Encyclopedia of Science & Technology Volume 9.pdf

Encyclopedia of Science & Technology Volume 9.pdf - I...

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Unformatted text preview: I I–spin — Ixodides I-spin A quantum-mechanical variable or quantum number applied to quarks and their compounds, the strongly interacting fundamental hadrons, and the compounds of those hadrons (such as nuclear states) to facilitate consideration of the consequences of the charge independence of the strong (nuclear) forces. This variable is also known as isotopic spin, isobaric spin, and isospin. The many strongly interacting particles (hadrons) and the compounds of these particles, such as nuclei, are observed to form sets or multiplets such that the members of the multiplet differ in their electric charge and magnetic moments, and other electromagnetic properties but are otherwise almost identical. For example, the neutron and proton, with electric charges that are zero and plus one (in units of the magnitude of the electron charge), form a set of two such states. The pions, one with a unit of positive charge, one with zero charge, and one with a unit of negative charge, form a set of three. It appears that if the effects of electromagnetic forces and the closely related weak nuclear forces (responsible for beta decay) are neglected, leaving only the strong forces effective, the different members of such a multiplet are equivalent and cannot be distinguished in their strong interactions. The strong interactions are thus independent of the different electric charges held by different members of the set; they are charge-independent. See ELEMENTARY PARTICLE; FUNDAMENTAL INTERACTIONS; HADRON; STRONG NUCLEAR INTERACTIONS. The I-spin (I) of such a set or multiplet of equivalent states is defined such that Eq. (1) is satisfied, N = 2I + 1 (1) where N is the number of states in the set. Another quantum number I3, called the third component of I-spin, is used to differentiate the numbers of a multi- plet where the values of I3 vary from +I to −I in units of one. The charge Q of a state and the value of I3 for this state are connected by the Gell-Mann-Okubo relation, Eq. (2), where Y, the charge offset, is called Q = I3 + Y 2 (2) hypercharge. For nuclear states, Y is simply the number of nucleons. Electric charge is conserved in all interactions; Y is observed to be conserved by the strong forces so that I3 is conserved in the course of interactions mediated by the strong forces. See HYPERCHARGE. Similarity to spin. This description of a multiplet of states with I-spin is similar to the quantummechanical description of a particle with a total angular momentum or spin of j (in units of , Planck’s constant divided by 2π). Such a particle can be considered as a set of states which differ in their orientation or component of spin jz in a z direction of quantization. There are 2j + 1 such states, where jz varies from −j to +j in steps of one unit. To the extent that the local universe is isotropic (or there are no external forces on the states that depend upon direction), the components of angular momentum in any direction are conserved, and states with different values of jz are dynamically equivalent. There is then a logical or mathematical equivalence between the descriptions of (1) a multiplet of states of definite I and different values of I3 with respect to charge-independent forces and (2) a multiplet of states of a particle with a definite spin j and different values of jz with respect to directionindependent forces. In each case, the members of the multiplet with different values of the conserved quantity I3 on the one hand and jz on the other are dynamically equivalent; that is, they are indistinguishable by any application of the forces in question. See ANGULAR MOMENTUM; SPIN (QUANTUM MECHANICS). 2 I-spin Relative intensities of virtual transitions determined by isobaric spin symmetry Transition Relative intensity p → n + π+ p → p + π0 n → n + π0 n → p + π− 2/3 1/3 1/3 2/3 Importance in reactions and decays. The charge independence of the strong interactions has important consequences, defining the intensity ratios of different charge states produced in those particle reactions and decays which are mediated by the strong interactions. A simple illustration is provided by the virtual transitions of a nucleon to a nucleon plus a pion, transitions which are of dominant importance in any consideration of nuclear forces. The neutron and proton form a nucleon I-spin doublet with I = 1 /2 ; the pions form an I-spin triplet with I = 1. If initially there are one neutron and one proton, with no bias in charge state or I3, and the strong forces responsible for the virtual transitions do not discriminate between states with different charge or different values of I3, then it follows that in the final system there must be equal probabilities of finding each charge member of the pion triplet and equal probabilities of finding a neutron or proton. This condition, that the strong interactions cannot