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Posts in the probability category


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Nuclear wave function in function of for the proton state, obtained by diagonalizing the self energy in the exact continuum used above. The first eigenvalue at -23.97 MeV (solid red line) is compared by the corresponding harmonic oscillator state multiplied by the square root of the spectroscopic factor (dashed red line), the second eigenvalue at -2.85 MeV (solid blue line) is similarly compared with harmonic oscillator state (dashed blue line). The spectroscopic factors are 0.78 and 0.21 respectively

A IMHO good picture to didactically illustrate the effect of many-body dynamics on nuclei.

I post it here since that it did not make it to the final version of the Proceeding for Pisa conference, but I think it illustrate nicely how, from the combination of several base state wavefunctions we build many-body wavefunctions which have different properties (are quenched, so posses spectroscopic factors, and have a completely different tail) from the harmonic oscillator starting point (dashed).

This is also why reaction dynamics are way different calculated with a complete set of many-body relation instead of a simple mean field picture.

IMHO would also be difficult to reproduce the richness of these wavefunctions with a single Wood Saxon, let alone an harmonic oscillator potential (you can notice that the decay of the is quite fat respect to the exponential of an harmonic oscillator eigenfunction).

Non-local optical potentials are the way to go! 😉

(absolutely objective and no conflict of interest there), more info here: arXiv:1612.01478 [nucl-th], and soon-to-be publication.

Enjoy.

Bayesian concept of probability is linked not with frequency, but with state of information. The processing of this information proceeds in a propositional sense. In fact there are semantic work related to the use of Bayesian statistic as foundation for programming languages (BLOG), First kind logic (MEBN , also look at the fun Of Starships and Klingon) and thus the foundation principles of Network-Centric warfare and commerce.

Property of Baysian calculation of proabability are sometimes difficult to grasp and very counter intuitive, interesting consideration can hide behind apparently trivial formulas that can help to answer questions like: If you know your neighbour has a son born on Tuesday, which is the probability your neighbour has two sons? (more…)