Atomic nucleus

From Wikipedia, the free encyclopedia

https://en.wikipedia.org/wiki/Atomic_nucleus 

A model of an atomic nucleus showing it as a compact bundle of protons (red) and neutrons (blue), the two types of nucleons. In this diagram, protons and neutrons look like little balls stuck together, but an actual nucleus (as understood by modern nuclear physics) cannot be explained like this, but only by using quantum mechanics. In a nucleus that occupies a certain energy level (for example, the ground state), each nucleon can be said to occupy a range of locations.

The atomic nucleus is the small, dense region consisting of protons and neutrons at the center of an atom, discovered in 1911 by Ernest Rutherford at the University of Manchester based on the 1909 Geiger–Marsden gold foil experiment. After the discovery of the neutron in 1932, models for a nucleus composed of protons and neutrons were quickly developed by Dmitri Ivanenko and Werner Heisenberg. An atom is composed of a positively charged nucleus, with a cloud of negatively charged electrons surrounding it, bound together by electrostatic force. Almost all of the mass of an atom is located in the nucleus, with a very small contribution from the electron cloud. Protons and neutrons are bound together to form a nucleus by the nuclear force.

The diameter of the nucleus is in the range of 1.70 fm (1.70×10⁻¹⁵ m) for hydrogen (the diameter of a single proton) to about 11.7 fm for uranium. These dimensions are much smaller than the diameter of the atom itself (nucleus + electron cloud), by a factor of about 26,634 (uranium atomic radius is about 156 pm (156×10⁻¹² m)) to about 60,250 (hydrogen atomic radius is about 52.92 pm).

The branch of physics involved with the study and understanding of the atomic nucleus, including its composition and the forces that bind it together, is called nuclear physics.

History

Main article: Rutherford model

The nucleus was discovered in 1911, as a result of Ernest Rutherford's efforts to test Thomson's "plum pudding model" of the atom. The electron had already been discovered by J. J. Thomson. Knowing that atoms are electrically neutral, J. J. Thomson postulated that there must be a positive charge as well. In his plum pudding model, Thomson suggested that an atom consisted of negative electrons randomly scattered within a sphere of positive charge. Ernest Rutherford later devised an experiment with his research partner Hans Geiger and with help of Ernest Marsden, that involved the deflection of alpha particles (helium nuclei) directed at a thin sheet of metal foil. He reasoned that if J. J. Thomson's model were correct, the positively charged alpha particles would easily pass through the foil with very little deviation in their paths, as the foil should act as electrically neutral if the negative and positive charges are so intimately mixed as to make it appear neutral. To his surprise, many of the particles were deflected at very large angles. Because the mass of an alpha particle is about 8000 times that of an electron, it became apparent that a very strong force must be present if it could deflect the massive and fast moving alpha particles. He realized that the plum pudding model could not be accurate and that the deflections of the alpha particles could only be explained if the positive and negative charges were separated from each other and that the mass of the atom was a concentrated point of positive charge. This justified the idea of a nuclear atom with a dense center of positive charge and mass.

Etymology

The term nucleus is from the Latin word nucleus, a diminutive of nux ('nut'), meaning 'the kernel' (i.e., the 'small nut') inside a watery type of fruit (like a peach). In 1844, Michael Faraday used the term to refer to the "central point of an atom". The modern atomic meaning was proposed by Ernest Rutherford in 1912. The adoption of the term "nucleus" to atomic theory, however, was not immediate. In 1916, for example, Gilbert N. Lewis stated, in his famous article The Atom and the Molecule, that "the atom is composed of the kernel and an outer atom or shell." Similarly, the term kern meaning kernel is used for nucleus in German and Dutch.

Principles

A figurative depiction of the helium-4 atom with the electron cloud in shades of gray. In the nucleus, the two protons and two neutrons are depicted in red and blue. This depiction shows the particles as separate, whereas in an actual helium atom, the protons are superimposed in space and most likely found at the very center of the nucleus, and the same is true of the two neutrons. Thus, all four particles are most likely found in exactly the same space, at the central point. Classical images of separate particles fail to model known charge distributions in very small nuclei. A more accurate image is that the spatial distribution of nucleons in a helium nucleus is much closer to the helium electron cloud shown here, although on a far smaller scale, than to the fanciful nucleus image. Both the helium atom and its nucleus are spherically symmetric.

The nucleus of an atom consists of neutrons and protons, which in turn are the manifestation of more elementary particles, called quarks, that are held in association by the nuclear strong force in certain stable combinations of hadrons, called baryons. The nuclear strong force extends far enough from each baryon so as to bind the neutrons and protons together against the repulsive electrical force between the positively charged protons. The nuclear strong force has a very short range, and essentially drops to zero just beyond the edge of the nucleus. The collective action of the positively charged nucleus is to hold the electrically negative charged electrons in their orbits about the nucleus. The collection of negatively charged electrons orbiting the nucleus display an affinity for certain configurations and numbers of electrons that make their orbits stable. Which chemical element an atom represents is determined by the number of protons in the nucleus; the neutral atom will have an equal number of electrons orbiting that nucleus. Individual chemical elements can create more stable electron configurations by combining to share their electrons. It is that sharing of electrons to create stable electronic orbits about the nuclei that appears to us as the chemistry of our macro world.

