相关论文: Relations Between Coefficients of Fractional Paren…

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…

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"…

A partial conservation of the seniority quantum number in $j=9/2$ shells has been found recently in a numerical application. In this paper a complete analytic proof for this problem is derived as an extension of the work by Zamick and P.…

A new procedure for the calculation of shell model coefficients of fractional parentage has been developed. This procedure is free of numerical diagonalization, orthogonalization, and even of grop theoretical classification of antisymmetric…

The concept of seniority plays a central role in nuclear structure physics by classifying many-body states according to the number of unpaired nucleons. While exact seniority conservation holds in single-$j$ systems with $j \leq 7/2$,…

We present analytic proofs of the properties of four particle states in the g9/2 shell which have seniority v=4 and angular momentum I=4 or 6.We show in particular that the number of pairs with angular momentum I is equal to one for these…

A discussion of the seniority quantum number in many-body systems is presented. The analysis is carried out for bosons and fermions simultaneously but is restricted to identical particles occupying a single shell. The emphasis of the paper…

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…

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…

For single-$j$ shells with $j={7/2}, {9/2}$ and 11/2, we relate the large probability of $I^+$ ground states to the largest (smallest) coefficients $\alpha^J_{I(v \beta)} = <nv \beta I |$ $A^{J \dagger} \cdot A^J | n v\beta I>$, where $n$…

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 find a relationship between coefficients of fractional parentage (cfp) obtained on the one hand from the principal parent method and on the other hand from a seniority classification. We apply this to the Redmond recursion formula 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…

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.…

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…

We introduce an algorithm to obtain coefficients of fractional parentage for light $p$-shell nuclei. The coefficients enable to use Jacobi coordinates in no-core shell model calculations separating off the center-of-mass motion. Fully…

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…

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…

There exist two uniquely defined $v=4$ states in systems within a $j=9/2$ subshell, which automatically conserve seniority and do not mix with other states. Here I show that the partial conservation of seniority plays an essential role in…

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…