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Nuclear Physics CSIR-NET prep notes
1 - Nuclear Radius
As we nucleaus is the core of the atom, where most of the mass of the atom is concentrated, and the nuclear radius is an essential concept in nuclear physics, as it represents the size of the atomic nucleus. It plays a significant role in understanding various nuclear phenomena, such as nuclear reactions, nuclear decay, and nuclear fission. This essay aims to provide a detailed explanation of the nuclear radius, its measurement, and its significance in nuclear physics.
The nuclear radius is the distance between the center of the nucleus and its outermost boundary, or the point at which the nuclear density decreases to a negligible value. The nuclear radius is much smaller than the atomic radius, which is the distance between the nucleus and the outermost electron in the atom. The atomic radius is typically on the order of angstroms (10^-10 meters), while the nuclear radius is on the order of femtometers (10^-15 meters).
Nuclear radius increases with the increase in the nucleons, i.e. atom with higher nucleons has higher radius than those of the lesser ones. However, this increase is not linear but follows a more complex trend due to the strong nuclear force that holds the nucleus together. The strong nuclear force is a short-range force that binds the nucleons together and is much stronger than the electromagnetic force that repels the positively charged protons from each other. As a result, the nuclear radius increases less rapidly than the number of nucleons, and the nuclear density decreases as the nucleus becomes larger.
Measurement of Nuclear Radius:
The measurement of nuclear radius is a challenging task due to the small size of the nucleus and the difficulty in probing its structure. Several methods have been developed to determine the nuclear radius experimentally, each with its advantages and limitations.
One of the most common methods for measuring nuclear radii is through electron scattering experiments. In this technique, high-energy electrons are directed at a thin foil of the element under investigation, and the scattered electrons are detected at different angles. The distribution of scattered electrons provides information about the size and shape of the nucleus. The advantage of this method is that it can be used for a wide range of nuclei and can provide information about the nuclear charge distribution. However, the electron scattering method is limited by the resolution of the detectors and the complexity of the nuclear structure.
Further information:
Another method for measuring nuclear radii is through the analysis of nuclear decay processes. In radioactive nuclei, the decay process involves the emission of particles from the nucleus, such as alpha or beta particles. The energy and momentum of these particles depend on the size and structure of the nucleus. By analyzing the decay products, one can determine the nuclear radius indirectly. The advantage of this method is that it can provide information about the excited states of the nucleus and the distribution of nuclear spins. However, the interpretation of the data can be complex, and the method is limited to radioactive nuclei.
A third method for measuring nuclear radii is through the study of nuclear collisions. In this technique, two nuclei are accelerated to high energies and made to collide with each other. The trajectory and energy of the scattered particles can provide information about the nuclear radius and the strength of the nuclear force. The advantage of this method is that it can provide information about the collision dynamics and the nuclear matter distribution. However, the interpretation of the data can be complex, and the method is limited to a small range of nuclei.
2 - Nuclear Spin and Parity
Spin is a quantum mechanical property that describes the intrinsic angular momentum of a nucleus, while parity is a quantum number that describes the symmetry properties of a nucleus under reflection. The spin and parity of a nucleus play a crucial role in determining its physical and chemical properties and are used extensively in nuclear physics research.
Spin:
The spin of a nucleus is a fundamental property that arises from the intrinsic angular momentum of its constituent particles, such as protons and neutrons. The spin of a nucleus is described using the quantum mechanical concept of angular momentum, which is a vector quantity that represents the rotation of an object around an axis. The magnitude of the angular momentum of a nucleus is proportional to its spin quantum number, denoted by the symbol I.
The spin quantum number can take on half-integer or integer values, depending on the number of protons and neutrons in the nucleus. For example, nuclei with an odd number of protons or neutrons have a half-integer spin, while nuclei with an even number of protons and neutrons have an integer spin. The spin quantum number is important in nuclear physics because it determines the magnetic moment of the nucleus, which is used in various experimental techniques, such as nuclear magnetic resonance (NMR) spectroscopy.
Parity:
The parity of a nucleus is a quantum number that describes its symmetry properties under reflection. A nucleus can be either even or odd parity, depending on whether it is symmetric or asymmetric under reflection. Parity is described using the quantum mechanical concept of parity operator, denoted by the symbol P, which changes the sign of the wave function of a nucleus under reflection.
The parity of a nucleus is related to the number of nucleons with spin up and spin down. For example, if a nucleus has an even number of nucleons with spin up and an even number of nucleons with spin down, it has an even parity. Conversely, if a nucleus has an odd number of nucleons with spin up and an even number of nucleons with spin down, it has an odd parity.
let $\psi$ (x,y,z) be a wave function representing the particle
then if $\psi$ (-x,-y,-z) = $\psi$ (x,y,z) : even parity
and if $\psi$ (-x,-y,-z) = - $\psi$ (x,y,z) : odd parity