Models of Fragment Production Chapter 1. Evaluation Criteria A. Stationary EQ statistical Models 3.

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Models of Fragment Production Chapter 1.
Evaluation Criteria A. Stationary (EQ)
statistical Models3. SMM or MMMC4. Thermal
Model5. Fisher model6. Lattice gas and
PercolationB. Kinetic statistical decay
models1. Standard Statistical models (SSM) -
GEMINI2. EESC. Microscopic dynamical
models1. Mean field models with
fluctuation2. Classical LJ drop
collisions3. QMD4. AMD5. FMD6.
CoMD
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Level 0 Requirements ETB - Must acquire
Energy of the Transition-State Barrier from
bath CDM - Must account for all Competing
Decay Modes EPF - Must not have
Extra-Physical Forces OtS - Must be open to
scrutiny (e.g., published or available code)
Level 1 Issues PRS - Plausible Reaction
Scenario exists to establish initial
conditions PTS - Plausible Time Scale
separation between rxn dynamics and decay PPA
- Plausible Physical Assumptions PMB -
Plausible MB correlations and evolution
thereof Pham - Plausible Hamiltonian that can
yield this state counting
Level 2 Questions CEO - Consistency with
Experimental Observations
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Evaluation Criteria for C Dynamical Models

• Level 0 Requirements
• MFNN - Mean field propagation and two-nucleon
  collisions
• Flct - Fluctuation/bifurcation/branching
• Pauli - Pauli principle should be satisfied.
• Level 1 Issues
• Pham - Plausible Hamiltonian
• PWF - Plausible approximation of quantum Wave
  Function
• PIBC - Plausible Initial and Boundary Conditions.
• PMB - Plausible MB correlations (e.g., pairing,
  quarteting)
• PEQ - Plausible description of ideal systems in
  EQuilibrium
• Level 2 Questions
• CEO - Consistency with Experimental Observations.
• FFM - When and how Fragments are ForMed.
• GdSt - Reasonable description of nuclear ground
  state properties.
• ERG - To what extent are identifiable degrees of
  freedom equilibrated.

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1) Standard Statistical Models - SSM
CDM Does not provide for Spinoidal
decomposition channel nor, until recently,
fragment expansion. Multiparticle Transition
states are not defined nor are the associated
transient delays. In principle this could be
done as it has been for fission. PTS No TS
separation between formation/EQ and decay likely
for mid-rapidity emission. ONLY plausible for PLF
or TLF decays or light-ion induced reactions. PMB
To some extent accounted for by level density
a(E) but this is not done systematically. CEO -
Massive fragment production observations. Requires upgraded concept of
compound nuclei, where thermal expansion is
accounted for and the role of the surface layer
may be critical. Not trivial, because of the
finite range of nuclear forces, momentum
dependence of the interaction and collectivity.
Large lower density regions may require coupling
to cluster preformation logic. The future of
this approach is the linking to DFT to get
nuclear shape (density of states) and cluster
properties.
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2) EESM
ETB - Fragment arrives at the saddle
configuration NOT at the expense of thermal bath
but by converting compressional energy into
translational. This makes the emission
non-statistical and therefore exo-statistical
arguments must be invoked. OtS - Code
unavailable. Published account is insufficient
for replicating published predictions. PRS -
Missing step of how the system arrives at the
initial state of an highly excited system at
ground-state matter density. Self-similar
expansion is unlikely to be justified in HI
reactions.
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3) SMM and MMMC
CDM - Most of the phase space available to
competition is excluded as the thermal expansion
of the matter is not allowed. EPF - Reliance on
the presence of an active wall at the boundary of
the freezeout volume. This active wall helps
populating parts of the phase space that would
otherwise be out of bounds for fragmentation.
PRS - Narrative used to describe, how the
system arrives at a freezeout configuration.
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4)Thermal Model

• PRS - Reliance on the presence of freezeout
  volume.
• PHam - No interaction between clusters.
  Interaction required to explore PS. It is unclear
  that this PS population could actually be
  generated by a real Hamiltonian. While the formal
  issue might not in practice turn out to be
  relevant it should be kept in mind. Comparison
  to dynamical models is required.

