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Alessandro De Angelis coauthored calculations of the transparency of intergalactic space to gamma rays. The work connects an assumed background photon population with energy-dependent optical depth and the attenuation of distant sources.^[ref]

High-energy photon propagation is affected by interactions with background radiation, including pair production. Interpreting a source's observed spectrum therefore requires both an emission model and a propagation model; a missing high-energy component need not originate entirely at the source.

For electrically neutral, fully ionized stellar matter with electrons and Positrons as its charged leptons, the electron fraction in stellar matter is the net electron number per baryon:Here $n_i$ is the number density of nuclear species $i$, $Z_i$ its atomic number, $A_i$ its mass number, and $n_b$ the total baryon number density. Charge neutrality equates the net negative lepton charge to the total proton charge. The subtraction of Positrons matters in hot matter containing abundant thermally produced Positrons; ordinary electron number alone need not equal nuclear charge.^[ref]

Neglecting small nuclear mass defect corrections, isotope mass fractions $X_i$ give $Y_e={\sum }_i{X}_i{Z}_i/A_i$. Pure fully ionized helium-4 therefore has $Y_e=1/2$. Strong interactions and electromagnetic reactions preserve this proton fraction, whereas electron capture and beta-plus decay reduce it and beta-minus decay can increase it. The total proton-to-neutron number ratio is $Y_e/(1-Y_e)$; electron-positron pair production changes neither of those baryon counts. If other charged leptons such as muons are appreciably populated, their charge must also be included in the neutrality equation.

A gamma ray is a high-energy photon, conventionally associated with a transition of an atomic nucleus, radioactive decay or a particle reaction. X-rays and gamma rays are both electromagnetic radiation; their energy ranges overlap, so the production mechanism can be more informative than an arbitrary energy boundary.

A nuclear energy level transition emits a gamma ray whose energy is approximately the level difference, with a correction for nuclear recoil. Detectors infer the incoming energy from interactions such as photoelectric absorption, Compton scattering and, above threshold, pair production. A measured gamma-ray spectrum can therefore identify nuclear transitions even when a detector does not absorb the entire photon energy in each event.

Pair production creates a particle and its antiparticle while conserving energy, momentum and relevant charges. For an electron–Positron pair, the available invariant energy must at least supply their combined rest mass, with additional kinetic energy and other final-state requirements included.

A single free photon in empty flat spacetime cannot produce just that pair: its four-momentum has zero invariant mass, while the massive pair has a positive invariant mass. A second photon or another participant, such as a nucleus taking recoil, can satisfy the full kinematics. The pair's charges cancel globally, but each outgoing particle can leave its own detector track. A laboratory-frame photon energy threshold therefore depends on the complete reaction, not only on writing twice the electron rest energy.

The following are the leading quantum electrodynamics diagrams. Solid arrows indicate fermion-number flow, and wavy lines indicate photons. The heavy source line represents a charged nucleus; its recoil allows four-momentum conservation.

For Compton scattering, $e^{-}\gamma \to e^{-}\gamma$, there are two diagrams: absorption of the incident photon followed along the electron line by emission of the outgoing photon, and the opposite ordering. These are the $s$- and $u$-channel electron propagators. Both scattering amplitudes are order $e^2$.

For bremsstrahlung, $e^{-}Z\to e^{-}Z\gamma$, a virtual photon transfers momentum between the electron and the source. The real photon is emitted before or after this interaction along the electron line. These two dominant external-field diagrams have scattering amplitudes of order $Z{e}^3$. A full finite-mass charged-target calculation also includes radiation from the target; it is suppressed in the heavy stationary-source approximation used here.

For nuclear-field pair production, $\gamma Z\to e^{-}{e}^{+}Z$, crossing the preceding diagrams gives two order-$Z{e}^3$ contributions, with the incoming real photon and the exchanged virtual photon in either order along the pair's fermion line. An isolated real photon cannot produce a massive pair in vacuum: its invariant squared mass is zero, whereas the pair has invariant squared mass at least $4m_e^2$. The source absorbs recoil momentum.

