Nuclear Physics: Isotopes, Nuclear Force & Plasma Physics

Unit 5 : Nuclear and Plasma Physics (AY: 2024-25) ================================================= **I-Introduction to Nuclear Physics:** 1. Terminology -------------- 1. *[(Atomic Number, Atomic Mass Number, Isotopes, Isobars, Isotones)]* A given atom is specified by the number of -neutr...

Unit 5 : Nuclear and Plasma Physics (AY: 2024-25) ================================================= **I-Introduction to Nuclear Physics:** 1. Terminology -------------- 1. *[(Atomic Number, Atomic Mass Number, Isotopes, Isobars, Isotones)]* A given atom is specified by the number of -neutrons: N -protons: Z -electrons: there are Z electron in neutral atoms The atomic mass number (A) = Z + N Atoms of the same element have same atomic number Z. **Isotopes:** Isotopes of the same element have different number of neutrons N. Hence, isotopes have same atomic number (Z) but different atomic mass number (A). Example: 11Na22 and **Isotones:** Isotones are the elements having same number of neutrons (N) but with different number of protons (different Z) and therefore different atomic mass number (A). Example: **Isobars:** Isobars are the elements having same atomic mass number (A) but with different atomic number (Z). Example: 6C14 and 7Na14 **Mirror nuclei**: Two isobars with proton and neutron number interchanged i.e., the number of protons in one is equal to the number of neutrons in the other, are called mirror nuclei. 2. **Nuclear Force**: The forces between nucleons, i.e., between proton and neutron, neutron and neutron are referred to as nuclear forces. Characteristics of nuclear force: ================================= 1. The nuclear force is the strongest among the four basic forces or interactions found in nature. 2. The nuclear force is powerfully attractive between nucleons at distances of about 1 femtometre (fm, or 1.0 × 10−15 metres), but it rapidly decreases to insignificance at distances beyond about 2.5 fm. At distances less than 0.7 fm, the nuclear force becomes repulsive. 3. Nuclear forces are charge independent i.e., force between two protons (p-p), the force between two neutrons (n-n) and the force between a neutron and a proton (n-p) are almost equal. 4. The nuclear force is spin-dependent i.e., nucleons with parallel spins have greater nuclear force than the ones with anti-parallel spins. 5. The strength of nuclear forces becomes saturated over a short distance i.e., nucleons interact only with their first neighbours and not beyond that. Origin of nuclear force: ======================== In 1935, Japanese physicist Yukawa postulated that nuclear forces result from the constant exchange of massive particles called mesons between two nucleons. According to Yukawa, because of short range nature of nuclear forces, a nucleon is surrounded by meson field.When a nucleon is brought near to another nucleon, a meson emitted by one may be absorbed by the other or vice-versa. This way there is a constant transfer of momentum from one nucleon to the other and hence a force is exerted between them. The emission of a meson ought to reduce the mass of a nucleon. However, this is not observed. Hence, the exchange of meson must take place in a short time that the uncertainty in energy is consistent with Heisenberg's uncertainty principle ∆E.∆t∼ ћ. This makes the experimental detection of meson exchange not possible and hence the mesons in the exchange process are referred to as virtual mesons. Nucleons interact with each other by exchange of pi mesons which can exist in three different forms. Its neutral form is called neutral pi meson or pion (π°), its negative form is called negative pion (π --) and its positive form is called positive pion (π +). Units, dimensions and physical constants ---------------------------------------- The mass of a nucleus is given in terms of a unit called the atomic mass unit (a.m.u.) which is equal to one-twelfth the mass of the carbon-12 atom. Since, the mass of one C12 atom in kilogram = (12 x 10-3)/NA where NA is Avogadro's number = 6.023 x 1023 mole-1 Therefore, 1 a.m.u. = (12 x 10-3)/(12 x 6.023 x 1023) = 1.66 x 10-27 kg. The atomic mass of an element is the average mass based on the natural isotopic combination. Thus, the atomic mass of carbon is not 12.00000 a.m.u but 12.01115 a.m.u due to the presence of different carbon isotopes in nature. It is also possible to express the units of mass in terms of energy units based on Einstein's mass energy relationship E = mc2 Therefore, the energy equivalent to one a.m.u. in terms of joules is E = 1 a.m.u. x c2 = 1.66 x 10-27 x 9 x 1016 = 1.494 x 10-10 J = 931.478 MeV Therefore, 1 a.m.u = 931.5 MeV. -Proton mass: 938.280 MeV/c2. -Neutron mass: 938.573 MeV/c2. -Electron mass: 0.511 MeV/c2. Basic Nuclear Properties ------------------------ According to Rutherford model, most of the mass of the atom is concentrated in a small spherical volume called the nucleus, and the electrons are distributed around the nucleus. The radius of the nucleus is about 10--13 cm and the spherical volume where electrons are distributed carries radius of about 10--8 cm. The protons and neutrons are the only constituents of the nucleus, which are called nucleons. 