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5) Fishers Model
ES - Considers forming fragments of liquid
within a volume filled with gas and not releasing
them to surrounding vacuum. CDM - Gaseous phase
is in fact free to go. EPF - A container is
implicit in considering gaseous phase close to
the condensation point. PRS - No depictable
scenario of arriving at Fishers point. PPA -
Origin and justification of the assumption that
the L-G surface free energy is a linear function
of temperature is missing. PHAM - No interaction
between clusters. Relation of physical
self-bound clusters unclear.
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6) lattice gas and percolation models
EB - Fragment formation is being equated to
fragment emission EPF - Reliance on the presence
of a containment vessel (lattice). PRS - Not
clear why it is relevant for the behavior of
non-contained nuclear matter. PMB To what
physical question is the cluster definition an
answer to? Pham As the Hamiltonian does not
depend on the precise position of the particles
violation of thermodynamics is not unexpected.
Unphysical/real Hamiltonian (for thermodyanmic
use.)
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1) Mean Field with Fluctuation
PWF No constraint on f(r,p). Semiclassical
aproximation. Pauli OK in principle, but ? in
practice. Flct Various implementations BOB,
?f2f(1-f), Small Ntest, ... 2,t2) ? Not clear how the total energy is
conserved. Not clear why bifurcation is absent
before MF instability. PIBC Applicable from t
-300 to 1-300 fm/c. Some ambiguity in
identifying fragments. Statistical decay is OK
only for nucleon evaporation. PEQ Caloric curve
has not been studied. Is it quantal? PMB No MB.
Not reliable for n, p, d, t, alpha... CEO Y(A) is
well reproduced, but light IMF's are not
enough. FFM Spinodal decomposition. Equal-size
fragmentation. ERG (N-Z)/A distribution is very
sharp.
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2) Classical MD
MFNN, Pauli, Flct, Pham, PWF, PMB Deterministic
Newtonian dynamics with two-body force. Not
justified for nuclear systems. But some general
features of fragmentation can be
studied. PEQ Liquid-gas phase transition
exists. But the statistics is classical by
definition. FFM Fragments can be recognized in an
early stage. EGO Chaos is often discussed. How
does it apply to quantum systems?
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3) QMD
Pauli Only in Pauli-blocking and initialization.
Pauli potential is artificial and has
side-effects. Flct By NN collisions and
initialization. PWF Wave packet, but ?x?p hbar/2. Usually ?p0. This is another practical
source of Flct. PIBC Applicable from t 0 to
0-300 fm/c. Ground state is not very
stable. Fragments often need to be recognized at
an early stage. PEQ Statistics is expected to be
classical. PMB Some classical MB? But not good
for n, p, d, t, alpha... CEO IMF yield is not
enough in some cases. FFM Fragments can be
identified at an early stage.
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4) AMD
Pauli No way to violate it. But some
approximation is introduced at several
places. Flct By NN collisions and wave packet
splitting. PWF Slater det of wave packets with
?x?p hbar/2. Change of wave packet shape is
considered by Flct (apprx). Not clear why Flct
should occur to form wave packets. PIBC Applicable
from t -infinity to infinity, in principle.
Ground state is uniquely determined and
completely stable. Description of statistical
decay has not been tested well. PEQ Consistent
with quantum statistics and phase
transition. PMB Some classical MB? But not very
good for n, p, d, t, ? (?). CEO IMF yield is good
if a reasonable Flct is chosen. ERG (N-Z)/A
distribution is similar to statistical prediction.
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5) FMD
Pauli No way to violate it. Flct Not yet. (Only
in b and the orientation of initial nuclei.)
Deterministic dynamics is not suitable for
fragmentation. PWF Slater det of wave packets
with variable width. Pham Based on realistic
nuclear force. Short range correlations are
considered. GdSt Good for nuclear structure
problems (with projections). PIBC Applicable from
t -infinity to infinity, in principle.
Ground state is uniquely determined and
completely stable. Description of statistical
decay has not been tested well. PEQ Consistent
with quantum statistics and phase
transition. Does it depend on the definition of
temperature? PMB Alpha clustering appears in
structure calc. No pairing?
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6) CoMD
Pauli Respected by introducing a stochastic
process. Not derived or justified form a first
principle. Flct NN collisions and the
collisions for Pauli. PWF Wave packet with ?x?p
practical source of Flct. PIBC Applicable from t
0 to 1-300 fm/c. Ground state is more
stable than QMD. What about statistical
decay? PEQ Has not been studied. Will be quantal
and fermionic? PMB Better than QMD for alpha.
Still too many nucleons. CEO Some
multifragmentation data are well reproduced.
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Additional QUESTIONS for discussion1. What is
the value of pure statistical models?2. What is
the value of the leptodermous expansion in this
NP?3. Assuming value what are the importance
Surface Effects? (See below.)

• Fragment formation always requires an increase
  in surface area.
• Both, statistical and dynamical models must be
  sensitive to the cost of such an increase,
  expressed in terms of surface free energy (SFE),
  manifesting itself as surface tension (ST).
• SFE decreases with increasing excitation energy.
  Eventually, vanishes (T.ne.Tc)
• SFE depends on the surface profile (in matter
  density), which in turn depends on the (finite)
  range of nuclear interactions.
• Surface profile changes with excitation energy
  (max. of entropy).
• No liquid-gas (L-G) separation in small systems
  interacting via finite range forces (truth
  neglected by all (?) L-G propositions).
• Vanishing of SFE (surface tension) should result
  in power-law distributions for fragment masses.
• A call for a look into the Physics of Hot Nuclear
  Surface