3,006 research outputs found

    Classification of states of single-jj fermions with JJ-pairing interaction

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    In this paper we show that a system of three fermions is exactly solvable for the case of a single-jj in the presence of an angular momentum-JJ pairing interaction. On the basis of the solutions for this system, we obtain new sum rules for six-jj symbols. It is also found that the "non-integer" eigenvalues of three fermions with angular momentum II around the maximum appear as "non-integer" eigenvalues of four fermions when II is around (or larger than) JmaxJ_{\rm max} and the Hamiltonian contains only an interaction between pairs of fermions coupled to spin J=Jmax=2j−1J=J_{\rm max}=2j-1. This pattern is also found in five and six fermion systems. A boson system with spin ll 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

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    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+0^+ ground states in even-even many-body systems

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    For single-jj shells with j=7/2,9/2j={7/2}, {9/2} and 11/2, we relate the large probability of I+I^+ ground states to the largest (smallest) coefficients αI(vβ)J=<nvβI∣\alpha^J_{I(v \beta)} = <nv \beta I | AJ†⋅AJ∣nvβI>A^{J \dagger} \cdot A^J | n v\beta I>, where nn is the particle number, vv is the seniority, β\beta is an additional quantum number, and II is the angular momentum of the state. Interesting regularities of the probabilities of I+I^+ ground states are noticed and discussed for 4-particle systems. Several counter examples of the 0+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 -

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    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 II States by Random Two-body Interactions

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    In this paper we study the behavior of energy centroids (denoted as EIˉ\bar{E_I}) of spin II states in the presence of random two-body interactions, for systems ranging from very simple systems (e.g. single-jj shell for very small jj) to very complicated systems (e.g., many-jj shells with different parities and with isospin degree of freedom). Regularities of EIˉ\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 EIˉ\bar{E_I}'s.Comment: four figures. to appear in Physical Review

    Nuclear Mass Dependence of Chaotic Dynamics in Ginocchio Model

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    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

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    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

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    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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