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Steady-state cosmology: from Einstein to Hoyle

Cormac O’Raifeartaigh, Simon Mitton
We recently reported the discovery of an unpublished manuscript by Albert Einstein in which he attempted a ‘steady-state’ model of the universe, i.e., a cosmic model in which the expanding universe remains essentially unchanged due to a continuous formation of matter from empty space. The manuscript was apparently written in early 1931, many years before the steady-state models of Fred Hoyle, Hermann Bondi and Thomas Gold. We compare Einstein’s steady-state cosmology with that of Hoyle, Bondi and Gold and consider the reasons Einstein abandoned his model. The relevance of steady-state models for today’s cosmology is briefly reviewed.
Read more at http://arxiv.org/ftp/arxiv/papers/1506/1506.01651.pdf

Carbon nucleus seen spinning in triangular state

Physicists have obtained important new evidence showing that the structure of the carbon-12 nucleus – without which there would be no life here on Earth – resembles that of an equilateral triangle. The evidence was obtained by physicists in the UK, Mexico and the US by measuring a new rapidly spinning rotational state of the nucleus. The finding suggests that the “Hoyle state” of carbon-12, which plays an important role in the creation of carbon in red giant stars, has the same shape too. Recent theoretical predictions, in contrast, had suggested that the Hoyle state is more like an obtuse triangle or “bent arm”.

All the carbon in the universe is created in red giant stars by two alpha particles (helium-4 nuclei) fusing to create a short-lived beryllium-8 nucleus, which then captures a third alpha particle to form carbon-12. But exactly how this reaction occurs initially puzzled physicists, whose early understanding of carbon-12 suggested that it would proceed much too slowly to account for the known abundance of carbon in the universe. Then in 1954 the British astronomer Fred Hoyle predicted that carbon-12 had a hitherto unknown excited state – now dubbed the Hoyle state – which boosts the rate of carbon-12 production.

Three years later the Hoyle state was confirmed experimentally by physicists working at Caltech. However, the precise arrangement of the protons and neutrons in the carbon-12 nucleus remains a matter of much debate. While some physicists feel that carbon-12 is best thought of as 12 interacting nucleons, others believe that the nucleus can be modelled as three alpha particles that are bound together. The rational for the latter model is that alpha particles are extremely stable and so are likely to endure within the carbon-12 nucleus. Continue reading Carbon nucleus seen spinning in triangular state

Carbon’s Hoyle state calculated at long last

This illustration shows how three helium-4 nuclei form a "bent arm" shape in a carbon-12 nucleus (Courtesy: North Carolina State University)

This illustration shows how three helium-4 nuclei form a “bent arm” shape in a carbon-12 nucleus (Courtesy: North Carolina State University)

By calculating the behaviour of protons and neutrons inside carbon nuclei from first principles, physicists in Germany and the US have identified the shape of carbon’s Hoyle state – which is an important step in the production of heavy elements inside stars. The researchers found the state to have an unusual bent structure, a finding that should help identify the forces at work in carbon production.

Carbon-12 comprises six protons and six neutrons and is a key step in nucleosynthesis – the process by which heavier elements are produced inside stars. Physicists studying stellar fusion in the 1940s and 1950s reckoned that carbon-12 forms when two helium-4 nuclei fuse to produce beryllium-8 – which then fuses with a third helium-4 nucleus.

There was a problem with this hypothesis, however. The energy of the fused particles is considerably higher than that of the ground state of carbon-12. This implies that the new particle is in fact extremely unlikely to form in this way – far too unlikely to account for the great abundance of carbon in the universe.

According to Hoyle
To overcome this apparent contradiction the British astronomer Fred Hoyle proposed in 1954 that carbon-12 has an excited state that had never been seen before. The idea is that carbon-12 would form readily in this state and then decay to its ground state, giving off a well defined amount of energy (7.6 MeV) in the process. This excited state was then observed three years later by researchers at the California Institute of Technology, when carrying out experiments involving beta decays of boron-12.

For the past 60 years nuclear physicists have been trying to understand the nature of this “Hoyle state”, which is not predicted by standard nuclear models. These models regard nuclei as being made up of individual protons and neutrons, and it was reckoned that the Hoyle state is better described as three helium-4 clusters.

Those clusters have now been identified by Ulf Meissner of the University of Bonn and colleagues, thanks to the number-crunching power of the JUGENE supercomputer in Jülich and a new form of Steven Weinberg’s “effective field theory”, which considers protons and nucleons as individual entities rather than as bound states of three quarks.

Space–time lattice
Weinberg’s theory reduces the number of particles that can be considered to make up a carbon-12 nucleus by a factor of three – from 36 to 12. Even 12, however, is too many for an analytical description of the nucleus. Instead, Meissner’s group combined the theory with numerical methods often used to describe the interaction of individual quarks via the strong force. This approach breaks down space and time into discrete chunks, constraining particles to exist only at the vertices of a space–time lattice and so radically simplifying the possible evolution of the particle system.

In a paper published in 2011, Meissner and co-workers described how they used this hybrid approach to identify the Hoyle state. To do this they first picked out carbon-12’s ground state, setting up vast numbers of configurations of the virtual protons and neutrons within JUGENE and then watching what happened as those configurations evolved in time.

