311 Acta Polytechnica CTU Proceedings 2(1): 311–320, 2015 311 doi: 10.14311/APP.2015.02.0311 Who Discovered the Hoyle Level? G. Shaviv1 1Department of Physics, Israel Institute of Technology, Haifa, Israel 32,000 Corresponding author: gioras@physics.technion.ac.il Abstract The prediction of Hoyle that the nucleus of 12C must have a resonance at 7.62MeV was the trigger to the Anthropic Principle. We review the history of the discovery of this level and investigate to what extent this was a genuine prediction. Keywords: anthropic principle - nuclear physics - stellar evolution. 1 Who Is Who Three dominant personalities were involved in the present story: Sir Fred Hoyle FRS (1915-2001), who was one of the greatest astrophysicists in the second half of the twentieth century with major contributions to Stellar structure (nuclear astrophysics - synthesis of the elements) and to Cosmology - (Steady state the- ory dubbed the name Big Bang) as well as planetary formation. William A. Fowler (1911-1995), who can be considered as the father of nuclear astrophysics and Edwin Salpeter (1924-2008) top theoretical astrophysi- cist, who has numerous seminal contributions in many astrophysical fields as well as in physics. Fred HoyleWilly FowlerEd Salpeter Edwin E, Salpeter William A. Fowler Fred Hoyle Figure 1: The dominant personalities involved in this story: The discovery of the triple α process. 2 What Is the Hoyle Level The synthesis of helium into carbon in stars proceeds via resonant reaction, namely the three α particles fuse into an excited energy level in the 12C nucleus. The rate of the reaction was calculated before the existence of this level was known and was found to be very low compared to the rate of destruction of 12C by collisions with α particles. As a consequence, it was impossible to predict the evolution off the main sequence towards the Red-Giant branch and the calculation implied that all the 12C is converted into 16O. But stars do evolve and we know that somehow carbon is synthesized. In view of the impass, Hoyle predicted therefore, that 12C has an energy level just at the right place and the reaction of carbon synthesis proceeds via this resonance level. The level was then discovered in the laboratory. This chain of events: prediction the existence of a nuclear level from astrophysical constraints, wa s considered as a big victory for astrophysics and the level was named the Hoyle level. 3 What Is the Anthropic Principle The Anthropic Principle is a philosophical hypothesis that measures of the physical Universe must be com- patible with the existence of conscious life that observes it. The phrase ”Anthropic Principle” appeared first in Brandon Carter’s contribution to the 1973 Krakow sym- posium honoring Copernicus’s 500th birthday. Carter argued as well, that humans do not occupy a privileged position in the Universe. The trigger to the idea that life as we know it, and the cosmos around us, ”are tuned”, emerged from Hoyle’s prediction of the existence of a special energy level in the nucleus of 12C. If such a level did not exist, argued Hoyle, life could not have develop in the cosmos, more accurately, 12C based life could not emerge. Was it really so amazing? Was it a full prediction? The basic astrophysical problem emerged when Hoyle and Schwarzschild calculated, in the early nineteen-fifties, the evolution of stars off the main se- quence into the red-giant using reaction rates known at the beginning of the nineteen fifties and got that as soon as 12C is synthesized from helium, it absorbs an- other α particle and becomes 16O leaving no carbon. The reaction forming 12C was much slower than the re- action that destroys it. If so, argued Hoyle, life should not exist! Alternatively, as 12C does exist in our uni- 311 http://dx.doi.org/10.14311/APP.2015.02.0311 G. Shaviv verse, there must be a resonance in this nucleus that accelerates the formation of carbon by many orders of magnitude. This was ’reverse engineering’ at its best. You know what should happen and find out how can it be. Could 12C be synthesized elsewhere? The only known alternative was the Big-Bang. But Hoyle ar- gued that all elements were synthesized in stars. On the other hand, Gamow argued that all elements were syn- thesized in the Big Bang. However, the various models of Big-Bang nucleosynthesis failed to produce elements like 12C and higher (in atomic weight), and left stars as the only cosmic site for synthesis of 12C and heavier nuclei. 4 The Nuclear Barrier Two nuclear barriers exist in the synthesis of the ele- ments from hydrogen up (see fig. 2). The barriers are the non existence of a stable A=5 and A=8 nuclei as shown in the figure. This means that the synthesis of the elements, if started from hydrogen, must jump over these nuclei.236 CHAPTER 8. HOW NATURE OVERCOMES ITS OWN BARRIERS Figure 8.1: The light elements in the N, Z plane. Sta- ble nuclei are painted brown. Unstable elements with long lifetime are painted yellow. Unstable nuclei with very short lifetime are painted red. The A=Z+N=5 and A=Z+N=8 nuclear barriers are shown as straight lines. The nuclear forces do not yield a stable nucleus for these combinations of protons and neutrons. There is only one nucleus with A=4 stable or unstable. Al- though it is very stable and has a large binding energy, it has no excited state, only the ground state. 1H Z N 1 2 3 4 1 2 3 4 5 6 7 8 5 6 7 8 14C 15N 16O 17O A=8 Barrier 18O 9 10 7Be 3.10-22s H He Li Be B C N O 5.10-21s 4.10-22s 8.10-19s10-17s 0.84s 177ms 8.7ms 8.10-22s 807ms 3.10-21s 119ms 12.3 yr 20.3m 5730yr 2.45s 0.75s 20ms 174ms 14ms 9ms 19.29s 11ms 9.97m 0 Finally, Bethe examined the triple body reaction, namely, the three ↵ particles interact simultaneously with one another to produce the carbon nucleus. Since collisions of an ↵-particle with one other particle, proton or alpha, do not lead to stable nuclei the alternative was to assume a triple collision of which three types were plausible: (a) 4He + 2p ! 6Be, (b) 24He + p ! 9B, and (c) 34He ! 12C. The first two reactions were rejected because they do not lead to a stable nucleus. The third reaction leads directly to 12C. However, Bethe knew from Eddington’s models that the temperatures in main sequence stars are around 2 ⇥ 107K, while the triple collision of ↵-particles requires according to Bethe’s estimates, temperatures of the order of 109K, which are way beyond the range of temperatures according to Eddington, in main sequence stars. Hence, Bethe dropped the idea of a three body reaction. In 1951 von Weizsacker1 discussed the problem and claimed that the energy source can still be gravi- tation if only the condensation is extremely large2, which is essentially a Milne type model. Weizsacker noted that there were giants among the old population of stars as defined by Baade. Namely, these stars must have a very long life time. Consequently, these stars must be low mass stars. If giants are main sequence stars which have exhausted their hydrogen fuel in the core and energy is not produced in the core any longer, then there need not be any temperature gradient in the core. Weizsacker thought that the fusion of H into He is the only process that could operate in stars because he believed that there is no way to overcome the A=5, 8 barriers. Consequently, nuclear energy was not an option for these stars because of the assumption that they exhausted their hydrogen and no other fusion can take place. From this point of view, Weizsacker put the giants and the white dwarfs in the same category of stars. Still, Weizsacker added a reservation that in view of results known at his time, there is a possibility for hydrogen burning outside the isothermal core3. However, the idea Weizsacker put forward was that the di↵erence between white dwarfs and giants should be that giants have masses above the Chandrasekhar 1von Weizsacker, C.F., ApJ, 114, 165, (1951) 2Jordan, P., Die herkunft der Sterne, 1947, p 38. 3Richardson, R.S. & Schwarzschild, M. ApJ, 108, 373, (1948) Gamow, G. & Teller, E., Phys. rev. , 55, 791, (1939) & Gamow, G. & Keller, G., Rev. Mod. Phys. ,17, 125, (1945) & Gamow, G. Phys. rev. 67, 120, (1945) Figure 2: The nuclear barriers at A=5 and A=8, namely the non existence of stable nuclei with these number of protons and neutrons. Many attempts and suggestions to overcome the barriers were suggested. We mention here only Bethe’s attempt, namely a three body reactions. Bethe knew from Eddington’s stellar models what are the central temperatures and densities in stars and soon realized that a 3-body reaction is much too rare under such con- ditions. We note that Eddington’s results were derived without reference to what is the energy source of stars (which he did not know but hypothesized, already in 1919, that it must be the fusion of hydrogen into he- lium). In fig. 3 we show the structure of all nuclei with N+Z=8. The instability of the A=8 nucleus implied that any fusion reaction leading to this nucleus will not create it. The so formed nucleus may live a short time but eventually it decays.8.1. UNSUCCESSFUL ATTEMPTS TO OVERCOME THE A=8 BARRIER 237 12B5 12C6 12N7 17.42MeV 13.37MeV β+ β- Energy The N+Z=12 system Z=5 Z=6 Z=7 τ1/2=11.00msτ1/2=20.20ms Figure 8.2: The A=12 nuclei system. The diagram explains why of all nuclei with 12 protons and neu- trons, the 12C is the most stable one. The other nu- clei with A=12 are all unstable and decay via �+ or �� into 12C. The energies above the ground state of carbon are given in MeV. Also given the half-lifetime of the unstable nuclei. After Ajzenberg-Selove and Lauritsen 2008. 