Nuclear Properties and Forces

• Unit 5 covers Nuclear and Plasma Physics
• The notes cover AY: 2024-25

Introduction to Nuclear Physics

• A given atom is specified by the number of neutrons (N) and protons (Z).
• Neutral atoms have Z electrons.
• The atomic mass number (A) is the sum of protons (Z) and neutrons (N): A = Z + N.
• Atoms of the same element share the same atomic number Z.

Terminology

• Isotopes: same Z, different N, thus different A.
• Example: 11Na22 and 11Na23
• Isotones: same N, different Z, thus different A.
• Example: 6C14 and 7N15
• Isobars: same A, different Z.
• Example: 6C14 and 7N14
• Mirror Nuclei: Two isobars where the number of protons and neutrons are interchanged.

Nuclear Force

• A nuclear force is the force between nucleons (protons and neutrons).
• The nuclear force is the strongest of the four basic interactions or forces.
• At distances of about 1 femtometer (fm, 1.0 x 10-15 meters), the nuclear force is powerfully attractive between nucleons.
• It rapidly decreases to insignificance beyond about 2.5 fm.
• The nuclear force becomes repulsive at distances less than 0.7 fm.
• Nuclear forces are charge independent.
• The force between two protons (p-p), two neutrons (n-n), a neutron, and a proton (n-p) are almost equal.
• Nuclear force is spin-dependent, whereby nucleons with parallel spins have greater nuclear force than those with antiparallel spins.
• The strength of nuclear forces becomes saturated over a short distance; nucleons interact only with their first neighbors.

Origin of Nuclear Force

• Yukawa postulated in 1935 that nuclear forces result from the exchange of mesons between two nucleons.
• A nucleon is surrounded by a meson field due to the short-range nature of nuclear forces.
• A meson emitted by one nucleon is absorbed by another, resulting in constant momentum transfer and exerted force.
• The exchange of mesons must occur in a short time, consistent with Heisenberg's uncertainty principle, making experimental detection impossible.
• Mesons in the exchange process are referred to as virtual mesons.
• Nucleons interact by exchanging pi mesons, existing in neutral (π0), negative (π-), and positive (π+) forms.

Units, Dimensions, and Physical Constants

• The atomic mass unit (a.m.u.) is used to express nuclear mass
• One a.m.u. is equal to one-twelfth the mass of a carbon-12 atom.
• 1 a.m.u. = 1.66 x 10-27 kg.
• The atomic mass of an element is an average mass based on natural isotopic combination.
• The atomic mass of carbon is 12.01115 a.m.u, not 12.00000 a.m.u because of carbon isotopes.
• Energy equivalent to one a.m.u: E = mc2
• E = 931.5 MeV.
• Proton mass: 938.280 MeV/c2
• Neutron mass: 938.573 MeV/c2
• Electron mass: 0.511 MeV/c2

Basic Nuclear Properties

• Most of an atom's mass is concentrated in the nucleus, with electrons distributed around the nucleus.
• Nucleus radius ≈ 10-13 cm
• Electron distribution radius ≈ 10-8 cm
• Protons and neutrons (nucleons) are the constituents of the nucleus.

Nuclear Radius and Density

• Nuclear size (volume) depends on its mass number (A).
• Assuming a spherical nucleus, the radius R = roA1/3.
• ro is between 1.2 x 10-13 cm and 1.48 x 10-13 cm.
• Nuclear density is independent of atomic mass number.
• Density is almost the same for all nuclei.

Nuclear Angular Momentum or Nuclear Spin

• Each nucleon has orbital and spin angular momenta.
• Magnitude of spin angular momentum is ħ/2 (ħ = h/2π).
• Spin axis has two states: parallel or antiparallel to a given direction (z-axis).
• Component of spin along z-axis is either ħ/2 or -ħ/2.
• Total angular momentum i of each nucleon is i = l ± s.
• l is the orbital angular momentum and s is the spin angular momentum.
• For nuclei with more than one nucleon, the total angular momentum of the nucleus is: I = L + S.
• I is a vector; its magnitude is the maximum possible component in any direction.
• Value of I is an integral multiple of ħ for nuclei with even mass numbers.
• Value of I is an odd half-integral multiple of ħ for nuclei with odd mass numbers.
• Even-even nuclei (even Z and N) carry I = 0.
• Total nuclear angular momentum I is also termed as nuclear spin.