1. [Nuclear radius and density]: The scattering of α-particles by the nucleus demonstrated that the size of any atom is almost constant, but the size (volume) of any nucleus depends on its mass number A. Assuming a nucleus to be in the form of a sphere, its radius R is given by The value of r0 is found to depend on the type of experiment. In general, it is between 1.2 x 10--13 cm and 1.48 x 10--13 cm. The density of nucleus is independent of atomic mass number and its value is almost the same for all nuclei. 2. Each nucleon in the nucleus is assumed to have both orbital and spinning motions just like an electron has in an atom. It means each nucleon has both orbital and spin angular momenta. The magnitude of the spin angular momentum is ћ/2 (ћ = h/2π). Its orientation in space can be described by only two states: the spin axis is either parallel or antiparallel to any given direction (say z-axis). So the component of spin along z-axis is either ћ /2 or -- ћ /2. In view of this, the total angular momentum *i* of each nucleon is where *l* is the orbital angular momentum and *s* is the spin angular momentum. For nuclei having more than one nucleon, *l* is replaced with *L* and *s* is replaced with *S*, which represent the corresponding total momentum of all the nucleons. Hence, the total angular momentum of the nucleus is given by *I* is actually a vector, whose magnitude is the maximum possible component in any given direction. The value of *I* is an integral multiple of ћ for the nuclei with even mass numbers, and it is an odd half-integral multiple of ћ for the nuclei with odd mass numbers. In particular, even- even nuclei (nuclei with both Z and N even) carry zero value of *I*. The total nuclear angular momentum *I* is also termed as nuclear spin. 3. A moving charged particle with intrinsic spin possesses an orbital and spin magnetic dipole moment. Inside a nucleus, a positively charged proton has both orbital and spin magnetic dipole moment while a neutron has only spin magnetic dipole moment. Hence, the resultant magnetic dipole moment μI of a nucleus is the vector sum of the magnetic dipole moments of all the nucleons and is given by where gI is the nuclear gyromagnetic ratio and μN is the nuclear magneton. The value of nuclear magnetons is 5.05 x 10--27 J/wb/m2. The measured values of μI are between --3μN and +10μN. When the magnetic moment of the nucleus is in the opposite direction to the direction of nuclear spin, μI carries negative values. The positive valve of μI means the directions of the magnetic moment of the nucleus is the same as that of the nuclear spin. The magnetic moment of a proton is +2.79276 μI, whereas that of neutron is --1.191315 μI. This indicates that the proton and neutron have a non-uniform charge distribution, which is also very complex. 4. The electric quadrupole moment is a measure of the deviation of the nucleus from its spherical symmetry. Under the situation of a deviation, the nucleus can be imagined to be an ellipsoid of revolution with its diameter 2b along the axis of symmetry and diameter 2a along the axis perpendicular to this. The quadrupole moment Q of the nucleus, when its electric charge is uniformly distributed throughout the ellipsoid, is given by Q = (2/5)Z(b2 - a2) Q is zero for the nuclei having spherical symmetry (a = b) and uniform charge distribution. The magnitude of electric quadrupole moment depends on the magnitude of nuclear charge Z, size of the nucleus (magnitudes of b and a) and the extent of deviation (difference in b and a) from spherical symmetry. 