8He 8Li 8Be 8B 8C 4He+4He -0.0918 3.03 11.35 16.9217.02 16.36 26.3228.09 Reference level Energy Z2 3 4 5 6 0 Figure 8.3: The energy levels of the nuclear system with A=8 for di↵erent atomic numbers Z. The nu- cleus 8B can decay into an excited state of 8Be, which may decay eventually to the 8Be ground state. But the ground state of 8Be is above the state of two free ↵ particles (colored green) and hence, the fast break- down of 8Be is unavoidable. Consequently, 8Be does not exist in nature. limiting mass4 and hence, have enough gravitational energy in the contraction towards extremely high densities, even as high as nuclear densities5. However, no detailed calculations were carried out, just speculation. Weizsacker attempts and ideas to explain the giants were typical to the hopeless situation in front of the insurmountable A=5, 8 barriers. In 1949 Gamow published a paper on Relativistic Cosmology6 in which he brought up an idea Wigner communicated to him in private. Another ingenious method of crossing the mass 5 crevasse was proposed by E. Wigner. It is known as the method of the ’nuclear chain bridge’. Wigner’s plan is that all that is required for building a chain bridge is an assumption that there was originally one single nucleus on the right-hand side of the crevasse. Such an assumption can easily be granted argued Gamow, since some building up is still maintained across the crevasse by the reaction 4He +3 T !7 Li + � in spite of the low probability of its occurrence. Gamow published his rejection of Wigner’s idea in a book7 just when the Salpeter and Hoyle started the work on the triple ↵ process which ended few years later with the detailed nuclear physics. Gamow gave no reference to where Wigner published his suggestion. 4Chandrasekhar, S., MNRAS, 95, 207, 226, 676, (1935) 5Nuclear densities are densities at which the nuclei touch each other. The radius of the nucleus is about 10�5 the radius of the atom, namely, the radius of the outer occupied electronic shells. The atom has an infinite number of electronic shells with radius increasing to infinity. But as the number of electrons in each atom is finite, they occupy only the lowest in energy levels and for this reason the actual atoms has a finite radius, the radius of the last occupied level. Normal matter densities on the earth are ⇠ 1g/cm3. If the matter is compressed to densities as high as 1015gm/cm3 the nuclei touch each other and form one gigantic nucleus. This is nuclear matter. 6Gamow. G., Rev. Mod. Phys., 21, 367, (1949) 7Gamow. G., The Creation of the Universe, Viking press, New York, 1952. Figure 3: The relative energies of the ground states of the N+Z=8 nuclei. The numbers are the energies in MeV relative to the ground state of 8Be, which has the lowest ground state energy of all A=8 nuclei. However, the state of two free α’s has still lower energy. Hence, there is no stable nucleus with A=8. 5 Why Nuclear Physicists Were Interested in the Problem? The fundamental problem in nuclear physics at the be- ginning of the nineteen thirties was the nuclear struc- ture. It was already known that the α particle is the most bound nucleus as it has the highest binding en- ergy per nucleon. Similarly, nuclei like 12C,16 O,20 Ne etc have a higher binding energy than their neighbor- ing nuclei. The question was therefore, are these so called α nuclei composed of α particles 238 CHAPTER 8. HOW NATURE OVERCOMES ITS OWN BARRIERS 8.2 The pursuit after the structure of the carbon nucleus Figure 8.4: Two possible structures of the carbon nucleus. On the left, the nucleons move randomly inside the nucleus. On the right, there are three clus- ters of ↵ particles and the ↵ particles move randomly inside the nucleus. Figure 8.5: The structure of 14N according to the revised ↵-particle nuclear model. The story starts as early as 1917, when Harkins8 observed that the binding energies of the so called ↵ nuclei, (12C,16O,20Ne,24Mg, . . . ) are particularly large. Consequently he suggested a periodic table for nuclei (cf. fig.??). The basis for this periodic table was Harkin’s idea that the basic building block of nuclei is the ↵-particle. Harkin’s original idea was put forward before the neutron was discovered. After the discovery of the neutral particle the model was modified to: the nucleus is made of a core of ↵ particles and up to 3 nucleons moving around it (cf. fig.??) Consequently, the following fundamental question was raised: to what extent a nucleus of type 4n+2 would yield a nucleus of type 4n, where n = 1, 2, 3, . . . and an ↵ particle, if bombarded with nucleus with atomic weight 2, namely a deuterium. In symbols the reaction is: 4n+2X2n+1 + 2D1 ! 4nY2n + ↵, where X is any nucleus and Y is the element the precedes the element X in the periodic table. The di↵erence between the two models is fundamental. The ↵ particle is fully symmetric and has zero spin, hence, it must follow the Bose-Einstein statistics. On the other hand, the protons and the neutrons both have spin 1/2 and hence, follow the Fermi-Dirac statistics. Obviously the behavior of the particles in the potential well and how they fill up the levels is completely di↵erent in two the cases. The di↵erence should express itself in the binding energy as well as in the energy levels. If there is a potential well and the particles moving inside obey the Fermi-Dirac statistics, we can expect periodicities in the properties. On the other hand, if the ↵ particles preserve their spin while they move in the nucleus, then they do not behave like bosons and can all stay in the same nuclear level. Obviously, the binding energy in such a case is larger than in the case of individual protons and neutrons (because in the latter case the nucleons are spread over many energy levels while in the first case they are all in the lowest most bound level.) The idea that nuclei are composed of ↵ particles emerges from the fact that the ↵ particles is extremely stable and we do not know that it has any excited levels. Like deuterium which is composed of a neutron and a proton does not have any excited state, only a ground state. Hence the helium nucleus is not unique from this point of view. The binding energy of a deuterium is 2.225MeV while that of an ↵ particle amounts to 28.3MeV, namely, significantly more than just two deuterium nuclei put together. It seems that the potential well inside which the ↵ particle resides is very deep and still does not posses any excited state. Lauritsen and Crane9 investigated this point in 1934 and indeed, did not discover any 8Harkins, W.D., J. Amer. Chem. Soc., 39, 856, (1917), Phys. Rev. 15, 85, (1920) 9Lauritsen C.C. & Crane, H.R. PRL, 46, 537, (1934) Figure 4: The two possible options for the structure of the carbon nucleus. On the left we see 12 nucleons moving independently of each other and on the right we see groups of 4 nucleons moving as a bound unit. or of just an equal number of protons and neutrons, as shown in fig. 4. In particular, is the excited state of 12C a three body state? Consequently, attempts to find the energy level structure of the excited 12C were 312 Who Discovered the Hoyle Level? carried out long before any astrophysical interest in the problem arose. Actually, even before Bethe discovered how the CN cycle powers the Sun (today we know that the CNO cycle contributes about 4% of the total energy produced by the Sun and the pp chain contributes the rest.) 6 The History of the Discovery of the 12C Nuclear Levels Already in 1933 Lewis et et al. experimented with the reaction:14N+2D → 12C+4He. The nucleus of 12C so formed has significantly more energy than the ground state as it forms in an excited state. The decay of the excited state to the ground is performed by one or more emissions of γ photons. In principle, if you measure the energy of the γ′s you can easily figure out the energies of the energy levels in the newly formed nucleus. Lewis et et al. did not measure any γ′s as they did not have the equipment, they however, discovered the emitted α particles. As they did not detect all particles emitted in the reaction they found that the emitted α particles have about half the energy difference and it was not known where the other half was lost. Lawrence et al (1935) repeated the experiment, again without any device to measure γ′s. However, they measured the energies of the α′s and found two groups of α particles having different energies, and so were able to infer that 12C has two energy levels: at 3.8MeV and 4.7MeV. Actually, the interpretation of the experiment was not complete. As shown in fig. 5, there are two possibilities to interpret this experiment. 0 0 3.8 3.8 8.5 4.7 Ground state 00 Figure 5: The interpretation of Lawrence et al. result. One alternative can be two levels at 3.8 and 8.5MeV with allows transitions between these two levels and forbidden transition directly from the 8.5Mev level to the ground state. The other alternative is two levels with allowed direct transition to the ground state and forbidden transition between the levels. Lawrence et al assumed the latter case but as we will see that in reality it was the first alternative. Crane and Lauritsen observed γ’s from the reaction: 11B+2D → 12C+p. These experiments which were car- ried out in the early 1930th made it clear that 12C has excited states but their energy was not known to better than ±1MeV . 8.5. BACK TO NEW DEVELOPMENTS IN THE STRUCTURE OF 12C 241 Table 8.1: Bethe’s estimate for the lifetime of the 8Be nucleus as a function of the energy excess above the state of two free ↵ particles (in seconds). The second row gives the crossing time. Energy excess in keV 50 100 200 300 400 R = 2.5 ⇥ 10�13cm 4 ⇥ 10�13 3 ⇥ 10�14 2 ⇥ 10�15 2 ⇥ 10�19 5 ⇥ 10�20 crossing time (sec) 4 ⇥ 10�22 2.8 ⇥ 10�22 2.0 ⇥ 10�22 1.6 ⇥ 10�22 1.4 ⇥ 10�22 R = 2.5 ⇥ 10�13cm 7 ⇥ 10�14 4 ⇥ 10�17 3 ⇥ 10�19 3 ⇥ 10�20 1 ⇥ 10�20 crossing time (sec) 8 ⇥ 10�22 5.6 ⇥ 10�22 4 ⇥ 10�22 3.2 ⇥ 10�22 2.8 ⇥ 10�22 8.5 Back to new developments in the structure of 12C Αα Αα3 +8 BeBe + 7.366 7.275 7.68 4.43 12C 7.1 7.8 Figure 8.6: The energy levels of the 12C nucleus relative to the rest mass energy of 8Be + ↵ and 3↵. The level at 7.68MeV can de- cay into a 8Be + ↵ or 3↵. The green color span the range where the various experiments gave an indication of an energy level. All energies are in MeV. The correct explanation was put forward five years later, in 1940, and by Gaerttner and Pardue25, then in the Kellogg radiation laboratory in Cal-Tech. Using the same nuclear reaction, 14N+2D ! 