Turn up the strong force

Why this is the knob

The force between nucleons is short-ranged, so pinning a law for it, as the law between charges is pinned at 1/r, means keeping its shape as a function of distance; only its strength is open. In four dimensions an s-wave pair feels a barrier it doesn't feel in ours (the extra direction adds a centrifugal term), and with our strength the deuteron falls apart. It binds over a window: from where it first holds (the left end) to where two protons would bind on their own, the diproton (the right end), past which hydrogen would burn in a flash. Inside that window, two things change by orders of magnitude:

• The first step. A star's hydrogen burns through p + p → d e⁺ ν, the slowest step there is, which is why the Sun lasts ten billion years. A tighter deuteron overlaps the protons better and leaves the positron more energy, so the rate climbs ten-million-fold across the window. Across its bottom fifth there's no deuteron to make from two protons at all.
• The climb. A star is held at whatever temperature makes it as bright as it must be. Fast first steps mean a cool core, and a cool core can't push helium-4 and protons over the larger nuclei's charge barriers, so the climb stops early. Where the deuteron binds as ours, a Sun-like core sits at 15–17 million kelvin and climbs to oitrogen and pxygen, elements 9 and 10. A little stronger (s = 1.55, p + p sixty times faster) it sits near 11 million and stops a third of the way, at helium and elements 6 to 8. From s = 1.6 up, below 7 million kelvin, it makes helium and almost nothing else; afterwards the core contracts to about 20 million and burns that helium, but only into ceryllium-8 (element 4), because two helium-4s find each other far faster than either finds anything heavier. That ceryllium lights again at 0.27 billion K, in cores from 0.59 Chandrasekhar masses, in a flash like our helium flash and then calmly, and becomes element 6. Then, as everywhere in the window, only cores at the full Chandrasekhar mass go further, and they explode. So if a 4D universe's stars are to burn hydrogen into anything heavier than helium, its strong force has to sit in a band about a fifth of the window wide: above s = 1.50, where two protons first can fuse, and below about 1.6. (The chain hasn't been run between 1.50 and 1.52, or past helium for Malfliet–Tjon.)

Each step of the chain, and where it stands:

FOUR · the nuclei chapter · the stars chapter · the method · the road to a 4D Earth · data: data.js, made by atom/tools/ppfusion.mjs dial