Scuola di Fisica Nucleare Raimondo Anni Secondo corso
description
Transcript of Scuola di Fisica Nucleare Raimondo Anni Secondo corso
![Page 1: Scuola di Fisica Nucleare Raimondo Anni Secondo corso](https://reader035.fdocumenti.com/reader035/viewer/2022081517/56815a72550346895dc7d6b8/html5/thumbnails/1.jpg)
Scuola di Fisica Nucleare Raimondo Anni
Secondo corso
Transizioni di fase liquido-gas nei nuclei
Maria Colonna LNS-INFN Catania
Otranto, 29 Maggio-3 Giugno 2006
Chomaz,Colonna,Randrup Phys. Rep. 389(2004)263Baran,Colonna,Greco,DiToro Phys. Rep. 410(2005)335
![Page 2: Scuola di Fisica Nucleare Raimondo Anni Secondo corso](https://reader035.fdocumenti.com/reader035/viewer/2022081517/56815a72550346895dc7d6b8/html5/thumbnails/2.jpg)
GasLiquid
Density
Big Bang T
empe
ratu
re
2020
0 M
eV Plasma
of Quarks and
Gluons Crab nebula July
5, 1054
Collisions
Heavy
Ion
1: nuclei 5?
Le Fasi della Materia Nucleare
Stelle1.5massa/sole
Neutron Stars
Ph. Chomaz
![Page 3: Scuola di Fisica Nucleare Raimondo Anni Secondo corso](https://reader035.fdocumenti.com/reader035/viewer/2022081517/56815a72550346895dc7d6b8/html5/thumbnails/3.jpg)
Osservazione sperimentale: frammentazione nucleare,rivelazione di frammenti di massa intermedia (IMF)in collisioni fra ioni pesanti alle energie di Fermi(30-80 MeV/A)
Obiettivi: stabilire connessione con transizione di faseliquido-gas, determinare diagramma di fase di materianucleareTermodinamica della transizione di fase in sistemi finiti
studiare il meccanismo di frammentazione e individuareosservabili che vi siano legate per ottenere informazionisul comportamento a bassa densita’ delle forze nucleari.Ex: osservabili cinematiche, massa, N/Z degli IMF
![Page 4: Scuola di Fisica Nucleare Raimondo Anni Secondo corso](https://reader035.fdocumenti.com/reader035/viewer/2022081517/56815a72550346895dc7d6b8/html5/thumbnails/4.jpg)
Transizioni di fase liquido-gas e segnali associati
Meccanismi di frammentazione Dinamica nucleare nella zona di co-esistenza Moti collettivi instabili, instabilita’ spinodale
Approcci dinamici per sistemi nucleari
Frammentazione in collisioni centrali e periferiche
Ruolo del grado di liberta’ di isospin
![Page 5: Scuola di Fisica Nucleare Raimondo Anni Secondo corso](https://reader035.fdocumenti.com/reader035/viewer/2022081517/56815a72550346895dc7d6b8/html5/thumbnails/5.jpg)
Phase co-existence
X, extensive variables:Volume, Energy, N
λ, intensive variables: temperature, pressure,chemical potential
Entropy S
![Page 6: Scuola di Fisica Nucleare Raimondo Anni Secondo corso](https://reader035.fdocumenti.com/reader035/viewer/2022081517/56815a72550346895dc7d6b8/html5/thumbnails/6.jpg)
Stability conditions
![Page 7: Scuola di Fisica Nucleare Raimondo Anni Secondo corso](https://reader035.fdocumenti.com/reader035/viewer/2022081517/56815a72550346895dc7d6b8/html5/thumbnails/7.jpg)
Spinodal instabilities are directly connected to first-order phase transitions and phase co-existence:a good candidate as fragmentationmechanism
V
Maxwell construction
λ pressure, X volume
![Page 8: Scuola di Fisica Nucleare Raimondo Anni Secondo corso](https://reader035.fdocumenti.com/reader035/viewer/2022081517/56815a72550346895dc7d6b8/html5/thumbnails/8.jpg)
F (free energy)
From the Van der Waals gas to
Nuclear Matter phase diagram
t0 < 0, t3 > 0
Mean-fieldapproximation
= ρ ρ < 0 instabilities
Canonical ensemble
F(ρ)
![Page 9: Scuola di Fisica Nucleare Raimondo Anni Secondo corso](https://reader035.fdocumenti.com/reader035/viewer/2022081517/56815a72550346895dc7d6b8/html5/thumbnails/9.jpg)
Phase diagram for classical systems
![Page 10: Scuola di Fisica Nucleare Raimondo Anni Secondo corso](https://reader035.fdocumenti.com/reader035/viewer/2022081517/56815a72550346895dc7d6b8/html5/thumbnails/10.jpg)
Two – component fluids ( neutrons and protons )
Y proton fraction = ρp/ρ
ρ ρμ= ρ( )
Mechanical inst.Chemical inst.
