Online text: opendatastructures.org/ods-python/5_2_LinearHashTable_Linear_.html

Section of Open Data Structures: An Introduction by Pat Morin, whose whole-book author is Pat Morin. The online Python edition is undated; 2013 in the parent record is the print-book publication year.

Cited passages: §5.2, opening description of direct slot storage and consecutive modular probing; three entry types and counters n and q; find, add, remove and correctness paragraphs distinguishing del from nil; resize and resetting q to n.

Institutional entry by International Union of Crystallography. Last edited 8 May 2018; original publication date unestablished.

Institutional entry by International Union of Crystallography. Last edited 17 November 2017; original publication date unestablished.

Entry in Online Dictionary of Crystallography by International Union of Crystallography. Last edited 24 February 2019; no original publication date is established.

Online text: dictionary.iucr.org/Reflection_conditions

Cited passages: Definition; Table 1: no centering condition for primitive cells; unmixed indices for all-face-centered cells.

Entry in Online Dictionary of Crystallography by International Union of Crystallography. Last edited 20 November 2017; no original publication date is established.

Online text: dictionary.iucr.org/Structure_factor

Cited passages: Definition: sum over unit-cell atoms, amplitudes and phases; Derivation: primitive one-scatterer model and addition of companion atoms.

Entry in Online Dictionary of Crystallography by International Union of Crystallography. Last edited 9 November 2017; no original publication date is established.

Online text: dictionary.iucr.org/Bragg%27s_law

Cited passages: Definition: interplanar spacing, glancing angle, wavelength and order; Direct derivation and Order of the reflection inspected for consistency; the worked examples and drawings were independently composed.

Entry in Online Dictionary of Crystallography by International Union of Crystallography. Institutional reference issued and hosted by the International Union of Crystallography; no individual byline is assigned. Last edited 11 December 2017; no original publication date is established.

Online text: dictionary.iucr.org/Miller_indices

Cited passages: Definition, Direct space, plane intercepts and primitive versus centered indexing; Definition, Reciprocal space, normal direction and inverse spacing. The entry uses reciprocal-length basis vectors; an angular reciprocal convention introduces a factor of $2\pi$.

Guanosine triphosphate is a nucleotide consisting of guanine, ribose, and three phosphate groups, abbreviated GTP. It is a precursor for RNA synthesis and an energy-coupling substrate in processes such as translation.

GTP-binding proteins also use the difference between GTP- and GDP-bound states as part of molecular switching. Hydrolysis changes the bound nucleotide state; regulatory proteins determine when that switch is activated and reset.

The initial minus final rest energy in a nuclear reaction; positive values represent energy available for outgoing kinetic energy in addition to the incident kinetic energy.

The effective area for a specified nuclear reaction channel at given incident energy. Multiplying incident particle flux, target count and this cross section gives an ideal event rate; target losses and detection efficiency require separate corrections.

Although the pion has spin zero, one-pion exchange depends on nucleon spin and isospin and includes a nuclear tensor force. Shorter-range and multiple-nucleon interactions also matter. The scalar Yukawa potential isolates a range mechanism rather than specifying the complete nuclear force.^[ref]

In 1935, Hideki Yukawa proposed a new massive exchange quantum to explain nucleon binding. His paper began with the inadequacy of an electron–neutrino exchange description of the binding strength. It then required a potential energy falling faster with distance than a Coulomb potential, introduced an exponentially decaying field, and related its inverse range to the exchange particle's rest mass. This was a theoretical proposal, not a detection with an apparatus of his own.^[ref]

The crucial idea is that a finite rest mass supplies a length scale even in empty space. In a scalar model, the static limit of a Klein-Gordon equation produces the modified Helmholtz equation. Its decaying Green's function gives the Yukawa potential. The derivation below isolates this range mechanism; one-pion exchange also carries spin and isospin structure.

The nuclear emulsion track experiment used developed photographic emulsions exposed to cosmic rays and inspected microscopically. Stopping pions gave daughter muon tracks with closely grouped ranges. Comparing penetrating muons with pion-induced nuclear breakup distinguished their interactions; this was not a direct static force measurement. The muon is a lepton, not Yukawa's strongly interacting meson.^[ref]

A nuclear reactor sustains and controls a nuclear chain reaction to produce heat or a useful neutron field. Nuclear fission supplies fresh neutrons; absorption and neutron leakage remove them. A steady neutron population requires a balance between production and losses, the condition of nuclear criticality.

The functions of its components are different. Fuel supplies fissioning atomic nuclei; control rods change neutron absorption; coolant transports heat. In a thermal reactor, a neutron moderator reduces neutron energies before subsequent reactions. Slowing neutrons and cooling the fuel are separate physical functions even when the same material performs both.

Chicago Pile-1 demonstrated a controlled self-sustaining chain reaction in 1942 using a uranium–graphite assembly and neutron-absorbing controls. The decisive observation was the neutron population's response to changing absorption, rather than generation of useful electrical power.^[ref] A power reactor adds heat-transfer and conversion equipment; decay heat persists after the chain reaction is stopped.

For two spherical fragments with the same proton fraction as the parent, let $(A_1,Z_1)=y(A,Z)$ and $(A_2,Z_2)=(1-y)(A,Z)$. In the semi-empirical mass formula without nuclear pairing, nucleon rest energies, the volume term and the nuclear symmetry energy cancel in the parent-minus-fragment mass difference. The remaining Q value is the displayed competition between increased surface energy and reduced nuclear Coulomb energy. Its symmetric value is positive whenThis is an energy-release condition, not the disappearance of a fission barrier or a prediction of a short mean lifetime.

The increase in a nucleus's collective deformation potential energy between a local minimum and a saddle on a path toward separated fragments. A positive final-state Q value does not remove this intermediate barrier. A nucleus can cross it after sufficient excitation energy, or undergo quantum tunnelling. The relevant barrier for neutron-induced fission belongs to the compound nucleus formed after capture, not automatically to the target before capture.

Nuclear fission without an incoming particle supplying the activation energy. A metastable atomic nucleus can tunnel through a fission barrier along collective deformation coordinates. The rate depends exponentially on a barrier action involving its height, width and collective inertia, so positive liquid-drop fission energy alone does not imply an observable rate.

The yield of fragments as a function of fragment mass number or mass fraction. Low-excitation actinide nuclear fission commonly gives two peaks, corresponding to complementary lighter and heavier fragments. Smooth liquid-drop fission energy by itself does not predict this yield: nuclear-shell structure and the dynamics of the descent toward scission matter. Increasing excitation can weaken shell effects and change the distribution. A two-peaked illustrative curve is therefore not a universal measured spectrum.

In a simple compound-nucleus picture, compare the neutron-capture excitation energy to the fission barrier of the capture product. If its neutron separation energy already exceeds the barrier, slow-neutron capture can lead to prompt fission without a positive kinetic-energy threshold. If it lies below, finite neutron kinetic energy is needed for appreciable over-barrier fission; sub-barrier tunnelling and detailed resonance widths soften a literal sharp-threshold picture.