Related papers: Number of spin-J states and odd-even staggering fo…
It is noted that in single j-shell calculations certain odd-spin states in even--even nuclei lie in a narrow energy band; likewise certain states in odd--odd nuclei.
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…
In this paper we study the enumeration of number (denoted as ${D_I}$) of spin $I$ states for fermions in a single-$j$ shell and bosons with spin $l$. We show that $D_I$ can be enumerated by the reduction from SU$(n+1)$ to SO(3). New…
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…
In the single j shell there is a two to one relationship between the spectra of certain even-even and neighbouring odd mass nuclei e.g. the calculated energy levels of J=0^+ states in ^{44}Ti are at twice the energies of corresponding…
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 show that a system of three fermions is exactly solvable for the case of a single-$j$ in the presence of an angular momentum-$J$ pairing interaction. On the basis of the solutions for this system, we obtain new sum rules…
Recent studies show that for systems with four identical fermions in the $j=9/2$ shell two special states, which have seniority $v=4$ and total spins I=4 and 6, are eigenstates of any two-body interaction. These states have good seniority…
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 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…
Analytical expressions of the total number of $J$ levels for three and four fermions in a nuclear $j^n$ shell are provided. The formulas were derived using a combination of sum rules for coefficients of fractional parentage, and "unusual"…
In this work we calculate the energies odd J$^{+}$ states in selectedeven-even nuclei-$^{44}$ Ti $^{52}$ Fe and $^{96}$Cd. Of particularinterest is the fact that in many cases the first T=0 and the first T=1 state are close in energy.…
For each of the (9/2), (11/2) and (13/2) single j shells we have only one state with J=j V=3 for a five particle system. For four identical particles there can be more than one state of seniority four. We note some ``ratio'' relations for…
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 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…
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…
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 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…
The fragmentation of thermalized sources is studied using a version of the Statistical Multifragmentation Model which employs state densities that take the pairing gap in the nuclear levels into account. Attention is focused on the…
We point out a simplicity that arises when we use an interaction in which only an energy with odd J is non-zero. The emphasis is on J= J_{max} and in particular J=9+ in the g_{9/2} shell. It is noted that high overlaps can be deceptive. In…