Related papers: Partial conservation of seniority in $j=9/2$ shell…
We investigate the energy spectrum of systems of two, three and four spin-1/2 fermions with short range attractive interactions both exactly, and within the scattering length approximation. The formation of molecular bound states and the…
We recently formulated a rule for isomeric states for a system of 4 nucleons with isospin T=1, namely that if the nucleons are in a single j shell then states with angular momenta J=2 and J=(2j-1) are either isomeric or ground states…
We investigate the spin structure of many-fermion systems with a spin-conserving two-body random interaction. We find a strong dominance of spin-0 ground states and considerable correlations between energies and wave functions of low-lying…
Results of a comprehensive shell model (SM) analyses, within the full $f_{5/2}pg_{9/2}$ model space, of the recently available experimental data [P. Ruotsalainen et al., Phy. Rec. C {88}, 024320 (2013)] with four $T=0$ bands and one $T=1$…
The seniority scheme has been shown to be extremely useful for the classification of nuclear states in semi-magic nuclei. The neutron-proton ($np$) correlation breaks the seniority symmetry in a major way. As a result, the corresponding…
We present a class of Hamiltonians $H$ for which a sector of the Hilbert space invariant under a Lie group $G$, which is not a symmetry of $H$, possesses the essential properties of many-body scar states. These include the absence of…
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.
Two-state spin systems is a classical topic in statistical physics. We consider the problem of computing the partition function of the systems on a bounded degree graph. Based on the self-avoiding tree, we prove the systems exhibits strong…
In this paper we obtain number of states with a given spin $I$ and a given isospin $T$ for systems with three and four nucleons in a single-$j$ orbit, by using sum rules of six-$j$ and nine-$j$ symbols obtained in earlier works.
We explore a generalization of nonrelativistic fermionic statistics that interpolates between bosons and fermions, in which up to $K$ particles may occupy a single-particle state. We show that it can be mapped exactly to $K$ flavors of…
We derive the spin Boltzmann equations for spin-1/2 fermions in a non-relativistic model with four-fermion contact interaction which conserves spin degrees of freedom. A great advantage of the model is that the spin matrix elements in…
It is well-known that the 2/5 state is unpolarized at zero Zeeman energy, while it is fully polarized at large Zeeman energies. A novel state with charge/spin density wave order for Composite Fermions is proposed to exist at intermediate…
We investigate analytically and numerically a random-matrix model for m fermions occupying l1 single-particle states with positive parity and l2 single-particle states with negative parity and interacting through random two-body forces that…
A possibility to produce bound states of several heavy fermions, which are bound together due to the Higgs exchange, is examined. It is shown that for 12 fermions, 6 fermions and 6 antifermions, occupying the lowest S_{1/2} shell this bound…
We present lattice results for spin-1/2 fermions at unitarity, where the effective range of the interaction is zero and the scattering length is infinite. We measure the spatial coherence of difermion pairs for a system of 6, 10, 14, 18,…
The spin$-1/2$ chain with ferromagnetic exchange $J_1 < 0$ between first neighbors and antiferromagnetic $J_2 > 0$ between second neighbors supports two spin-Peierls (SP) instabilities depending on the frustration $\alpha = J_2/\vert…
Excited states in low-energy spectra in $^{70-76}$Ni are considered. To this end, pairing forces in form of surface delta interaction are employed to account for formation of the ground state multiplet with seniority $\nu = 2$ states. The…
We consider symmetries which arise when two-body interaction matrix elements with isopin T=0 are set equal to a constant in a single-j -shell calculation. The nucleus ^{96} Cd is used as an example.
Recently we proposed [62] a fast computing scheme for generalized seniority on spherical single-particle basis. This work redesigns the scheme to make it applicable to deformed single-particle basis. The algorithm is applied to the…
We propose a simple approach to predict the angular momentum I ground state (I g.s.) probabilities of many-body systems that does not require the diagonalization of hamiltonians with random interactions. This method is found to be…