Gravitational evidence requires much more nonbaryonic matter than can be supplied by ordinary luminous material or by the baryon abundance permitted by nucleosynthesis. A stable, electrically neutral massive particle is a plausible cold component. Thermal production followed by cosmological particle freeze-out gives an additional motivation: an annihilation rate near a weak-interaction scale can leave an appreciable relic abundance. This is a mechanism and search hypothesis, not proof that the dark matter must be a WIMP or have any particular elastic-scattering cross section.

The plotted regions are conditional WIMP interpretations of different measurements. The experiments use different targets and distinguish signal from background differently:

The plot also includes CRESST experiment, whose cryogenic calcium-tungstate modules combine phonon and scintillation-light signals. Different nuclei contribute to its recoil interpretation. Its excess region is another conditional candidate region, not an extra confirmed detection.^[ref]

Around ten GeV, the shaded regions favour cross sections roughly $10^{-41}$–$10^{-40}\mathrm{c}{\mathrm{m}}^2$, while the XENON100 solid curve and the improved low-mass CDMS curve cut into or exclude much of those regions under the common elastic, spin-independent WIMP-nucleus scattering interpretation expressed per nucleon. There is tension within that shared model; the plot does not show mutually confirmed discoveries. electron backgrounds, threshold response, nuclear-recoil quenching factors, channeling assumptions and the halo velocity distribution can shift interpretations. Changing the interaction model can also alter target comparisons, but cannot establish a WIMP by assertion. The 100-live-day XENON100 result itself reported candidates compatible with estimated background.^[ref]

For a rough dimensional event estimate, $1\mathrm{c}{\mathrm{m}}^2=10^{-4}{\mathrm{m}}^2$ givesIf a collider production cross section had this value, that small yield, before acceptance and backgrounds, would not support a likely discovery. The plotted nuclear-scattering cross section is not the LHC production cross section, however. Converting between them needs a mediator, couplings, parton distributions and production kinematics; a light stable WIMP would normally be inferred from missing transverse momentum with a visible recoil object, not a visible WIMP track. The mass makes pair production kinematically accessible, but the plot and integrated collider luminosity alone do not decide discovery probability.

For the relic estimate, define $M=m{c}^2$ and $\theta =k_{B}T$. The sharp-freeze-out relic dilution model givesAssume stable particles, no subsequent annihilation, and $RT=\mathrm{constant}$. Conserved comoving particle number then givesThe present rest-energy density and its critical fraction areThus the supplied toy model yields a cosmologically substantial density, of the right broad scale to motivate a dark-matter candidate. It is not an independent precision prediction: $P$ is imposed and the abundance depends exponentially on it. If entropy degrees of freedom change, entropy conservation instead gives an extra factor $g_{\ast s,0}/g_{\ast s,f}$ in $n_0$ when using the photon temperature. The species content needed to evaluate that correction is not supplied. A realistic calculation also follows residual annihilations with the abundance Boltzmann equation rather than stopping exactly at equilibrium freeze-out.

Nuclear-field pair creation is $\gamma Z\to e^{-}{e}^{+}Z$. A virtual photon exchanged with the nucleus supplies recoil momentum, while the real photon and virtual photon attach to the electron line joining the outgoing pair. The figure shows a representative graph. The second attachment ordering must be included in the full amplitude. A real photon cannot create a free massive pair in vacuum: its invariant mass is zero, whereas $(p_{e^{-}}+p_{e^{+}}{)}^2\ge 4m_e^2$. Nuclear recoil resolves that kinematic obstruction and permits energy-momentum conservation.

At low charged-lepton energy, collisional ionization and excitation dominate over radiation. A slowing Positron also eventually annihilates, usually yielding photons. Low-energy photons lose energy through Compton scattering and, at sufficiently low energy, photoelectric absorption; pair production is kinematically unavailable below its threshold.

