Spectrosopic Study of Baryons

Baryons are the combination of three quarks(antiquarks) configured by qqq(q¯q¯q¯). They are fermions and obey the Pauli’s principal so that the total wave function must be anti-symmetric. The SU(5) flavor group includes all types of baryons containing zero, one, two or three heavy quarks. The Particle Data Froup (PDG) listed the ground states of most of these baryons and many excited states in their summary Table. The radial and orbital excited states of the baryons are important to calculate, from that the Regge trajectories will be constructed. The quantum numbers will be determined from these slopes and intersects. Thus, we can help experiments to determine the masses of unknown states. The other hadronic properties like decays, magnetic moments can also play a very important role to emphasize the baryons. It is also interesting to determine the properties of exotic baryons nowadays.

Modern State of the Pauli Exclusion Principle and the Problems of Its Theoretical Foundation

The Pauli exclusion principle (PEP) can be considered from two aspects. First, it asserts that particles that have half-integer spin (fermions) are described by antisymmetric wave functions, and particles that have integer spin (bosons) are described by symmetric wave functions. It is called spin-statistics connection (SSC). The physical reasons why SSC exists are still unknown. On the other hand, PEP is not reduced to SSC and can be consider from another aspect, according to it, the permutation symmetry of the total wave function can be only of two types: symmetric or antisymmetric. They both belong to one-dimensional representations of the permutation group, while other types of permutation symmetry are forbidden. However, the solution of the Schrödinger equation may have any permutation symmetry. We analyze this second aspect of PEP and demonstrate that proofs of PEP in some wide-spread textbooks on quantum mechanics, basing on the indistinguishability principle, are incorrect. The indistinguishability principle is insensitive to the permutation symmetry of wave function. So, it cannot be used as a criterion for the PEP verification. However, as follows from our analysis of possible scenarios, the permission of states with permutation symmetry more general than symmetric and antisymmetric leads to contradictions with the concepts of particle identity and their independence. Thus, the existence in our Nature particles only in symmetric and antisymmetric permutation states is not accidental, since all symmetry options for the total wave function, except the antisymmetric and symmetric, cannot be realized. From this an important conclusion follows, we may not expect that in future some unknown elementary particles that are not fermions or bosons can be discovered.

ISGUR–WISE FUNCTION IN A QCD POTENTIAL MODEL WITH COULOMBIC POTENTIAL AS PERTURBATION

We study heavy light mesons in a QCD inspired quark model with the Cornell potential [Formula: see text]. Here we consider the linear term br as the parent and [Formula: see text], i.e. the Coloumbic part as the perturbation. The linear parent leads to Airy function as the unperturbed wave function. We then use the Dalgarno method of perturbation theory to obtain the total wave function corrected up to first order with Coulombic piece as the perturbation. With these wave functions, we study the Isgur–Wise function and calculate its slope and curvature.

Theoretical Oscillator Strengths for nS–mP Transitions in Mg

Theoretical oscillator strengths for the 3s ns1,3S–3s mp1,3P transitions of Mg are reported for n,m = 3,4,…,7.The results are based on an MCHF approximation to the total wave function which includes the correlation of the outer two electrons.

Theoretical Oscillator Strengths for nP → nD Transitions in Mg

Theoretical oscillator strengths for the transitions 3s np1,3P → 3s md1,3D of Mg are reported for n = 3,4, … and m = 3,4,…The results are based on an MCHF approximation to the total wave function which includes the correlation of the outer two electrons.

A GROUP-THEORETICAL TREATMENT OF ELECTRONIC, VIBRATIONAL, TORSIONAL, AND ROTATIONAL MOTIONS IN THE DIMETHYLACETYLENE MOLECULE

The Hamiltonian for the dimethylacetylene molecule is expressed in terms of a set of coordinates which allow a separation of the molecular wave function into an electronic part, a vibrational part, a torsional part, and a rotational part. Symmetry species are introduced which can be used to classify separately any one of the parts of the molecular wave function as well as the total wave function itself. These symmetry species correspond not only to the single-valued representations of the group proposed by Longuet-Higgins for the dimethylacetylene molecule, but also to double-valued representations of that group. The use of these symmetry species and of the corresponding selection rules is illustrated by the example of an optical transition which would correspond to a [Formula: see text] transition in the linear portion of the dimethylacetylene molecule.

Über die Symmetrie-Eigenschaften der reduzierten Dichtematrizen und der natürlichen Spin-Orbitale und Spin-Geminale (der natürlichen Ein- und Zwei-Elektronen-Funktionen)

The density operator (density matrix) of a quantum mechanical system can be decomposed into operators which transform as irreducible representations of the symmetry group in coordinate and spin space. Each of these components has a physical meaning connected with the expectation values of certain operators. The reduced density matrices can be decomposed in a completely analogous way.The symmetry properties of the total wave function give rise to degeneracies of the eigenvalues of the reduced density matrices. These degeneracies can be removed by requiring that the natural spin orbitals (NSO, defined as the eigenfunctions of the first order density matrix), as well as the natural spin geminais (NSG, the eigenfunctions of the second order density matrix) and their spinless counterparts transform as irreducible representations of the symmetry group and are eigenfunctions of S2 and Sz.In many important cases this requirement is compatible with the original definition of the NSO, the NSG etc. e. g., when there is no spatial degeneracy of the total wave function and when the Z-component of the total spin vanishes. When these conditions are not fulfilled an alternative definition of the NSO and the NSG is proposed.