A neutron may pass by a nucleus with a probability determined by the nuclear interaction distance, or be absorbed, or undergo scattering that may be either coherent or incoherent. [1] The interference effects in coherent scattering can be computed via the coherent scattering length of neutrons, being proportional to the amplitude of the spherical scattered waves according to Huygens–Fresnel theory. This scattering length varies by isotope (and by element as the weighted arithmetic mean over the constituent isotopes) in a way that appears random, whereas the X-ray scattering length is just the product of atomic number and Thomson scattering length, thus monotonically increasing with atomic number. [1] [2]
The scattering length may be either positive or negative. The scattering cross-section is equal to the square of the scattering length multiplied by 4π, [3] i.e. the area of a circle with radius twice the scattering length. In some cases, as with titanium and nickel, it is possible to mix isotopes of an element whose lengths are of opposite signs to give a net scattering length of zero, in which case coherent scattering will not occur at all, while for vanadium already the opposite signs of the only naturally occurring isotope's two spin configurations give a near cancellation. However, neutrons will still undergo strong incoherent scattering in these materials. [1]
There is a large difference in scattering length between protium (-0.374) and deuterium (0.667). By using heavy water as solvent and/or selective deuteration of the probed molecule (exchanging the naturally occurring protium by deuterium) this difference can be leveraged in order to image the hydrogen configuration in organic matter, which is nearly impossible with X-rays due to their small sensitivity to hydrogen's single electron. [4] On the other hand, neutron scattering studies of hydrogen-containing samples often suffer from the strong incoherent scattering of natural hydrogen.
element | protons | isotope | neutron scattering length bcoh (fm) | coherent cross-section σcoh (barn) | incoherent cross-section σinc (barn) | absorption cross-section σa (barn) |
---|---|---|---|---|---|---|
Hydrogen | 1 | 1 [2] [5] | -3.74 [1] [2] [5] [6] | 1.758 [1] | 79.7, [6] 80.27 [1] | 0.33, [6] 0.383 [1] |
Hydrogen | 1 | 2 | 6.67 [1] [2] [5] [6] | 5.592 [1] | 2.0, [6] 2.05 [1] | 0.0005 [1] [6] |
Boron | 5 | natural | 5.30 [1] | 3.54 [1] | 1.70 [1] | 767.0 [1] |
Carbon | 6 | 12 | 6.65 [1] [2] [5] [6] | 5.550 [1] | 0.0, [6] 0.001 [1] | 0.0035, [6] 0.004 [1] |
Nitrogen | 7 | 14 | 9.36, [1] 9.40, [2] 9.4 [5] [6] | 11.01 [1] | 0.3, [6] 0.5 [1] | 1.9 [1] [6] |
Oxygen | 8 | 16 | 5.80, [2] 5.8 [1] [5] [6] | 4.232 [1] | 0.0, [6] 0.000 [1] | 0.00019, [6] 0.0002 [1] |
Aluminum | 13 | natural | 3.45, [1] 3.5 [6] | 1.495 [1] | 0.0, [6] 0.008 [1] | 0.23, [6] 0.231 [1] |
Silicon | 14 | natural | 4.2 [6] [7] | 0.0 [6] | 0.17 [6] | |
Phosphorus | 15 | 30 | 5.10 [2] | |||
Sulfur | 16 | 32 | 2.80, [2] 2.8 [5] | |||
Titanium | 22 | natural | -3.44, [1] -3.4 [6] [7] | 1.485 [1] | 2.87, [1] 3.0 [6] | 6.09, [1] 6.1 [6] |
Vanadium | 23 | natural | -0.38 [1] | 0.018 [1] | 5.07 [1] | 5.08 [1] |
Chromium | 24 | natural | 3.64 [1] | 1.66 [1] | 1.83 [1] | 3.05 [1] |
Manganese | 25 | 55 (natural) | -3.73 [1] | 1.75 [1] | 0.4 [1] | 13.3 [1] |
Iron | 26 | natural | 9.45, [1] 9.5 [6] | 11.22 [1] | 0.4 [1] [6] | 2.56, [1] 2.6 [6] |
Nickel | 28 | natural | 10.3 [1] | 13.3 [1] | 5.2 [1] | 4.49 [1] |
Copper | 29 | natural | 7.72 [1] | 7.485 [1] | 0.55 [1] | 3.78 [1] |
Zirconium | 40 | natural | 7.16, [1] 0.72 [6] | 6.44 [1] | 0.02, [1] 0.3 [6] | 0.18, [6] 0.185 [1] |
Niobium | 41 | 93 (natural) | 7.054 [1] | 6.253 [1] | 0.0024 [1] | 1.15 [1] |
Molybdenum | 42 | natural | 6.72 [1] | 5.67 [1] | 0.04 [1] | 2.48 [1] |
Cadmium | 48 | natural | 4.87 [1] | 3.04 [1] | 3.46 [1] | 2520 [1] |
Tin | 50 | natural | 6.23 [1] | 4.87 [1] | 0.022 [1] | 0.626 [1] |
Cerium | 58 | natural | 4.8 [6] | 0.0 [6] | 0.63 [6] | |
Gadolinium | 64 | natural | 6.5 [1] | 29.3 [1] | 151 [1] | 49700 [1] |
Tantalum | 73 | natural | 6.91 [1] | 6.00 [1] | 0.01 [1] | 20.6 [1] |
Tungsten | 74 | natural | 4.86 [1] | 2.97 [1] | 1.63 [1] | 18.3 [1] |
Gold | 79 | 197 | 7.60 [2] | |||
Lead | 82 | natural | 9.41 [1] | 11.115 [1] | 0.003 [1] | 0.171 [1] |
Thorium | 90 | 232 (natural) | 9.8 [6] | 0.00 [6] | 7.4 [6] | |
Uranium | 92 | natural | 8.42 [1] [6] | 8.903 [1] | 0.00, [6] 0.005 [1] | 7.5, [6] 7.57 [1] |
