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

Solvability of eigenvalues in jn configurations

Eigenvalues of eigenstates in jn configurations (n identical nucle- ons in the j -orbit) are functions of two-body energies. In some cases they are linear combinations of two-body energies whose coe+/-cients are independent of the interaction and are rational non-negative num- bers. It is shown here that a state which is an eigenstate of any two-body interaction has this solvability property. This includes, in particular, any state with spin J if there are no other states with this J in the jn configuration. It is also shown that eigenstates with solvable eigenvalues have definite seniority v and thus, exhibit partial dynamical symmetry

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-

A new effective interaction for the trapped Fermi gas

We apply the configuration-interaction method to calculate the spectra of two-component Fermi systems in a harmonic trap, studying the convergence of the method at the unitary interaction limit. We find that for a fixed regularization of the two-body interaction the convergence is exponential or better in the truncation parameter of the many-body space. However, the conventional regularization is found to have poor convergence in the regularization parameter, with an error that scales as a low negative power of this parameter. We propose a new regularization of the two-body interaction that produces exponential convergence for systems of three and four particles. From the systematics, we estimate the ground-state energy of the four-particle system to be (5.05 +- 0.024)hbar omega.Comment: 4 pages, 3 figure

Spin-aligned neutron-proton pairs in N=ZN=Z nuclei

A study is carried out of the role of the aligned neutron-proton pair with angular momentum J=9 and isospin T=0 in the low-energy spectroscopy of the $N=Z$ nuclei $^{96}$Cd, $^{94}$Ag, and $^{92}$Pd. Shell-model wave functions resulting from realistic interactions are analyzed in terms of a variety of two-nucleon pairs corresponding to different choices of their coupled angular momentum $J$ and isospin $T$. The analysis is performed exactly for four holes ($^{96}$Cd) and carried further for six and eight holes ($^{94}$Ag and $^{92}$Pd) by means of a mapping to an appropriate version of the interacting boson model. The study allows the identification of the strengths and deficiencies of the aligned-pair approximation.Comment: 5 figures, 7 tables, accepted for publication in Physical Review

The Rhesus Macaque Corticospinal Connectome

The corticospinal tract (CST), which carries commands from the cerebral cortex to the spinal cord, is vital to fine motor control. Spinal cord injury (SCI) often damages CST axons, causing loss of motor function, most notably in the hands and legs. Our preliminary work in rats suggests that CST circuitry is complex: neurons whose axons project to the lower cervical spinal cord, which directly controls hand function, also send axon collaterals to other locations in the nervous system and may engage parallel motor systems. To inform research into repair of SCI, we therefore aimed to map the entire projection pattern, or “connectome,” of such cervically-projecting CST axons. In this study, we mapped the corticospinal connectome of the Rhesus macaque - an animal model more similar to humans, and therefore more clinically relevant for examining SCI. Comparison of the Rhesus macaque and rat CST connectome, and extrapolation to the human CST connectome, may improve targeting of treatments and rehabilitation after human SCI. To selectively trace cervically-projecting CST motor axons, a virus encoding a Cre-recombinase-dependent tracer (AAV-DIO-gCOMET) was injected into the hand motor cortex, and a virus encoding Cre-recombinase (AAV-Cre) was injected into the C8 level of the spinal cord. In this intersectional approach, the gCOMET virus infects many neurons in the cortex, but gCOMET expression is not turned on unless the nucleus also contains Cre-recombinase, which must be retrogradely transported from axon terminals in the C8 spinal cord. Thus, gCOMET is only expressed in neurons that project to the C8 spinal cord, and it proceeds to fill the entire neuron, including all axon collaterals. Any gCOMET-labeled axon segments observed in other regions of the nervous system are therefore collaterals of cervically-projecting axons. gCOMET-positive axons were immunohistochemically labeled, and axon density was quantified using a fluorescence microscope and Fiji/ImageJ software. Specific regions of interest were chosen for analysis because of their known relevance in motor function in humans, and for comparison to results of a similar study in rats. Results in the first monkey have revealed both similarities and differences between the monkey and rodent CST connectome. Analyses of additional monkeys are ongoing. The final results will provide detailed information about differences between rodent and primate CST, will serve as a baseline for examining changes in the CST connectome after SCI, and will provide guidance for studies targeting treatment and functional recovery after SCI

Über Natur. Ein philosophischer Essay

Die Autorin klärt in ihrem philosophischen Essay darüber auf, was Natur aus naturwissenschaftlicher Perspektive ausmacht und stellt in diesem Kontext die Frage nach der menschlichen Stellung in der abstrakt gefassten Natur. Doch mehr als ein Zweig der irdischen Fauna bleibt den Menschen nicht, resümiert die Autorin, allenfalls in ihren emotional überheblichen Einbildungen