12C+↵, Gaerttner and Pardue discovered that on top of the emerging ↵, also � rays at 1.9, 3.1, 4.0, 5.3 and 7.0MeV were produced and explained their origin as due to excited levels in 12C at energies of 4.32 and 7.2 ± 0.4MeV above the ground state. The authors even stated that the level at 7.2MeV is weakly coupled with the ground state, namely, the probability for a transition from the 7.2MeV state to the ground state is very small and was not observed. Here we note that the energy of 8Be + ↵ is 7.367MeV above the ground state of 12C. Hence only a level above this rest mass energy plus the kinetic energy can be directly reached by the 8Be+↵. At stellar temperatures of the order of 108 � 109K the nuclei have kinetic energy of about 0.01 � 0.1MeV, so that the kinetic energy is not the dominant one.26 We conclude that for the colliding 8Be and ↵-particle to enter into an energy level of 12C, the energy must be above 7.366MeV but not by very much. The knowledge of the structure of the 12C nucleus at that time is shown in fig.??. The green zone spans the uncertainty in the location of the energy level just above the energy of 8Be+↵ or 3↵. Since the reaction rate is very sensitive to the exact value of the energy level, accurate positions are mandatory. Most nuclear reactions at low energy have two quite independent steps: formation and decay. • The formation: So far we discussed the probability of formation. Due to the strong interaction between the particles and the relatively long time the particles stay together, the 0nucleus forgets how the particular level was reached0. The newly formed excited 12C lives for a while, exactly like the 8Be nucleus lives for a while, before it decays. Nuclear physicists call the new nucleus the 0compound nucleus0. • The decay: The new nucleus may have several modes of decay. It can disintegrate back into the original constituents or lose energy in one way or another and descend into a bound state, provided there is one, or even the ground state. No bound nucleus can be formed without any loss of energy. The most common way of losing energy is by emitting a �, however, other ways, though with lower probabilities, exist. 25Gaerttner, E.R., & Pardue, L.A. , Phys. Rev., 57, 386, (1940) 26The relevant particles are those with energies equal to the Gamow peak and not with the average energy. Figure 6: The structure of the 12C nucleus as known in 1940. The level at 7.68MeV can decay into a 8Be+α or 3α. The green color spans the range where the var- ious experiments gave an indication of an energy level. All energies are in MeV. In 1940 Gaerttner & Pardue of the Kellogg labo- ratory at Caltech investigated the reaction 14N+2D → 12C+α and discovered that on top of the emitted α particles also γs with energies 1.9,3.1,4.0,5.3 & 7.0 MeV were emitted. It became clear already at this epoch that there exists a level at ∼ 7.2MeV but it is weakly cou- pled to the ground state, namely the transition to the ground state was too weak to be observed! Hence, only an upper limit to the rate of transition could be found. The implication was that indeed, if the reaction product goes to excite this level in 12C, then extremely few 12C nuclei would decay from this state to the ground state. It appeared therefore, that from stellar nucleosynthesis this is not likely to be the way 12C forms. But this question of transition probability was not yet raised. In the same year Holloway and Moore (1940) re- peated the experiment 14N+2D → 12C+4He and con- firmed the existence of the levels at 4.37 & 7.62MeV and suggested that in most cases the (excited) 12C∗ disin- tegrates by emitting an α particle. They wrote that: The corresponding excited state of 12C would be unsta- ble against α emission, but it is still easily conceivable that such a state could not actually emit an α because 313 G. Shaviv of selection rules. Clearly, in the first case this is not the way to form carbon while if carbon is formed in this way we can claim that astrophysical situation implies that the channel in which 12C∗ disintegrates by emit- ting an α may exist but along with the decay to the ground state. As for our particular reaction, what Holloway and Moore argued was that in the reaction 8Be+α↔12 C+γ the compound nucleus disintegrates mostly into the in- coming channel. Terrell (1950) examined the 9Be+α → 12C+n and found no evidence for excited states in 12C. In the same year Johnson (1952) investigated the 11B+2D→ 12C+n reaction and found the 4.4 & 9.6MeV levels but not the one around 7MeV. It should be realized that these ex- periments are very difficult and tricky and hence no wonder that it took such a long time to find the accu- rate structure of the nucleus of 12C. In 1950 Hornyak et al. summarized the known data of the 12C nuclear structure as depicted in fig. 6. The 7.86MeV level is shown but very weak, namely only rare transitions into it, and hence a problem to experimen- talists. Lauritsen and Fowler were co-authors on this paper. In 1951 Miller & Cameron followed the motion of 8Be nuclei in nuclear emulsion and observed their de- cay. They found a lifetime of 5 ± 1 × 10−14sec. This lifetime is 106 times longer than the two α’s mutual crossing time. This was the paper that put an end to a long line of papers that claimed alternatively that 8Be is unstable and unstable. Miller & Cameron succeeded to watch the motion of the 8Be nucleus in emulsion and see its decay. We mentioned above that α-like nuclei are expected to be more bound than their neighbors. Here we have a nucleus composed of just two α nuclei and it is unstable! 7 The Wrong Solution Some people claim that Salpeter, who discovered the basis for the triple alpha process, must share the credit with Öpik. Öpik, according to this claim, solved the problem of the helium fusion to carbon already in 1951. The trouble was, so goes the claim, that Öpik published his paper in the Proc. Royal Irish Acad. 1951. A sel- dom visited by astrophysicists journal. But Öpik’s paper is wrong and not identical with that of Salpeter. Öpik, who had many important and very original contributions, apparently did not read the nuclear literature or ignored it, because he ignored the fact the 8Be is unstable, a fact known already in 1951. So Öpik assumed a 3 body collision. The α + α penetration takes about 0.8 × 10−20sec and the third α must collide within this time. Clearly, the lifetime of 8Be as assumed by Öpik, is off by a factor of 106. This factor enters into the rate. Moreover, despite the fact that the energy level in the 8Be continuum was al- ready known, Öpik overlooked it. Öpik assumed that He burning lasts 1014sec. The question then was at what temperature would helium burning last this time and with his wrong reaction rate Öpik derived that he- lium burning takes place at 6 × 108K. This is known today as far off and it implies a discrepancy between the formation of 8Be via two α′s and the formation of 12C, as we will shortly see. Öpik’s paper did not attract the astrophysical community and from its publication in 1951 till 2009 Öpik’s paper was cited just once, and it was by Salpeter... In 1972 Marshal Wrubel wrote a review on Ernst Öpik’s contributions to Red Giants and did not men- tion his contribution to the 3α process. The uncertainty in the energy levels prevailed in 1950. Guier and Roberts looked at: 9Be+α → 12C +n and claimed the level is at 7.8MeV. The experiment was repeated with Bertini joining the team, and no level was observed. In 1952 Azjenberg & Lauritsen prepared a compila- tion of all the experiments and provided the following summary in fig. 7. Our particular level is well marked. 246 CHAPTER 8. HOW NATURE OVERCOMES ITS OWN BARRIERS in a figure which provided the structure of energy levels in 12C. As can be seen from fig.??, a level at 4.43MeV and a level at 7.5MeV appeared as well as the quantum numbers J = 2+ and J = 0, respectively49. No parity is assigned to the upper level. The only reference given for this information is 0cloud-chamber investigation0 without the details of the paper. However, the only researchers to apply a cloud chambers on a close problem were Crane, Delsasso, Fowler and Lauritsen50 back in 1935. Figure 8.12: The structure of 12C as was known in 1952. For the ease of reading this heavy with data figure, we marked energy level at 7.5MeV with red and the level of 8Be +↵ is marked with green. Note that the spin of the level is given, indicating that the 8Be+↵ can create the excited 12C nucleus. It is this coincidence which led later to philosophical hypothesis. From Ajzenberg and Lauritsen 1952. The data on the quantum numbers of the energy levels is important. It was well known that the ground state of 12C is J = 0+. It is also well known that a transition from a J = 0+ to J = 0+ is strictly forbidden. The spin of the photon is 1. Hence a zero spin to a zero spin tran- sition does not leave room for the photon, so that angular momentum can be con- served. Hence, if a bound carbon nucleus is to be the end product, it is not su�- cient to have this energy level because no direct transition from the 7.5MeV state to the ground state is possible. Another en- ergy level above the ground state and be- low the level at 7.5MeV must exist and must have the right quantum numbers so that the transition to the ground state can go through an intermediate state. 8.9 Salpeter - The solution is two plus one In the early nineteen fifties, Willy Fowler, who was already then the insa- tiable force behind the Kellogg laboratory, in CalTech, consulted extensively Hans Bethe, who was at Cornell. After a while, Bethe agreed to send to Fowler one of his best young men and Edwin Salpeter (1924- 2008) was his choice. Salpeter spent the summer of 1951 in the Kellogg Laboratory. It is during this and subsequent stays that Salpeter carried out his research on how helium can be synthesized into carbon. On October 1952 Salpeter submitted his first short paper to the Astrophysical Journal51. In the same month of October, the Physical Review published a paper by Ajzenberg and Lauritsen, who worked in the same Kellogg Laboratory, in which the resonance level in 12C was marked at 7.5MeV and with quantum number assignment of J = 0. No parity was given. Salpeter submitted his paper after returning 49In 1950 Azjenberg and Lauritsen had the level at 7.MeV and it is not clear why the level 0moved0 half an MeV upward. 50Crane, H.R., Delsasso, L.A., Fowler, W.A., & Lauritsen, C.C., Phys. Rev. 48, 100, (1935) 51Salpeter, E.E. ApJ, 115, 326, (1952) Figure 7: The structure of the 12C nucleus as sum- marized in 1952. The energy level under discussion is marked in red and is at 7.5MeV. Note that the authors assigned the level J = 0, which is identical with that of the ground state. But 0→ 0 transitions are forbidden. 314 Who Discovered the Hoyle Level? 