5. When nuclear masses are measured, it is found that they are less than the sum of the masses of the neutrons and protons of which they are composed. This decrease in mass (∆M) is converted into energy ∆E = ∆Mc2. This energy is called the binding energy (B). The binding energy B of a nucleus is the energy required to break the nucleus into free neutrons and protons. For a nucleus of mass M containing Z protons and N neutrons, the binding energy B is defined as, where Mp and Mn represent the masses of free proton and neutron, respectively. A graph of the binding energy per nucleon (B/A) as a function of the mass number (A) is called binding energy curve. The interesting conclusions that can be drawn from this plot of B/A against A (atomic mass number) is given below: i. The magnitude of average B/A is approximately 8.8 MeV i.e., B/A does not depend on A. In other words, B/A appears to be approximately independent of the overall size of a nucleus. ii. B/A falls off at small values of A. This is because very light nuclei have a larger fraction of their nucleons residing on the surface rather than inside. This reduces iii. B/A falls off at large values of A. This is due to Coulomb effect. Between every pair of protons, there is a Coulomb repulsion which increases as Z2. For naturally occurring nuclei, Z2 increases faster than A and so the Coulomb effect cannot be adequately compensated by an increase in A. iv. B/A against A plot is peaked around A ∼ 60. When the binding energy is increased, energy in other forms can be released, since a decrease in M corresponds to conversion of mass into energy. These considerations highlight the importance of fission and fusion reactions, which are basic in the production of nuclear energy. v. The peak of this plot corresponds to Fe. This explains for the large abundance of Fe in nature. vi. The magnitude of binding is strong for mass numbers 4, 8, 12, 16, 20 and 24 i.e., mass numbers which are multiples of four particles (2 neutrons + 2 protons). This effect is due to a pairing force which exists between pairs of neutrons and pairs of protons. vii. The value of B/A against A plot shows discontinuities at neutron or proton number values 2, 4, 8, 20, 50, 82 and 126. These numbers are termed as nuclear magic numbers. At these values of neutron or proton numbers, the binding energy is found to be unusually large. Large binding energy means high stability. This high stability is reflected in high abundance of isotopes with these proton numbers and isotones with these neutron numbers. [Nuclear Stability] Certain isotopes are more stable than others. Their stability is determined by the ratio of the number of neutrons to the number of protons in the nucleus termed as the Segre plot. At low atomic masses, the stable ratio is approximately 1:1. At about an atomic mass number of 20 this starts to increase until it is around 1.5:1 for the very heavy elements. This is due to the fact that with higher numbers of protons more neutrons are needed due to the repulsion of the protons from electrostatics. This ratio is not exact but represents a \"band of stability\" around which unstable isotopes cluster. There are a large number of unstable isotopes both above the band (too high a number of neutrons) and below the band (too high a number of protons). At some point there are no longer any stable isotopes regardless of the neutron to proton ratio. This can be seen at very high atomic numbers. Above mass 208 there are no stable isotopes. The isotopes on both sides of the stability curve are radioactive, which decay in such a way that the final product lies on the stability curve and is now stable. The total binding energy of a nucleus depends not only on the ratio N/Z but also on whether these numbers of neutrons and protons are odd or even. This is called odd-even effect. All the stable nuclei can be classified into four groups, namely even-even, even-odd, odd-even and odd-odd, based on number of protons and neutrons, respectively. Even-even nuclei having even number of mass number A are the most abundant, i.e., these nuclei are most stable, whereas odd-odd nuclei are very few. The stability of odd-even and even-odd lies between the two extremes. Data collected for stable nuclei suggests that nucleons tend to form neutron-proton pairs. This is called pairing of nucleons, according to which nuclei that satisfy the condition A/2 = Z or A = 2Z are more strongly bound together and any deviation from A = 2Z should decrease the binding energy. 7. [Nuclear Models] In the absence of a detailed theory of nuclear structure, attempts were made to correlate the nature of variation of binding energy per nucleon in terms of various models. Several models were proposed. Each of them were based on a set of simplifying assumptions and hence, was useful in a limited way only. The nuclear models include the shell or independent particle model, liquid drop model, collective nuclear model and the optical model for nuclear reactions. The shell model and the liquid drop models are the most important and useful models of nuclear structure. II -- PLASMA PHYSICS ==================== Basic concepts of Plasma physics: Plasma as a state of matter, Applications of plasma physics. Plasma as a state of matter =========================== In the ancient phlogiston theory there was a classification of the