 | This article has multiple issues. Please help improve it or discuss these issues on the talk page . (Learn how and when to remove these template messages)
|
The Pandya theorem is a good illustration of the richness of information forthcoming from a judicious use of subtle symmetry principles connecting vastly different sectors of nuclear systems. It is a tool for calculations regarding both particles and holes.
Pandya theorem provides a theoretical framework for connecting the energy levels in jj coupling of a nucleon-nucleon and nucleon-hole system. It is also referred to as Pandya Transformation or Pandya Relation in literature. It provides a very useful tool for extending shell model calculations across shells, for systems involving both particles and holes.
The Pandya transformation, which involves angular momentum re-coupling coefficients (Racah-Coefficient), can be used to deduce one-particle one-hole (ph) matrix elements. By assuming the wave function to be "pure" (no configuration mixing), Pandya transformation could be used to set an upper bound to the contributions of 3-body forces to the energies of nuclear states.
It was first published in 1956 as follows:
Nucleon-Hole Interaction in jj Coupling
S.P. Pandya, Phys. Rev. 103, 956 (1956). Received 9 May 1956
A theorem connecting the energy levels in jj coupling of a nucleon-nucleon and nucleon-hole system is derived, and applied in particular to Cl38 and K40.
Since it is by no means obvious how to extract "pairing correlations" from the realistic shell-model calculations, Pandya transform is applied in such cases. The "pairing Hamiltonian" is an integral part of the residual shell-model interaction. The shell-model Hamiltonian is usually written in the p-p representation, but it also can be transformed to the p-h representation by means of the Pandya transformation. This means that the high-J interaction between pairs can translate into the low-J interaction in the p-h channel. It is only in the mean-field theory that the division into "particle-hole" and "particle-particle" channels appears naturally.
Some features of the Pandya transformation are as follows:
Pandya theorem establishes a relation between particle-particle and particle-hole spectra. Here one considers the energy levels of two nucleons with one in orbit j and another in orbit j' and relate them to the energy levels of a nucleon hole in orbit j and a nucleus in j. Assuming pure j-j coupling and two-body interaction, Pandya (1956) derived the following relation:
This was successfully tested in the spectra of
Figure 3 shows the results where the discrepancy between the calculated and observed spectra is less than 25 keV.
In physics and chemistry, a nucleon is either a proton or a neutron, considered in its role as a component of an atomic nucleus. The number of nucleons in a nucleus defines the atom's mass number.
Rutherfordium is a synthetic chemical element; it has symbol Rf and atomic number 104. It is named after physicist Ernest Rutherford. As a synthetic element, it is not found in nature and can only be made in a particle accelerator. It is radioactive; the most stable known isotope, 267Rf, has a half-life of about 48 minutes.
In nuclear physics, atomic physics, and nuclear chemistry, the nuclear shell model utilizes the Pauli exclusion principle in order to model the structure of atomic nuclei in terms of energy levels. The first shell model was proposed by Dmitri Ivanenko in 1932. The model was developed in 1949 following independent work by several physicists, most notably Maria Goeppert Mayer and J. Hans D. Jensen, who shared half of the 1963 Nobel Prize in Physics for their contributions.
Moscovium is a synthetic chemical element; it has symbol Mc and atomic number 115. It was first synthesized in 2003 by a joint team of Russian and American scientists at the Joint Institute for Nuclear Research (JINR) in Dubna, Russia. In December 2015, it was recognized as one of four new elements by the Joint Working Party of international scientific bodies IUPAC and IUPAP. On 28 November 2016, it was officially named after the Moscow Oblast, in which the JINR is situated.
Flerovium is a superheavy synthetic chemical element; it has symbol Fl and atomic number 114. It is an extremely radioactive synthetic element, named after the Flerov Laboratory of Nuclear Reactions of the Joint Institute for Nuclear Research in Dubna, Russia, where the element was discovered in 1999. The lab's name, in turn, honours Russian physicist Georgy Flyorov. IUPAC adopted the name on 30 May 2012. The name and symbol had previously been proposed for element 102 (nobelium), but was not accepted by IUPAC at that time.
In quantum physics and chemistry, quantum numbers describe values of conserved quantities in the dynamics of a quantum system. Quantum numbers correspond to eigenvalues of operators that commute with the Hamiltonian—quantities that can be known with precision at the same time as the system's energy—and their corresponding eigenspaces. Together, a specification of all of the quantum numbers of a quantum system fully characterize a basis state of the system, and can in principle be measured together.
In nuclear physics, a magic number is a number of nucleons such that they are arranged into complete shells within the atomic nucleus. As a result, atomic nuclei with a 'magic' number of protons or neutrons are much more stable than other nuclei. The seven most widely recognized magic numbers as of 2019 are 2, 8, 20, 28, 50, 82, and 126.
