Annihilation: Reorganization and Energy Accounting

01Conjugate cores reorganizing into final modes

ASD explains annihilation as conjugate localized cores releasing their separate locking and, together with surrounding fields, transferring energy and momentum into allowed final states. The two-photon result for a resting electron pair is a conservation solution under specified center-of-momentum conditions. Its detector readout must additionally use Chapter 4’s common background, action scale and detector energy account.

ASD describes annihilation as reorganization of localized cores and their surrounding fields. Separate conjugate closed structures release their locking, transferring energy and momentum into permitted propagating modes and other final states. Energy does not vanish or cancel as two opposite materials; the field organization carrying it changes.

An electron–positron channel depends on relative momentum, orientation, spin, overlap, environment and coupling. A bound state can form first and decay through allowed channels. The manuscript’s conceptual sequence connects these stages without replacing evolution:

02Canceling charge constrains channels rather than rates

$N_{\rm em}$ is candidate electromagnetic degree. Its zero sum permits final states without separated charged cores. Other invariants, barriers, angular momentum and boundaries in the complete configuration space still constrain the transition. Arbitrary opposite-charge particles are not thereby antiparticles, and neutrality does not imply automatic annihilation.

Fixed-amplitude fields can rearrange local positive and negative density in a neutral sector. Variable-amplitude fields may pass through reduced amplitude or undefined orientation. The actual equations determine accessibility; canceling labels cannot calculate a probability.

03Energies and directions in a two-photon channel

Select a two-photon electron–positron final state with zero initial total momentum, negligible relative kinetic and binding energy, and no other participants. Conservation gives

$m_e$ is intrinsic electron mass and $\mathbf p_i,E_i$ the momentum and energy of photon $i$ in the same background. From $\mathbf p_2=-\mathbf p_1$ and $E_i=c|\mathbf p_i|$, the photon energies are equal. Total energy $2m_ec^2$ then fixes each to $m_ec^2$. Opposite directions follow from precisely these conditions.

The approximate $511\,\mathrm{keV}$ uses the existing measured mass rather than predicting it or specifying universal annihilation photon energies. A zero-momentum isolated pair cannot become a single free photon, since that photon cannot have both nonzero energy and zero momentum.

04Center-of-momentum and laboratory accounts

If total momentum remains zero but relative kinetic or binding energy matters, use the complete $E_{\rm tot}$. In the selected two-photon channel each energy is $E_{\rm tot}/2$, not necessarily $m_ec^2$. This is the center-of-momentum description or condition.

In a laboratory with $\mathbf P_{\rm tot}\ne0$, keep both energy and direction relations:

Energies generally differ and directions need not be opposite. Squaring the momentum sum and combining it with total energy gives

where $\vartheta$ is the angle between final photons. This is algebra within the same conservation account, not a dynamical angular distribution or an added radiation channel. Recoil participants or external fields must be included when present.

05Field readjustment and complete energy allocation

Initial energy includes cores, motion, binding and participating fields. When the source changes, its longitudinal accompanying field readjusts dynamically rather than being deleted instantaneously throughout space. For one system boundary and initial and final times, the manuscript gives

$E_{{\rm out},\gamma}$ is photon energy, $E_{{\rm out},{\rm other}}$ other allowed final-state energy, $E_{\rm recoil}$ recoil, and $\Delta E_{\rm background}$ the final-minus-initial background energy within the selected boundary. Avoid double counting; assign remaining near fields consistently, and determine the background difference’s sign from the process.

Connecting an outgoing final state to a readout also requires detector absorption. Outgoing energy uses the common background and reference calibration above. During absorption, internal excitation, changes in detector motion, recoil and work by any apparatus maintaining that motion belong to the same system. The detector page converts average absorbed power and a fixed effective trigger energy into a long-term event rate only under its stated material-response and recording conditions. Reaction energy, the allocation in one absorption event and accumulated counts must therefore be connected in sequence, with accompanying-field energy counted once across these levels.

Longitudinal degrees of freedom permit field reorganization without implying mandatory undetected longitudinal radiation. Free-wave production, power and branching ratios require the same coupling and selection rules and are constrained by energy balance. Existing three-photon channels likewise need consistent rotational representations, discrete symmetries and reaction coupling. Positronium channel and lifetime measurements are requirements, not independently calculated ASD rates.

Proton–antiproton reactions involve more complex strong connections and final states, so cannot inherit the special stationary electron-pair picture. Species and complete conjugate correspondence determine which reaction is being studied.

06One dynamics for forward and reverse processes

If the microscopic action has the necessary reversibility, creation and annihilation must use the same coupling and match initial and final states, momenta, spin and fields under the actual time-reversal rules. Spatial parity is not that correspondence, and conservation alone does not determine reciprocal transition strengths.

Rates also involve incident flux, distributions, final phase space and environment. OP-MAT-007 tracks joint dynamics and annihilation requirements the observational interface. Core unlocking, near-field adjustment and distant energy transport must be calculated together to obtain a reaction result from the ASD picture.

07Outgoing propagation and absorption are different comparisons

For each already formed outgoing photon, (4.94)–(4.95) assert that, without real exchange in a static background, wavelength and local action scale change by the same factor while frequency changes inversely, preserving $E_\gamma^*=h_\gamma\nu_\gamma$. This follows one propagating excitation; photons created from different initial kinetic energies, bound states or emission conditions can have different intrinsic energies.

Absorption instead uses (4.100), $E_\gamma^*+E_D^{\rm in}+E_{\rm env}^{\rm in}=E_D^{\rm out}+E_{\rm env}^{\rm out}$. The detector energy $E_D$ includes internal and motional energy, while $E_{\rm env}$ includes the recoil, fields and drive that actually participate. Invariant pre-absorption intrinsic energy does not imply identical internal heat for every moving detector. Action and material standards, together with the detection article, specify the path from a two-photon final state to readouts.