8 Salpeter Enters the Game Salpeter entered the game in 1951 just after the pub- lication of the Bethe-Salpeter equation. It was upon Fowler’s request for help in the theory, that Bethe de- cided to send his distinguished young physicist Salpeter to the Kellogg laboratory at Caltech. Salpeter spent two summers in Caltech. On October 1951 Salpeter submitted his first paper to the ApJ: 12C had no level around 7.6MeV. On October 1951 Ajzenberg & Lau- ritsen submitted a paper to Physical Review in which 12C had a level at 7.5MeV with J=0 (no known parity). Two of the most important results for the triple alpha process were published at the same time by people from the same laboratory in two different journals and no ci- tation was given to one another. They simply did not know of each other. When Gamow considered in 1938 the possible en- ergy source of MS stars he assumed, in an attempt to overcome the A=5 barrier, that: 24He ↔ 8Be, namely the reaction is in a dynamic equilibrium and assumed 8Be to be stable. Salpeter was unaware of this publica- tion of Gamow but knew already that 8Be is unstable. So Salpeter, facing the same dilemma as Gamow, as- sumed that the two α′s go into the 95KeV level (which was known already to Salpeter) in the continuum and the so formed nucleus lives long enough (just 10−14sec which were inferred from the width of the level) for a third α to collide and create a 12C nucleus. Salpeter realized that 10−14sec is orderes of magnitude longer than the two α′s self-crossing time and hence his treat- ment was justified because 8Be lives a long time before it decays and the assumption of equilibrium is fully jus- tified. If so, there is no need for a cross section! Next, Salpeter assumed that the 12C nucleus ”somehow de- cays” in flight (no level in 12C was known to certainly exists) into the ground state of 12C. Salpeter stressed that he assumed no resonances in 12C,16 O,20 Ne,24 Mg . . .. Salpeter felt uneasy about it and wrote that: The nuclear γ-ray width for the forma- tion of 12C (but not the one for 8Be) is required. This width has not yet been measured, and the position of resonance levels was not known accurately enough and an estimate of 0.1eV was used for this width. Hence the correct production rate could be smaller by a factor of as much as 10 or larger by as much as 1000. Thus the reaction rate known in the literature was estimated ignoring the possible existence of unknown resonances. Two comments: In 1954 Öpik wrote a paper about WD and the 3α. He wrote that: the lifetime of the temporary nucleus 8Be formed is assumed equal to ∼ 8 × 10−21sec being an estimate of the duration of penetration. The lifetime of true 8Be is probably much shorter, about 10−22sec . . . No resonance capture is as- sumed in this case. Moreover, Öpik complained that Salpeter did not cite him and added: His method of calculation is not quite clear from his brief note. It seems that the reaction 2α → 8Be∗ he has treated in a manner similar to ours, where as in 8Be+4He → 12C +γ he has postulated a resonance process. The outcome is a formula yielding 1.4× 1013 times higher an energy generation with practically similar temperature as our formula. How many errors can be written in a single sentence? 8.12. THE NEW EXPERIMENT 249 7.59 4.43 0+ 2+ 0+ Gγ Gγ4.43 3.16 12C Figure 8.13: The status of the level structure of 12C after Beghian et al. 1953. Figure 8.14: The clear evidence for the two groups of � rays as discovered by Beghian et al. 1953. known and documented by researchers from Kellogg, as described before. However, many of the required details were still missing and above all Fowler did not trust the experimental results. The abstract was presented in the American Physical Society in Albuquerque, New Mexico, September 2-7, 1953. The sensational paper was the last one in the last session. The session itself was on nuclear physics not astrophysics. It was a victory to astrophysics and Hoyle, in particular in front of skeptical Fowler63, that the location of a nuclear level that wandered so much from one experiment to the other, could be determined from observing the stars. Shortly after, two papers were published, one by the exper- imentalists in the Physical Review and one by the theoretician in the Astrophysical Journal Supplement. This triumph forged the Fowler-Hoyle collaboration that contributed immensely to nuclear astrophysics for many years to come. The exact reference is an abstract by Hoyle, Dunbar et al.64 with the title: A State in 12C Predicted from Astrophysical Evidence. The idea was that: the observed 0cosmic0 ratio of He:C:O can be made to fit the yield calculated for these reactions if the reaction 8Be + ↵ ! 12C + � has a resonance near 0.31MeV, corresponding to a level at 7.68MeV in 12C. The abstract also claimed that: A level had previously been reported at 7.5MeV, based on Ajzenberg and Lauritsen 1952. In the same abstract they report about the experiment which led to the discovery of the level at 7.68 ± 0.03MeV. The mode of decay of the level is not discussed. 8.12 The new experiment Dunbar et al.65 repeated the 14N + 2H ! 12C + ↵ experiment once more using a new special double focusing magnetic spectrometer and discovered that the excited level is at 7.68 ± 0.03MeV as can be seen from fig.??. Unfortunately, they did not give the quantum numbers of the levels, and it was impossible to determine whether the reaction a stable 12C could be formed. This sophisticated and accurate experiment settled for good the question where is the level but could not answer the crucial question: can a stable 12C be formed? 63Salpeter, E.E., Publ. Astron. Soc. Australia, 25, 1, (2008) 64Hoyle, F., Dunbar, D.N.F., Wenzel, W.A. & Whaling, W., Phys. Rev, 92, 1095, (1953) 65Dunbar,D.N.F., Pixley, R.E., Wenzel, W.A., & Whaling,W., Phys. Rev, 92, 649, (1953) Figure 8: The very nice discovery of the energy levels by Beghian et al (1953). In 1953 Beghian et al investigated the 9Be+α → 12C+n reaction. They detected two groups of γ rays: at 3.16MeV and at 4.43MeV and concluded that: 12C has two levels: at 4.43 & 7.59MeV (The first alternative is shown in fig. 5) . They did not find any γ rays with energies close to 7.5MeV. Hence they concluded that the probability of the 7.59MeV level to decay to the ground state is < 1/2500. Willy Fowler did not trust any of the previous measurements of the carbon level and searched for a way to carry out a trustful experi- ment. 8.12. THE NEW EXPERIMENT 249 7.59 4.43 0+ 2+ 0+ Gγ Gγ4.43 3.16 12C Figure 8.13: The status of the level structure of 12C after Beghian et al. 1953. Figure 8.14: The clear evidence for the two groups of � rays as discovered by Beghian et al. 1953. known and documented by researchers from Kellogg, as described before. However, many of the required details were still missing and above all Fowler did not trust the experimental results. The abstract was presented in the American Physical Society in Albuquerque, New Mexico, September 2-7, 1953. The sensational paper was the last one in the last session. The session itself was on nuclear physics not astrophysics. It was a victory to astrophysics and Hoyle, in particular in front of skeptical Fowler63, that the location of a nuclear level that wandered so much from one experiment to the other, could be determined from observing the stars. Shortly after, two papers were published, one by the exper- imentalists in the Physical Review and one by the theoretician in the Astrophysical Journal Supplement. This triumph forged the Fowler-Hoyle collaboration that contributed immensely to nuclear astrophysics for many years to come. The exact reference is an abstract by Hoyle, Dunbar et al.64 with the title: A State in 12C Predicted from Astrophysical Evidence. The idea was that: the observed 0cosmic0 ratio of He:C:O can be made to fit the yield calculated for these reactions if the reaction 8Be + ↵ ! 12C + � has a resonance near 0.31MeV, corresponding to a level at 7.68MeV in 12C. The abstract also claimed that: A level had previously been reported at 7.5MeV, based on Ajzenberg and Lauritsen 1952. In the same abstract they report about the experiment which led to the discovery of the level at 7.68 ± 0.03MeV. The mode of decay of the level is not discussed. 8.12 The new experiment Dunbar et al.65 repeated the 14N + 2H ! 12C + ↵ experiment once more using a new special double focusing magnetic spectrometer and discovered that the excited level is at 7.68 ± 0.03MeV as can be seen from fig.??. Unfortunately, they did not give the quantum numbers of the levels, and it was impossible to determine whether the reaction a stable 12C could be formed. This sophisticated and accurate experiment settled for good the question where is the level but could not answer the crucial question: can a stable 12C be formed? 63Salpeter, E.E., Publ. Astron. Soc. Australia, 25, 1, (2008) 64Hoyle, F., Dunbar, D.N.F., Wenzel, W.A. & Whaling, W., Phys. Rev, 92, 1095, (1953) 65Dunbar,D.N.F., Pixley, R.E., Wenzel, W.A., & Whaling,W., Phys. Rev, 92, 649, (1953) Does not exist! Figure 9: The structure of 12C after Beghian et al dis- covery. The direct transition from the 7.59MeV to the ground state is forbidden. 315 G. Shaviv The symmetry of the 12C ground state leads to a J = 0+ state. The state at question appears to have also J = 0+. Angular momentum conservation do not allow the 0+ state to decay into the ground state which is also 0+. Hence, if eventually the decay of this state leads to the ground state, there must be another inter- mediate level below the 7.59MeV one with the proper spin, to which this level can decay. Hoyle never men- tioned these requirements nor allowed and forbidden transitions. He tacitly assumed that the 7.69MeV level ’somehow’ decays to the ground state. 