differentiate among the members of an isobaric spin multiplet, determines the relative intensities of the transitions (see table). Using the same kind of argument, it is easy to see that the conditions of equal intensity of each member of a multiplet cannot be fulfilled in a transition from an initial doublet to a final state of a doublet and a quartet. Therefore, none of the individual transitions is allowed by charge independence, though charge or I3 is conserved in the decays. In general, decays are allowed for a transition A → B + C only if inequality (3) is satisfied. This is analogous to the |I(B) + I(C)| ≥ |I(A)| ≥ |I(B) − I(C)| (3) vector addition rule for spin or angular momentum; the strong interactions conserve I-spin in the same manner as angular momentum is conserved. See SELECTION RULES (PHYSICS). Classification of states. I-spin considerations provide insight into the total energies or masses of nuclear and particle states. The fundamental constituents of nuclei are the nucleons, the neutron and proton–spin-1/2 fermions which must obey the Pauli exclusion principle to the effect that the sign of the wave function that describes a set of identical fermions must change sign upon exchange of any two fermions. Similarly, hadrons are described as compounds of quarks, which are also spin-1/2 fermions. The two fermions that make up an I-spin doublet can be considered as different charge states of a basic fermion, even as states with the spin in the plus and minus direction of quantization are consid- ered as different spin states of the fermion. The extended Pauli exclusion principle then requires that the wave function amplitude change sign upon exchange of spin direction, charge, and spatial coordinates for two (otherwise) identical fermions. See EXCLUSION PRINCIPLE. A space state u(r) of two identical fermions, where r is the vector distance between the two particles, will be even upon exchange of the two particles if u(r) has an even number of nodes, and will be odd under exchange if there is an odd number of nodes. With more nodes, the space wavelength is smaller, and the momentum and energy of the particles are larger. The lowest energy state must then have no spatial nodes and must be even under spatial interchange. From the Pauli principle, the whole wave function must be odd, and then the exchange under spin and I−spin coordinates must be odd. Using this kind of argument, the low-mass (low-energy) states of light nuclei can be classified in terms of their I-spin symmetries. An application of the same principle, that the space wave function of the lowest state must be even under exchange, was an important element in the discovery of a new quantum number (labeled color) for quarks, the elementary constituent of the hadrons, and concomitantly the unfolding of a deeper understanding of fundamental particles. Basis for charge independence. The basis for the symmetry described by I-spin is to be found in the quark structure of the strongly interacting particles and the character of the interactions between quarks. All of the strongly interacting particles are quark compounds; the conserved fermions, such as the neutron and proton, are made up of three quarks; the bosons, such as the π mesons, are quark-antiquark pairs. There are six significantly different quarks arranged in three pairs of charge +2/3 and charge −1/3 particles, (u2/3, d−1/3), (c2/3, s−1/3), and (t2/3, b−1/3), called up and down, charm and strange, and, top and bottom. The quarks interact through their strong interacting color charges that couple the quarks to gluons in a manner analogous to the coupling of electrical charge to photons. Rather than one kind of electrical charge, and its negative, quarks have three kinds of color charges (conventionally labeled r for red, y for yellow, and b for blue), and their negatives. Even as there are three different colors, there are 3 × 3 − 1 = 8 different gluons labeled with color and anticolor (with the so-called white combination ruled out), rather than the one photon that carries the electromagnetic forces. Since each kind of quark carries exactly the same sets of color charge, the strong forces between two quarks are exactly the same as the forces between two other quarks. However, the simple consequences of this color independence of the strong forces are largely obviated by the fact that the six quarks have different masses. Hence, the  + hyperon, (uus), is appreciably heavier than the proton, (uud), even as the s-quark is heavier than the d-quark, though the quark-quark forces holding the systems together are the same. Ice cream However, the masses of the two lightest quarks, the u and d, are almost the same, differing by only a few electron masses. Then, for the many situations that this small difference can be neglected, the u and d quarks cannot be differentiated by the strong forces; that is, the neutron (duu) and proton (ddu) are identical under the strong forces, which is just the symmetry described by I-spin. There are some effects