states of matter: i. e., "earth", "water", "air", and "fire". While the phlogiston theory had certain basic defects, it did properly enumerate the four states of matter -- solid, liquid, gas, and plasma. It is estimated that more than 99% of the matter in the universe exists in a plasma state. As the temperature of any solid material is raised, its state changes from solid to liquid and then to gas. If we increase the temperature of a gas beyond a certain limit, it enters a regime where the thermal energy of its constituent particle is so great that the electrostatic forces, which ordinarily bind electrons to atomic nuclei, are overcome. Instead of hot gas composed of electrically neutral atoms, we then have a mixed population of charged and neutral particles. With increasing temperature, the number of ionized particles increases and the ionized gas starts behaving differently. After the fraction of ionized particles is sufficiently high the ionized gas starts exhibiting the collective behavior and the state of matter is plasma, and it is neither solid nor liquid nor gas. Plasma is thus defined as a quasi-neutral gas of charge and neutral particles, which exhibits collective behavior. Here are some familiar examples of plasmas: 1. Lightning, Aurora Borealis, and electrical sparks. All these examples show that when an electric current is passed through plasma, the plasma emits light (electromagnetic radiation). 2. Neon and fluorescent lights, etc. Electric discharge in plasma provides a rather efficient means of converting electrical energy into light. 3. Flame. The burning gas is weakly ionized. The characteristic yellow color of a wood flame is produced by 579 nm transitions (D lines) of sodium ions. 4\. Nebulae, interstellar gases, the solar wind, the earth's ionosphere, the Van Allen belts. These provide examples of a diffuse, low temperature, ionized gas. 5\. The sun and the stars. Controlled thermonuclear fusion in a hot, dense plasma provides us with energy (and entropy!) on earth. Plasma Production ================= A plasma can be produced by raising the temperature of a substance until a reasonably high fractional ionization is obtained. Under thermodynamic equilibrium conditions, the degree of ionization and the electron temperature are closely related. Although plasmas in local thermodynamic equilibrium are found in many places in nature, as is the case for many astrophysical plasmas, they are not very common in the laboratory. Plasmas can also be generated by ionization processes that raise the degree of ionization much above its thermal equilibrium value. There are many different methods of creating plasmas in the laboratory and, depending on the method, the plasma may have a high or low density, high or low temperature, it may be steady or transient, stable or unstable, and so on. In what follows, a brief description is presented of the most commonly known processes of photoionization and electric discharge in gases. In the photoionization process, ionization occurs by absorption of incident photons whose energy is equal to, or greater than, the ionization potential of the absorbing atom. The excess energy of the photon is transformed into kinetic energy of the electron-ion pair formed. For example, the ionization potential energy for the outermost electron of atomic oxygen is 13.6 eV, which can be supplied by radiation of wavelength smaller than about 91 nm, i.e., in the far ultraviolet. Ionization can also be produced by x-rays or gamma rays, which have much smaller wavelengths. The Earth\'s ionosphere, for example, is a natural photoionized plasma. In a gas discharge, an electric field is applied across the ionized gas, which accelerates the free electrons to energies sufficiently high to ionize other atoms by collisions. One characteristic of this process is that the applied electric field transfers energy much more efficiently to the light electrons than to the relatively heavy ions. The electron temperature in gas discharges is therefore usually higher than the ion temperature, since the transfer of thermal energy from the electrons to the heavier particles is very slow. When the ionizing source is turned off, the ionization decreases gradually because of recombination until it reaches an equilibrium value consistent with the temperature of the medium. In the laboratory the recombination usually occurs so fast that the plasma completely disappears in a small fraction of a second Applications ============ Plasma processing of materials is now becoming a critical technology not only in the electronics industry but also in the aerospace, automotive, steel, biomedical, textile, optics and paper industries. Due to the diversity of