Core contraction

The evolution of a. star after it leaves the red-giant phase depends to some extent on its mass. If it is not more than about 1.4 M it may contract appreciably again and then enter an oscillatory phase of its life before becoming a white dwarf (p. 7). When core contraction following helium and carbon depletion raises the temperature above I0 K the y-ray.s in the stellar assembly become sufficiently energetic to promote the (endothermic) reaction Ne(y,a) 0. The a-paiticle released can penetrate the coulomb barrier of other neon nuclei to form " Mg in a strongly exothermic reaction ... 

An important advantage of ECP basis sets is their ability to incorporate approximately the physical effects of relativistic core contraction and associated changes in screening on valence orbitals, by suitable adjustments of the radius of the effective core potential. Thus, the ECP valence atomic orbitals can approximately mimic those of a fully relativistic (spinor) atomic calculation, rather than the non-relativistic all-electron orbitals they are nominally serving to replace. The partial inclusion of relativistic effects is an important physical correction for heavier atoms, particularly of the second transition series and beyond. Thus, an ECP-like treatment of heavy atoms is necessary in the non-relativistic framework of standard electronic-structure packages, even if the reduction in number of... 

When helium fusion comes to an end at the centre of the star, its carbon/ oxygen core contracts and the temperature rises. At a temperature slightly below 1 billion K, carbon is ignited. 

Fig. 5.4. Schematic evolution of the internal structure of a star with 25 times the mass of the Sun. The figure shows the various combustion phases (shaded) and their main products. Between two combustion phases, the stellar core contracts and the central temperature rises. Combustion phases grow ever shorter. Before the explosion, the star has assumed a shell-like structure. The centre is occupied by iron and the outer layer by hydrogen, whilst intermediate elements are located between them. CoUapse followed by rebound from the core generates a shock wave that reignites nuclear reactions in the depths and propels the layers it traverses out into space. The collapsed core cools by neutrino emission to become a neutron star or even a black hole. Most of the gravitational energy liberated by implosion of the core (some 10 erg) is released in about 10 seconds in the form of neutrinos. (Courtesy of Marcel Amould, Universite Libre, Brussels.)...

If the star is massive enough, the force of gravity resumes core contraction, and this in turn leads to ever higher temperatures and densities. Core contraction is accompanied by expansion of the envelope, for reasons which have not yet been fully elucidated, initiating a new visual stage in the star s life. Its countenance is transformed as it mutates into a red giant. 

As the core contracts, it gets hotter, and once it reaches about a hundred million degrees the fusion of helium atoms becomes possible. This produces carbon, oxygen, and neon. (The intervening elements beryllium, boron, nitrogen, and fluorine are less stable, and decay to other elements.)... 

The red giant stage ends when helium in the core is exhausted. Again the core contracts and the thermal structure of the star becomes unstable. Convective mixing again reaches down toward the layers that have experienced nuclear burning. This mixing event is... 

Sir, if the pressure in the center decreases, doesn t that make the Sun s core contract under the weight of the rest of the Sun ... 

As hydrogen in the core is depleted, nuclear reactions switch off, and the core contracts. Hydrogen-rich material outside the core is compressed and heated... 

When the core hydrogen abundance drops to Xc < 0.5, any further increases in Tc fail to compensate for the drop in energy generation and the whole star starts to contract. As nuclear reactions are extinguished, the convective core vanishes, but only when Xc gravitational energy, with the core contracting on a thermal timescale tx 2 x 106 years. 

At the end of the neon burning the core is left with a mixture of alpha particle nuclei ieO and 24Mg. After this another core contraction phase ensues and the core heats up, until at Tg 2, ieO begins to react with itself ... 

The method works as follows. The mass velocity, Darwin and spin-orbit coupling operators are applied as a perturbation on the non-relativistic molecular wave-functions. The redistribution of charge is then used to compute revised Coulomb and exchange potentials. The corrections to the non-relativistic potentials are then included as part of the relativistic perturbation. This correction is split into a core correction, and a valence electron correction. The former is taken from atomic calculations, and a frozen core approximation is applied, while the latter is determined self-consistently. In this way the valence electrons are subject to the direct influence of the relativistic Hamiltonian and the indirect effects arising from the potential correction terms, which of course mainly arise from the core contraction. 

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