The configuration that lasted the longest, being the most stable, was the ground state. Identifying the Hoyle state was a bit trickier since it involved stopping the simulation at some earlier point in time and then disentangling the various states that remained. Despite the challenges of calibrating their simulation using scattering and other data, their calculated values for the energy of the carbon-12 ground state and the Hoyle state agreed very well with experiment.

“Bent arm” shape
Now in this latest work, the team has calculated the structure of those states using a more sophisticated representation of the nuclear wavefunction. Likening the nucleons and groups of nucleons to LEGO bricks, Meissner says that “before we had bricks of just one size and now we have a whole series of different-sized bricks that we can use to construct more complex structures”.

Building up those structures, the group found that in the ground state, carbon-12 consists of three helium-4 clusters arranged in a compact equilateral-triangle formation, whereas in the Hoyle state the three clusters form an obtuse triangle or “bent arm” shape. This more open configuration, the researchers explain, results from the extra energy in the system.

One exciting aspect of the research, according to Morton Hjorth-Jensen of the University of Oslo in Norway, is that it should allow scientists to understand which part of the strong force dictates the carbon-12 decay. This is important because the force in fact consists of several elements, including some that deform the shape of nuclei. “Hoyle predicted his state on the basis of the anthropic principle, arguing that if the state didn’t exist we wouldn’t be here,” he says. “But we now want to understand the structure of this state in terms of its basic constituents and forces.”

Experimental tests
Meanwhile, David Jenkins of York University in the UK points out that the latest work makes a number of explicit predictions that could, in principle, be tested experimentally, including the existence of a number of electromagnetic transitions involving the Hoyle state. But he adds that these transitions are very weak and therefore hard to measure. “Such experiments will be no less challenging than the theoretical achievement,” he says, “but renewed effort is warranted given the strong topical interest.”

According to Meissner there is also more theoretical work to be done. One job, he says, is to reduce the spacings in their virtual lattice, in order to make more precise calculations. Another is to investigate larger nuclei, such as oxygen-16, as well as the reactions that give rise to these nuclei – in this case carbon-12 combining with a helium-4 nucleus. “This is a very important reaction in the sequence that generates life-giving molecules,” he adds.
The latest work is published in Physical Review Letters
Read more: http://physicsworld.com/cws/article/news/2013/jan/03/carbons-hoyle-state-calculated-at-long-last

The carbon challenge

1. Helium burning

Figure 1: Synthesis of carbon in a burning star. Two alpha particles react to form beryllium-8. Beryllium-8 and an alpha particle react to form carbon-12, proceeding via the Hoyle state. This state in carbon-12 is a “resonance” in the beryllium-8 plus alpha-particle system. Once the resonant state is formed, it tends to decay by breaking up into beryllium-8 and an alpha particle. However, approximately four out of ten thousand decays bring the excited carbon-12 nucleus to its stable ground state.

“…In the first-generation stars the ash resulting from hydrogen burning via the p-p chain is entirely helium-4, the creation of heavier elements having been blocked by the instabilities at A=5 and A=8. These are referred to as the mass gaps.
Since carbon-12, the fourth most abundant nuclear species observed in the universe, could not synthesized in its observed abundances in the early universe, the site for its creation has to be in stars. Thus, a major question in the early studies of nucleosynthesis was how the stability gaps were bridged to create carbon-12 using only helium. While the simultaneous interaction of three α-particles to form carbon-12 is energetically possible, the probability for this direct process is much to small to account for the observed carbon-12 abundances.
The solution of this problem was provided in principle by Salpeter and Opik, who proposed that carbon-12 was created via a two-step process. In the first step, two a-particles combine to form beryllium-8 in its ground state.
The ground state of beryllium-8 is known to be unstable against decay into two α-particles with a lifetime of 10-16 s, which is the reason for the mass-8 stability gap. However, as Salpeter pointed out, this lifetime is long compared with the 10-19 s transit time of two α-particles with kinetic energies corresponding to Q.
As a result, a small concentration of beryllium-8 nuclei builds up in equilibrium with the decay products, two α-particles.
The actual equilibrium concentration of beryllium-8 in a helium environment can be calculated using the Saha equation.
For typical values, the Saha equation leads to one beryllium-8 nucleus for every 109 helium-4 nuclei.
In the second step, Salpeter suggested that, since the first step provides an appreciable concentration of beryllium-8 nuclei, these nuclei capture an additional α-particle, thus completing the carbon-12 creation process.
Since the combined effect of these two steps is to transform three α-particles into a carbon-12 nucleus, this set of reactions is referred to as the triple-α process:

3α —> 12C

Assuming the triple-α process to be the correct mechanism for synthesis of 12C, Hoyle showed that the amount of 12C produced in this way is insufficient to expalin the obseved abundance.
To surmount this difficulty, Hoyle suggested that sufficient 12C nuclei could be synthesized if the 8Be(α,γ)12C reaction took place through an s-wave resonance near the 8Be + α threshold, since the existence of such a resonance would greatly accelerate the rate of triple-α process….. Continue reading The carbon challenge