![Page 11: Scuola di Fisica Nucleare Raimondo Anni Secondo corso](https://reader035.fdocumenti.com/reader035/viewer/2022081517/56815a72550346895dc7d6b8/html5/thumbnails/11.jpg)
In asymmetric matter phase co-existence happens between phases with different asymmetry: The iso-distillation effect, a new probe for theoccurrence of phase transitions
Phase co-existence in asymmetric matter
![Page 12: Scuola di Fisica Nucleare Raimondo Anni Secondo corso](https://reader035.fdocumenti.com/reader035/viewer/2022081517/56815a72550346895dc7d6b8/html5/thumbnails/12.jpg)
Phase diagram in asymmetricmatter
Two-dimensional spinodal boundariesfor fixed values of the sound velocity
In asymmetric matter phase co-existence happens between phases with different asymmetry: The iso-distillation effect, a new probe for the occurrence of phase transitions
![Page 13: Scuola di Fisica Nucleare Raimondo Anni Secondo corso](https://reader035.fdocumenti.com/reader035/viewer/2022081517/56815a72550346895dc7d6b8/html5/thumbnails/13.jpg)
Phase transition inasymmetric matter
![Page 14: Scuola di Fisica Nucleare Raimondo Anni Secondo corso](https://reader035.fdocumenti.com/reader035/viewer/2022081517/56815a72550346895dc7d6b8/html5/thumbnails/14.jpg)
Phase transitions in finite systems
Probability P(X) for asystem in contact with a reservoir
Bimodality, negative specific heat
![Page 15: Scuola di Fisica Nucleare Raimondo Anni Secondo corso](https://reader035.fdocumenti.com/reader035/viewer/2022081517/56815a72550346895dc7d6b8/html5/thumbnails/15.jpg)
Lattice-gas canonical ensemblefixed V
Isochore ensemble
Curvature anomalies and bimodality
![Page 16: Scuola di Fisica Nucleare Raimondo Anni Secondo corso](https://reader035.fdocumenti.com/reader035/viewer/2022081517/56815a72550346895dc7d6b8/html5/thumbnails/16.jpg)
Hydrodynamical instabilities in classical fluids
Navier-Stokes equation Continuity equation
Linearization
= ρ ρ
Link between dynamics and thermodynamics !