More comprehensive data is available from NIST [8] and Atominstitut of Vienna. [9]
Atoms are the basic particles of the chemical elements. An atom consists of a nucleus of protons and generally neutrons, surrounded by an electromagnetically bound swarm of electrons. The chemical elements are distinguished from each other by the number of protons that are in their atoms. For example, any atom that contains 11 protons is sodium, and any atom that contains 29 protons is copper. Atoms with the same number of protons but a different number of neutrons are called isotopes of the same element.
A chemical element is a chemical substance that cannot be broken down into other substances by chemical reactions. The basic particle that constitutes a chemical element is the atom. Chemical elements are identified by the number of protons in the nuclei of their atoms, known as the element's atomic number. For example, oxygen has an atomic number of 8, meaning that each oxygen atom has 8 protons in its nucleus. Two or more atoms of the same element can combine to form molecules, in contrast to chemical compounds or mixtures, which contain atoms of different elements. Atoms can be transformed into different elements in nuclear reactions, which change an atom's atomic number.
Deuterium (or hydrogen-2, symbol 2
H
or D, also known as heavy hydrogen) is one of two stable isotopes of hydrogen (the other being protium, or hydrogen-1). The nucleus of a deuterium atom, called a deuteron, contains one proton and one neutron, whereas the far more common protium has no neutrons in the nucleus. Deuterium has a natural abundance in Earth's oceans of about one atom of deuterium among every 6,420 atoms of hydrogen (see heavy water). Thus deuterium accounts for approximately 0.0156% by number (0.0312% by mass) of all the naturally occurring hydrogen in the oceans (i.e., 4.85×1013 tonnes of deuterium – mainly in form of HOD and only rarely in form of D2O – in 1.4×1018 tonnes of water), while protium accounts for 99.98%. The abundance of deuterium changes slightly from one kind of natural water to another (see Vienna Standard Mean Ocean Water)
Heavy water is a form of water whose hydrogen atoms are all deuterium rather than the common hydrogen-1 isotope that makes up most of the hydrogen in normal water. The presence of the heavier hydrogen isotope gives the water different nuclear properties, and the increase in mass gives it slightly different physical and chemical properties when compared to normal water.
The neutron is a subatomic particle, symbol
n
or
n0
, which has a neutral charge, and a mass slightly greater than that of a proton. Protons and neutrons constitute the nuclei of atoms. Since protons and neutrons behave similarly within the nucleus, they are both referred to as nucleons. Nucleons have a mass of approximately one atomic mass unit, or dalton, symbol Da. Their properties and interactions are described by nuclear physics. Protons and neutrons are not elementary particles; each is composed of three quarks.
Nucleosynthesis is the process that creates new atomic nuclei from pre-existing nucleons and nuclei. According to current theories, the first nuclei were formed a few minutes after the Big Bang, through nuclear reactions in a process called Big Bang nucleosynthesis. After about 20 minutes, the universe had expanded and cooled to a point at which these high-energy collisions among nucleons ended, so only the fastest and simplest reactions occurred, leaving our universe containing hydrogen and helium. The rest is traces of other elements such as lithium and the hydrogen isotope deuterium. Nucleosynthesis in stars and their explosions later produced the variety of elements and isotopes that we have today, in a process called cosmic chemical evolution. The amounts of total mass in elements heavier than hydrogen and helium remains small, so that the universe still has approximately the same composition.
Small-angle neutron scattering (SANS) is an experimental technique that uses elastic neutron scattering at small scattering angles to investigate the structure of various substances at a mesoscopic scale of about 1–100 nm.
A neutron source is any device that emits neutrons, irrespective of the mechanism used to produce the neutrons. Neutron sources are used in physics, engineering, medicine, nuclear weapons, petroleum exploration, biology, chemistry, and nuclear power.