Magnetic Dipole Moment of Nucleus

• A moving charged particle with intrinsic spin possesses an orbital and spin magnetic dipole moment.
• A positively charged proton has orbital and spin magnetic dipole moment.
• A neutron has only spin magnetic dipole moment.
• The resultant magnetic dipole moment μ of a nucleus is the vector sum of the magnetic dipole moments of all nucleons: μ = gI μN I
• gI is the nuclear gyromagnetic ratio, μN is the nuclear magneton.
• Nuclear magneton value = 5.05 x 10-27 J/wb/m2.
• Measured values of μ are between -3 μN and +10 μN.
• Negative μ means magnetic moment opposes nuclear spin direction.
• Positive μ means magnetic moment is in the same direction as nuclear spin.
• Magnetic moment of a proton = +2.79276 μN
• Magnetic moment of a neutron = -1.191315 μN
• Suggests non-uniform charge distribution in protons and neutrons.

Electric Quadrupole Moment

• Measures the deviation of the nucleus from its spherical symmetry.
• Under deviation, the nucleus is imagined to be an ellipsoid.
• The diameter is 2b along symmetry axis and 2a along the axis perpendicular to this.
• Quadrupole moment Q of the nucleus is Q = (2/5)Z(b2 - a2) when electric charge is uniformly distributed.
• Q = 0 for nuclei having spherical symmetry (a = b) and uniform charge distribution.
• Magnitude of electric quadrupole moment depends on: nuclear charge Z, size of the nucleus (magnitudes of b and a), and extent of deviation (difference in b and a).

Binding Energies of Nuclei

• Nuclear masses are less than the sum of the masses of their constituent neutrons and protons.
• Mass decrease (ΔM) is converted into energy: E = ΔMc².
• Energy is called the binding energy (B).
• Binding energy B required to break the nucleus into free neutrons and protons.
• For a nucleus of mass M with Z protons and N neutrons, binding energy B is B = (ZMp + NMn – M)c2, Mp and Mn are the masses of free proton and neutron, respectively.
• Graphing binding energy per nucleon (B/A) against mass number (A) yields the binding energy curve.
• Average B/A ≈ 8.8 MeV
• Magnitude is approximately independent of A
• B/A decreases for small A values.
• Light nuclei have a larger fraction of nucleons on the surface, reducing the B/A value.
• B/A decreases as A increases due to the Coulomb effect.
• Coulomb repulsion between protons increases as Z2. Naturally occurring nuclei: Z2 increases faster than A.
• The Coulomb effect cannot be compensated by an increase in A.
• The B/A vs A plot peaks around A ≈ 60.
• Increased binding energy means energy release via mass conversion.
• Highlights the significance of fission and fusion reactions, which are basic in the production of nuclear energy is highlighted.
• Fe corresponds to the peak of this plot and explains for the large abundance of it.
• Strong magnitude of binding for mass numbers which are multiples of four particles (2 neutrons + 2 protons): 4, 8, 12, 16, 20, and 24.
• Effect is due to a pairing force existing between neutron pairs and proton pairs.
• B/A vs A plot shows discontinuities at neutron/proton numbers: 2, 4, 8, 20, 50, 82, and 126 which are termed as nuclear magic numbers .
• Large binding energy at these values signifies high stability.
• 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, which is determined by the neutron-to-proton ratio
• Segre plot.
• Stable ratio is approximately 1:1 at low atomic masses.
• Ratio increases to around 1.5:1 for heavy elements, beginning at atomic mass 20.
• With a larger number of protons, more neutrons are needed because of the repulsion from electrostatics.
• A bandwidth of stability is marked by this ratio around which unstable isotopes cluster.
• Unstable isotopes lie above and below the band which indicates respectively too hihg or low numbers of neutrons.
• Above mass 208 have no stable isotopes.
• Isotopes on both sides of stability curve are radioactive
• Radioactive isotopes decay in such a way that the final product lies on the stability curve and is now stable.
• 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 = odd-even effect .
• Stable nuclei can be classified into four groups: even-even, even-odd, odd-even, and odd-odd.
• Even-even nuclei are the most abundant and even-odd nuclei are the least abundant.
• Nucleons tend to form neutron-proton pairs = pairing of nucleons.
• Nuclei are more strongly bounded which satisfy A = Z or A/2 = Z together.
• Decreased binding energy should decrease any deviation from A = 22

Nuclear Models

• Attempts to correlate variations, where in absence of a detailed theory of nuclear structure binding energy per nucleon prompted nuclear models.
• Models were based on simplifying assumptions and hence, were useful in a limited way only.
• 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.

