3,006 research outputs found

### Classification of states of single-$j$ fermions with $J$-pairing interaction

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 for six-$j$ symbols. It is also found that the "non-integer" eigenvalues
of three fermions with angular momentum $I$ around the maximum appear as
"non-integer" eigenvalues of four fermions when $I$ is around (or larger than)
$J_{\rm max}$ and the Hamiltonian contains only an interaction between pairs of
fermions coupled to spin $J=J_{\rm max}=2j-1$. This pattern is also found in
five and six fermion systems. A boson system with spin $l$ exhibits a similar
pattern.Comment: to be published in Physical Review

### General pairing interactions and pair truncation approximations for fermions in a single-j shell

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 pairing interaction, eigenvalues are found to be approximately integers
for a large array of states, in particular for those with total angular momenta
I le 2j. For I=0 eigenstates of four fermions in a single-j shell we show that
there is only one non-zero eigenvalue. We address these observations using the
nucleon pair approximation of the shell model and relate our results with a
number of currently interesting problems.Comment: a latex text file and 2 figures, to be publishe

### Towards understanding the probability of $0^+$ ground states in even-even many-body systems

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 $n$ is the particle number, $v$ is the seniority, $\beta$ is an
additional quantum number, and $I$ is the angular momentum of the state.
Interesting regularities of the probabilities of $I^+$ ground states are
noticed and discussed for 4-particle systems. Several counter examples of the
$0^+$ ground state (0GS) predominance are noticed for the first time.Comment: 5 pages, 1 figure. Phys. Rev. C64, in pres

### Analytic approach to nuclear rotational states: The role of spin - A minimal model -

We use a simple field theory model to investigate the role of the nucleon
spin for the magnetic sum rules associated with the low-lying collective
scissors mode in deformed nuclei. Various constraints from rotational symmetry
are elucidated and discussed. We put special emphasis on the coupling of the
spin part of the M1 operator to the low lying collective modes, and investigate
how this coupling changes the sum rules.Comment: 15 pages, 4 figure

### Energy Centroids of Spin $I$ States by Random Two-body Interactions

In this paper we study the behavior of energy centroids (denoted as
$\bar{E_I}$) of spin $I$ states in the presence of random two-body
interactions, for systems ranging from very simple systems (e.g. single-$j$
shell for very small $j$) to very complicated systems (e.g., many-$j$ shells
with different parities and with isospin degree of freedom). Regularities of
$\bar{E_I}$'s discussed in terms of the so-called geometric chaoticity (or
quasi-randomness of two-body coefficients of fractional parentage) in earlier
works are found to hold even for very simple systems in which one cannot assume
the geometric chaoticity. It is shown that the inclusion of isospin and parity
does not "break" the regularities of $\bar{E_I}$'s.Comment: four figures. to appear in Physical Review

### Nuclear Mass Dependence of Chaotic Dynamics in Ginocchio Model

The chaotic dynamics in nuclear collective motion is studied in the framework
of a schematic shell model which has only monopole and quadrupole degrees of
freedom. The model is shown to reproduce the experimentally observed global
trend toward less chaotic motion in heavier nuclei. The relation between
current approach and the earlier studies with bosonic models is discussed.Comment: 11 Page REVTeX file, 2 postscript figures, uuencode

### Housework and childcare in Italy: a persistent case of gender inequality

This article focuses on the gender gap in housework and childcare in Italian couples. Italian women still carry out three-quarters of domestic work and two-thirds of childcare. We focus on three possible theoretical explanations for the persistence of the gendered division of labor: time availability, relative resources, and conformity with traditional gender ideology. Time Use data from the 2008/09 Survey edition have been used: we considered couples, married or in consensual unions, with at least one child under 14 years of age and with the mother employed

### Critical-Point Symmetry in a Finite System

At a critical point of a second order phase transition the intrinsic energy
surface is flat and there is no stable minimum value of the deformation.
However, for a finite system, we show that there is an effective deformation
which can describe the dynamics at the critical point. This effective
deformation is determined by minimizing the energy surface after projection
onto the appropriate symmetries. We derive analytic expressions for energies
and quadrupole rates which provide good estimates for these observables at the
critical point.Comment: 12 pages, 2 figures, 2 tables, Phys. Rev. Lett. in pres

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