Towards understanding the probability of 0+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

Energy Centroids of Spin II 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

Perovskite Manganites Hosting Versatile Multiferroic Phases with Symmetric and Antisymmetric Exchange Strictions

Complete magnetoelectric (ME) phase diagrams of orthorhombic $R$MnO$_{3}$ with and without magnetic moments on the $R$ ions have been established. Three kinds of multiferroic ground states, the $ab$-cycloidal, the $bc$-cycloidal, and the collinear $E$-type phases, have been identified by the distinct ME responses. The electric polarization of the $E$-type phase dominated by the symmetric spin exchange ($bm{S}_{i} cdot bm{S}_{j}$) is more than 10 times as large as that of the $bc$-cycloidal phase dominated by the antisymmetric one ($bm{S}_{i} times bm{S}_{j}$), and the ME response is enhanced near the bicritical phase boundary between these multiferroic phases of different origins. These findings will provide an important clue for the development of the magnetically induced multiferroics.Comment: 5 pages, 3 figure

Lattice-form dependent orbital shape and charge disproportionation in charge- and orbital-ordered manganites

The orbital shapes and charge disproportionations at nominal Mn$^{3+}$ and Mn$^{4+}$ sites for the charge- and orbital-ordered phases have been studied on half-doped manganites Pr(Sr$_{0.1}$Ca$_{0.9}$)$_2$Mn$_2$O$_7$ and Eu$_{0.5}$Ca$_{1.5}$MnO$_4$ with double-layer and single-layer Mn-O networks, respectively, by means of x-ray structural analyses, in comparison with Pr$_{0.5}$Ca$_{0.5}$MnO$_3$ with the pseudo cubic network. In a single-layer Eu$_{0.5}$Ca$_{1.5}$MnO$_4$ system, the ($y^2-z^2$)/($z^2-x^2$)-type orbital shape is observed, while the ($3y^2-r^2$)/($3x^2-r^2$)-type orbital shape in a pseudo cubic Pr$_{0.5}$Ca$_{0.5}$MnO$_3$ system. In a double-layer Pr(Sr$_{0.1}$Ca$_{0.9}$)$_2$Mn$_2$O$_7$ system, the orbital shape is found to undergo a large change upon thermally induced rotation of orbital stripe. Furthermore, clear charge disproportionation is observed for the pseudo cubic and double-layer systems, while not in the single-layer system. These results indicate that the orbital shape and charge disproportionation are sensitive to the dimension of Mn-O network.Comment: 12 page, 5 figures, 11 table

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

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

Residual proton-neutron interactions and the NpNnN_{\rm p} N_{\rm n} scheme

We investigate the correlation between integrated proton-neutron interactions obtained by using the up-to-date experimental data of binding energies and the $N_{\rm p} N_{\rm n}$, the product of valence proton number and valence neutron number with respect to the nearest doubly closed nucleus. We make corrections on a previously suggested formula for the integrated proton-neutron interaction. Our results demonstrate a nice, nearly linear, correlation between the integrated p-n interaction and $N_{\rm p} N_{\rm n}$, which provides us with a firm foundation of the applicability of the $N_{\rm p} N_{\rm n}$ scheme to nuclei far from the stability line.Comment: four pages, three figures, Physical Review C, in pres

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