![Page 17: Scuola di Fisica Nucleare Raimondo Anni Secondo corso](https://reader035.fdocumenti.com/reader035/viewer/2022081517/56815a72550346895dc7d6b8/html5/thumbnails/17.jpg)
Collective motion in Fermi fluids
Derivation of fluid dynamics from a variational approach
Phase S is additive, Φ Slater determinant
-
E = energy density functional
δI (with respect to S) = 0
![Page 18: Scuola di Fisica Nucleare Raimondo Anni Secondo corso](https://reader035.fdocumenti.com/reader035/viewer/2022081517/56815a72550346895dc7d6b8/html5/thumbnails/18.jpg)
For a given collective mode ν…
(μ = dE/dρ)
Ph.Chomaz et al., Phys. Rep. 389(2004)263V.Baran et al., Phys. Rep. 410(2005)335
![Page 19: Scuola di Fisica Nucleare Raimondo Anni Secondo corso](https://reader035.fdocumenti.com/reader035/viewer/2022081517/56815a72550346895dc7d6b8/html5/thumbnails/19.jpg)
= ρ ρ
ρ ρμ= ρ( )
U(ρ) = dfpot/dρ mean-field potential
1 + F0 = N dμ/dρ
![Page 20: Scuola di Fisica Nucleare Raimondo Anni Secondo corso](https://reader035.fdocumenti.com/reader035/viewer/2022081517/56815a72550346895dc7d6b8/html5/thumbnails/20.jpg)
ρA =
The nuclear matter case
Plane waves for Sν
Landau parameter F0
![Page 21: Scuola di Fisica Nucleare Raimondo Anni Secondo corso](https://reader035.fdocumenti.com/reader035/viewer/2022081517/56815a72550346895dc7d6b8/html5/thumbnails/21.jpg)
Linearized transport equations: Vlasov
U(ρ) = dEpot/dρ mean-field potential , f(r,p,t) one-body distribution function
(μ = dE/dρ)
0
![Page 22: Scuola di Fisica Nucleare Raimondo Anni Secondo corso](https://reader035.fdocumenti.com/reader035/viewer/2022081517/56815a72550346895dc7d6b8/html5/thumbnails/22.jpg)
Dispersion relation in nuclear matter
s= ω/kvF
![Page 23: Scuola di Fisica Nucleare Raimondo Anni Secondo corso](https://reader035.fdocumenti.com/reader035/viewer/2022081517/56815a72550346895dc7d6b8/html5/thumbnails/23.jpg)
Growth time and dispersion relation
Instability diagram
![Page 24: Scuola di Fisica Nucleare Raimondo Anni Secondo corso](https://reader035.fdocumenti.com/reader035/viewer/2022081517/56815a72550346895dc7d6b8/html5/thumbnails/24.jpg)
Two-component fluids
τ = 1 neutrons, -1 protonsρ’=ρn - ρp
![Page 25: Scuola di Fisica Nucleare Raimondo Anni Secondo corso](https://reader035.fdocumenti.com/reader035/viewer/2022081517/56815a72550346895dc7d6b8/html5/thumbnails/25.jpg)
Dispersion relation
A new effect: Isospin distillation dρp/dρn >ρp/ρn The liquid phase is more symmetric (as seen in phase co-existence)
![Page 26: Scuola di Fisica Nucleare Raimondo Anni Secondo corso](https://reader035.fdocumenti.com/reader035/viewer/2022081517/56815a72550346895dc7d6b8/html5/thumbnails/26.jpg)
Finite nuclei
Linearized Schroedinger equation (RPA)for dilute systems
α = density dilution
![Page 27: Scuola di Fisica Nucleare Raimondo Anni Secondo corso](https://reader035.fdocumenti.com/reader035/viewer/2022081517/56815a72550346895dc7d6b8/html5/thumbnails/27.jpg)
Instabilities in nuclei
Collective modesYLM(θ,φ)
The role of charge asymmetry(neutron-rich systems)
![Page 28: Scuola di Fisica Nucleare Raimondo Anni Secondo corso](https://reader035.fdocumenti.com/reader035/viewer/2022081517/56815a72550346895dc7d6b8/html5/thumbnails/28.jpg)
neutrons
protons
total
neutrons protons
Isospin distillation in nuclei
![Page 29: Scuola di Fisica Nucleare Raimondo Anni Secondo corso](https://reader035.fdocumenti.com/reader035/viewer/2022081517/56815a72550346895dc7d6b8/html5/thumbnails/29.jpg)