where the mass difference, equal to about two pion masses, between the s and u quark, or the s and d quark, can be neglected, or for which corrections can be calculated. For such effects twofold symmetries like I−spin, called, respectively, V-spin and U-spin, are useful. In principle, similar broken symmetries exist for compounds of the heavier quarks, but the symmetry breaking that follows from their much larger mass differences so obscures the underlying symmetry that it is not useful. See COLOR (QUANTUM MECHANICS); GLUONS; QUANTUM CHROMODYNAMICS; QUARKS; SYMMETRY LAWS Robert K. Adair (PHYSICS). Bibliography. F. Halzen and A. Martin, Quarks and Leptons, 1984; N. A. Jelley, Fundamentals of Nuclear Physics, 1990; G. Kane, Modern Elementary Particle Physics, updated ed., 1993; L. B. Okun, Leptons and Quarks, 1980, paper 1985; S. S. Wong, Introductory Nuclear Physics, 2d ed., 1999. Ice cream A commercial dairy food made by freezing while stirring a pasteurized mix of suitable ingredients. The product may include milk fat, nonfat milk solids, or milk-derived ingredients; other ingredients may include corn syrup, water, flavoring, egg products, stabilizers, emulsifiers, and other non-milk-derived ingredients. Air incorporated during the freezing process is also an important component. The structure of ice cream is complex. It consists of solid, gaseous, and liquid phases; ice crystals and air cells are dispersed throughout the liquid phase, which also contains fat globules, milk proteins, and other materials. Composition. In the United States, ice cream composition is regulated by Federal Frozen Dessert Standards of Identity, which set forth minimum composition requirements of not less than 10% milk fat and not less than 20% total milk solids. Ice cream must weigh not less than 4.5 lb/gal (0.54 kg/liter) and must contain not less than 1.6 lb food solids/gal (0.26 kg/liter). In the case of bulky flavors, the fat may be not less than 8%, nor can the total milk solids be less than 16% in the finished food. Ingredient and nutritional-requirements labeling is included in the standards. The composition of ice cream may vary depending on whether it is an economy brand satisfying minimal requirements, a trade brand of average composition, or a premium brand of superior composition. The components by weight of an average-composition ice cream are 12% fat, 11% nonfat milk solids, 15% sugar, and 0.3% vegetable gum stabilizer. An average serving of 4 fl oz (120 ml) of vanilla ice cream with 10% milk fat provides about 135 calories, 0.4 oz (11.2 g) fat, 0.8 oz (22.4 g) protein, 0.56 oz (15.9 g) carbohydrate, 0.003 oz (88 mg) calcium, 0.0024 oz (67 mg) phosphorus, 270 International Units vitamin A, and 0.0000058 oz (0.164 mg) riboflavin. Thus, a serving of ice cream provides more than 10% of the U.S. Recommended Daily Dietary Allowance (USRDA) for riboflavin and calcium and about 5% of the USRDA for protein for adults and teenagers. See NUTRITION. French ice cream may contain a relatively high fat content, have a slight yellow color, and contain egg yolk solids. Both this product and ice cream carry the same requirements. French ice cream must contain not less than 1.4% egg yolk solids for plain flavor and not less than 1.12% for bulky flavors. It is usually sold as a soft-serve product but may be sold as a prepackaged hardened product. Gelato is Italian for ice cream; it commonly increases in volume by only one-third on freezing. The composition of ice milk is similar to that of ice cream except that it must contain more than 2% but not more than 7% milk fat, not less than 11% total milk solids, and not less than 1.3 lb food solids/gal (0.15 kg/liter). Sherbet is made with about 1 part ice cream mix to 4 parts water ice mix and is manufactured in the same way as ice cream. It must weigh not less than 6 lb/gal (0.7 kg/liter). Sherbet contains not less than 1% or more than 2% fat, and total milk solids of not less than 2% or more than 5% by weight of the finished food; it must also contain 0.35% edible citric or natural fruit acid. A sherbet made with addition of egg yolk is known as frappe. Frozen dairy desserts. Products classed as frozen dairy desserts include French ice cream, frozen custard, ice milk, sherbet, water ice, frozen dairy confection, dietary frozen dairy dessert, and mellorine (imitation ice cream). Most of these desserts can be sold in the soft-serve form, as they are when first removed from the freezer at about 20◦F (−7◦C), or in the hard form as they are when the temperatures are reduced to about 8◦F (−13◦C). A frozen dessert mix is the combination of ingredients, usually in the liquid form and ready to be frozen. Dry mixes must be dissolved in water before freezing. Unflavored mixes may be flavored before freezing, as with vanilla and chocolate, or may have flavorings added to the soft frozen product as it exits the freezer, as with fruit, nut, and candy type desserts. Water ice is made from water, sugar, corn sweeteners, fruit juices, flavorings, and stabilizers. It