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-

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

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

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

Certainty in ascending sensory signals - The unexplored driver of analgesic placebo response.

Previous frameworks have failed to adequately explain the observed correlation between within-subject variability in pain reporting and analgesic placebo response. These relationships have been observed in both clinical and experimental setups. Within-subject variability of clinical pain scores is traditionally assessed based on daily pain diaries collected during the pre-intervention stage. Experimental variability can be assessed by the Focused Analgesia Selection Test (FAST), which calculates the relationship between noxious stimuli administrated at various intensities and pain reports. The variability, either clinical or experimental, has been shown to predict the placebo response. In explaining the placebo response, Bayesian Brain Hypothesis (BBH) posits that pain perception (posterior), is composed of certainty (precision) of expectations (priors due to belief or conditioning) and incoming sensory information (likelihood), with the bulk of research focused on the precision of priors. Virtually all placebo analgesia research has focused on the priors and their certainty, rather than on the certainty of the likelihood, mainly because it cannot be assessed directly. We propose that the within-subject variability, as encapsulated by the FAST, is a proxy for certainty in (or, precision of) ascending sensory signals, and our results suggest that it could not only be assessed, but also manipulated. If true, our hypothesis will facilitate new lines of research and could potentially promote precision analgesic medicine by use of variability of pain scores as a diagnostic method to identify pain patients who will benefit from specific treatments

The Tamm-Dancoff Approximation as the boson limit of the Richardson-Gaudin equations for pairing

A connection is made between the exact eigen states of the BCS Hamiltonian and the predictions made by the Tamm-Dancoff Approximation. This connection is made by means of a parametrised algebra, which gives the exact quasi-spin algebra in one limit of the parameter and the Heisenberg-Weyl algebra in the other. Using this algebra to construct the Bethe Ansatz solution of the BCS Hamiltonian, we obtain parametrised Richardson-Gaudin equations, leading to the secular equation of the Tamm-Dancoff Approximation in the bosonic limit. An example is discussed in depth.Comment: Submitted to the proceedings of the Group28 conference (Newcastle-upon-Tyne, UK). Journal of Physics: Conference Serie

Emotional response to images of wind turbines: a psychophysiological study of their visual impact on the landscape

YesSocial acceptance for wind turbines is variable, providing a challenge to the implementation of this energy source. Psychological research could contribute to the science of climate change. Here we focus on the emotional responses to the visual impact of wind turbines on the landscape, a factor which dominates attitudes towards this technology. Participants in the laboratory viewed images of turbines and other constructions (churches, pylons and power-plants) against rural scenes, and provided psychophysiological and self-report measures of their emotional reactions. We hypothesised that the emotional response to wind turbines would be more negative and intense than to control objects, and that this difference would be accentuated for turbine opponents. As predicted, the psychophysiological response to turbines was stronger than the response to churches, but did not differ from that of other industrial constructions. In contrast with predictions, turbines were rated as less aversive and more calming compared with other industrial constructions, and equivalent to churches. Supporters and non-supporters did not differ significantly from each other. We discuss how a methodology using photo manipulations and emotional self-assessments can help estimate the emotional reaction to the visual impact on the landscape at the planning stage for new wind turbine applications.This work was partly funded by an ESRC First Grant RES-061-25-0512 to D

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

The general harmonic-oscillator brackets: compact expression, symmetries, sums and Fortran code

We present a very simple expression and a Fortran code for the fast and precise calculation of three-dimensional harmonic-oscillator transformation brackets. The complete system of symmetries for the brackets along with analytical expressions for sums, containing products of two and three brackets, is given.Comment: 13 pages, accepted for publication in Nuclear Physics