The electron critical energy $E_c$ is the energy where mean bremsstrahlung and collisional losses are equal. With $-(dE/dx{)}_{\mathrm{rad}}\simeq E/X_0$ and a slowly varying collisional loss,Above this energy, radiation and pair creation multiply shower particles efficiently. Below it, charged particles mainly deposit their energy by collisions and the shower dies out. Critical energy is material dependent; it is not a new photon-production threshold.

Interpret the terminal infall speed as the free-fall speed from a radius much larger than the neutron star radius $R_{\ast }=12\mathrm{km}$. In the Newtonian estimate,For fully ionized hydrogen with electrons and protons at a common temperature, there are two particles per atom and $\mu =(m_p+m_e)/2\simeq m_p/2$. The result of e then yieldsThis is the thermal energy scale $k_B{T}_d$ per particle. In the same classical monatomic gas approximation, the mean random kinetic energy per particle is $3k_B{T}_d/2\simeq 59\mathrm{MeV}$. Before the shock wave, the bulk kinetic energy per proton is $m_p{v}_u^2/2=G{M}_{\ast }{m}_p/R_{\ast }\simeq 208\mathrm{MeV}$. Distinguishing these quantities avoids an ambiguity in “particle energy”. If only the ions support the downstream pressure because electrons have not equilibrated, $\mu \simeq m_p$ instead gives $k_B{T}_i\simeq 78\mathrm{MeV}$; that is a different, two-temperature assumption.

These are estimates within the question's Newtonian, $\gamma =5/3$ model. Its self-consistency is poor here: $2G{M}_{\ast }/(R_{\ast }{c}^2)\simeq 0.443$, and $39\mathrm{MeV}$ is much larger than the electron rest energy $0.511\mathrm{MeV}$. Relativistic electrons, electron–positron pair production, radiation, unequal species temperatures, and general relativity can alter the equation of state and shock wave structure. In particular, the numerical $39\mathrm{MeV}$ must not be presented as a precision surface temperature prediction.

A radio pulsar is a rapidly rotating, magnetized neutron star whose emission beam periodically crosses the line of sight. Collapse of a massive stellar core can leave such a compact remnant. Angular-momentum conservation during contraction helps explain rapid rotation, while amplified magnetic fields and a plasma-filled magnetosphere enable particle acceleration and beamed emission. The pulses are not repeated stellar contractions. Not every newborn neutron star is seen as a radio pulsar, because emission, beaming and observational selection matter.

rotation supplies energy to radiation and the magnetized wind. With approximately constant moment of inertia $I$,An ideal fixed magnetic-dipole torque has $\dot{\Omega }=-K{\Omega }^3$. Its integration givesso the pulsar characteristic age ${\tau }_c=P/(2\dot{P})$ approximates the true age only for a short birth period, constant torque coefficient and braking index three. Real magnetospheres, field evolution and kinematic contributions to observed $\dot{P}$ complicate both age and inferred magnetic field.

As the star spins down, the available accelerating potential falls. If particle acceleration and pair production can no longer sustain the radio-emitting magnetosphere, the object crosses a model-dependent pulsar death line and ceases to be detectable as an ordinary radio pulsar. It still exists as a cooling neutron star; “death” refers to the emission state, not disappearance of the star. The death boundary is not a precisely universal spin period.

In a surviving binary, later Roche-lobe overflow from a companion can create an accretion disc. Transferred angular momentum spins the old neutron star up, and the accretion luminosity can produce an X-ray binary. Long accretion episodes can produce millisecond rotation, commonly accompanied by a smaller inferred external magnetic field. After mass transfer declines, the radio pulsar can switch on again as a recycled pulsar, often with a white dwarf companion. Other binary histories can leave a second neutron star, an ablated companion or an isolated recycled object; there is no single obligatory evolutionary sequence.

A direct observational bridge is the coherent approximately $2.49\mathrm{ms}$ X-ray pulsation discovered with RXTE in SAX J1808.4-3658, an accretion-powered binary. It demonstrated an accreting neutron star rotating at a rate appropriate to recycled millisecond radio pulsars.^[ref] Timing analysis must correct orbital Doppler shifts, telescope and solar-system timing, and instrumental aliases. Radio dispersion, sky coverage and beaming selection affect demographic inferences. The sequence is rotational pulsar spin-down, possible loss of radio activity, and possible accretion-driven recycling—not a necessary path for every neutron star.