contains no milk solids. Sorbet is similar; in addition it contains finely divided fruit and is whipped while being frozen. There is no federal standard for sorbet in the United States. Dietary frozen desserts are comparatively low in calories. Ice milk commonly contains about onethird the fat of ice cream. Proposed U.S. Federal Standards permit 2–5% fat in ice milk and establish a category of light (lite) ice cream with 5–7% fat. To provide frozen desserts for diabetics, sugar (sucrose) 3 4 Ice cream is replaced with nonnutritive sweeteners, and complex carbohydrates, such as sorbitol, are added to provide desirable texture. Mellorine is manufactured in a process similar to that for ice cream, but is not limited to milk-derived nonfat solids and may be composed of animal or vegetable fat or both, only part of which may be milk fat. It contains not less than 6% fat and not less than 2.7% protein by weight. Frozen dairy confections are produced in the form of individual servings and are commonly referred to as novelties, including bars, stick items, and sandwiches. These constitute an important segment of the industry. Soft frozen dairy products make up about 9.6% of the total frozen desserts produced in the United States. Per capita consumption is 5 qt (4.7 liters) per year. The soft frozen product is usually drawn from the freezer at 18 to 20◦F (−8 to −7◦C) and is served directly to the consumer. Ice milk accounts for about three-fourths of the soft-serve products that are manufactured in the United States. These products usually vary from 2 to 7% fat, 11 to 14% nonfat milk solids, 13 to 18% sugar, and have about 0.4% stabilizer. Frozen custard and ice cream are also important soft-serve products. Commercial manufacture. In ice cream manufacture the basic ingredients are blended together (see illus.). The process ranges from small-batch operations, in which the ingredients are weighed or measured by hand, to large automated operations, where the ingredients, all in liquid form, are metered into the mix-making equipment. The liquid materials, including milk, cream, concentrated milk, liquid sugar syrup, and water, are mixed. The dry solids, such as nonfat dry milk, dried egg yolk, stabilizer, and emulsifier, are blended with the liquid ingredients. This liquid blend is known as the mix. Following the blending operation, the mix is pasteurized, homogenized, cooled, and aged. Pasteurization destroys all harmful microorganisms and improves the storage properties of the ice cream. See PASTEURIZATION. The hot mix is pumped from the pasteurizer through a homogenizer, which reduces the fat globules to less than 2 micrometers in diameter. Homogenization is accomplished by forcing the mix through the homogenization valves under pressure in the range 1500–3000 lb/in.2 (103–207 kilopascals). This phase of the manufacturing process results in a uniform, smooth product and limits churning of the fat during the freezing process. The mix is cooled immediately to 32–40◦F (0–4◦C); then it is aged 4–12 h in order to permit development of favorable hydration and particle orientation effects, which serve to improve the body and texture in the finished ice cream. Soluble flavoring materials are usually added to the mix just before the freezing process, but fruits, nuts, and candies are not added until the ice cream is discharged from the freezer. In the United States, popular flavors of ice cream include vanilla, chocolate, strawberry, butter pecan, and “cookies ‘n cream” (broken cookies are blended into the ice cream), and there are many other flavors. Neapolitan is one-third each of vanilla, chocolate, and strawberry extruded simultaneously into one container. Ice cream is frozen in batch or continuous cartons and wrappers dry receiving flavors, fruits, and nuts ingredients condensed blend cream liquid receiving cane suger corn suger water fruit and nuts mix storage 0° to 4°C blending pasteurizing 68°C for 30 min 79°C for 25 s flavoring cooling 0° to4° C homogenizing 71°C pump pump packaging and wrapping –4°C freezing –6°C pump pump ◦ ◦ Flow chart for ice cream processing. F = ( C × 1.8) + 32. (Arbuckle and Co.) hardening –43° to –46°C storage –23° to –29°C Ice field freezers. The continuous freezing process is more effective, as it freezes more rapidly and produces a product with finer texture. Continuous freezers vary in capacity from 85 gal (323 liters) to more than 2000 gal (7600 liters) per hour. During freezing, air is incorporated into the mix, resulting in increased volume. This increase in volume is called overrun. The drawing temperature of the ice cream from the freezer is about 21◦F (−6◦C). The ice cream is packaged at this temperature and cooled further to about −20◦F (−29◦C) in a hardening room, where it is stored until marketed. The ice cream industry of the United States has been described as a high-volume, highly automated, progressive, very competitive industry composed of large and small factories. It has d...
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