Protons define the entire charge of a nucleus, and hence its chemical identity. Neutrons are electrically neutral, but contribute to the mass of a nucleus to nearly the same extent as the protons. Neutrons can explain the phenomenon of isotopes (same atomic number with different atomic mass). The main role of neutrons is to reduce electrostatic repulsion inside the nucleus.

Composition and shape

Protons and neutrons are fermions, with different values of the strong isospin quantum number, so two protons and two neutrons can share the same space wave function since they are not identical quantum entities. They are sometimes viewed as two different quantum states of the same particle, the nucleon. Two fermions, such as two protons, or two neutrons, or a proton + neutron (the deuteron) can exhibit bosonic behavior when they become loosely bound in pairs, which have integer spin.

In the rare case of a hypernucleus, a third baryon called a hyperon, containing one or more strange quarks and/or other unusual quark(s), can also share the wave function. However, this type of nucleus is extremely unstable and not found on Earth except in high-energy physics experiments.

The neutron has a positively charged core of radius ≈ 0.3 fm surrounded by a compensating negative charge of radius between 0.3 fm and 2 fm. The proton has an approximately exponentially decaying positive charge distribution with a mean square radius of about 0.8 fm.

The shape of the atomic nucleus can be spherical, rugby ball-shaped (prolate deformation), discus-shaped (oblate deformation), triaxial (a combination of oblate and prolate deformation) or pear-shaped.

Forces

Nuclei are bound together by the residual strong force (nuclear force). The residual strong force is a minor residuum of the strong interaction which binds quarks together to form protons and neutrons. This force is much weaker between neutrons and protons because it is mostly neutralized within them, in the same way that electromagnetic forces between neutral atoms (such as van der Waals forces that act between two inert gas atoms) are much weaker than the electromagnetic forces that hold the parts of the atoms together internally (for example, the forces that hold the electrons in an inert gas atom bound to its nucleus).

The nuclear force is highly attractive at the distance of typical nucleon separation, and this overwhelms the repulsion between protons due to the electromagnetic force, thus allowing nuclei to exist. However, the residual strong force has a limited range because it decays quickly with distance (see Yukawa potential); thus only nuclei smaller than a certain size can be completely stable. The largest known completely stable nucleus (i.e. stable to alpha, beta, and gamma decay) is lead-208 which contains a total of 208 nucleons (126 neutrons and 82 protons). Nuclei larger than this maximum are unstable and tend to be increasingly short-lived with larger numbers of nucleons. However, bismuth-209 is also stable to beta decay and has the longest half-life to alpha decay of any known isotope, estimated at a billion times longer than the age of the universe.

The residual strong force is effective over a very short range (usually only a few femtometres (fm); roughly one or two nucleon diameters) and causes an attraction between any pair of nucleons. For example, between a proton and a neutron to form a deuteron [NP], and also between protons and protons, and neutrons and neutrons.

Halo nuclei and nuclear force range limits

The effective absolute limit of the range of the nuclear force (also known as residual strong force) is represented by halo nuclei such as lithium-11 or boron-14, in which dineutrons, or other collections of neutrons, orbit at distances of about 10 fm (roughly similar to the 8 fm radius of the nucleus of uranium-238). These nuclei are not maximally dense. Halo nuclei form at the extreme edges of the chart of the nuclides—the neutron drip line and proton drip line—and are all unstable with short half-lives, measured in milliseconds; for example, lithium-11 has a half-life of 8.8 ms.

Halos in effect represent an excited state with nucleons in an outer quantum shell which has unfilled energy levels "below" it (both in terms of radius and energy). The halo may be made of either neutrons [NN, NNN] or protons [PP, PPP]. Nuclei which have a single neutron halo include ¹¹Be and ¹⁹C. A two-neutron halo is exhibited by ⁶He, ¹¹Li, ¹⁷B, ¹⁹B and ²²C. Two-neutron halo nuclei break into three fragments, never two, and are called Borromean nuclei because of this behavior (referring to a system of three interlocked rings in which breaking any ring frees both of the others). ⁸He and ¹⁴Be both exhibit a four-neutron halo. Nuclei which have a proton halo include ⁸B and ²⁶P. A two-proton halo is exhibited by ¹⁷Ne and ²⁷S. Proton halos are expected to be more rare and unstable than the neutron examples, because of the repulsive electromagnetic forces of the halo proton(s).

Nuclear models

Main article: Nuclear structure

Although the standard model of physics is widely believed to completely describe the composition and behavior of the nucleus, generating predictions from theory is much more difficult than for most other areas of particle physics. This is due to two reasons:

• In principle, the physics within a nucleus can be derived entirely from quantum chromodynamics (QCD). In practice however, current computational and mathematical approaches for solving QCD in low-energy systems such as the nuclei are extremely limited. This is due to the phase transition that occurs between high-energy quark matter and low-energy hadronic matter, which renders perturbative techniques unusable, making it difficult to construct an accurate QCD-derived model of the forces between nucleons. Current approaches are limited to either phenomenological models such as the Argonne v18 potential or chiral effective field theory.
• Even if the nuclear force is well constrained, a significant amount of computational power is required to accurately compute the properties of nuclei ab initio. Developments in many-body theory have made this possible for many low mass and relatively stable nuclei, but further improvements in both computational power and mathematical approaches are required before heavy nuclei or highly unstable nuclei can be tackled.