9 1953 Kellogg Phase I When Martin Schwarzschild and Fred Hoyle tried to evolve main sequence stars off the main sequence and derive the Red Giant, the modeling failed and they could not get the Red Giant branch. Beside the fail- ure to derive the branch, there was a problem with the composition. The rate of 12C + α (carbon conversion into 16O) was much greater than the rate of carbon for- mation and hence no carbon was left after helium burn- ing. The model moved from helium to oxygen leaving no carbon. Hence, Hoyle argued that there should be a level at about 7.6MeV which accelerates the reaction and leads to the formation of carbon (relative to its destruction). Hoyle spoke only on the energy of the level and he knew at what energy in 12C it should be because he assumed it takes place via 8Be + α. This is exactly the level we discuss here. 250 CHAPTER 8. HOW NATURE OVERCOMES ITS OWN BARRIERS 8.13 Hoyle: We must have Carbon in our Universe! In 1954 Hoyle published an extensive research on the synthesis of the heavy elements66 and discussed the synthesis of carbon as the starting point. This is the same paper in which Hoyle proposed how the synthesized elements spread in the galaxy, see sec. ??. Hoyle followed Salpeter and assumed the dynamic equilibrium for ↵ + ↵ *) 8Be and applied statistical mechanics to find the abundance of the beryllium. As Salpeter did not provide the equation and only quoted the result, Hoyle cited himself for the equation of equilibrium.67 In that paper Hoyle discussed the formation of the heavy elements under statistical equilibrium. No mention of Gamow’s 1938 paper and his equilibrium 8Be. Figure 8.15: Dunbar’s et al. 1953 result. A beau- tiful manifestation of the predicted 7.68MeV level. Once carbon is synthesized it can absorb an additional ↵ particle and become oxygen, which in turn can again absorb an ↵ particle and become neon: 12C + ↵ ! 16O + � followed by 16O + ↵ ! 20Ne + �. In principle, the 20Ne can capture another ↵ particle to form 24Mg, but the increasing Coulomb barrier reduces the rate so much that it is permissible to neglect the ↵ capture past oxygen. The crucial point is therefore, that carbon and oxygen are synthesized at the same time and not one after the other. Thus, on one hand the carbon is synthesized and on the other it is destroyed. By the end of the day, the final amount of carbon depends on the ratio between the rate of formation and the rate of destruction. Hence, Hoyle defined a parameter:  = A ⇥ Rate(12C + ↵ ! 16O) Rate(3↵ ! 12C) where A is a numerical factor, so that relevant values of  will be of the order of unity. Clearly,  depends on the temperature as well as on the properties of the energy levels in carbon and oxygen. Of all the data which enters into the expression for , it is most sensitive to the Eres = E � E(8Be + ↵) because  ⇠ e �Eres kBT = e � (E�E(8Be+↵)) kBT , where E is the energy of the level in the 12C nucleus. All energies are above the ground state of 12C. The energy dependence is exponential. Assuming the Salpeter’s rate for the triple ↵ reaction and the problematic (see later) subsequent reaction 12C + ↵ !16 O, Hoyle solved for the abundances of carbon and the results are shown in fig. ??. It can be seen from the figure that when  = 1/9 the amount of carbon produced by the time the helium is exhausted, is 1/3 which corresponds to an abundance ratio of C/O=1/2, the value Hoyle took as the observed cosmic value. Also, one can see that a small variation in  from 1/3 to 1/15 spans a carbon abundance which covers the observed value. On the other hand, if there would be no resonance at all in 12C, the value of  would have been orders of magnitude smaller and no carbon would be left at the 66Hoyle, F., ApJS, 1, 121, (1954) 67Hoyle, F., MNRAS, 106, 343, (1946) Figure 10: The structure of 12C after Dunbar et al discovery. When Hoyle came to Kellogg in the first time he convinced Ward Whaling to look for this level and in- deed Whaling went to the lab and found the level ex- actly where Hoyle claimed it must be. The level was rediscovered! Hoyle spoke about the energy of the missing in cal- culation level and did not discuss any spin, selection rules etc. The abstract was presented in the American Physical Society meeting in Albuquerque, NM, Sep 2-7, 1953. The paper was presented in the session on nuclear physics not astrophysics. It was a victory for Hoyle in particular in front of skeptical Fowler. 10 How Did Hoyle Predict the Nuclear Level in 12C Hoyle assumed the that κ defined as: κ = A Rate(12C + α→16 O + γ) Rate(3α→ γ) = destruction formation is given and calculated the resulting mass fraction of 12C after the burning of helium into carbon. Hoyle ob- tained in this way the results shown in fig. 11. It is easily seen that κ � 1 (the destruction is much faster than formation) yields no carbon at the end of helium burning. 8.14. THE KELLOGG LABORATORY GROUP PHASE II 251 end of the helium burning.If the formation of 12C is much slower than its destruction, the end product if almost pure 16O. Figure 8.16: The formation of carbon from helium as a function of Hoyle’s parameter . This is the figure which convinced Hoyle that 12C should have a resonance. In addition, Hoyle carried out the inverse cal- culation in a style which is known today as 0reverse engineering0, namely what must T and Eres be so as to get the observed abundance, and he found T = 1.4 ⇥ 108K and Eres = 0.33MeV (above the rest mass of 8Be + ↵) which corresponds to E = 7.705MeV in the 12C nucleus. In summary, Hoyle was able to apply astro- physical arguments to solve the problem of the car- bon energy level, the exact location of which wan- dered from one experiment to the other. Shortly after the idea that such a resonance must exist or else, the cosmos will have no carbon to support life the way we are familiar with, was born. The fan- tastic story about how astrophysical consideration led to the prediction of a nuclear level triggered the invention of the anthropic principle68. 8.14 The Kellogg Laboratory group phase II Hoyle’s victory was not complete. Cook et al.69 found it necessary to carry out a new experiment again because the Experimental evidence on the character of the 7.7MeV 12C state is not entirely clear. It seems well established that the state does not radiate directly to the ground state but rather cascades via the 4.43MeV state. Furthemore, Cook et al added that one must (a) Make sure that the 12C level can be formed by 8Be+↵. The prerequisite for that are the right spin and parity and that there is a non vanishing probability that it decays by emitting these particles. (b) It must have a finite probability to decay to the lower excited state or the ground state. These questions should be best explored by bombarding 8Be with ↵ particles, but since 8Be is unstable, recourse must be made to study the two possible modes of decay of the excited state of 12C, namely 12C⇤ ! 8Be + ↵ and 12C⇤ ! 12C + �. Then one has to rely on the principle of reversibility of nuclear reactions. Indeed, Hoyle did not predict the quantum numbers of the level and without these the prediction is not terribly powerful The experiment Cook et al. was innovative and di↵ered substantially from all previous ones. They created the radioactive isotope 12B, which has an energy of 13.378MeV above the ground state of 12C and decays via a � decay (in contrast to a � decay) into all excited levels of 12C with lower energy and in particular into the two relevant levels for our discussion here, cf. fig.??. Special arrangement was prepared to detect the emitted ↵’s using a strong focusing magnetic spectrometer. The basic problem Cook et al. faced with the 7.68MeV level was the following: It was established before that there is no direct transition to the ground state. On the other hand, no one observed that this level disintegrates into 8Be + ↵70. There were merely conflicting estimates of the probability to emit 68The anthropic principle is a philosophical claim that the Universe must be compatible with the existence of life as is observed. 69Cook, C.W., Fowler, W.A., Lauritsen, C.C. & Lauritsen, T., Phys. Rev., 107, 508, (1957) 70Recall, nuclear reactions under astrophysical conditions are usually very slow because the energies are low. So the 8Be+↵ yielding 12C and decaying back to the products was hopelessly slow and hence, not observed Figure 11: The argument by Hoyle that the resonance must exist. The paper by Hoyle, Dunbar et al had the title: A state in 12C Predicted from Astrophysical Evidence. The abstract also admitted that: A level had previously been reported at 7.5MeV, based on Ajzenberg and Lau- ritsen 1952. . on the other hand, the decay mode of the level - a crucial point - was not discussed at all. Beghian discovery of the 7.59MeV level was overlooked. But Hoyles victory was not complete - his friends did not accept the idea. Could Hoyle invert the pro- cess and learn nuclear physics from the stars? Cook, Fowler, T. Lauritsen and C.C. Lauritsen 1957 argued that:Experimental evidence on the character of the 7.7MeV state is not entirely clear. It seems well es- tablished that the state does not radiate directly to the ground state but rather cascades via the 4.43MeV state. The authors added that: one must (a) make sure that the level can be formed by 8Be + α. The spins should 316 Who Discovered the Hoyle Level? agree. (b) It must have a finite probability to decay to the ground state. Note: the direct reaction cannot be investigated in the lab because the rate is very slow. Consequently, the 12C level must be populated indirectly. Cooks et al. had a sever technical problems: On one hand: It was established that there is no direct way to the ground state. On the other hand no one observed that the compound 12C nucleus disintegrates into 8Be∗ + α. There were conflicting estimates of the probability to emit an α. Uebergang and independently Steffen, got that the excited 12C nucleus emits α at about << 50% of the cases while Bent et al and inde- pendently Hornyak got that it emits an α in >> 97% of the cases. 252 CHAPTER 8. HOW NATURE OVERCOMES ITS OWN BARRIERS an ↵ particle. On one hand, Uebergang71 and Ste↵en et al.72 estimated the probability to be ⌧ 50% and on the other hand, Bent et al.73 and Hornyak74 estimated it to be � 97%. Figure 8.17: Cook et al. 1957 created the ra- dioactive nucleus 12B which decays into 12C. Most of the decays go into the ground state and only 1.3% go into the investigated level. Cook et al. managed to get only an upper limit to the probability of decay into 8Be + ↵. Since this was by far the most probably mode of decay of this level, the exact value was crucial. So here they were forced to rely on Russell, Phillips and Reich75 and Heydenburg and Tem- mer76 who found an upper limit which was about 250 times smaller than predicted. With the improved (lower) upper limit they were able to reach their most important result, namely, that the probability for � decay to the 4.43MeV level is: 0.001- 0.0028. Very small but not zero. Next they found that the probability to decay through the emission of an electron-positron pair is about 10�5 and hence negligible. 