Effective shell-model hamiltonians from realistic nucleon-nucleon potentials within a perturbative approach

This paper discusses the derivation of an effective shell-model hamiltonian starting from a realistic nucleon-nucleon potential by way of perturbation theory. More precisely, we present the state of the art of this approach when the starting point is the perturbative expansion of the Q-box vertex function. Questions arising from diagrammatics, intermediate-states and order-by-order convergences, and their dependence on the chosen nucleon-nucleon potential, are discussed in detail, and the results of numerical applications for the p-shell model space starting from chiral next-to-next-to-next-to-leading order potentials are shown. Moreover, an alternative graphical method to derive the effective hamiltonian, based on the Z-box vertex function recently introduced by Suzuki et al., is applied to the case of a non-degenerate (0+2) hbaromega model space. Finally, our shell-model results are compared with the exact ones obtained from no-core shell-model calculations.Comment: 40 pages, 22 figures, 4 tables. Accepted for publication in Annals of Physic

Randomised Prior Feedback Modulates Neural Signals of Outcome Monitoring

Substantial evidence indicates that decision outcomes are typically evaluated relative to expectations learned from relatively long sequences of previous outcomes. This mechanism is thought to play a key role in general learning and adaptation processes but relatively little is known about the determinants of outcome evaluation when the capacity to learn from series of prior events is difficult or impossible. To investigate this issue, we examined how the feedback-related negativity (FRN) is modulated by information briefly presented before outcome evaluation. The FRN is a brain potential time-locked to the delivery of decision feedback and it is widely thought to be sensitive to prior expectations. We conducted a multi-trial gambling task in which outcomes at each trial were fully randomised to minimise the capacity to learn from long sequences of prior outcomes. Event-related potentials for outcomes (Win/Loss) in the current trial (Outcomet) were separated according to the type of outcomes that occurred in the preceding two trials (Outcomet-1 and Outcomet-2). We found that FRN voltage was more positive during the processing of win feedback when it was preceded by wins at Outcomet-1 compared to win feedback preceded by losses at Outcomet-1. However, no influence of preceding outcomes was found on FRN activity relative to the processing of loss feedback. We also found no effects of Outcomet-2 on FRN amplitude relative to current feedback. Additional analyses indicated that this effect was largest for trials in which participants selected a decision different to the gamble chosen in the previous trial. These findings are inconsistent with models that solely relate the FRN to prediction error computation. Instead, our results suggest that if stable predictions about future events are weak or non-existent, then outcome processing can be determined by affective systems. More specifically, our results indicate that the FRN is likely to reflect the activity of positive affective systems in these contexts. Importantly, our findings indicate that a multifactorial explanation of the nature of the FRN is necessary and such an account must incorporate affective and motivational factors in outcome processing