# EkEk ∆ δ A I of rigid Gap parameters from moments of Inertia

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14-Jan-2016Category

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Triune Pairing RevelationLuciano G. Moretto&Augusto Macchiavelli

even-oddmass differences Critical temperatures from level densitiesSuperfluid momentsof inertiaAnomalous Quasi Particle Spectrum Ek

Ground State Masses

Hence even odd mass differences A

Anomalous Moments of Inertia in rotational nucleiI

of rigid

Gap parameters from moments of InertiaMemories.Gilbert and Cameron0lnElnE/T

BnLow energy level counting ..exponential?Neutron resonances . 1 pointHigher energy..Fermi gas

Global Solution : matching a Fermi Gas to an exponential dependence

Away from shells TG.C. TCr pairing = 2/3.5

Level densities, actinides6

Universal 1st Order Low Energy Phase Transition in Atomic Nuclei Luciano G. Moretto Hallmark of 1st order phase transition in micro-canonical systems?

Linear Dependence of Entropy with Energy !

or

(E)0510E (MeV)This is universally observed in low energy nuclear level densitiesT is the micro-canonical temperature characterizing the phase transitionEnergy goes in, Temperature stays the sameCan a thermostat have a temperature other than its own?

Is T0 just a parameter?

According to this, a thermostat, can have any temperature lower than its own!

T = Tc = 273Kor0 T 273K?8What causes the phase transition? In non magic nuclei Pairing

In magic nuclei Shall gap

= 1.76 TCrBCS Phase TransitionTCrT02nd orderNearly 1st order?

Fixed energy cost per quasi particle up to criticality : little blocking ? # quasi particle at TCr

Energy at criticality!Pairing: Fixed Energy cost/ quasi particle up to TCR ! Is this consistent with blocking?

goes down (k-) goes up Proof:=0ggxxfor x=0 ECr/QCr= 0for x>0 ECr/QCr 0

1st order phase transition implies two phases

Superfluid phase gas of independent quasi particles superfluid

What fixes the transition temperature?constant entropy per quasi particle Remember Sackur Tetrode

Entropy / Quasi Particle

Testing the picture:Even-Odd horizontal shift.

should be compared with even-odd mass differences

b) Relationship between the above shift and the slope 1/T

c) Vertical shift or entropy excess

Low energy level densities for nuclei away from shells vademecum for beginners..Get TCr from =12/A1/2

Write ln(E)=S(E)=E/T

Shift horizontally by or 2 for odd or odd-odd nuclei Ek

Ek

Pairing

Shell Model

Spectra with any gap

quasi particles vacuum N slots

Entropy/particle

Let us compare.

Entropy/ quasi particle

Good enough!!!!6-7 levels/ quasi particle

ConclusionsThe universal linear dependence of S=ln with E at low energies is a clear cut evidence of a first order phase transition

In non magic nuclei the transition is due to pairing. The coexisting phases are a) superfluid; b) ideal gas of quasi particles

In magic nuclei the transition is due to the shell gap . AD MULTOS ANNOS, ALDO.WITH FRIENDSHIPLow Energy Level DensitiesEln

Condensation energyGilbert and Cameron did empirically the match between linear and square root dependence.

In so doing they extracted TCR !

Memories.Gilbert and Cameron0lnElnE/T

BnLow energy level counting ..exponential?Neutron resonances . 1 pointHigher energy..Fermi gas

Global Solution : matching a Fermi Gas to an exponential dependence

Away from shells TG.C. TCr pairing = 2/3.53