Related papers: Irreducible tensor form of three-particle operator…
General formulas of the two-electron operator representing either atomic or effective interactions are given in a coupled tensorial form in relativistic approximation. The alternatives of using uncoupled, coupled and antisymmetric…
A general method is described for finding algebraic expressions for matrix elements of any one- and two-particle operator for an arbitrary number of subshells in an atomic configuration, requiring neither coefficients of fractional…
The atomic third-order open-shell many-body perturbation theory is developed. Special attention is paid to the generation and algebraic analysis of terms of the wave operator and the effective Hamiltonian as well. Making use of…
The tensorial form of the spin-other-orbit interaction operator in the formalism of second quantization is presented. Such an expression is needed to calculate both diagonal and off-diagonal matrix elements according to an approach, based…
The irreducible tensor operators and their tensor products employing Racah algebra are studied. Transformation procedure of the coordinate system operators act on are introduced. The rotation matrices and their parametrization by the…
General method is suggested to find non-relativistic and relativistic matrix elements of one- and two-electron operators for any number of open shells in atom, requiring neither coefficients of fractional parentage nor unit tensors. It is…
An operator form of the 3N bound state is proposed. It consists of eight operators formed out of scalar products in relative momentum and spin vectors, which are applied on a pure 3N spin 1/2 state. Each of the operators is associated with…
We study a commuting triple of bounded operators $(A, B, P)$ which has the tetrablock as a spectral set.
We study the problem of calculating two-loop three-point diagrams with irreducible numerators (i.e. numerators which cannot be expressed in terms of the denominators). For the case of massless internal particles and arbitrary (off-shell)…
Tensor representation (TR) for wave function (WF) of three-nucleon bound state with the total angular momentum I=1/2 is discussed. The WF in TR has 16 complex components depending on vectors of relative momenta. Constraints on the WF…
We consider various systematic ways of defining unbounded operator valued integrals of complex functions with respect to (mostly) positive operator measures and positive sesquilinear form measures, and investigate their relationships to…
We study the breaking of rotational symmetry on the lattice for irreducible tensor operators and practical methods for suppressing this breaking. We illustrate the features of the general problem using an $\alpha$ cluster model for…
We show how to construct embedding space three-point functions for operators in arbitrary Lorentz representations by employing the formalism developed in arXiv:1905.00036 and arXiv:1905.00434. We study tensor structures that intertwine the…
The pseudo-SU(3) model is extended to explicitly include the spin and proton-neutron degrees of freedom. A general formalism for evaluating matrix elements of one-body and two-body tensor operators within this framework is presented. The…
Traditional theory of many-electron atoms and ions is based on the coefficients of fractional parentage and matrix elements of tensorial operators, composed of unit tensors. Then the calculation of spin-angular coefficients of radial…
Using the multipole expansion of electromagnetic (EM) field, we present the angular magnetoelectric (AME) coupling in irreducible tensor form. We evaluate the matrix elements when the radiation source is described by electronic transitions…
We derive the recurrence relation of irreducible tensor operator for O(4) in using the Wigner-Eckart theorem. The physical process like radiative transitions in atomic physics, nuclear transitions between excited nuclear states can be…
A typical quantum experiment has a bunch of apparatuses placed so that quantum systems can pass between them. We regard each use of an apparatus, along with some given outcome on the apparatus (a certain detector click or a certain meter…
Using the irreducible tensor-operator technique, we establish the relation between different forms of spin tomograms. Quantizer and dequantizer operators are presented in simple explicit forms and are specified for the low-spin states. The…
The general tensorial form of the orbit-orbit interaction operator in the formalism of second quantization is presented. Such an expression is needed to calculate both diagonal and off-diagonal matrix elements with respect to…