoing a particle which results in an hydrogen is of the order of IMF = 10—103 at LHD, so muon enhancement of the continuum muon phase—space distribution in stripping, if it occurs, does not have any impact on the cycling the vicinity of the 06 particle [9]. rate of the muon. During the slow—down process, substantial energy is available to strip the muon from the a particle. Like the 3.3 Impact of direct fusion mechanisms on sticking energy loss rate, the stripping rate is also proportional to the measurements density. For one—step processes we find In our opinion, present data suggest the existence of a sticking side cycle of MuCF which becomes particularly active at high E0=3.5MeV . cog“ = of exp[—J iLn] . (5) density and/or at low temperature. A recent analysis of the results of Ef=0 ( ) the dry system [5] further suggests that the direct pseudo-resonant reaction dominates the fusion cycle in dense, low temperature The stripping fraction is therefore essentially a ratio of the muon environment, and is potentially the cause of the apparent variation stripping cross section and the energy loss weighted electron of sticking with changes of LHD temperatures. Interest in the in— ionization cross section (stopping power S). The complete flight fusion was in part stimulated by the suggestion that a tepid treatment of the muon re—activation process is actually more plasma might be a suitable environment for MuCF to take place complex [8] than the above eq. (5), valid for low density in [11]. Despite some critical technical errors of this work, the idea of which only one-step processes play a role. Normally, the excited tepid plasma offers an interesting path to study MuCF and we return state populations are coupled by radiative, Auger and Coulomb to this point at the end of the following section. induced de-excitation and Stark mixing processes. The multiple- The non—resonant continuum of nuclear cit—0m states exists step processes involving radiative transitions are the source of a both above and below the d + 011)]s threshold (up to weak density dependence in cos. —l7.60 MeV). The continuum exists as a consequence of the 25 Should the muon be bound at any time to the a particle, there coupling of the dtu channel to the any continuum, and the will be some muonic X—ray transitions. These arise either from stationary states may easily be constructed as the R matrix is well .l Rat'elski and H.E Rai'elski
known for this system. This global stationary continuum geometric definition of the first interaction point in the thin penetrates deep into the (12‘ region near to the 3-body Coulomb internal target and avoids the use of tritium. eigenenergies, with resonantly enhanced amplitude, and generally Even though there is no evidence as yet that MuCF will ever has an amplitude ~ 10—4 smaller away from these eigenenergies become a viable energy alternative, several workers, in [5]. Furthermore, just below (and above) the d + (Itt)ls recognition of the observation that the fusion yield and cost of threshold, the amplitude diverges weakly as the energy of the dip energy production are strongly systein—Llepemlent, began the system approaches the d + (nu).s threshold. In order to be able to conceptual MuCF-fusion reactor design. There are numerous involve this near threshold continuum in the nuclear reaction schemes, of which all but one have been scarcely more than a processes, there must be other bodies to pick up the (small) conceptual study. The original idea which started the race to the surplus energy. Hence these reactions are of particular importance MuCF reactor system was the hybrid scheme: the fusion— at high density. A comparison of the data with theory [5] plutonium breeder system [14] which consists of an accelerator suggests that the pseudo—resonant direct fusion reaction (of (I or better I), a pion—producing target, a converter and mechanism is indeed responsible for the smallness of the blankets. The beam at 0.8 GeV/nucleon is injected into the 4 cm observed sticking. diameter x 2 m long cylindrical pion-producing (Be) target. The estimated energy cost per negative pion is 5.7 GeVbeam. The pions produced are guided into a converter which is a 40 cm 4. Muon production and reactor schemes diameter X 40 m long cylinder with an 11 Tesla magnetic field At present, the practical path to produce high-intensity cheap parallel to the cylinder. Also, a magnetic mirror to reduce the loss muon beams as required in MuCF is believed to proceed via of backward pions, and an electric field parallel to the magnetic hadronic interactions, that is via the production of negative pion field are employed. A converter efficiency of up to n = 83% is beams in collisions of (neutron—rich light) nuclei. In addition to believed to be attainable. However, pion loss due to absorption