ELEMENTS OF NEUTRON SCATTERING

ELEMENTS OF NEUTRON SCATTERING • Basic properties of neutrons, comparison with x-ray photons • Neutron sources • Neutron detectors • “Classical” neutron scattering • Magnetic scattering • Inelastic scattering

Basic properties of neutrons, comparison with x-ray photons • Neutron sources • Neutron detectors • “Classical” neutron scattering • Magnetic scattering • Inelastic scattering

Nuclear fission In reactors, fission takes place when a fissile nucleus (always 235U or 239Pu in practice, although there are a few others) captures a neutron, the nucleus splits into two nearly equal-mass fragments (in large variety) that together carry about 160 MeV of kinetic energy. On average, the process also promptly (~10-15 sec) produces about 2.5 neutrons for each fission. Fission neutrons actually “evaporate” from the initially highly excited fragments and have average energies of about 2 MeV. Each fission event produces a total of approximately 190 MeV of energy: fission fragment and neutron kinetic energy, beta radiation (mostly e– because fission fragments usually have too many neutrons), and photons (g rays), all of which appears as heat in the reactor fuel and surroundings, and neutrino energy, which escapes. A small fraction (~ 0.5%) of neutrons appear after a few seconds delay time. The delayed neutrons are essential for reactor control. One neutron of the 2.5 goes on to cause another fission, usually (after a few microseconds) slowing down to energies at which the fission cross-section is large. Capture in control rods and parasitic processes absorb about 0.5 neutron per fission. This leaves about 1 neutron per fission useable for external purposes. In round numbers, fission reactors require dissipating about 200 MeV of heat energy for each useful neutron produced. Most (but not all) reactors used for slow-neutron scattering research operate in a steady mode.

E is in MeV The energy distribution of prompt fission neutrons

Nuclear spallation In accelerator-driven spallation sources, high-energy particles (invariably protons of ~ 1. GeV energy) from the accelerator impinge on a thick target of dense, high-mass-number materials, e.g., uranium, tungsten, tantalum, or mercury. Here they collide, leaving highly excited nuclei. Neutrons, protons, and pions that emerge from collisions with sufficient energy proceed to collide again and leave further excited nuclei. The excited nuclei shed their energy by promptly evaporating particles (by far, predominantly neutrons) until there is too little left for that process.

spallation (approx. 40 neutrons per nucleus) internal cascade Thick-target yields of neutrons as a function of incident proton energy and target material

The energy and angular distribution of neutrons emerging from a tantalum target irradiated by 1-GeV protons. The target is 31 cm long, 7 cm wide and 20 cm high.

Moderators

Paths of neutrons in a research reactor. Several fast neutrons (red) emerge from each fission (heavy dots) and proceed to collide, losing energy in each collision (progressively less red) until they cause another fission, disappear by non-fission absorption (a), or travel into the reflector. In the reflector-moderator, neutrons collide repeatedly, losing energy (less red, more green) until they come into thermodynamic equilibrium with the moderator medium (thermal neutrons, green) and live for a long time. Some return to the core to cause another fission. Others find their way into the neutron beams.

A cavity-type cold moderator. Thermal neutrons (green) enter the 25-K liquid hydrogen from the 300-K D2O moderator. There, they collide numerous times, losing energy at each collision (less green), and come into equilibrium with the hydrogen at 25 K (blue). The reentrant cavity acts as a hohlraum, allowing neutrons to rattle around within, promoting thermal equilibration but permitting cold neutrons to emerge efficiently into the neutron beams. The diagram exaggerates the thickness of the L-H2 layer in relation to the diameter of the cavity and omits the necessary plumbing arrangements.

A hot-neutron source. Thermal neutrons (green) from the 300-K D2O moderator enter the block of vacuum-insulated graphite, heated by gamma rays and fast neutrons to about 2000°C. There they collide, gaining energy in collisions (progressively yellower), and come into thermodynamic equilibrium with the hot graphite. They emerge as hot neutrons (orange) and travel into the neutron beams.

