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

Classification of states of single-jj fermions with JJ-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

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

Ferroelectric polarization flop in a frustrated magnet MnWO4_4 induced by magnetic fields

The relationship between magnetic order and ferroelectric properties has been investigated for MnWO$_4$ with long-wavelength magnetic structure. Spontaneous electric polarization is observed in an elliptical spiral spin phase. The magnetic-field dependence of electric polarization indicates that the noncollinear spin configuration plays a key role for the appearance of ferroelectric phase. An electric polarization flop from the b direction to the a direction has been observed when a magnetic field above 10T is applied along the b axis. This result demonstrates that an electric polarization flop can be induced by a magnetic field in a simple system without rare-earth f-moments.Comment: 9 pages, 4 figure

Number of states for nucleons in a single-jj shell

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.Comment: to be published in Physical Review