What I Learned Today

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Posts in the nuclear physics 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.


Github returns

I am setting up and using the public github repository after many years. I decided to start releasing some old projects publicly, since seems apparent I will never have time to write anymore papers, nor to polish the code.

Eventually, at least for these little "didactic" subprojects, I will start to do little explanatory videos, or blogposts, instead of articles just to save times and make the process more fluid.

So, with the philosophy of releasing as process, not as product, here it is the first project on Pairing Vibration RPA:


Enjoy and let me know.

Theorical ArXiv of Cook and Rossi

There are several aspects of the paper of Norman Cook and Andrea Rossi that scream "amateurish": from layout to typos (hoping they're so), from historical concepts to bibliography, I'm not certainly the only one to have noted them.

But is the scientific thesis to be flawed, even without considering the disputed history of E-cat and LENR and possible prejudices one can have on the author and its reasons.


Beta decay logft

The comparative half life ft is useful to compare the strength of the and electron-capture processes over different nuclei. -decay half lives can span several orders of magnitude, from fraction of seconds to thousands of time the age of the universe. Some of these striking differences are due to relatively trivial energetic conditions, but the more interesting from a nuclear structure point of view are due to the wavefunction superposition and the angular momentum coupling.

The comparative half life ft is useful to purge from energetic and kinematic details the reaction and analyze just the nuclear structure behind. For example superallowed decays, that go from a ground to a ground state, should have very similar structure overall conditions, thus similar ft, even if the half life vary by orders of magnitude. And in fact the value of for all the known superallowed decays even if the half life span from few seconds to few milliseconds.

The comparative half life is given by

where the Matrix element for superallowed, for allowed, and lesser for forbidden type of decays (superallowed, allowed and forbidden type of decays are dependent on the eventual unit of angular momentum and parity the radiation has to carry away, cf. Wikipedia for a list), and

thus, considering ft in the unit of seconds we have

with C the square matrix element in natural unit.

Making use of the ft value expressed in second we can deduce a common value in the Beta-decay jargon that is the logft, that is now trivially

Common example of values of logft are, ~ 3.5 for superallowed decays (as specified above), ~5.5 for allowed, ~8 for first forbidden and ~11 for second forbidden.

Check Appendix A of Towner and Hardy


Ta-180 is the rarest isotope of Nature's rarest element. It exists only in an a long-lived (10^15y half life) isomer (Jpi=9-; E=75 keV). Potential s-process production path is easy to point out, but the survival of this fragile piece of nature at finite temperature is unlikely...

The mysteries of strange Nature's sons can be investigated with a combination of the thermodynamic of s-process sites, p-process and neutrino nucleosynthesis.

The three Borromean rings.

The three Borromean rings.

There are some properties of few-body systems that are "Universal", so shared between all few-body systems that feel an attractive interaction (with certain boundary properties for defining eventual spin-orbit and isospin).

An example of this behavior are the Efimov states of three-body systems: when an interaction loosely bound two bodies, the three-body system have a precise spectrum of excitation. This spectrum is observed in three nucleons systems like Helium-3 and Triton, since the two-body system, the deuteron, is loosely bound (for nuclear scales).

Moreover Efimov states can predict that even when two-body subsystems are unbound, three-body counterpart can form bound states. This is the so-called Borromean systems, from the coat of arms of Borromeo family of the lake Maggiore, where three rings interweave such as to take one out you have to break the whole system.

There is no bound 5-nucleons nucleus (Litium-5 or Helium-5 are unbound systems). Is that an Universal property of the nuclear force that make impossible to form 5-body systems, or is just an accident?

Today I learned from J. Kirscher that seems just an accident and there are no Efimov-like properties expected from the properties of non-existent 5-body systems.