8.15 Salpeter-1957: Completing the job Salpeter’s second and updated paper77 was submitted together with the Cook et al. paper and the two papers were published back to back. At the time, beginning of 1957, the spin of the 7.68MeV level was not yet certain though very recent ex- periments seemed to provide the final proof of the quan- tum numbers of this level. Fregeau and Hofstadter78 were interested in using high energy electron beams to investi- gate the surface of nuclei and they considered that the 12C would be an ideal case. So they bombarded 12C with high energy electrons. This and subsequent works of this type won for Hofstadter the 1961 Nobel prize.79 Fregeau and Hofstadter treated already in 1955(!) the 4.43MeV and 7.68MeV levels of carbon as so well established, that they did not give any reference to prior experiments. As for the spin of the 7.68MeV level, they state that: J = 0+ is not inconsistent with the experimental results that they found. The levels emerged very nicely in their electron scattering experiments. On the other hand, Salpeter argued that the only possibilities were 0+ or 2+. If the 2+ was assumed then the probability for electron-positron decay (symbolized in nuclear physics as �e±) could be theoret- ically calculated and it was found to be 1000 smaller than the one obtained if 0+ was assumed and this 71Uebergang, R.G., Australian J. Phys.,7, 279, (1954) 72Ste↵en, K.G., Hinrichs, O., & Neuert, H., Zeit. f. Phys., 145, 156, (1956) 73Bent, R. D., Bonner, T. W., McCrary, J. H., Ranken, W. A., Phys. Rev., 100, 771, (1955) 74Hornyak, W.,F., Bull. Am. Phys. Soc. Ser, II, 1, 197, (1956) 75Russell, J. L., Phillips, G. C., & Reich, C. W., Phys. Rev. 104, 135, 143, (1956) 76Heydenburg, N.P. & Temmer, G.M., Phys. Rev., 104, 123, (1956) 77Salpeter, E.E., Phys. Rev., 107, 516, (1957) 78Fregeau, J.H., & Hofstadter, R., Phys. Rev., 99, 1503, (1955). Ibid. 104, 225, (1956) 79The citation of the prize read for his pioneering studies of electron scattering in atomic nuclei and for his thereby achieved discoveries concerning the structure of the nucleons . Figure 12: The final experiment by Cook et al. 1957: creates the nucleus 12B and follow its decay into the 7.653MeV level (only 1.3%). To overcome the problems Cook et al 1957 cre- ated the radioactive nucleus 12B which decays into 12C. Most of the decay goes into the ground state and only 1.3% decays into the investigated level. 11 1957 Salpeter Finishes the Job Remaining problems: What is the spin of the 7.68MeV state? Fregeau & Hofstadter (1955) using electrons scattering from the nucleus (an experiment for which Hofstadter got the Nobel prize 1961), claimed that J=0+ is not inconsistent with experiment. So Salpeter assumed J = 0+ or 2+. The latter yields a result which is about 1000 smaller than the first one. 8.15. SALPETER-1957: COMPLETING THE JOB 253 result contradicted the result of the Cal Tech experiment80. Now came the critical question, what is the probability to decay back into the incoming channel, 8Be + ↵. Salpeter resorted to the Wigner theory81 and calculated an upper limit for the case 0+ which was 40% higher than the one adopted by Cook et al. The other possibility was proven by Salpeter to contradict the experimental results. To further provide support to his estimates of the probabilities, Salpeter derived the probabilities by assuming the ↵ model for the 8Be nucleus. The numbers agreed. 3α 8 Be+α Q1=0.278 Q2=0.094 J=0+ J=2+ J=0+ 7.654 4.43 0 Γα Γe+e-Γγ Figure 8.18: The structure of 12C assumed by Salpeter in 1957. �↵ is the probability of decay emitting an ↵ particle, �� is the probability of decay emitting a � photon and �e± is the prob- ability to decay by emitting an electron positron pair. This is after Salpeter obtained the improved results of Cook et al. 1957. Finally came the question what is the probability �� to decay into the bound 4.43MeV level. After all, this was the dominant mode to form a stable carbon nucleus. Again, the estimate depended on the model for the car- bon nucleus. If one assumed that the carbon nucleus was made of three ↵ particles, one got a very small probability to decay into the first excited state. So after some lengthy theoretical discussion Salpeter adopted that the probabil- ity to decay into the ground state plus the probability to decay into excited state, namely the total probability to decay into the ground state, was 0.00014, quite small. Salpeter made an additional crucial assumption. Since the probability to decay back into the incoming channel (8Be+↵) is by far the largest, or in other words, the leak- age to modes of decay other than the mode of formation is extremely small, it is permitted to assume an equilibrium 8Be + ↵ *) 12C ⇤ . The unbound 2 ↵’s are reluctant to ab- sorb a third ↵ and become bound. Once this is done and statistical mechanics can be used to calculate the abun- dance of the 12C nuclei, the details of the nuclear reaction became irrelevant! The probability to form carbon in the ground state is then the number of carbon nuclei in the excited state (as obtained form the equilibrium condition) times the probability that they decay to the ground state of carbon. At the end of January 1955 the American Physical Society had its annual meeting in New York. In a session on Reactions of Transmutation and Nuclear Energy Level, Salpeter presented preliminary results on the e↵ect of the 7.68MeV82. By now, Salpeter became aware of the Ajzenberg and Lauritsen coming up summary (it appeared in his paper as 0to be published0) of the energy levels of 12C and derived for the first time the full reaction rate. Hayakawa et al.83 got the information from Salpeter, who also informed them about the probability that the 7.68MeV excited state decays to the 4.43MeV level, and submitted their paper to the Progress in Theoretical Physics Japan, on July 1956 to be published November 1956. Salpeter’s paper, on the other hand, was submitted March 1957 to be published July 1957, that is to say, over a year later. So before Salpeter managed to publish his results in a journal, Hayakawa et al. published the calculation of the rate including the excited state of 12C and wrote that: This rate is about 106 times larger than that given by Salpeter. They meant Salpeter 1952. They continued to state that: Such a great di↵erence is due mainly to the fact that he did not take the e↵ect of the recently discovered resonance level in 12C into account. This is one of the most important conclusion obtained in our work. It may have been the most important 80Most recent result: Chemykh, M. and 5 authors, Proc.13th Int. Symposium Capture Gamma-Ray Spect., AIP Conf. Proc. 2009 is �± e = 6.2 ⇥ 10�5eV . 81Blatt, J., & Weisskopf, V., Theoretical Nuclear Physics, John Wiley & Sons, Inc. NY, 1952. 82Salpeter, E.E., Phys. Rev. 98, 1183, (1955) 83Hayakawa, S., Hayashi, C., Imoto, M., & Kikuchi, K. Prog. Theor. Physics, 16, 507, (1956) Figure 13: The part of the energy schemes of the 12C nucleus relevant to the 3α reactions as was finally as- sumed by Salpeter in his final paper in 1957 The structure of 12C as assumed by Salpeter in 1957, is given in fig. 13. Γα is the probability of decay emit- ting an α particle, Γγ is the probability of decay emit- ting a γ photon and Γe± is the probability to decay by emitting an electron-positron pair. This is a rare mode of decay and of no importance to our story here. This was the structure of 12C after Salpeter obtained the improved results of Cook et al 1957. Salpeter made some critical assumptions: The dis- integration channel 12C∗ decaying back into 8Be + α is the dominant channel and all other possibilities are very small leakages. Consequently, Salpeter assumed a dynamic equilibrium, namely 12C∗ ↔8 Be + α. If so, the concentration of 12C is determined from the equilibrium (small sensitivity to the energy of the level) and all the uncertainty is in the small leakage to the other channels. In particular, the is no need for a cross section,to evaluate the rate. The reaction is in a statis- tical equilibrium. On January 1955 Salpeter presented the results in the New York meeting of the Physical Society. By now he became aware of the Ajzenberg & Lauritsen old re- sult and cited it. Fowler won the 1983 Nobel prize (with Chan- drasekhar) for contributions to nuclear astrophysics, but Fowler’s Nobel speech was one long discussion about . . . Hoyles contributions. As for Salpeter, Fowler commented that he ignored the 7.68MeV state - which is a very wrong claim. He ignored it when it was un- known to him. Fowler was a great experimental nuclear physicists but without knowledge in statistical mechan- ics and he did not like that ’the nuclear physics’ was eliminated from the problem. 317 G. Shaviv Hoyle and Salpeter shared the 1997 Crafoord prize1 in particular for the physics of the triple α reaction. The process is called today the Salpeter process and the energy level is called the Hoyle level. Fight for priority: Salpeter informed Hayakawa et al. about the probability that the 7.68MeV state de- cays into the 4.43MeV state. Hayakawa et al hurried and submitted their paper to Progress of Theoretical Physics Japan in July 1956 in which they made just this claim. The journal published on November 1956. Salpeter published his work only in 1957. Surpris- ingly the japanese authors claimed that: This (meaning theirs) rate is 106 times greater than given by Salpeter 1952. Such a great difference is due mainly due to the fact that he did not take into account the 12C resonance. They did not mention that it was Salpeter who told them about his work and the 12C level..... 