Flux spectra at the source surfaces of the three moderators of the FRM-II reactor

Spectrum of a poisoned room-temperature polyethylene moderator at IPNS

Brightness & Fluxes for Neutron & X-Ray Sources

Reactor ILL, Grenoble http://www.ill.fr/index_ill.html • The double wall of the reactor • The reactor's overhead crane • The gantry crane • The reactor operations hall • The experimental hall overhead crane • The experimental hall • Spectrometer • View into the reactor core • The reactor core (plan) • The main reactor pool • The storage pool • The heat exchanger

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IN20:

What does it mean to “detect” a neutron? • Need to produce some sort of measurable quantitative (countable) electrical signal • Can’t directly “detect” slow neutrons • Need to use nuclear reactions to “convert” neutrons into charged particles • Then we can use one of the many types of charged particle detectors • Gas proportional counters and ionization chambers • Scintillation detectors • Semiconductor detectors

Nuclear Reactions for Neutron Detectors • n + 3He 3H + 1H + 0.764 MeV • n + 6Li 4He + 3H + 4.79 MeV • n + 10B 7Li* + 4He7Li + 4He + 0.48 MeV  +2.3 MeV (93%)7Li + 4He +2.8 MeV ( 7%) • n + 155Gd  Gd* -ray spectrum  conversion electron spectrum • n + 157Gd  Gd* -ray spectrum  conversion electron spectrum • n + 235U  fission fragments + ~160 MeV • n + 239Pu  fission fragments + ~160 MeV most common

Gas detectors ~25,000 ions and electrons produced per neutron (~410-15 coulomb)

MAPS Detector Bank

Scintillation Detectors photons per neutron Li glass (Ce) ~7,000 ZnS (Ag) - LiF ~160,000

GEM Detector Module

Semiconductor Detectors ~1,500,000 holes and electrons produced per neutron (~2.410-13 coulomb)

scattering length for neutrons

consequences: structure of the same molecule seen by neutrons, clouds of nuclear density are denoted in blue, H atoms are detected (purple) structure of a molecule seen by x-rays, clouds of electron density are denoted in red, H atoms are not detectes

radiography (shadow projection) neutrons (the plastic parts are detected (H-rich)) x-rays (not sensitive to the plastic parts)

Scattering from a set of nuclei bi depends on the nucleus (isotope, orientation of spin relatively to the neutron spin etc.). Statistical averaging yields: Coherent and incoherent parts of the cross-section Total cross-sections

Example: • scattering from a single isotope with the spin quantum number j. Two possible orientations of the neutron spin exist: • parallel spins: • antiparallel spins: the scattering length is b+ the scattering length is b- probabilities of these two states are and the average scattering lengths For proton with j=1/2: 

Various isotopes in the sample:

Thermal Neutrons, 8 keV X-Rays, Low Energy Electrons:Absorption by Matter

Magnetic Scattering • The magnetic moment of the neutron interacts with B fields caused, for example, by unpaired electron spins in a material – Both spin and orbital angular momentum of electrons contribute to B – Expressions for cross sections are more complex than for nuclear scattering • Magnetic interactions are long range and non-central – Nuclear and magnetic scattering have similar magnitudes – Magnetic scattering involves a form factor – FT of electron spatial distribution • Electrons are distributed in space over distances comparable to neutron wavelength • Elastic magnetic scattering of neutrons can be used to probe electron distributions – Magnetic scattering depends only on component of B perpendicular to Q – For neutrons spin polarized along a direction z (defined by applied H field): • Correlations involving Bz do not cause neutron spin flip • Correlations involving Bx or By cause neutron spin flip – Coherent & incoherent nuclear scattering affects spin polarized neutrons • Coherent nuclear scattering is non-spin-flip • Nuclear spin-incoherent nuclear scattering is 2/3 spin-flip • Isotopic incoherent scattering is non-spin-flip

Magnetic Neutron Scattering is a Powerful Tool • In early work Shull and his collaborators: – Provided the first direct evidence of antiferromagnetic ordering – Confirmed the Neel model of ferrimagnetism in magnetite (Fe3O4) – Obtained the first magnetic form factor (spatial distribution of magnetic electrons) by measuring paramagnetic scattering in Mn compounds – Produced polarized neutrons by Bragg reflection (where nuclear and magnetic scattering scattering cancelled for one neutronspin state) – Determined the distribution of magnetic moments in 3d alloys by measuring diffuse magnetic scattering – Measured the magnetic critical scattering at the Curie point in Fe • More recent work using polarized neutrons has: – Discriminated between longitudinal & transverse magnetic fluctuations – Provided evidence of magnetic solitons in 1-d magnets – Quantified electron spin fluctuations in correlated-electron materials – Provided the basis for measuring slow dynamics using the neutron spin-echo technique…..etc

Theory of magnetic neutron scattering for pedestrians: Interaction of the magnetic moment of neutron with the magnetic field produced by a moving electron Interaction potential: Magnetic dipole moment of the neutron: gn 1.913 is the gyromagnetic factor of neutron, is the spin operator of neutron The magnetic field produced by a moving electron magnetic dipole moment of electron differential cross-section of magnetic neutron scattering

ELEMENTS OF NEUTRON SCATTERING