Historically, experiments have been compared to relatively crude models that are necessarily imperfect. None of these models can completely explain experimental data on nuclear structure.

The nuclear radius (R) is considered to be one of the basic quantities that any model must predict. For stable nuclei (not halo nuclei or other unstable distorted nuclei) the nuclear radius is roughly proportional to the cube root of the mass number (A) of the nucleus, and particularly in nuclei containing many nucleons, as they arrange in more spherical configurations:

The stable nucleus has approximately a constant density and therefore the nuclear radius R can be approximated by the following formula,

${\displaystyle R=r_0{A}^{1/3}}$

where A = Atomic mass number (the number of protons Z, plus the number of neutrons N) and r₀ = 1.25 fm = 1.25 × 10⁻¹⁵ m. In this equation, the "constant" r₀ varies by 0.2 fm, depending on the nucleus in question, but this is less than 20% change from a constant.

In other words, packing protons and neutrons in the nucleus gives approximately the same total size result as packing hard spheres of a constant size (like marbles) into a tight spherical or almost spherical bag (some stable nuclei are not quite spherical, but are known to be prolate).

Models of nuclear structure include:

Cluster model

The cluster model describes the nucleus as a molecule-like collection of proton-neutron groups (e.g., alpha particles) with one or more valence neutrons occupying molecular orbitals.

Liquid drop model

Main article: Semi-empirical mass formula

Early models of the nucleus viewed the nucleus as a rotating liquid drop. In this model, the trade-off of long-range electromagnetic forces and relatively short-range nuclear forces, together cause behavior which resembled surface tension forces in liquid drops of different sizes. This formula is successful at explaining many important phenomena of nuclei, such as their changing amounts of binding energy as their size and composition changes (see semi-empirical mass formula), but it does not explain the special stability which occurs when nuclei have special "magic numbers" of protons or neutrons.

The terms in the semi-empirical mass formula, which can be used to approximate the binding energy of many nuclei, are considered as the sum of five types of energies (see below). Then the picture of a nucleus as a drop of incompressible liquid roughly accounts for the observed variation of binding energy of the nucleus:

Volume energy. When an assembly of nucleons of the same size is packed together into the smallest volume, each interior nucleon has a certain number of other nucleons in contact with it. So, this nuclear energy is proportional to the volume.

Surface energy. A nucleon at the surface of a nucleus interacts with fewer other nucleons than one in the interior of the nucleus and hence its binding energy is less. This surface energy term takes that into account and is therefore negative and is proportional to the surface area.

Coulomb energy. The electric repulsion between each pair of protons in a nucleus contributes toward decreasing its binding energy.

Asymmetry energy (also called Pauli Energy). An energy associated with the Pauli exclusion principle. Were it not for the Coulomb energy, the most stable form of nuclear matter would have the same number of neutrons as protons, since unequal numbers of neutrons and protons imply filling higher energy levels for one type of particle, while leaving lower energy levels vacant for the other type.

Pairing energy. An energy which is a correction term that arises from the tendency of proton pairs and neutron pairs to occur. An even number of particles is more stable than an odd number.

Shell models and other quantum models

Main article: Nuclear shell model

A number of models for the nucleus have also been proposed in which nucleons occupy orbitals, much like the atomic orbitals in atomic physics theory. These wave models imagine nucleons to be either sizeless point particles in potential wells, or else probability waves as in the "optical model", frictionlessly orbiting at high speed in potential wells.

In the above models, the nucleons may occupy orbitals in pairs, due to being fermions, which allows explanation of even/odd Z and N effects well known from experiments. The exact nature and capacity of nuclear shells differs from those of electrons in atomic orbitals, primarily because the potential well in which the nucleons move (especially in larger nuclei) is quite different from the central electromagnetic potential well which binds electrons in atoms. Some resemblance to atomic orbital models may be seen in a small atomic nucleus like that of helium-4, in which the two protons and two neutrons separately occupy 1s orbitals analogous to the 1s orbital for the two electrons in the helium atom, and achieve unusual stability for the same reason. Nuclei with 5 nucleons are all extremely unstable and short-lived, yet, helium-3, with 3 nucleons, is very stable even with lack of a closed 1s orbital shell. Another nucleus with 3 nucleons, the triton hydrogen-3 is unstable and will decay into helium-3 when isolated. Weak nuclear stability with 2 nucleons {NP} in the 1s orbital is found in the deuteron hydrogen-2, with only one nucleon in each of the proton and neutron potential wells. While each nucleon is a fermion, the {NP} deuteron is a boson and thus does not follow Pauli Exclusion for close packing within shells. Lithium-6 with 6 nucleons is highly stable without a closed second 1p shell orbital. For light nuclei with total nucleon numbers 1 to 6 only those with 5 do not show some evidence of stability. Observations of beta-stability of light nuclei outside closed shells indicate that nuclear stability is much more complex than simple closure of shell orbitals with magic numbers of protons and neutrons.