Plasma Physics

• Plasma is a state of matter
• Plasma, solid, liquid, and gas are the four states of matter after earth, water, air and fire
• Estimated, over 99% of the matter in the universe exists in the plasma state.
• When any material is heated, its state changes from solid to liquid to gas.
• Increasing the temperature of gas beyond limits leads to a regime where the thermal energy dominates electrostatic forces.
• Instead of neutral atoms, there is a mixed population of charged and neutral particles.
• Increasing temperature is related to increasing ionized particles, changing the behavior of ionized gas. After the fraction of ionized particles starts exhibiting the collective behavior, it forms plasma
• Solid, liquid and gas properties aren't in plasma that is defined as exhibiting collective behavior.
• Lightning, Aurora Borealis, and electrical sparks are examples that show the light emission when an electric current is passed.
• Electric discharge is used in Neon and florescent lights to convert electrical energy into light.
• Burning gas (flame) is weakly ionized; 579 nm transitions (D lines) of sodium ions produce the characteristic yellow color from a wood flame
• The solar wind, nebulae, interstellar gases, the earth's ionosphere, and the Van Allen belts are example of a diffuse, low temperature, ionized gas .
• Controlled thermonuclear fusion provides energy on earth through hot, dense plasma.

Plasma Production

• Raising the temperature of a substance until a reasonably high fractional ionization is obtained can produce plasma.

• A plasma can be produced by raising the temperature of a substance until a reasonably high fractional ionization is obtained.

• In particular, the electron temp ionization determines the relationship between the degree of ionization and electron temperature.

• Some astrophysical plasmas and local thermodynamic equilibrium and natural plasmas, are common in the lab. Plasmas can be generated for more raise in the degree of ionization.

• Many methods are for creating plasmas in the laboratory with a high or low density, high or low temperature, steady or transient, stable or unstable.

• The most common processes are photoionization and electric discharge in gases.

• In photoionization, 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 will be transformed intokinetic energy

• The ionization potential energy for the outermost electron of atomic oxygen is 13.6 eV.

• Energy can be supplied by radiation of wavelength of 91nm, i.e in the far ultra violet. X-rays or gamma rays can produce ionization.

• Earth’s ionosphere is photoionized plasma,

• A gas discharge is an electric field over ionized gas, which accelerates the free electrons to energies sufficiently high to ionize other atoms by collisions.

• Applied electric field transfers energy Light electrons than relatively heavy ions .

• Electron temperature exceeds the ion temperature in gas discharge,transfer of thermals energy electrons to the heavier particles is slow .When ionizing source is turned off, the ionization decreases gradually because of recombination until it reaches an equilibrium value in the lab the recombination happens fast so the plasma disappearsin a small fraction of a second .

Applications

• Plasma processing of materials is becoming a critical technology across diverse industries: electronics, aerospace, automotive, biomedical, textile, optics and paper.
• Plasma processing has a broad range of applications.
• The uniformity of surface treatment is industrial-level plasma processing of materials.
• Technological challenge: developing surface processes to meet required specifications (uniformity/rate) and transferring/scaling processes.

Etching (Sputtering)

• Energetic ions strike solid surface

• Atoms are ejected.

• Used to etch solids.

• In sputter etching, the substate to be etched (the target) is placed on one electrode of the system.

• Glow discharge: generated in low-pressure gas and accelerated ions strike the target which can be excited by a DC, RF or microwave electric field.

• Can enhance plasma density.

• Inert gas as argon is used.

• Reactive gasses can also be used (reactive sputter etching).

• Plasmas are generated with RF or microwave voltages from kHz to GHz.

• Plasma etching refers to processes where chemical reactions are at work.

Deposition/coating

• Sputter coating can be a deposition process as well as an etching process.

• Sputter coating: material removes from the target, subsequently redepositing on a substrate.

• Common method of thin-film deposition metals like tungsten and molybdenum.

• Reactive sputter coating utilizes reactive gases when inert gases are used for deposit modified coatings.

• silicon nitride films can be deposited using a Si target and an N2 plasma.

• Glow discharge cleaning: it's like sputtering where impurities on the material surface process is used for vacuum surfaces and medical instruments

High Voltage Engineering

• Have been largely replaced by Solid-Stage Technology but they still dominate high-power average systems and have attained peak power: >100 Mw,average power: >≥1and operating frequencies up to hundreds of GHz.
• microwave tube is a high performance solid that has widespread applications in radar, communications and cooking such as in microwave ovens (magnetron tubes).
• Amplifier tubes and communicating satellites which is most often traveling through waves can be high energy plasma

Environmental engineering

• High energy plasma is a chemical catalyst and and has been used in industrial pollutants (S02) and volatile organic compounds.
• Toluene and automobile emissions have been verified with processing of levels of radio active waste and reduces the volume.
• Plasmas can be used in hazardous waste treatment, PCBs, dioxins, nerve gas and pesticides

Laser induced plasma

• Pprocesses include bond breaking during ionization and excitation.

• These bond-breaking mechanisms can generate a laser pulse in the form of energy.

• has been used for differentdiagnostic and technological applications as detection, thin film deposition, and elemental identification.

• Atomic or molecule species specify organic, inorganic or biological materials. This allows applications in defense and public health.

• Can potentially provide and produce fast sensor systems explosive trace and a pathogen biological agent