12 Is This the Entire Story? Is this the entire story? No! What about the structure of 16O? Following Hoyle, we treated the reaction 12C + α16 → O + γ as well established. However, this is not the case. In 1974 Dyer and Barnes from CalTech attempted to mea- sure the 12C+α reaction. The next attempt was carried out in 1982 when Kettner et al. from Münster measured the reaction and discovered that it is 3 to 5 times faster then what Dyer and Barnes from Caltech found. As a consequence, the most abundant specie at the end of helium burning was found to be 16O and not 20Ne as the formation of 16O is faster than its destruction. Langanke and Koonin (1983) criticized the analysis and the conclusions of the experimenters and repeated the very long theoretical analysis of the experimental data. However, they could not resolve the discrepancy between the Caltech data (Dryer and Barnes) and the Münster data (Kettner et al.) and fitted each experi- ment separately. Thus, the Münster data was 1.5 time higher than that of Caltech, which in turn was 3 times higher than what stellar modelers used. As Lankange and Koonin wrote, such higher values , as those found in Münster and Caltech, lead to 16O rather than 12C, as the final product of helium burning, and in this way cast a shadow on Hoyles argument. In fig. 15 we show a comparison between two recent experimental result and a theoretical fit. The red arrow shows the energy range in stars where this reaction takes place. So far this experimental discrepancy is not sett led. 8.18. CARBON STRUCTURE IS HALF THE STORY: THE 12C + ↵ !16 O + � REACTION 255 very high. Due to the fact that these levels are rather wide86, they all contribute to the rate of the reaction. Consequently, the locations of the levels up to about 10MeV are important for the rate of 8Be + ↵ at T < 109K. The higher in energy levels corresponds to such a high energy range that by the time the colliding species have enough energy to reach these levels, the temperature is so high that all nuclei disintegrate and hence, cannot fuse any further. In 1994 Freer at el87 investigated whether the 12C 7.65MeV level could decay directly into 3 ↵ in contrast of a decay to 8Be + ↵ first and then the 8Be would break into 2 ↵s. The results for this direct decay is less than 4%. This was an additional experimental proof that the triple alpha is not a three body reaction. The problems in getting accurate value for the probability for the 7.68MeV level transition to the 4.43MeV one continued to annoy physicists. The recent values are: Alburger88 (3.3±0.9)⇥10�4, Hall and Tanner89 (3.5±1.2)⇥10�4, Seeger and Kavanagh90 (2.8±0.3)⇥10�4, and Mak et al.91 (4.30±0.2)⇥10�4. It is di�cult to achieve high accuracy! 8.18 Carbon structure is half the story: The 12C+↵ !16 O+� reaction Αα12C+ 6.049 6.130 6.917 7.1157.162 J=1- J=2+ J=3- J=0+ J=0+ O16 Figure 8.19: The struc- ture of the oxygen nu- cleus 1952. Based on Ajzenberg and Lauritsen 1952. We come to the destruction of carbon. The existence of excited levels in 16O was discovered by Burcham and Freeman92, who used the reaction 19F + p ! 16O + ↵ and found the 6.94MeV and the 7.15MeV levels. They however, did not determine the quantum numbers of the level. In 1950 Millar, Bartholomew and Kinsey93 investigated the � rays from the decay of 16N ! 16O + e�. This radioactive isotope is produced in the cooling water of nuclear reactors via the reaction 16O + n ! 16N + p. The half lifetime of the isotope is 7.35 sec. The energy of 16N is so high that it can decay into the first two levels of 16O by emission of an electron. Thus, they discovered � rays which corresponded to the level at 6.133 ± 0.011MeV and 7.10 ± 0.02MeV. These results were in good agreement with the values found by Chao, Tollestrup, Fowler and Lauritsen94 of 6.136 ± 0.030MeV and 7.111 ± 0.03MeV. To complicate the issue, they did not discover � rays which would correspond to the level at 6.91MeV. They were however, able to determine the quantum numbers of the level as J = 1�. The situation became complicated once more. The 12C + ↵ have a rest- mass energy of 7.162MeV, while the closest energy level in the 16O nucleus is at 7.115MeV, that is to say, just below the threshold of the colliding particles. Because all energy levels save the ground state, are not stable they have a certain width in energy. The width �E is related to the lifetime �t through the relation �E�t ⇠ h̄. The 7.115MeV level in 16O is su�ciently wide to extend into energies slightly above the 86According to the Uncertainty Principle, the width of the level is connected to the life time of the system in that level. From a nuclear reaction point of view it means that if the energy of the colliding particles is within the wide range of the level, and not just equal to the prescribed energy, the reaction can proceed. 87Freer, M., Wuosmaa, A.H., Betts, R.R., Henderson, D.J., Wilt, P., Zurmuhle, R.W., Balamuth, D.P., Barrow, S., Benton, D., Li, Q., Liu, Z., & Miao, Y., Phys. Rev. C, 49, 1751, (1994) 88Alburger, D.E., Phys. Rev., 124, 193, (1961), who used the reaction 10B + 3He ! 12C + p. 89Hall & Tanner , Nuclear Phys.,53, 673, (1964), who used the reaction 10B + 3He ! 12C + p. 90Seeger, P.A. & Kavanagh, R.W., Nucl. Phys., 46, 577, (1963), who used the reaction 14N + 2D ! 12C + ↵ 91Mak, H.-B., and 4 co-authors, Phys. Rev. C,12, 1158, (1975) 92Freeman, J.M. & Baxter, A.S., Nature,162, 696, (1948). Burcham, W.E., & Freeman, J.M., Phys. Rev. 75, 1756, (1949) 93Millar, C. H. , Bartholomew, G. A. & Kinsey, B. B., PRL, 81, 150, (1951) 94Chao, C. Y. ,Tollestrup, A. V. , Fowler, W. A. & Lauritsen, C. C. , Phys. Rev. 79, 108, (1950) Figure 14: The structure of 16O based on Ajzenberg & Lauritsen 1952. The partial width of the relevant level at 7.115MeV is not known because it is a very difficult measurement. The uncertainty in the level is marked by the grey zone around the level. The diffi- culty stems from the fact that the level lies just below the continuum and hence extremely difficult to feed in. The next question is where carbon is synthesized? Or what happens if the carbon level were at another energy? would carbon still be formed? The answer is 256 CHAPTER 8. HOW NATURE OVERCOMES ITS OWN BARRIERS 12C + ↵ threshold. Thus the carbon plus the alpha combine to form the excited oxygen nucleus via the upper tail of the level. On the other hand, as the width of the level is large, the probability to breakup into 12C + ↵ is very small and as a matter of fact, was never observed. In 1974 Dyer and Barnes95 from CalTech attempted to measure the 12C + ↵. The next attempt was in 1982 when Kettner et al.96 from Münster measured the reaction and discovered that it is 3 to 5 times faster then what Dyer and Barnes from Caltech found. As a consequence, the most abundant specie at the end of helium burning was found to be 16O and not 20Ne Langanke and Koonin97 criticized the analysis and the conclusions of the experimenters and repeated the very long theoretical analysis of the experimental data. They could not resolve the discrepancy between the Caltech data (Dryer and Barnes) and the Münster data (Kettner et al.) and fitted each experiment separately. Thus, the Münster data98 was 1.5 time higher than that of Caltech, which in turn was 3 times higher than what stellar modelers use. As Lankange and Koonin wrote Such higher values , as those found in Münster and Caltech, lead to 16O rather than 12C, as the final product of helium burning, and in this way cast a shadow on Hoyle’s argument. Figure 8.20: The measured capture probability (in units of nano-barns) by the Munster (1982) and the Kellogg (1974) laboratories. The arrow marks the energy range at which the reaction take place in stars. The continuous lines are the theoretical fit by Langanke and Koonin 1983 and it includes the e↵ect of the resonance. 0 2 4 6 8 10 0.8 1 1.2 1.4 1.6 1.8 2 2.2 2.4 Temperature in 109K 12C+α 16O+γ Ra tio of pr ed ic te d re ac tio n ra te s Kunz et al(2002) Caughlan & Fowler (1988) Figure 8.21: The ratio between the newest rate calculated by Kunz et al (2002) and the standard rate compiled by Caughlan and Fowler (1988) used in many calculation of stellar evolution. The ratio is given as a function of the temperature. 95Dyer, P. & Barnes, C. A., Nuc. Phys. A233, (1974) 96Kettner, K.U. and 8 co-authors, Z. Phys. A, 308, 73, (1982) 97Langanke, K. & Koonin, S.E., Nuc. Phys. A410, 334, (1983). Ibid. Nuc. Phys., A439, 384, (1985). The first paper was published when Langanke was still in Munster. The second paper was published after he joined Koonin in Caltech 98The probability for this reaction to take place at thermal energies (T = 2 ⇥ 108 or 300keV) was given by S(300keV ) = 350 keV barn (Münster), 240 keV barn (Caltech) and 80 keV barn in standard nucleosynthesis calculations at that time. Figure 15: The measured capture probability (in units of nano-barns) by the Munster (1982) and the Kel- logg(1974) laboratories. The arrow marks the energy range at which the reaction takes place in stars. The continuous lines are the theoretical fit by Langanke & Koonin 1983 and it includes the effect of the resonance. 1 The Crafoord Prize in astronomy and mathematics, bio- sciences, geosciences or polyarthritis research is awarded by the Royal Swedish Academy of Sciences annually according to a rotat- ing scheme. The prize sum of SEK 4 million makes the Crafoord one of the worlds largest scientific prizes. 