For larger nuclei, the shells occupied by nucleons begin to differ significantly from electron shells, but nevertheless, present nuclear theory does predict the magic numbers of filled nuclear shells for both protons and neutrons. The closure of the stable shells predicts unusually stable configurations, analogous to the noble group of nearly-inert gases in chemistry. An example is the stability of the closed shell of 50 protons, which allows tin to have 10 stable isotopes, more than any other element. Similarly, the distance from shell-closure explains the unusual instability of isotopes which have far from stable numbers of these particles, such as the radioactive elements 43 (technetium) and 61 (promethium), each of which is preceded and followed by 17 or more stable elements.

There are however problems with the shell model when an attempt is made to account for nuclear properties well away from closed shells. This has led to complex post hoc distortions of the shape of the potential well to fit experimental data, but the question remains whether these mathematical manipulations actually correspond to the spatial deformations in real nuclei. Problems with the shell model have led some to propose realistic two-body and three-body nuclear force effects involving nucleon clusters and then build the nucleus on this basis. Three such cluster models are the 1936 Resonating Group Structure model of John Wheeler, Close-Packed Spheron Model of Linus Pauling and the 2D Ising Model of MacGregor.

Dye laser

From Wikipedia, the free encyclopedia

https://en.wikipedia.org/wiki/Dye_laser 

Close-up of a table-top CW dye laser based on rhodamine 6G, emitting at 580 nm (yellow). The emitted laser beam is visible as faint yellow lines between the yellow window (center) and the yellow optics (upper-right), where it reflects down across the image to an unseen mirror, and back into the dye jet from the lower left corner. The orange dye-solution enters the laser from the left and exits to the right, still glowing from triplet phosphorescence, and is pumped by a 514 nm (blue-green) beam from an argon laser. The pump laser can be seen entering the dye jet, beneath the yellow window.

A dye laser is a laser that uses an organic dye as the lasing medium, usually as a liquid solution. Compared to gases and most solid state lasing media, a dye can usually be used for a much wider range of wavelengths, often spanning 50 to 100 nanometers or more. The wide bandwidth makes them particularly suitable for tunable lasers and pulsed lasers. The dye rhodamine 6G, for example, can be tuned from 635 nm (orangish-red) to 560 nm (greenish-yellow), and produce pulses as short as 16 femtoseconds. Moreover, the dye can be replaced by another type in order to generate an even broader range of wavelengths with the same laser, from the near-infrared to the near-ultraviolet, although this usually requires replacing other optical components in the laser as well, such as dielectric mirrors or pump lasers.

Dye lasers were independently discovered by P. P. Sorokin and F. P. Schäfer (and colleagues) in 1966.

In addition to the usual liquid state, dye lasers are also available as solid state dye lasers (SSDL). These SSDL lasers use dye-doped organic matrices as gain medium.

Construction

The internal cavity of a linear dye-laser, showing the beam path. The pump laser (green) enters the dye cell from the left. The emitted beam exits to the right (lower yellow beam) through a cavity dumper (not shown). A diffraction grating is used as the high-reflector (upper yellow beam, left side). The two meter beam is redirected several times by mirrors and prisms, which reduce the overall length, expand or focus the beam for various parts of the cavity, and eliminate one of two counter-propagating waves produced by the dye cell. The laser is capable of continuous wave operation or ultrashort picosecond pulses (trillionth of a second, equating to a beam less than ⁠1/3⁠ of a millimeter in length).

A ring dye laser. P-pump laser beam; G-gain dye jet; A-saturable absorber dye jet; M0, M1, M2-planar mirrors; OC–output coupler; CM1 to CM4-curved mirrors.

A dye laser uses a gain medium consisting of an organic dye, which is a carbon-based, soluble stain that is often fluorescent, such as the dye in a highlighter pen. The dye is mixed with a compatible solvent, allowing the molecules to diffuse evenly throughout the liquid. The dye solution may be circulated through a dye cell, or streamed through open air using a dye jet. A high energy source of light is needed to 'pump' the liquid beyond its lasing threshold. A fast discharge flashtube or an external laser is usually used for this purpose. Mirrors are also needed to oscillate the light produced by the dye's fluorescence, which is amplified with each pass through the liquid. The output mirror is normally around 80% reflective, while all other mirrors are usually more than 99.9% reflective. The dye solution is usually circulated at high speeds, to help avoid triplet absorption and to decrease degradation of the dye. A prism or diffraction grating is usually mounted in the beam path, to allow tuning of the beam.

Because the liquid medium of a dye laser can fit any shape, there are a multitude of different configurations that can be used. A Fabry–Pérot laser cavity is usually used for flashtube pumped lasers, which consists of two mirrors, which may be flat or curved, mounted parallel to each other with the laser medium in between. The dye cell is often a thin tube approximately equal in length to the flashtube, with both windows and an inlet/outlet for the liquid on each end. The dye cell is usually side-pumped, with one or more flashtubes running parallel to the dye cell in a reflector cavity. The reflector cavity is often water cooled, to prevent thermal shock in the dye caused by the large amounts of near-infrared radiation which the flashtube produces. Axial pumped lasers have a hollow, annular-shaped flashtube that surrounds the dye cell, which has lower inductance for a shorter flash, and improved transfer efficiency. Coaxial pumped lasers have an annular dye cell that surrounds the flashtube, for even better transfer efficiency, but have a lower gain due to diffraction losses. Flash pumped lasers can be used only for pulsed output applications.

