Related papers: Classification of states of single-$j$ fermions wi…
We investigate Hamiltonians with attractive interactions between pairs of fermions coupled to angular momentum J. We show that pairs with spin J are reasonable building blocks for the low-lying states. For systems with only a J = Jmax…
We had previously used techniques involving isospin to count the number of states for three identical fermions in a single j shell with total angular momentum I=j. We generalize this to all I, but the main thrust of this work is to consider…
In this paper we study $J$-pairing Hamiltonian and find that the sum of eigenvalues of spin $I$ states equals sum of norm matrix elements within the pair basis for four identical particles such as four fermions in a single-$j$ shell or four…
We propose closed-form expressions of the distributions of magnetic quantum number $M$ and total angular momentum $J$ for three and four fermions in single-$j$ orbits. The latter formulas consist of polynomials with coefficients satisfying…
We present in this paper empirical formulas for the number of angular momentum I states for three and four identical fermions or bosons. In the cases with large I we prove that the number of states with the same ${\cal M}$ and n but…
In this talk I shall introduce our recent works on general pairing interactions and pair truncation approximations for fermions in a single-j shell, including the spin zero dominance, features of eigenvalues of fermion systems in a single-j…
Using a generalization of Cayley's hyperdeterminant as a new measure of tripartite fermionic entanglement we obtain the SLOCC classification of three-fermion systems with six single particle states. A special subclass of such three-fermion…
A quantum mechanical three-body problem for two identical fermions of mass $m$ and a distinct particle of mass $m_1$ in the universal limit of zero-range two-body interaction is studied. For the unambiguous formulation of the problem in the…
We qualify the main features of the spectrum of the Hamiltonian of point interaction for a three-dimensional quantum system consisting of three point-like particles, two identical fermions, plus a third particle of different species, with…
For systems with three and four fermions within a single-j shell, analytical expressions for the state energies are presented from a decomposition of the angular momentum. In some important cases the expressions acquire a very simple form.…
In a previous work we considered the number of pairs of particles with angular momentum J12 for systems with angular momentum zero.Here we extend the work to states of any total angular momentum.We find simplified relations satisfied for a…
In this work, new recursion relations for the number of spin-J states for identical particles in a single-j shell are presented. Such relations are obtained using the generating-function technique, which enables one to exhibit an odd-even…
We consider a quantum mechanical three-particle system made of two identical fermions of mass one and a different particle of mass $ m $, where each fermion interacts via a zero-range force with the different particle. In particular we…
The existence of states with angular momenta $I = 4$ and~6 of four fermions in an angular momentum $j = 9/2$ shell that are stationary for any rotationally invariant two-body interaction despite the presence of other states with the same…
We consider either 3 spinless bosons or 3 equal mass spin-1/2 fermions, interacting via a short range potential of infinite scattering length and trapped in an isotropic harmonic potential. For a zero-range model, we obtain analytically the…
We study a three-body system with zero-range interactions in a one-dimensional harmonic trap. The system consists of two spin-polarized fermions and a third particle which is distinct from two others (2+1 system). First we assume that the…
Spin density matrices of the system, containing arbitrary even number N of indistinguishable fermions with spin S = 1/2, described by antisymmetric wave function, have been calculated. The indistinguishability and the Pauli principles are…
We introduce and study an exactly solvable model of several species of fermions in which particles interact pairwise through a mutual magnetic field; the interaction operates only between particles belonging to different species. After an…
Spectroscopic labels for a few particles with spin that are harmonically trapped in one-dimension with effectively zero-range interactions are provided by quantum numbers that characterize the symmetries of the Hamiltonian: permutations of…
We count the number of pairs in the single $j-$shell model of $^{44}$Ti for various interactions. For a state of total angular momentum $I$, the wave function can be written as $\Psi=\sum_{J_P J_N} D(J_P J_N) [(j^2)_{J_P}(j^2)_{J_N}]_I$,…