Landau-Vlasov (BUU-BNV) equation
Boltzmann-Langevin(BL) equation
![Page 30: Scuola di Fisica Nucleare Raimondo Anni Secondo corso](https://reader035.fdocumenti.com/reader035/viewer/2022081517/56815a72550346895dc7d6b8/html5/thumbnails/30.jpg)
Effect of instabilitieson trajectories
![Page 31: Scuola di Fisica Nucleare Raimondo Anni Secondo corso](https://reader035.fdocumenti.com/reader035/viewer/2022081517/56815a72550346895dc7d6b8/html5/thumbnails/31.jpg)
Fluctuation correlations
![Page 32: Scuola di Fisica Nucleare Raimondo Anni Secondo corso](https://reader035.fdocumenti.com/reader035/viewer/2022081517/56815a72550346895dc7d6b8/html5/thumbnails/32.jpg)
Linearization of BL equation
O-1 overlap matrix
![Page 33: Scuola di Fisica Nucleare Raimondo Anni Secondo corso](https://reader035.fdocumenti.com/reader035/viewer/2022081517/56815a72550346895dc7d6b8/html5/thumbnails/33.jpg)
Development of fluctuations inpresence of instabilities
![Page 34: Scuola di Fisica Nucleare Raimondo Anni Secondo corso](https://reader035.fdocumenti.com/reader035/viewer/2022081517/56815a72550346895dc7d6b8/html5/thumbnails/34.jpg)
Fragment formation in BL treatment
Growth of instabilities
Exponential increase
![Page 35: Scuola di Fisica Nucleare Raimondo Anni Secondo corso](https://reader035.fdocumenti.com/reader035/viewer/2022081517/56815a72550346895dc7d6b8/html5/thumbnails/35.jpg)
Approximate BL treatment ---- BOB dynamics
Growth of instabilities(comparison BL-BOB)
(Brownian One Body, Stochastic Mean Field (SMF), …)
![Page 36: Scuola di Fisica Nucleare Raimondo Anni Secondo corso](https://reader035.fdocumenti.com/reader035/viewer/2022081517/56815a72550346895dc7d6b8/html5/thumbnails/36.jpg)
Applications to nuclear fragmentation
Some examples of reactions
Xe + Sn , E/A = 30 - 50 MeV/A
Sn + Sn, 50 MeV/A
Au + Au 30 MeV/A
p + Au 1 GeV/A
Sn + Ni 35 MeV/A
E*/A ~ 5 MeV , T ~ 3-5 MeV
LBLMSUTexas A&MGANILGSILNS
![Page 37: Scuola di Fisica Nucleare Raimondo Anni Secondo corso](https://reader035.fdocumenti.com/reader035/viewer/2022081517/56815a72550346895dc7d6b8/html5/thumbnails/37.jpg)
Some examples of trajectories as predicted bySemi-classical transport equations (BUU)
Is the spinodal region attained in nuclear collisions ?
La + Cu 55 AMeVLa + Al 55 AMeV
![Page 38: Scuola di Fisica Nucleare Raimondo Anni Secondo corso](https://reader035.fdocumenti.com/reader035/viewer/2022081517/56815a72550346895dc7d6b8/html5/thumbnails/38.jpg)
Expansion and dissipation in TDHF simulations:both compression and heat are effective
Vlasov
![Page 39: Scuola di Fisica Nucleare Raimondo Anni Secondo corso](https://reader035.fdocumenti.com/reader035/viewer/2022081517/56815a72550346895dc7d6b8/html5/thumbnails/39.jpg)
Expansion dynamics in presenceof fluctuations
Stochastic mean-fieldSMF (BL like) results
![Page 40: Scuola di Fisica Nucleare Raimondo Anni Secondo corso](https://reader035.fdocumenti.com/reader035/viewer/2022081517/56815a72550346895dc7d6b8/html5/thumbnails/40.jpg)
Compression and expansion in Antisymmetrized-Molecular Dynamics simulations (AMD)
Thermal expansion in MD(classical) simulations
![Page 41: Scuola di Fisica Nucleare Raimondo Anni Secondo corso](https://reader035.fdocumenti.com/reader035/viewer/2022081517/56815a72550346895dc7d6b8/html5/thumbnails/41.jpg)
Fragmentation studies
RPA predictions
SMF calculations
![Page 42: Scuola di Fisica Nucleare Raimondo Anni Secondo corso](https://reader035.fdocumenti.com/reader035/viewer/2022081517/56815a72550346895dc7d6b8/html5/thumbnails/42.jpg)