A ring laser design is often chosen for continuous operation, although a Fabry–Pérot design is sometimes used. In a ring laser, the mirrors of the laser are positioned to allow the beam to travel in a circular path. The dye cell, or cuvette, is usually very small. Sometimes a dye jet is used to help avoid reflection losses. The dye is usually pumped with an external laser, such as a nitrogen, excimer, or frequency doubled Nd:YAG laser. The liquid is circulated at very high speeds, to prevent triplet absorption from cutting off the beam. Unlike Fabry–Pérot cavities, a ring laser does not generate standing waves which cause spatial hole burning, a phenomenon where energy becomes trapped in unused portions of the medium between the crests of the wave. This leads to a better gain from the lasing medium.

Operation

The dyes used in these lasers contain rather large organic molecules which fluoresce. Most dyes have a very short time between the absorption and emission of light, referred to as the fluorescence lifetime, which is often on the order of a few nanoseconds. (In comparison, most solid-state lasers have a fluorescence lifetime ranging from hundreds of microseconds to a few milliseconds.) Under standard laser-pumping conditions, the molecules emit their energy before a population inversion can properly build up, so dyes require rather specialized means of pumping. Liquid dyes have an extremely high lasing threshold. In addition, the large molecules are subject to complex excited state transitions during which the spin can be "flipped", quickly changing from the useful, fast-emitting "singlet" state to the slower "triplet" state.

The incoming light excites the dye molecules into the state of being ready to emit stimulated radiation; the singlet state. In this state, the molecules emit light via fluorescence, and the dye is transparent to the lasing wavelength. Within a microsecond or less, the molecules will change to their triplet state. In the triplet state, light is emitted via phosphorescence, and the molecules absorb the lasing wavelength, making the dye partially opaque. Flashlamp-pumped lasers need a flash with an extremely short duration, to deliver the large amounts of energy necessary to bring the dye past threshold before triplet absorption overcomes singlet emission. Dye lasers with an external pump-laser can direct enough energy of the proper wavelength into the dye with a relatively small amount of input energy, but the dye must be circulated at high speeds to keep the triplet molecules out of the beam path. Due to their high absorption, the pumping energy may often be concentrated into a rather small volume of liquid.

Since organic dyes tend to decompose under the influence of light, the dye solution is normally circulated from a large reservoir. The dye solution can be flowing through a cuvette, i.e., a glass container, or be as a dye jet, i.e., as a sheet-like stream in open air from a specially-shaped nozzle. With a dye jet, one avoids reflection losses from the glass surfaces and contamination of the walls of the cuvette. These advantages come at the cost of a more-complicated alignment.

Liquid dyes have very high gain as laser media. The beam needs to make only a few passes through the liquid to reach full design power, and hence, the high transmittance of the output coupler. The high gain also leads to high losses, because reflections from the dye-cell walls or flashlamp reflector cause parasitic oscillations, dramatically reducing the amount of energy available to the beam. Pump cavities are often coated, anodized, or otherwise made of a material that will not reflect at the lasing wavelength while reflecting at the pump wavelength.

A benefit of organic dyes is their high fluorescence efficiency. The greatest losses in many lasers and other fluorescence devices is not from the transfer efficiency (absorbed versus reflected/transmitted energy) or quantum yield (emitted number of photons per absorbed number), but from the losses when high-energy photons are absorbed and reemitted as photons of longer wavelengths. Because the energy of a photon is determined by its wavelength, the emitted photons will be of lower energy; a phenomenon called the Stokes shift. The absorption centers of many dyes are very close to the emission centers. Sometimes the two are close enough that the absorption profile slightly overlaps the emission profile. As a result, most dyes exhibit very small Stokes shifts and consequently allow for lower energy losses than many other laser types due to this phenomenon. The wide absorption profiles make them particularly suited to broadband pumping, such as from a flashtube. It also allows a wide range of pump lasers to be used for any certain dye and, conversely, many different dyes can be used with a single pump laser.

• 
  A cuvette used in a dye laser. A thin sheet of liquid is passed between the windows at high speeds. The windows are set at Brewster's angle (air-to-glass interface) for the pump laser, and at Brewster's angle (liquid-to-glass interface) for the emitted beam.
   
• 
  Stokes shift in Rhodamine 6G during broadband absorption/emission. In laser operation, the Stokes shift is the difference between the pump wavelength and the output.

CW dye lasers

Continuous-wave (CW) dye lasers often use a dye jet. CW dye-lasers can have a linear or a ring cavity, and provided the foundation for the development of femtosecond lasers.

Narrow linewidth dye lasers

Multiple prisms expand the beam in one direction, providing better illumination of a diffraction grating. Depending on the angle unwanted wavelengths are dispersed, so are used to tune the output of a dye laser, often to a linewidth of a fraction of an angstrom.

Dye lasers' emission is inherently broad. However, tunable narrow linewidth emission has been central to the success of the dye laser. In order to produce narrow bandwidth tuning these lasers use many types of cavities and resonators which include gratings, prisms, multiple-prism grating arrangements, and etalons.