Photon radiotherapy uses indirectly ionizing photons. Their Compton scattering, photoelectric effect and, at higher energy, pair production create charged particles that deposit energy. A megavoltage beam has a dose-build-up region followed by a gradual decline and substantial exit dose. Multiple shaped beams or intensity-modulated radiotherapy distribute this dose around a target.

Proton therapy uses directly ionizing charged particles with a finite particle range and a Bragg peak. Tuning beam energy controls depth and scanning controls lateral delivery; multiple energies cover a finite target thickness. Reduced distal and integral normal-tissue dose is a potential advantage. Limitations include range uncertainty, Multiple Coulomb scattering, nuclear secondary production, motion-dependent delivery, and a variable relative biological effectiveness, particularly near the distal edge. A physical dose advantage must be assessed against target coverage and clinically relevant toxicity; it does not by itself establish superior tumour control.

For photons, the total mass attenuation coefficient sums contributions from photoelectric absorption, Compton scattering, coherent Rayleigh scattering, and pair production in nuclear or electronic fields when above their thresholds. At sufficiently high photon energies, photonuclear reactions can also contribute. Attenuation counts removal from the incident narrow beam, including scattering without complete local deposition of the original energy.

In water at both specified energies, Compton scattering dominates. At $140\mathrm{keV}$, photoelectric absorption and coherent Rayleigh scattering make smaller contributions; at $511\mathrm{keV}$ these are still less important. Nuclear-field pair production is impossible below $2m_e{c}^2=1.022\mathrm{MeV}$, so it occurs in neither example. The positrons used to produce the fluorine-18 annihilation radiation do not change that threshold for interactions of its $511\mathrm{keV}$ photons in water.

Strictly, $\mu$ is a linear attenuation coefficient, whereas $\mu /\rho$ is a mass attenuation coefficient; the source's wording blurs these units. The mass energy-absorption coefficient ${\mu }_{\mathrm{en}}/\rho$ weights the fraction of incident photon energy transferred to charged particles and retained after radiative losses, rather than simply counting all removals. Coherent scattering contributes attenuation with negligible energy transfer. A photon deflected by Compton scattering can carry much of the original energy away. One often writes ${\mu }_{\mathrm{en}}=(1-g){\mu }_{\mathrm{tr}}$, with $g$ the fraction of secondary charged-particle kinetic energy lost radiatively. Under charged-particle equilibrium, multiplying photon energy fluence by ${\mu }_{\mathrm{en}}/\rho$ gives the absorbed dose; that equilibrium condition matters near interfaces and in buildup regions.^[ref]

A nuclear reaction initiated by absorption or scattering of a photon. Such channels may contribute to attenuation at photon energies above their relevant nuclear thresholds; they are distinct from atomic photoelectric absorption and electron–positron pair production.

The Positron is the antiparticle of the electron, with equal rest mass and spin but electric charge $+e$. It can be created in beta-plus decay or in a sufficiently energetic pair production process.

An electron and Positron can undergo electron-positron annihilation. For the two-photon channel from a pair initially at rest, conservation of momentum requires opposite photon directions and each photon has energy $m_e{c}^2$, neglecting binding. Initial motion or a different allowed final state changes that simple picture. Annihilation is conversion of the initial particles' energy into other excitations, not disappearance of conserved energy or charge.

A model-dependent boundary in spin-period and spin-down parameter space beyond which particle acceleration and pair production cannot maintain a specified radio-emission mechanism. Crossing it means loss of an emission state, not destruction of the neutron star. Selection and beaming obscure an exact empirical universal boundary.

The study of interactions involving two incoming photons. Channels include elastic light-by-light scattering and pair production. A nonlinear response in a material and the direct vacuum QED process have different physical mechanisms.