Neutron diffraction or elastic neutron scattering is the application of neutron scattering to the determination of the atomic and/or magnetic structure of a material. A sample to be examined is placed in a beam of thermal or cold neutrons to obtain a diffraction pattern that provides information of the structure of the material. The technique is similar to X-ray diffraction but due to their different scattering properties, neutrons and X-rays provide complementary information: X-Rays are suited for superficial analysis, strong x-rays from synchrotron radiation are suited for shallow depths or thin specimens, while neutrons having high penetration depth are suited for bulk samples.
Neutron scattering, the irregular dispersal of free neutrons by matter, can refer to either the naturally occurring physical process itself or to the man-made experimental techniques that use the natural process for investigating materials. The natural/physical phenomenon is of elemental importance in nuclear engineering and the nuclear sciences. Regarding the experimental technique, understanding and manipulating neutron scattering is fundamental to the applications used in crystallography, physics, physical chemistry, biophysics, and materials research.
Hydrogen (1H) has three naturally occurring isotopes, sometimes denoted 1
H
, 2
H
, and 3
H
. 1
H
and 2
H
are stable, while 3
H
has a half-life of 12.32(2) years. Heavier isotopes also exist, all of which are synthetic and have a half-life of less than one zeptosecond (10−21 s). Of these, 5
H
is the least stable, while 7
H
is the most.
In nuclear physics, the concept of a neutron cross section is used to express the likelihood of interaction between an incident neutron and a target nucleus. The neutron cross section σ can be defined as the area in cm2 for which the number of neutron-nuclei reactions taking place is equal to the product of the number of incident neutrons that would pass through the area and the number of target nuclei. In conjunction with the neutron flux, it enables the calculation of the reaction rate, for example to derive the thermal power of a nuclear power plant. The standard unit for measuring the cross section is the barn, which is equal to 10−28 m2 or 10−24 cm2. The larger the neutron cross section, the more likely a neutron will react with the nucleus.
Powder diffraction is a scientific technique using X-ray, neutron, or electron diffraction on powder or microcrystalline samples for structural characterization of materials. An instrument dedicated to performing such powder measurements is called a powder diffractometer.
Nuclear binding energy in experimental physics is the minimum energy that is required to disassemble the nucleus of an atom into its constituent protons and neutrons, known collectively as nucleons. The binding energy for stable nuclei is always a positive number, as the nucleus must gain energy for the nucleons to move apart from each other. Nucleons are attracted to each other by the strong nuclear force. In theoretical nuclear physics, the nuclear binding energy is considered a negative number. In this context it represents the energy of the nucleus relative to the energy of the constituent nucleons when they are infinitely far apart. Both the experimental and theoretical views are equivalent, with slightly different emphasis on what the binding energy means.
Neutron spin echo spectroscopy is an inelastic neutron scattering technique invented by Ferenc Mezei in the 1970s and developed in collaboration with John Hayter. In recognition of his work and in other areas, Mezei was awarded the first Walter Haelg Prize in 1999.
In chemistry, the hydron, informally called proton, is the cationic form of atomic hydrogen, represented with the symbol H+
. The general term "hydron", endorsed by the IUPAC, encompasses cations of hydrogen regardless of their isotopic composition: thus it refers collectively to protons (1H+) for the protium isotope, deuterons (2H+ or D+) for the deuterium isotope, and tritons (3H+ or T+) for the tritium isotope.
In physics, the atomic form factor, or atomic scattering factor, is a measure of the scattering amplitude of a wave by an isolated atom. The atomic form factor depends on the type of scattering, which in turn depends on the nature of the incident radiation, typically X-ray, electron or neutron. The common feature of all form factors is that they involve a Fourier transform of a spatial density distribution of the scattering object from real space to momentum space. For an object with spatial density distribution, , the form factor, , is defined as
Isotopes are distinct nuclear species of the same chemical element. They have the same atomic number and position in the periodic table, but differ in nucleon numbers due to different numbers of neutrons in their nuclei. While all isotopes of a given element have almost the same chemical properties, they have different atomic masses and physical properties.
Deuterium-depleted water (DDW) is water which has a lower concentration of deuterium than occurs naturally at sea level on Earth.
The discovery of the neutron and its properties was central to the extraordinary developments in atomic physics in the first half of the 20th century. Early in the century, Ernest Rutherford developed a crude model of the atom, based on the gold foil experiment of Hans Geiger and Ernest Marsden. In this model, atoms had their mass and positive electric charge concentrated in a very small nucleus. By 1920, isotopes of chemical elements had been discovered, the atomic masses had been determined to be (approximately) integer multiples of the mass of the hydrogen atom, and the atomic number had been identified as the charge on the nucleus. Throughout the 1920s, the nucleus was viewed as composed of combinations of protons and electrons, the two elementary particles known at the time, but that model presented several experimental and theoretical contradictions.