The first narrow linewidth dye laser, introduced by Hänsch, used a Galilean telescope as beam expander to illuminate the diffraction grating. Next were the grazing-incidence grating designs and the multiple-prism grating configurations. The various resonators and oscillator designs developed for dye lasers have been successfully adapted to other laser types such as the diode laser. The physics of narrow-linewidth multiple-prism grating lasers was explained by Duarte and Piper.

Chemicals used

Rhodamine 6G Chloride powder; mixed with methanol; emitting yellow light under the influence of a green laser

Some of the laser dyes are rhodamine (orange, 540–680 nm), fluorescein (green, 530–560 nm), coumarin (blue 490–620 nm), stilbene (violet 410–480 nm), umbelliferone (blue, 450–470 nm), tetracene, malachite green, and others. While some dyes are actually used in food coloring, most dyes are very toxic, and often carcinogenic. Many dyes, such as rhodamine 6G, (in its chloride form), can be very corrosive to all metals except stainless steel. Although dyes have very broad fluorescence spectra, the dye's absorption and emission will tend to center on a certain wavelength and taper off to each side, forming a tunability curve, with the absorption center being of a shorter wavelength than the emission center. Rhodamine 6G, for example, has its highest output around 590 nm, and the conversion efficiency lowers as the laser is tuned to either side of this wavelength.

A wide variety of solvents can be used, although most dyes will dissolve better in some solvents than in others. Some of the solvents used are water, glycol, ethanol, methanol, hexane, cyclohexane, cyclodextrin, and many others. Solvents can be highly toxic, and can sometimes be absorbed directly through the skin, or through inhaled vapors. Many solvents are also extremely flammable. The various solvents can also have an effect on the specific color of the dye solution, the lifetime of the singlet state, either enhancing or quenching the triplet state, and, thus, on the lasing bandwidth and power obtainable with a particular laser-pumping source.

Adamantane is added to some dyes to prolong their life.

Cycloheptatriene and cyclooctatetraene (COT) can be added as triplet quenchers for rhodamine G, increasing the laser output power. Output power of 1.4 kilowatt at 585 nm was achieved using Rhodamine 6G with COT in methanol-water solution.

Excitation lasers

Flashlamps and several types of lasers can be used to optically pump dye lasers. A partial list of excitation lasers include:

• Copper vapor lasers
• Diode lasers
• Excimer lasers
• Nd:YAG lasers (mainly second and third harmonics)
• Nitrogen lasers
• Ruby lasers
• Argon ion lasers in the CW regime
• Krypton ion lasers in the CW regime

Ultra-short optical pulses

R. L. Fork, B. I. Greene, and C. V. Shank demonstrated, in 1981, the generation of ultra-short laser pulse using a ring-dye laser (or dye laser exploiting colliding pulse mode-locking). This kind of laser is capable of generating laser pulses of ~ 0.1 ps duration.

The introduction of grating techniques and intra-cavity prismatic pulse compressors eventually resulted in the routine emission of femtosecond dye laser pulses.

Applications

An atomic vapor laser isotope separation experiment at LLNL. Green light is from a copper vapor pump laser used to pump a highly tuned dye laser which is producing the orange light.

Dye lasers are very versatile. In addition to their recognized wavelength agility these lasers can offer very large pulsed energies or very high average powers. Flashlamp-pumped dye lasers have been shown to yield hundreds of Joules per pulse and copper-laser-pumped dye lasers are known to yield average powers in the kilowatt regime.

Dye lasers are used in many applications including:

• astronomy (as laser guide stars),
• atomic vapor laser isotope separation
• manufacturing
• medicine
• spectroscopy

In laser medicine these lasers are applied in several areas, including dermatology where they are used to make skin tone more even. The wide range of wavelengths possible allows very close matching to the absorption lines of certain tissues, such as melanin or hemoglobin, while the narrow bandwidth obtainable helps reduce the possibility of damage to the surrounding tissue. They are used to treat port-wine stains and other blood vessel disorders, scars and kidney stones. They can be matched to a variety of inks for tattoo removal, as well as a number of other applications.

In spectroscopy, dye lasers can be used to study the absorption and emission spectra of various materials. Their tunability, (from the near-infrared to the near-ultraviolet), narrow bandwidth, and high intensity allows a much greater diversity than other light sources. The variety of pulse widths, from ultra-short, femtosecond pulses to continuous-wave operation, makes them suitable for a wide range of applications, from the study of fluorescent lifetimes and semiconductor properties to lunar laser ranging experiments.

Tunable lasers are used in swept-frequency metrology to enable measurement of absolute distances with very high accuracy. A two axis interferometer is set up and by sweeping the frequency, the frequency of the light returning from the fixed arm is slightly different from the frequency returning from the distance measuring arm. This produces a beat frequency which can be detected and used to determine the absolute difference between the lengths of the two arms.

Baryogenesis

From Wikipedia, the free encyclopedia
https://en.wikipedia.org/wiki/Baryogenesis

In physical cosmology, baryogenesis (also known as baryosynthesis) is the physical process that is hypothesized to have taken place during the early universe to produce baryonic asymmetry, the observation that only matter (baryons) and not antimatter (antibaryons) is detected in universe other than in cosmic ray collisions. Since it is assumed in cosmology that the particles we see were created using the same physics we measure today, and in particle physics experiments today matter and antimatter are always symmetric, the dominance of matter over antimatter is unexplained.

