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PPT – Models of Fragment Production Chapter 1. Evaluation Criteria A. Stationary EQ statistical Models 3. PowerPoint presentation | free to download - id: 1366f-YzE4Z

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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

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

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.

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.

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.

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.

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.

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.

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.)

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.

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?

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.

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.

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?

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.

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