Effective three-body interactions in nuclei

It is shown that the three-body forces in the $1f_{7/2}$ shell, for which recently evidence was found on the basis of spectroscopic properties of the Ca isotopes and $N=28$ isotones, can be most naturally explained as an effective interaction due to excluded higher-lying shells, in particular the $2p_{3/2}$ orbit.}Comment: 5 pages, 1 tables, accepted for publication in Europhysics Letter

Relations Between Coefficients of Fractional Parentage

For each of the (9/2), (11/2) and (13/2) single j shells we have only one state with J=j V=3 for a five particle system. For four identical particles there can be more than one state of seniority four. We note some ``ratio'' relations for the coefficients of fractional parentage for the four and five identical particle systems

Seniority conservation and seniority violation in the g_{9/2} shell

The g_{9/2} shell of identical particles is the first one for which one can have seniority-mixing effects. We consider three interactions: a delta interaction that conserves seniority, a quadrupole-quadrupole (QQ) interaction that does not, and a third one consisting of two-body matrix elements taken from experiment (98Cd) that also leads to some seniority mixing. We deal with proton holes relative to a Z=50,N=50 core. One surprising result is that, for a four-particle system with total angular momentum I=4, there is one state with seniority v=4 that is an eigenstate of any two-body interaction--seniority conserving or not. The other two states are mixtures of v=2 and v=4 for the seniority-mixing interactions. The same thing holds true for I=6. Another point of interest is that the splittings E(I_{max})-E(I_{min}) are the same for three and five particles with a seniority conserving interaction (a well known result), but are equal and opposite for a QQ interaction. We also fit the spectra with a combination of the delta and QQ interactions. The Z=40,N=40 core plus g_{9/2} neutrons (Zr isotopes) is also considered, although it is recognized that the core is deformed.Comment: 19 pages, 9 figures; RevTeX4. We have corrected the SDI values in Table1 and Fig.1; in Sect.VII we have included an explanation of Fig.3 through triaxiality; we have added comments of Figs.10-12 in Sect.IX; we have removed Figs.7-

Competition of different coupling schemes in atomic nuclei

Shell model calculations reveal that the ground and low-lying yrast states of the $N=Z$ nuclei $^{92}_{46}$Pd and $^{96}$Cd are mainly built upon isoscalar spin-aligned neutron-proton pairs each carrying the maximum angular momentum J=9 allowed by the shell $0g_{9/2}$ which is dominant in this nuclear region. This mode of excitation is unique in nuclei and indicates that the spin-aligned pair has to be considered as an essential building block in nuclear structure calculations. In this contribution we will discuss this neutron-proton pair coupling scheme in detail. In particular, we will explore the competition between the normal monopole pair coupling and the spin-aligned coupling schemes. Such a coupling may be useful in elucidating the structure properties of $N=Z$ and neighboring nuclei.Comment: 10 pages, 7 figures, 1 table. Proceedings of the Conference on Advanced Many-Body and Statistical Methods in Mesoscopic Systems, Constanta, Romania, June 27th - July 2nd 2011. To appear in Journal of Physics: Conference Serie

Alternate Derivation of Ginocchio-Haxton relation [(2j+3)/6]

We address the problem, previously considered by Ginocchio and Haxton (G-H), of the number of states for three identical particles in a single j-shell with angular momentum J=j. G-H solved this problem in the context of the quantum Hall effect. We address it in a more direct way. We also consider the case J=j+1 to show that our method is more general, and we show how to take care of added complications for a system of five identical particles.Comment: 7 pages, RevTeX4; submitted to Phys. Rev.

Fermionic Symmetries: Extension of the two to one Relationship Between the Spectra of Even-Even and Neighbouring Odd mass Nuclei

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 levels in ^{43}Ti(^{43}Sc) with J=j=7/2. Here an approximate extension of the relationship is made by adopting a truncated seniority scheme i.e. for ^{46}Ti and ^{45}Sc we get the relationship if we do not allow the seniority v=4 states to mix with the v=0 and v=2 states. Better than that, we get very close to the two to one relationship if seniority v=4 states are admixed perturbatively. In addition, it is shown that the higher isospin states do not contain seniority 4 admixtures.Comment: 11 pages, RevTex file and no figures, typos added, references changed and changed content

Degeneracies when only T=1 two-body interactions are present

In the nuclear f_7/2 shell, the nucleon-nucleon interaction can be represented by the eight values E(J)=, J=0,1,...,7, where for even J the isospin is 1, and for odd J it is 0. If we set the T=0 (odd J) two-body matrix elements to 0 (or to a constant), we find several degeneracies which we attempt to explain in this work. We also give more detailed expressions than previously for the energies of the states in question. New methods are used to explain degeneracies that are found in {45}Ti (I=25/2- and 27/2-), {46}V (I=12^+_1 and 13^+_1, as well as I=13^+_2 and 15+), and {47}V (I=29/2- and 31/2-).Comment: 21 pages; RevTeX4. We have filled in some holes, mainly including more equations for the 44Ti Sectio

JJ-pairing interaction, number of states, and nine-jj sum rules of four identical particles

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 bosons with spin $l$. We relate number of states to sum rules of nine-$j$ coefficients. We obtained sum rules for nine-$j$ coefficients $$and$$ summing over (1) even $J$ and $K$, (2) even $J$ and odd $K$, (3) odd $J$ and odd $K$, and (4) both even and odd $J,K$, where $j$ is a half integer and $l$ is an integer.Comment: 6 pages, no figure, updated version, to be published. Physical Review C, in pres

Generalized seniority from random Hamiltonians

We investigate the generic pairing properties of shell-model many-body Hamiltonians drawn from ensembles of random two-body matrix elements. Many features of pairing that are commonly attributed to the interaction are in fact seen in a large part of the ensemble space. Not only do the spectra show evidence of pairing with favored J=0 ground states and an energy gap, but the relationship between ground state wave functions of neighboring nuclei show signatures of pairing as well. Matrix elements of pair creation/annihilation operators between ground states tend to be strongly enhanced. Furthermore, the same or similar pair operators connect several ground states along an isotopic chain. This algebraic structure is reminiscent of the generalized seniority model. Thus pairing may be encoded to a certain extent in the Fock space connectivity of the interacting shell model even without specific features of the interaction required.Comment: 10 pages, 7 figure

Isoscalar g Factors of Even-Even and Odd-Odd Nuclei

We consider T=0 states in even-even and odd-odd N=Z nuclei. The g factors that emerge are isoscalar. We find that the single j shell model gives simple expressions for these g factors which for even-even nuclei are suprisingly close to the collective values for K=0 bands. The g factors of many 2+ in even-even nuclei and 1+ and 3+ states in odd-odd nuclei have g factors close to 0.5