A number of theoretical mechanisms are proposed to account for this discrepancy, namely identifying conditions that favour symmetry breaking and the creation of normal matter (as opposed to antimatter). This imbalance has to be exceptionally small, on the order of 1 in every 1630000000 (≈2×10⁹) particles a small fraction of a second after the Big Bang. After most of the matter and antimatter was annihilated, what remained was all the baryonic matter in the current universe, along with a much greater number of bosons. Experiments reported in 2010 at Fermilab, however, seem to show that this imbalance is much greater than previously assumed. These experiments involved a series of particle collisions and found that the amount of generated matter was approximately 1% larger than the amount of generated antimatter. The reason for this discrepancy is not yet known.

Most grand unified theories explicitly break the baryon number symmetry, which would account for this discrepancy, typically invoking reactions mediated by very massive X bosons (X) or massive Higgs bosons (H⁰
). The rate at which these events occur is governed largely by the mass of the intermediate X or H⁰
particles, so by assuming these reactions are responsible for the majority of the baryon number seen today, a maximum mass can be calculated above which the rate would be too slow to explain the presence of matter today. These estimates predict that a large volume of material will occasionally exhibit a spontaneous proton decay, which has not been observed. Therefore, the imbalance between matter and antimatter remains a mystery.

Baryogenesis theories are based on different descriptions of the interaction between fundamental particles. Two main theories are electroweak baryogenesis, which would occur during the electroweak phase transition, and the GUT baryogenesis, which would occur during or shortly after the grand unification epoch. Quantum field theory and statistical physics are used to describe such possible mechanisms.

Baryogenesis is followed by primordial nucleosynthesis, when atomic nuclei began to form.

Background

The majority of ordinary matter in the universe is found in atomic nuclei, which are made of neutrons and protons. There is no evidence of primordial antimatter. In the universe about 1 in 10,000 protons are antiprotons, consistent with ongoing production due to cosmic rays. Possible domains of antimatter in other parts of the universe is inconsistent with the lack of measurable of gamma radiation background.

Furthermore, accurate predictions of Big Bang nucleosynthesis depend upon the value of the baryon asymmetry factor (see § Relation to Big Bang nucleosynthesis). The match between the predictions and observations of the nucleosynthesis model constrains the value of this baryon asymmetry factor. In particular, if the model computed with equal amounts of baryons and antibaryons, they annihilate each other so completely that not enough baryons are left to create nucleons.

There are two main interpretations for this disparity: either the universe began with a small preference for matter (total baryonic number of the universe different from zero), or the universe was originally perfectly symmetric, but somehow a set of particle physics phenomena contributed to a small imbalance in favour of matter over time. The goal of cosmological theories of baryogenesis is to explain the baryon asymmetry factor using quantum field theory of elementary particles.

Sakharov conditions

In 1967, Andrei Sakharov proposed a set of three necessary conditions that a baryon-generating interaction must satisfy to produce matter and antimatter at different rates. These conditions were inspired by the recent discoveries of the cosmic microwave background and CP-violation in the neutral kaon system. The three necessary "Sakharov conditions" are:

• Baryon number ${\displaystyle B}$ violation.
• C-symmetry and CP-symmetry violation.
• Interactions out of thermal equilibrium.

Baryon number violation is a necessary condition to produce an excess of baryons over anti-baryons. But C-symmetry violation is also needed so that the interactions which produce more baryons than anti-baryons will not be counterbalanced by interactions which produce more anti-baryons than baryons. CP-symmetry violation is similarly required because otherwise equal numbers of left-handed baryons and right-handed anti-baryons would be produced, as well as equal numbers of left-handed anti-baryons and right-handed baryons.  Finally, the last condition, known as the out-of-equilibrium decay scenario, states that the rate of a reaction which generates baryon-asymmetry must be less than the rate of expansion of the universe. This ensures the particles and their corresponding antiparticles do not achieve thermal equilibrium due to rapid expansion decreasing the occurrence of pair-annihilation. The interactions must be out of thermal equilibrium at the time of the baryon-number and C/CP symmetry violating decay occurs to generate the asymmetry.

In the Standard Model

The Standard Model can incorporate baryogenesis, though the amount of net baryons (and leptons) thus created may not be sufficient to account for the present baryon asymmetry. There is a required one excess quark per billion quark-antiquark pairs in the early universe in order to provide all the observed matter in the universe. This insufficiency has not yet been explained, theoretically or otherwise.

Baryogenesis within the Standard Model requires the electroweak symmetry breaking to be a first-order cosmological phase transition, since otherwise sphalerons wipe out any baryon asymmetry that happened up to the phase transition. Beyond this, the remaining amount of baryon non-conserving interactions is negligible.

The phase transition domain wall breaks the P-symmetry spontaneously, allowing for CP-symmetry violating interactions to break C-symmetry on both its sides. Quarks tend to accumulate on the broken phase side of the domain wall, while anti-quarks tend to accumulate on its unbroken phase side. Due to CP-symmetry violating electroweak interactions, some amplitudes involving quarks are not equal to the corresponding amplitudes involving anti-quarks, but rather have opposite phase (see CKM matrix and Kaon); since time reversal takes an amplitude to its complex conjugate, CPT-symmetry is conserved in this entire process.