318 Who Discovered the Hoyle Level? given in fig. 16 for low mass stars and fig. 17 for high mass stars. We see that ’moving’ the level quite sig- nificantly changes the dominant stellar mass at which carbon is formed but not in a way that would required a revision of our ideas.258 CHAPTER 8. HOW NATURE OVERCOMES ITS OWN BARRIERS -150 -100 -50 0 50 100 150 0.0001 0.001 0.01 0.1 1 10 100 1000 10000 C/ O ΔE-KeV M=1.3Msun M=5Msun Figure 8.22: The C/O ratio and obtained in the evolution of low mass stars (1.3M� and 5.0M�) upon a hypothetical change in the location of the resonance in 12C. -100 -50 0 50 100 2 4 6 8 10 ΔE-KeV C/ O M=15Msun M=25Msun Figure 8.23: The C/O ratio and obtained in the evolution of high mass stars (15M� and 25M�) upon a hypothetical change in the location of the resonance in 12C. 8.20 The C/O ratio today - observations and what they imply Not a single star without oxygen or without carbon was discovered. Detailed observations have shown that the abundance ratio C/O varies from star to star. Gradually it became clear that there is no universal value for the C/O abundance ratio which was the basis for Hoyle’s analysis and di↵erent stars expose di↵erent ratios. For example, stars with extra high abundance of carbon do not show extra high abundances of oxygen107. Examination of the gases ejected from low mass stars shows that when the metals are more abundance by about 50% the C/O ratio is lower by about 50%.108 The C/O ratio appears to be higher in stars with low abundance of heavy elements.109 Finally, the C/O appears to vary in low mass stars from 0.2 to 13110. In short, the picture is more complicated and the last word has not yet been said. 8.21 The structure of 12C and the ↵ model: Retrospect In 1971 Brink111 concluded from the nuclear cluster model that 0our0 state forms a linear chain of three ↵-particles. Further indication (from bombardment by electrons), imply that this state has an unusually large radius112. These properties enhance the probability of decay into three ↵ particles. This conclusion was supported in 1997 when Pichler, Oberhummer, Csoto and Moskowski113 who concluded that the 0+ level is a genuine three alpha resonance. If so, one would expect that the level would decay directly into three ↵’s and then Salpeter’s equation for the nuclear statistical equilibrium may need a change. But the probability of decay directly into three alpha appears to be only about 4%. The reason for this is purely statistical, the phase space of 8Be+↵ is that much bigger than the 3↵ mode, in layman terminology: all possible modes of decay have equal probabilities and the number of ways the system can decay into 8Be + ↵ is much larger that the number of di↵erent ways it can decay into 3↵s. 107Bujarrabal, V. & Cernicharo, J., A&A, 288, 551, (1994) 108Wang, W. & Liu, X.-W., MNRAS, 381, 669, (2007) 109Wahlin, R., and 6 co-authors, Memorie della Societa Astronomica Italiana, 77, 955, (2006) 110Cohen, M. & Barlow, M. J., MNRAS, 362, 1199, (2005) 111Brink, in The Alpha Particle Model of Light Nuclei, Proc. ”Enrico Fermi” school course XXXVII, Varenna, 1966. 112Takigawa, N., & Arima, A., Nucl. Phys., A168, 593, (1971) 113Pichler, R., Oberhummer,H., Csoto, A., and Moskowski, S.A., Nucl. Phys. A618, 55, (1997) Figure 16: The C/O ratio obtained in the evolution of low mass stars (1.3M� and 5.0M�) upon a hypothetical change in the location of the resonance in 12C. We did not discuss the possible decay of the ex- cited nucleus 12C∗ to 3α. We can, however, repeat Hoyle’s argument and argue that the observations im- ply that this decay, though possible energetically and should take place, is very rare and hence neglected.258 CHAPTER 8. HOW NATURE OVERCOMES ITS OWN BARRIERS -150 -100 -50 0 50 100 150 0.0001 0.001 0.01 0.1 1 10 100 1000 10000 C/ O ΔE-KeV M=1.3Msun M=5Msun Figure 8.22: The C/O ratio and obtained in the evolution of low mass stars (1.3M� and 5.0M�) upon a hypothetical change in the location of the resonance in 12C. -100 -50 0 50 100 2 4 6 8 10 ΔE-KeV C/ O M=15Msun M=25Msun Figure 8.23: The C/O ratio and obtained in the evolution of high mass stars (15M� and 25M�) upon a hypothetical change in the location of the resonance in 12C. 8.20 The C/O ratio today - observations and what they imply Not a single star without oxygen or without carbon was discovered. Detailed observations have shown that the abundance ratio C/O varies from star to star. Gradually it became clear that there is no universal value for the C/O abundance ratio which was the basis for Hoyle’s analysis and di↵erent stars expose di↵erent ratios. For example, stars with extra high abundance of carbon do not show extra high abundances of oxygen107. Examination of the gases ejected from low mass stars shows that when the metals are more abundance by about 50% the C/O ratio is lower by about 50%.108 The C/O ratio appears to be higher in stars with low abundance of heavy elements.109 Finally, the C/O appears to vary in low mass stars from 0.2 to 13110. In short, the picture is more complicated and the last word has not yet been said. 8.21 The structure of 12C and the ↵ model: Retrospect In 1971 Brink111 concluded from the nuclear cluster model that 0our0 state forms a linear chain of three ↵-particles. Further indication (from bombardment by electrons), imply that this state has an unusually large radius112. These properties enhance the probability of decay into three ↵ particles. This conclusion was supported in 1997 when Pichler, Oberhummer, Csoto and Moskowski113 who concluded that the 0+ level is a genuine three alpha resonance. If so, one would expect that the level would decay directly into three ↵’s and then Salpeter’s equation for the nuclear statistical equilibrium may need a change. But the probability of decay directly into three alpha appears to be only about 4%. The reason for this is purely statistical, the phase space of 8Be+↵ is that much bigger than the 3↵ mode, in layman terminology: all possible modes of decay have equal probabilities and the number of ways the system can decay into 8Be + ↵ is much larger that the number of di↵erent ways it can decay into 3↵s. 107Bujarrabal, V. & Cernicharo, J., A&A, 288, 551, (1994) 108Wang, W. & Liu, X.-W., MNRAS, 381, 669, (2007) 109Wahlin, R., and 6 co-authors, Memorie della Societa Astronomica Italiana, 77, 955, (2006) 110Cohen, M. & Barlow, M. J., MNRAS, 362, 1199, (2005) 111Brink, in The Alpha Particle Model of Light Nuclei, Proc. ”Enrico Fermi” school course XXXVII, Varenna, 1966. 112Takigawa, N., & Arima, A., Nucl. Phys., A168, 593, (1971) 113Pichler, R., Oberhummer,H., Csoto, A., and Moskowski, S.A., Nucl. Phys. A618, 55, (1997) Figure 17: The C/O ratio obtained in the evolution of high mass stars (15M� and 25M�) upon a hypothetical change in the location of the resonance in 12C. 13 In Retrospect In 1985 Arnet and Thielemann questioned the logic of Hoyles original argument as the synthesized carbon may be fused into heavier nuclei or locked in WDs. Hence, we should re-think how carbon is synthesized and it is not clear that any remnant of the Anthropic Princi- ple will prevail. However, Hoyle’s reverse engineering methodology is right: If we see carbon in Nature, there should be a way to synthesize it! Today, the principle has its own life and the origin which triggered it is mostly forgotten. In any case the old justification that lead to its inception is not that valid. The story is told in more detail in Shaviv (2011). References [1] Ajzenberg, F. & Lauritsen, T., Rev. Mod. Phys.24, 321, (1952) In 1950 Azjenberg and Lauritsen had the level at 7.MeV and it is not clear why the level ?moved? half an MeV upward. [2] Beghian, L.E., Halban, H.H., Husain, T., & Sanders, L.G., PRL, 90, 1129, (1953) Submitted April, 1953 and published June 1953. [3] Bethe, H.A. , Rev. Mod. Phys., 9, 167, (1937). This extensive review of nuclear physics earned justifiably the title The Bethes Bible. doi:10.1103/RevModPhys.9.69 [4] Bothe, W., & Becker, H., Zeits. f. Physik, 76, 421, (1932) doi:10.1007/BF01336726 [5] Cook, C.W., Fowler, W.A., Lauritsen, C.C. & Lauritsen, T., Phys. Rev., 107, 508, (1957) doi:10.1103/PhysRev.107.508 [6] Crane,H.R., Delsasso, L.A., Fowler & Lauritsen, C.C., Phys. Rev.,46, 1109, (1934) doi:10.1103/PhysRev.46.1109.2 [7] Crane,H.R., & Lauritsen, C.C., Phys. Rev.,45, 497, (1934) [8] Dyer, P. & Barnes, C. A., Nuc. Phys. A233, 495, (1974) doi:10.1016/0375-9474(74)90470-9 [9] Gaerttner, E.R., & Pardue, L.A. , Phys. Rev., 57, 386, (1940) doi:10.1103/PhysRev.57.386 [10] Gamow, G., Phys. Rev., 53, 595, (1938) doi:10.1103/PhysRev.53.595 [11] Guier, W.H., & Roberts, J.H. , Phys. Rev. 79, 719, (1950) doi:10.1103/PhysRev.79.719 [12] Hayakawa, S., Hayashi, C., Imoto, M., & Kikuchi, K. Prog. Theor. Physics, 16, 507, (1956) doi:10.1143/PTP.16.507 [13] Holloway, M.G., & Moore, B.L., Phys. Rev., 58, 847, (1940) doi:10.1103/PhysRev.58.847 [14] Hornyak, W.F., Lauritsen, T., Morrison, P. & Fowler, W.A., Rev. Mod. Phys., 22, 291, (1950) doi:10.1103/RevModPhys.22.291 [15] Kettner, K.U. and 8 co-authors, Z. Phys. A, 308, 73, (1982) 319 http://dx.doi.org/10.1103/RevModPhys.9.69 http://dx.doi.org/10.1007/BF01336726 http://dx.doi.org/10.1103/PhysRev.107.508 http://dx.doi.org/10.1103/PhysRev.46.1109.2 http://dx.doi.org/10.1016/0375-9474(74)90470-9 http://dx.doi.org/10.1103/PhysRev.57.386 http://dx.doi.org/10.1103/PhysRev.53.595 http://dx.doi.org/10.1103/PhysRev.79.719 http://dx.doi.org/10.1143/PTP.16.507 http://dx.doi.org/10.1103/PhysRev.58.847 http://dx.doi.org/10.1103/RevModPhys.22.291 G. Shaviv [16] Kunz, R. and 7 co-authors, ApJ, 567, 643, (2002) doi:10.1086/338384 [17] Johnson, V.R., Phys. Rev., 86, 302, (1952) doi:10.1103/PhysRev.86.302 [18] Langanke, K. & Koonin, S.E., Nuc. Phys. A410, 334, (1983). Ibid. Nuc. Phys., A439, 384, (1985). [19] Lawrence, E.O., McMillan, E., & Henderson, M.C., Phys. Rev, 47, 273, (1935) [20] Lewis, G.N., Livingston,M.S., & Lawrence, E.O., PRL, 44, 55, (1933) [21] Miller, C., & Cameron, A.G.W., Phys. Rev., 81, 316, (1951) [22] Öpik E. Proc. Roy. Irish Acad. A54, 49, (1951). The paper was published over a year after it was read before the Irish Academy. [23] Öpik, E.J., MSRSL, 1, 131, (1954), Les Processus Nuclaires dans les Astres, Communications prsentes au cinquime Colloque International dAstrophysique tenu Liege les 10-12 Septembre. [24] Shaviv,G. The Synthesis of the Elements: The Astrophysical Quest for Nucleosynthesis and What It Can Tell Us About the Universe (Astrophysics and Space Science Library) , Springer, 2011. [25] Terrell, J., Phys. Rev., 80, 1076, (1950) [26] Wrubel, M.H., Irish AJS, 10, 77, (1972) DISCUSSION TZUMI HACHISU: Is the carbon-burning C/O ra- tio still uncertain? GIORA SHAVIV: The reduced width of the 16O level is still unknown and there are only guess on its value. Sp any C/O ratio between 1/4 - to -3/4 is to my mind plausible. In 2002 Kunz et al. carried out an extensive theo- retical analysis based primarily on Kunzs experimental PhD thesis. The result of Kunz et differs significantly from Caughlan & Fowler known tables at low temper- ature which are the relevant temperatures for quiet he- lium burning. However, it is not the last word on the subject. 320 http://dx.doi.org/10.1086/338384 http://dx.doi.org/10.1103/PhysRev.86.302 Who Is Who What Is the Hoyle Level What Is the Anthropic Principle The Nuclear Barrier Why Nuclear Physicists Were Interested in the Problem? The History of the Discovery of the 12C Nuclear Levels The Wrong Solution Salpeter Enters the Game 1953 Kellogg Phase I How Did Hoyle Predict the Nuclear Level in 12C 1957 Salpeter Finishes the Job Is This the Entire Story? In Retrospect