in the composition of the beam and target, the 73'“ production cost the pion—producing target is not allowed for. The reactor vessel depends also on the geometry of the target, projectile beam has an average radius of 10 cm and a length of 19 m, containing energy, and the external fields used to channel pions out of the a DT mixture at 0.5 LHD with a tritium concentration of Ct = 0.3 target volume. Monte Carlo simulations show that the and requires at least 20 kg of tritium. The fusion neutrons are hypothetical energy cost per primary pion is slowly rising with absorbed in a lithium and 238U blanket to breed the plutonium the energy even for a neutron beam. There is a pronounced and tritium. For the time being, even when discounting complex energy cost minimum for a proton beam around 3 GeV/c2: like physics and engineering issues, it is hardly conceivable that such for neutrons, at high energies too much of the initial energy is a scheme could be implemented, considering the needed tritium becoming part of the kinetic motion of the produced particles; inventory (requires a prior disarmament of superpowers) and the and for protons at low energies there are losses arising from need for a large plutonium breeding effort with numerous occasional stopping without inelastic hadronic interaction [12, plutonium reactors. 13]. Another significant effect arises considering the density of In order to avoid the hybrid fission-fusion scheme, we need to the neutron—rich target: if the It" produced are moderated rapidly increase the fusion yield per muon, eq. (2), which requires the to atomic velocity, their binding and subsequent capture in the reduction of (03‘. Equation (5) shows that in actual technological target material will precede the natural decay into muons. applications of MuCF there are a priori two paths to reduce final Consequently, only in a (on average) very dilute target will the sticking through regeneration: we can seek conditions with losses to n" absorption be moderate. The lowest pion energy cost reduced stopping power, or we can attempt to re—accelerate the is around 2 GeV/7t" for a deuterium beam of 2—5 GeV/nucleon ay‘l' ion. For the latter there has not yet been a workable proposal on an infinite low-density tritium target [13]. made. More natural is to seek environments in which the stopping Given these operational constraints, a storage ring — internal power is reduced. While in a first approximation S is independent target scheme for muon production — has been proposed [12]. A of particle density, it is well known that it is greatly varying with proton beam (5 GeV) is kept in a storage ring, there is an internal temperature, once we are above the molecular dissociation target of small integrated stopping power and external targets for energy. A comprehensive study of this effect has been carried out the secondary 7r" showers. When a nuclear collision occurs, a by Jandel et al. [15], and it seems that a significant enhancement shower of particles is produced in a well—defined spot of the of muon regeneration could occur in dense plasma with a internal target. The primary particle shower, other than n", is temperature above 100 eV. Indeed, up to 10 000 fusions per directed to the external targets where further It" production muon appear possible in dense degenerate hydrogen plasmas occurs. The most optimistic calculation gives an energy cost of [15]. This would suggest that we turn much of our attention to 2.7 GeVbeam per It“ for a 5 GeV proton beam on internal and tepid but dense plasmas such as those which can potentially be 26 external Be targets. This scheme presents an energy advantage in reached in schemes involving inertial confinements. It is terms of the energy cost per muon, which is due to the good interesting to note that we need not concern ourselves with the ] Rafelski and II E Rafelski
energy needed to forln the MuCF plasma: if the beam energy cost called scientific break—even has been exceeded; that is, the per muon is of several giga—electronvolts, then the debris of the amount of fusion energy release by a single muon during its beam used to produce muons and contained in the secondary catalytic cycle exceeds the minimal energy required to make the positively-charged particle shower would suffice to compress the muon, which is 2 mucz. However, major critical improvements in fusion target. Such a conceptual system is somewhat reminiscent MuCF need to be made, if this scientific break—even were to lead of the ion—driven inertial fusion, with the difference that because to economically useful applications. For one, the 150 fusions of the catalysis the temperatures required are substantially lower, were reached at cryogenic temperatures in liquid hydrogen targets but the required confinement time must be longer than the