Though some of their amplitudes have opposite phases, both quarks and anti-quarks have positive energy, and hence acquire the same phase as they move in space-time. This phase also depends on their mass, which is identical but depends both on flavor and on the Higgs VEV which changes along the domain wall. Thus certain sums of amplitudes for quarks have different absolute values compared to those of anti-quarks. In all, quarks and anti-quarks may have different reflection and transmission probabilities through the domain wall, and it turns out that more quarks coming from the unbroken phase are transmitted compared to anti-quarks.

Thus there is a net baryonic flux through the domain wall. Due to sphaleron transitions, which are abundant in the unbroken phase, the net anti-baryonic content of the unbroken phase is wiped out as anti-baryons are transformed into leptons. However, sphalerons are rare enough in the broken phase as not to wipe out the excess of baryons there. In total, there is net creation of baryons (as well as leptons).

In this scenario, non-perturbative electroweak interactions (i.e. the sphaleron) are responsible for the B-violation, the perturbative electroweak Lagrangian is responsible for the CP-violation, and the domain wall is responsible for the lack of thermal equilibrium and the P-violation; together with the CP-violation it also creates a C-violation in each of its sides.

Relation to Big Bang nucleosynthesis

See also: Baryon asymmetry

The central question to baryogenesis is what causes the preference for matter over antimatter in the universe, as well as the magnitude of this asymmetry. An important quantifier is the asymmetry parameter, given by

$${\displaystyle \eta =\frac{n_{\text{B}}-n_{\overline{\text{B}}}}{n_{\gamma }},}$$ where n_B and n_B refer to the number density of baryons and antibaryons respectively and n_γ is the number density of cosmic background radiation photons.

According to the Big Bang model, matter decoupled from the cosmic background radiation (CBR) at a temperature of roughly 3000 kelvin, corresponding to an average kinetic energy of 3000 K / (10.08×10³ K/eV) = 0.3 eV. After the decoupling, the total number of CBR photons remains constant. Therefore, due to space-time expansion, the photon density decreases. The photon density at equilibrium temperature T is given by $${\displaystyle \begin{array}{rl}{n}_{\gamma }& =\frac{1}{{\pi }^2}{\left(\frac{k_{\text{B}}T}{\hslash c}\right)}^3{\int }_0^{\mathrm{\infty }}\frac{x^2}{e^x-1}dx\\ & =\frac{2\zeta (3)}{{\pi }^2}{\left(\frac{k_{\text{B}}T}{\hslash c}\right)}^3\\ & \approx 20.3{\left(\frac{T}{1\mathrm{K}}\right)}^3{\text{cm}}^{-3},\end{array}}$$ with k_B as the Boltzmann constant, ħ as the Planck constant divided by 2π and c as the speed of light in vacuum, and ζ(3) as Apéry's constant. At the current CBR photon temperature of 2.725 K, this corresponds to a photon density n_γ of around 411 CBR photons per cubic centimeter.

Therefore, the asymmetry parameter η, as defined above, is not the "best" parameter. Instead, the preferred asymmetry parameter uses the entropy density s, $${\displaystyle {\eta }_s=\frac{n_{\text{B}}-n_{\overline{\text{B}}}}{s}}$$ because the entropy density of the universe remained reasonably constant throughout most of its evolution. The entropy density is $${\displaystyle s\stackrel{\mathrm{d}\mathrm{e}\mathrm{f}}{=}\frac{\mathrm{e}\mathrm{n}\mathrm{t}\mathrm{r}\mathrm{o}\mathrm{p}\mathrm{y}}{\mathrm{v}\mathrm{o}\mathrm{l}\mathrm{u}\mathrm{m}\mathrm{e}}=\frac{p+\rho }{T}=\frac{2{\pi }^2}{45}{g}_{\text{⁎}}(T)T^3,}$$ with p and ρ as the pressure and density from the energy density tensor T_μν, and g_⁎ as the effective number of degrees of freedom for "massless" particles at temperature T (in so far as mc² ≪ k_BT holds), $${\displaystyle g_{\text{⁎}}(T)=\sum _{i=\mathrm{b}\mathrm{o}\mathrm{s}\mathrm{o}\mathrm{n}\mathrm{s}}{g}_i{\left(\frac{T_i}{T}\right)}^3+\frac{7}{8}\sum _{j=\mathrm{f}\mathrm{e}\mathrm{r}\mathrm{m}\mathrm{i}\mathrm{o}\mathrm{n}\mathrm{s}}{g}_j{\left(\frac{T_j}{T}\right)}^3,}$$ for bosons and fermions with g_i and g_j degrees of freedom at temperatures T_i and T_j respectively. At the present epoch, s = 7.04 n_γ.

Other models

B-meson decay

Another possible explanation for the cause of baryogenesis is the decay reaction of B-mesogenesis. This phenomenon suggests that in the early universe, particles such as the B-meson decay into a visible Standard Model baryon as well as a dark antibaryon that is invisible to current observation techniques.

Asymmetric Dark Matter

The asymmetric dark matter proposal investigates mechanisms that would explain the abundance of dark matter but lack of dark antimatter as the consequence of the same effect as would explain baryogenesis.