Related papers: Alternate derivation of the Ginocchio--Haxton rela…
We address the problem, previously considered by Ginocchio and Haxton (G-H), of the number of states for three identical particles in a single j-shell with angular momentum J=j. G-H solved this problem in the context of the quantum Hall…
We consider 2 neutrons and 2 protons in the g_{9/2} shell.Wave functions and energy levels are obtained for various interactions. The wave functions for states with total angular momentum I greater or equal to 10 are not affected by what…
For a system with three identical nucleons in a single-$j$ shell, the states can be written as the angular momentum coupling of a nucleon pair and the odd nucleon. The overlaps between these non-orthonormal states form a matrix which…
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…
It is noted that the simple interaction in isospin variables $a (1/4 - t(i)\cdot t(j))$, in a single $j$ shell calculation, can also be written with angular momentum variables. For the configuration $(j^2) J_A$ for even $J_A$ the isospin is…
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…
We solve the N-body Calogero problem, \ie N particles in 1 dimension subject to a two-body interaction of the form $\half \sum_{i,j}[ (x_i - x_j)^2 + g/ {(x_i - x_j)^2}]$, by constructing annihilation and creation operators of the form $…
It is noted that in a calculation with 4 nucleons with isospin 1 in a single j shell (f_{7/2}, g_{9/2}, h_{11/2}) the state with median angular momentum J = (J_{max}+1)/2 lies very low in energy becoming either an isomeric state or a ground…
A new angular momentum projection for systems of particles with arbitrary spins is formulated based on the Heine-Stieltjes correspondence, which can be regarded as the solutions of the mean-field plus pairing model in the strong pairing…
The onset of hyperons in the core of neutron stars and the consequent softening of the equation of state have been questioned for a long time. Controversial theoretical predictions and recent astrophysical observations of neutron stars are…
We propose a new scenario of neutrino masses with a Higgs triplet $(\xi^{++},\xi^+,\xi^0)$ in a theory of large extra dimensions. Lepton number violation in a distant brane acts as the source of a very small trilinear coupling of $\xi$ to…
A generalized uncertainty relation for an entangled pair of particles is obtained if we impose a symmetrization rule for all operators that we should use when doing any calculation using the entangled wave function of the pair. This new…
It is here noted that in a calculation with four nucleons with isospin T=1 in a single J shell the states with angular momentum J=(J(max)+1)/2 lie very low and become either isomeric states or ground states.
Growing non-singular solution of 6-dimensional Einstein equations for the 4-brane in infinite transversal 2-space is found. This solution provides gravitational trapping of matter and 4-dimensional gravity on the brane without extra…
We consider the problem to single out a particular state among $2^n$ orthogonal pure states. As it turns out, in general the optimal strategy is not to measure the particles separately, but to consider joint properties of the $n$-particle…
The covariant spectator (or Gross) equations for the bound state of three identical spin 1/2 particles, in which two of the three interacting particles are always on shell, are developed and reduced to a form suitable for numerical…
Let $k$ be a natural number and let $c=2.134693\ldots$ be the unique real solution of the equation $2c=2+\log (5c-1)$ in $[1,\infty)$. Then, when $s\ge ck+4$, we establish an asymptotic lower bound of the expected order of magnitude for the…
By means of a general classification of the different kinds of matter of nature form a chain from the world of the subatomic particles to the large bodies of the universe, the galaxies. Then, it proposes a new baryonic force for the…
The $2N$-dimensional quantum problem of $N$ particles (e.g. electrons) with interaction $\beta/r^2$ in a two-dimensional parabolic potential $\omega_0$ (e.g. quantum dot) and magnetic field $B$, reduces exactly to solving a…
The familiar Greenberger-Horne-Zeilinger (GHZ) states can be rewritten by entangling the Bell states for two qubits with a state of the third qubit, which is dubbed entangled entanglement. We show that in this way we obtain all 8…