muon and it is clear that in a normal reactor environment we could lifetime (say 5 us). probably not yet reach this fusion yield. On the other hand, the energy cost per muon is at present estimated at ~ 3 Gewm. Thus, we have to reduce at least by one order of magnitude the 5. Fusion with muons energy cost of muon production or/and enhance fusion MuCF Even if the dt MuCF—based economic power production can yield, before a MuCF approach to fusion energy can seriously be be achieved, the dt reaction poses known health and technological considered as a viable fusion alternative. problems and requires a significant inventory of tritium, as we We have shown that the recent advances in MuCF took this need to stop muons in a DT target. Ironically, the aneutronic, and field of research to a point at which the progress needed to reach non-tritium pcl reaction is suppressed in rate by the relatively high energy-related applications appears to be small in comparison to Q value, which suppresses the muon conversion probability. In improvements needed in more conventional fusion approaches, view of these insights, it is imperative to seek alternatives to such as plasma fusion or inertial confinement fusion. The MuCF hydrogen MuCF fusion, seeking in particular those cases which has reached the scientific break-even point, and the economical would have a near threshold nuclear state into which nuclei could break—even point may be as close as a factor 10 improvement in fuse, converting the muon. Due to the screening effect of the the catalyzed fusion yield per muon and/or reduction in energy muon cloud and the small reduced mass of the proton, the needed to produce a muon. However, as discussed in detail in this Coulomb penetration factor in direct reactions pp + Z remains of survey, there is a good reasons to believe that MuCF energy yield acceptable size for practically all reactions of interest. The most has also reached the point near the limits posed by the interesting system for such a consideration is the pp + 7Be, since combination of practicable approaches with the fundamental laws the p — 7Be cluster structure in the resulting 8B reaction product of physics, and hence further improvement is believed to be is nearly as large as the muon orbit. However, 7Be is a radioactive exceedingly difficult. Given the recent advances in understanding nucleus and even with its several months lifespan, unsuitable for we take the position that. in principle, a much greater than MuCF: and, furthermore, most of the nuclear reaction energy already achieved number of fusions per muon is possible. A limit would be carried off by the energetic neutrino emanating from the to the fusion yield per muon always arises in a particular context 8B decay to 8Be (which is also the solar neutrino in the solar envisaged for the likely fusion apparatus and is based on the neutrino problem). But a similar case is the p + 9Be system, limited knowledge of the complex catalyzed fusion cycle. which has a nuclear state 30 keV below threshold, and which Therefore, it is conceivable that an ingenious and practicable idea after fusion dissociates in cluster combinations of or + or + (l. is born during the research in issues related to MuCF, providing The key drawback of this and other similar cases is that once the the needed breakthrough. Hence, research in MuCF will always muon is transferred to a deeply bound state in the Z > 1 nucleus, have the potential of reaching some significant energy-related it is lost from the cycle of fusions. Clearly, this obstacle, if looked application. Apart from a wide intrinsic value of this field of upon superficially, precludes even one fusion per muon, as the research, it is also from this general interest perspective that the conventional wisdom would imply that the muon is primarily particle community must judge the matter. transferred to the more bound Z > 1 system. However, the significance of non—molecular in—flight scavenging can be reduced to manageable proportions by working with optimized very small partial concentrations CZ of Z > 1 light nuclei. One can search for situations in which the branching ratio, in say pp collision with a Z nucleus, is tilted towards the nuclear reaction, either in molecular processes [16], or as it appears to be equally of interest, in direct fusion reactions. Let us now sum up the current energetics of the muon Acknowledgement releases 17.6 MeV and hence The work of J. Rafelski was in part supported by the US catalyzed dt reaction. Every fusion 27 the maximal energy yield per muon is presently 2.7 GeV Department of Energy, Division of Basic Energy Sciences, stemming from a record yield of ~ 150 fusions. Thus, the so- Advanced Energy Projects. J. Rafelski and H E Rafelski
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