In physics, a parity transformation is the flip in the sign of one spatial coordinate. In three dimensions, it can also refer to the simultaneous flip in the sign of all three spatial coordinates :
In quantum mechanics, angular momentum coupling is the procedure of constructing eigenstates of total angular momentum out of eigenstates of separate angular momenta. For instance, the orbit and spin of a single particle can interact through spin–orbit interaction, in which case the complete physical picture must include spin–orbit coupling. Or two charged particles, each with a well-defined angular momentum, may interact by Coulomb forces, in which case coupling of the two one-particle angular momenta to a total angular momentum is a useful step in the solution of the two-particle Schrödinger equation. In both cases the separate angular momenta are no longer constants of motion, but the sum of the two angular momenta usually still is. Angular momentum coupling in atoms is of importance in atomic spectroscopy. Angular momentum coupling of electron spins is of importance in quantum chemistry. Also in the nuclear shell model angular momentum coupling is ubiquitous.
In quantum physics, the spin–orbit interaction is a relativistic interaction of a particle's spin with its motion inside a potential. A key example of this phenomenon is the spin–orbit interaction leading to shifts in an electron's atomic energy levels, due to electromagnetic interaction between the electron's magnetic dipole, its orbital motion, and the electrostatic field of the positively charged nucleus. This phenomenon is detectable as a splitting of spectral lines, which can be thought of as a Zeeman effect product of two relativistic effects: the apparent magnetic field seen from the electron perspective and the magnetic moment of the electron associated with its intrinsic spin. A similar effect, due to the relationship between angular momentum and the strong nuclear force, occurs for protons and neutrons moving inside the nucleus, leading to a shift in their energy levels in the nucleus shell model. In the field of spintronics, spin–orbit effects for electrons in semiconductors and other materials are explored for technological applications. The spin–orbit interaction is at the origin of magnetocrystalline anisotropy and the spin Hall effect.
A three-body force is a force that does not exist in a system of two objects but appears in a three-body system. In general, if the behaviour of a system of more than two objects cannot be described by the two-body interactions between all possible pairs, as a first approximation, the deviation is mainly due to a three-body force.
The Jahn–Teller effect is an important mechanism of spontaneous symmetry breaking in molecular and solid-state systems which has far-reaching consequences in different fields, and is responsible for a variety of phenomena in spectroscopy, stereochemistry, crystal chemistry, molecular and solid-state physics, and materials science. The effect is named for Hermann Arthur Jahn and Edward Teller, who first reported studies about it in 1937.
The QCD vacuum is the quantum vacuum state of quantum chromodynamics (QCD). It is an example of a non-perturbative vacuum state, characterized by non-vanishing condensates such as the gluon condensate and the quark condensate in the complete theory which includes quarks. The presence of these condensates characterizes the confined phase of quark matter.
The nuclear force is a force that acts between hadrons, most commonly observed between protons and neutrons of atoms. Neutrons and protons, both nucleons, are affected by the nuclear force almost identically. Since protons have charge +1 e, they experience an electric force that tends to push them apart, but at short range the attractive nuclear force is strong enough to overcome the electrostatic force. The nuclear force binds nucleons into atomic nuclei.
Understanding the structure of the atomic nucleus is one of the central challenges in nuclear physics.
The light-front quantization of quantum field theories provides a useful alternative to ordinary equal-time quantization. In particular, it can lead to a relativistic description of bound systems in terms of quantum-mechanical wave functions. The quantization is based on the choice of light-front coordinates, where plays the role of time and the corresponding spatial coordinate is . Here, is the ordinary time, is one Cartesian coordinate, and is the speed of light. The other two Cartesian coordinates, and , are untouched and often called transverse or perpendicular, denoted by symbols of the type . The choice of the frame of reference where the time and -axis are defined can be left unspecified in an exactly soluble relativistic theory, but in practical calculations some choices may be more suitable than others.
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 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.
Unbiunium, also known as eka-actinium or element 121, is a hypothetical chemical element; it has symbol Ubu and atomic number 121. Unbiunium and Ubu are the temporary systematic IUPAC name and symbol respectively, which are used until the element is discovered, confirmed, and a permanent name is decided upon. In the periodic table of the elements, it is expected to be the first of the superactinides, and the third element in the eighth period. It has attracted attention because of some predictions that it may be in the island of stability. It is also likely to be the first of a new g-block of elements.
In nuclear physics, ab initio methods seek to describe the atomic nucleus from the bottom up by solving the non-relativistic Schrödinger equation for all constituent nucleons and the forces between them. This is done either exactly for very light nuclei or by employing certain well-controlled approximations for heavier nuclei. Ab initio methods constitute a more fundamental approach compared to e.g. the nuclear shell model. Recent progress has enabled ab initio treatment of heavier nuclei such as nickel.
Unbihexium, also known as element 126 or eka-plutonium, is a hypothetical chemical element; it has atomic number 126 and placeholder symbol Ubh. Unbihexium and Ubh are the temporary IUPAC name and symbol, respectively, until the element is discovered, confirmed, and a permanent name is decided upon. In the periodic table, unbihexium is expected to be a g-block superactinide and the eighth element in the 8th period. Unbihexium has attracted attention among nuclear physicists, especially in early predictions targeting properties of superheavy elements, for 126 may be a magic number of protons near the center of an island of stability, leading to longer half-lives, especially for 310Ubh or 354Ubh which may also have magic numbers of neutrons.