applications, plasma processing will in the near future, have to cover a broad range of geometries, dimensions, chemical systems, electromagnetic designs and plasma-surface interactions. In addition, at the industrial level, plasma processing of materials usually imposes the uniformity of the surface treatment. In this situation, the technological challenge consists in developing surface processes able to meet the required specifications, especially in terms of uniformity and processing rate, and furthermore, the possibility of transferring processes from one reactor to another, or more generally, scaling processes from a small to a large reactor. Etching (Sputtering) ==================== When an energetic ion strikes a solid surface, one or more atoms can be ejected from the solid. This process is called sputtering (or sometimes ion milling) and is used to etch solids. In sputter etching, the sub- state to be etched (the target) is placed on one electrode of the system. A glow discharge is generated in a low-pressure gas. The ions, accelerated through the sheath, strike and sputter the target. The discharge can be excited by a DC, RF or microwave electric field in many different configurations. Magnetic fields can be used to enhance plasma density. Typically, an inert gas such as argon is used. But reactive gasses can also be used (reactive sputter etching). Plasma etching. Though sputtering is technically "plasma etching," the term usually refers to processes where chemical reactions are at work. Many plasma etching systems (called etching tools) operate over a wide range of gas pressures. Plasmas are generated with RF or microwave voltages ranging in frequency from kHz to GHz. Deposition/coating Sputter coating. Sputtering can be used as a deposition process as well as an etching process. Sputter coating removes material from a target, which is then redeposited on a substrate. This is a common method of thin film deposition for metals such as molybdenum or tungsten. While inert gases are typically used, reactive sputter coating utilizes reactive gases to deposit modified coatings. For example, silicon nitride (Si3N4) films can be deposited using a Si target and an N2 plasma. Plasma Surface Cleaning ======================= Glow discharge cleaning is similar to sputtering, except that impurities on the surface of the material are removed. This process is used to clean such things as vacuum surfaces and medical instruments. High Voltage Engineering ======================== Vacuum tubes have largely been replaced by solid-state technology. However, they still dominate in high power microwave systems. Modern microwave tubes have attained peak powers \> 100 MW, average powers z 1 MW, and operating frequencies up to hundreds of GHz. These are performance levels solid-state devices may never attain. Microwave tubes have widespread applications in radar, communications and microwave cooking. For example, microwave ovens are powered by magnetron tubes, and communications satellites contain amplifier tubes, most often Travelling Wave Tubes (TWTs). Environmental engineering ========================= High energy plasma particles can be used to catalyze chemical reactions. This can be useful in processing pollutants and hazardous waste. Plasma waste processing has been applied to industrial pollutants such as sulfur dioxide (S02) and nitrogen- oxygen compounds (NO,), solvents such as acetone and trichloroethylene and volatile organic compounds such as toluene and automobile emissions. Plasmas have also been used to process low-level radioactive waste via verification. This is where the material is reduced in volume and transformed into a glassy obsidian. The vitrified substance has much lower leachability than unprocessed material. Other hazardous wastes with potential for plasma treatment are PCBs, dioxins, nerve gas and pesticides Laser induced plasma ==================== Plasma ignition processes include bond breaking during ionization and excitation; these bond breaking mechanisms can generate a laser pulse in the form of energy. Laser induced plasma has been used for different diagnostic and technological applications as detection, thin film deposition, and elemental identification. The possible interferences of atomic or molecular species are used to specify organic, inorganic or biological materials which allows critical applications in defense (landmines, explosive, forensic (trace of explosive or organic materials), public health (toxic substances pharmaceutical products), or environment (organic wastes). Laser induced plasma for organic material potentially provides fast sensor systems for explosive trace and pathogen biological agent detection and analysis.