Fragment reconstruction
Experimental observables :IMF multiplicity, charge distributions, Kinetic energies, IMF-IMF correlations …
![Page 43: Scuola di Fisica Nucleare Raimondo Anni Secondo corso](https://reader035.fdocumenti.com/reader035/viewer/2022081517/56815a72550346895dc7d6b8/html5/thumbnails/43.jpg)
Confrontation with experimental data
Compilation of experimentaldata on radial flowOnset of nuclear explosionaround 5-7 MeV/u
From two-fragment correlation Function Fragment emission timeOnset of radial expansionIMF emission probability
p + Au
![Page 44: Scuola di Fisica Nucleare Raimondo Anni Secondo corso](https://reader035.fdocumenti.com/reader035/viewer/2022081517/56815a72550346895dc7d6b8/html5/thumbnails/44.jpg)
Nuclear caloric curves and critical behaviour
J.Natowitz et al. Lattice-gas calculations
![Page 45: Scuola di Fisica Nucleare Raimondo Anni Secondo corso](https://reader035.fdocumenti.com/reader035/viewer/2022081517/56815a72550346895dc7d6b8/html5/thumbnails/45.jpg)
Further evidences of multifragmentation as a process happening inside the co-existence zone
Kinetic energy fluctuations Negative specific heat
M.D’Agostino et al., NPA699(2002)795
![Page 46: Scuola di Fisica Nucleare Raimondo Anni Secondo corso](https://reader035.fdocumenti.com/reader035/viewer/2022081517/56815a72550346895dc7d6b8/html5/thumbnails/46.jpg)
Comparison with the INDRA data:central reactions
Charge distribution
Largest fragment distribution
![Page 47: Scuola di Fisica Nucleare Raimondo Anni Secondo corso](https://reader035.fdocumenti.com/reader035/viewer/2022081517/56815a72550346895dc7d6b8/html5/thumbnails/47.jpg)
Fragment kinetic energies :Comparison between calculations and data
Uncertainties ………Pre-equilibrium emissionExc.energy estimationImpact parameter Ground state …..
But typical shape wellreproduced !
![Page 48: Scuola di Fisica Nucleare Raimondo Anni Secondo corso](https://reader035.fdocumenti.com/reader035/viewer/2022081517/56815a72550346895dc7d6b8/html5/thumbnails/48.jpg)
129Xe + 119Sn 50 AMeV
129Xe + 119Sn 32 AMeV
Event topology
![Page 49: Scuola di Fisica Nucleare Raimondo Anni Secondo corso](https://reader035.fdocumenti.com/reader035/viewer/2022081517/56815a72550346895dc7d6b8/html5/thumbnails/49.jpg)
A more sophisticated analysis: IMF-IMF velocity correlations
Event topology:
Structure of fragments at freeze-out:
Uniform distribution orbubble-like shape ?
![Page 50: Scuola di Fisica Nucleare Raimondo Anni Secondo corso](https://reader035.fdocumenti.com/reader035/viewer/2022081517/56815a72550346895dc7d6b8/html5/thumbnails/50.jpg)
Relics of spinodal instabilities:Events with equal-size fragmentsG.Tabacaru et al., EPJA18(2003)103
Fragment size correlations
For each event: <Z>, ΔZΔZ 0 Relics of equal size fragment partitions !
![Page 51: Scuola di Fisica Nucleare Raimondo Anni Secondo corso](https://reader035.fdocumenti.com/reader035/viewer/2022081517/56815a72550346895dc7d6b8/html5/thumbnails/51.jpg)
In the outer part of the star,(stellar crust), densities aresimilar to nuclear case.Star modelized in terms of n,p,e,ν.
Evolution of the crust duringthe cooling process.
Spinodal decomposition in other fields
Ideal hadronic gas
Bag with quarks and nucleonsmixture
Onset of spinodal decomposition:development of characteristic patterns in ε (azimuthal multipolarity)
Influence on flow coefficients
QGP
Neutron stars
J.Randrup, PRL92(2004)122301