Proton–proton chains and solar neutrinos

The ordinary pp gateway produces a deuteron, a positron, and an electron neutrino from two protons. Its weak conversion makes it slow compared with many subsequent electromagnetic captures. Deuterium can capture another proton to form helium three. A competing pep gateway consumes an electron with two protons and supplies a different neutrino line. The relative rates depend on the plasma conditions; assigning every hydrogen-burning neutrino to the ordinary pp reaction would miss this distinction.

In the pp-I termination, two helium-three nuclei fuse into one helium-four nucleus and return two protons. Preparing the two intermediates initially used six protons, but two are recycled, so only four are consumed net. Including positron annihilation with surrounding electrons, the net bookkeeping consumes two electrons and emits two neutrinos per newly made helium-four nucleus. Charge, baryon number, and lepton number all balance. The associated atomic-mass energy release must not then have annihilation energy added a second time.

The pp-II route uses helium three and an existing helium-four nucleus to make beryllium seven. Electron capture then makes lithium seven and a neutrino, and a proton reaction returns two helium-four nuclei. One of those replaces the original helium-four participant; only one is newly produced net. In the pp-III route, proton capture on beryllium seven produces boron eight, whose beta decay supplies a higher-energy neutrino spectrum before the light products complete the route.

A completed pp-I cycle normally has two gateway neutrinos. A pp-II or pp-III cycle normally has one gateway neutrino and one from its later weak step, with pep substitutions or small additional branches requiring separate accounting. A high-energy neutrino detector therefore does not directly count all helium production. Intermediate abundances and competing destruction rates determine branch fractions. The short lifetime of one intermediate does not identify the slowest rate controlling the complete conversion throughput.

At a distance from an isotropic source, a neutrino production rate divided by sphere area gives a number flux, provided losses or direction-dependent emission are neglected. Neutrino flavor evolution changes the electron-flavor fraction arriving at a detector, so an electron-neutrino event rate also requires survival probabilities, cross sections, efficiencies, and the source spectrum. A source neutrino count is therefore neither an observed count rate nor a direct measurement of a particular fusion cross section without a model connecting those quantities.

The usual luminosity comparison assumes the burning network is close to a stationary state. A changing reservoir of helium three or another intermediate can delay the relation between gateway reactions and newly completed helium nuclei. Photon transport also delays a star's surface response, whereas escaping neutrinos probe ongoing core reactions more directly. These timing distinctions matter when interpreting a hypothetical transient or comparing different epochs. The simple arithmetic below deliberately specifies a stationary ideal source rather than asserting a complete solar model.