The Master Formula · Parameter by Parameter

The Five Parameters

The Master Formula of Neutrinovoltaics, published by Holger Thorsten Schubart on 2024, expresses the electrical power output of a neutrinovoltaic device as a single integral over five physical factors. Each factor answers one question — how much invisible radiation arrives, how strongly it couples to the absorber, how hard it pushes, how fast that push travels through the lattice, and how efficiently the motion becomes directed current. Follow any parameter to a page devoted to its physics, its numbers, and the experiments behind it.

P(t) = \eta \cdot \int_{V} \Phi_{\text{eff}}(\mathbf{r},t) \cdot \sigma_{\text{eff}}(E)\; dV

The canonical Schubart Master Formula — power as an efficiency-weighted volume integral of the effective radiation field and the effective interaction cross-section.

The five parameters below are the expanded physical representation of this canonical base equation — a decomposition that makes each physical contribution explicit:

P(t) = \int \Phi(E,\theta,t)\,\sigma(E)\,\Delta p\,v_{\text{ph}}\,\eta_{\text{conv}}\;dE\,d\theta

Expanded physical (spectral–transport) representation — the integral, over energy E and incidence angle θ, of five factors multiplied together.

For the full context and derivation of the formula, see the Master Formula overview.

Five parameters, one integral

Read the integrand left to right and it tells a physical story. Radiation of energy $E$ arrives from every direction $\theta$ ; a fraction of it couples to the graphene–silicon absorber; each coupling delivers a mechanical push; that push propagates as a lattice wave; and a share of the resulting motion is rectified into current. Summing over all energies and angles gives a single number — continuous power in watts.

\Phi(E,\theta)

Radiation Flux Density

How much invisible radiation arrives, resolved by energy and incidence angle — essentially constant, day and night.

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\sigma(E)

Scattering Cross-Section

How strongly radiation of energy E couples to the absorber — coherently enhanced by the nucleus.

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\Delta p

Momentum Transfer

The mechanical push each interaction delivers into the lattice — the seed of every vibration.

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v_{\text{ph}}

Phonon Velocity

The speed at which lattice vibrations travel through graphene — exceptionally fast, and central to transport.

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\eta_{\text{conv}}

Conversion Efficiency

The fraction of captured motion the structure turns into usable directed current — the main engineering target.

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P

Power Output

The result — the continuous electrical power in watts, once the five factors are integrated over E and θ.

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Every parameter page is built in three depths — an intuitive reading, the underlying physics, and the formal mathematics — and extended with derivations, limiting cases and engineering implications. Read as far as you like; the intuition stands on its own.

Why these five? Any honest estimate of power from a radiation field must answer five questions — how much arrives, how strongly it couples, how hard it pushes, how fast the disturbance travels, and how efficiently it is converted. The Master Formula assigns exactly one symbol to each, which keeps the model transparent and every assumption inspectable.

Scientific context. The Master Formula rests on established, Nobel-recognised physics — neutrino oscillation (2015 Nobel Prize, Kajita and McDonald), coherent elastic neutrino–nucleus scattering, and the electronic properties of graphene (2010 Nobel Prize, Geim and Novoselov). The Neutrino Energy Group frames the remaining task honestly: independent validation of full-scale net output is an ongoing part of the normal scientific process, and these pages present each parameter with its real experimental foundation so the reasoning can be followed step by step.