Giovanni POLLAROLO - unisalento.itgpco/scuola/terzo/pollarolo/nanni2.pdf · Giovanni POLLAROLO Dipartimento di Fisica Teorica, Universit`a di TORINO e INFN Sezione di Torino. ...

Introduction GRAZING Fusion Applications MNT End

Elementi di teoria delle reazioni nucleari con ionipesanti. Applicazioni

Giovanni POLLAROLO

Dipartimento di Fisica Teorica, Universita di TORINOe INFN Sezione di Torino

Introduction GRAZING Fusion Applications MNT End

HI reactions

HI reactions, a short overview

Introduction GRAZING Fusion Applications MNT End

HI reactions

HI reactions, a short overview

TRANSFER REACTIONSEVAPORATION

are possible for opt. Qval

For stable nuclei onlyNEUTRON PICK-UP andPROTON STRIPPING

Introduction GRAZING Fusion Applications MNT End

HI reactions

HI reactions, a short overview

TRANSFER REACTIONSEVAPORATION

are possible for opt. Qval

For stable nuclei onlyNEUTRON PICK-UP andPROTON STRIPPING

Lfus >> LldORBITING

FUSION-FISSION

Introduction GRAZING Fusion Applications MNT End

HI reactions

Macro-Microscopic approach

Transport equationsfor the exchange of massand charge.

friction forcesfor energy and angularmomentum dissipation

GRAZING

It uses a microscopicapproach.

It calculates the evolution ofthe reaction by using theintrinsic properties of the twocolliding nuclei:

surface modeslow lying modeshigh lying modes

transfer channels(microscopic formfactorfor transfer)

Introduction GRAZING Fusion Applications MNT End

HI reactions

Macro-Microscopic approach

σFriction (transport equation)

Z (Elos) DISSIPATION

Transport equationsfor the exchange of massand charge.

friction forcesfor energy and angularmomentum dissipation

GRAZING

It uses a microscopicapproach.

It calculates the evolution ofthe reaction by using theintrinsic properties of the twocolliding nuclei:

surface modeslow lying modeshigh lying modes

transfer channels(microscopic formfactorfor transfer)

Introduction GRAZING Fusion Applications MNT End

HI reactions

Macro-Microscopic approach

σFriction (transport equation)

Z (Elos) DISSIPATION

Transport equationsfor the exchange of massand charge.

friction forcesfor energy and angularmomentum dissipation

GRAZING

It uses a microscopicapproach.

It calculates the evolution ofthe reaction by using theintrinsic properties of the twocolliding nuclei:

surface modeslow lying modeshigh lying modes

transfer channels(microscopic formfactorfor transfer)

Introduction GRAZING Fusion Applications MNT End

HI reactions

Macro-Microscopic approach

σFriction (transport equation)

Z (Elos) DISSIPATION

Transport equationsfor the exchange of massand charge.

friction forcesfor energy and angularmomentum dissipation

GRAZING

It uses a microscopicapproach.

It calculates the evolution ofthe reaction by using theintrinsic properties of the twocolliding nuclei:

surface modeslow lying modeshigh lying modes

transfer channels(microscopic formfactorfor transfer)

Introduction GRAZING Fusion Applications MNT End

Trasferimento

Trasferimento di massa

Per iniziare a capire il ruolo del trasferimento di massaconsideriamo semplice esempio: cioe di avere N modi indipendentidi trasferire un nucleone.

pk per trasferire una particella(1− pk) per rimanere nello stesso stato

la probabilita di trasferire n nucleoni ( per semplicita p =< pk >)si calcola facilmente:

p0 = (1− p)N

p1 = Np(1− p)N−1

· · · = · · ·

pn =

(Nn

)pn(1− p)N−n

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Trasferimento

Trasferimento di massa

Da cui si calcola subito:

< n >= Np

(∆n)2 = Np(1− p) ∆n =√

< n >

Poisson distribution

Se il numero N di canali aperti (modi di trasferimento) e granderispetto al numero n di particelle trasferite allora la distribuzioneBINOMIALE puo essere approssimata con una distribuzione diPOISSON cioe:

Pn =< n >n

n!e−<n>

Introduction GRAZING Fusion Applications MNT End

Trasferimento

Trasferimento di massa

Da cui si calcola subito:

< n >= Np

(∆n)2 = Np(1− p) ∆n =√

< n >

Poisson distribution

Se il numero N di canali aperti (modi di trasferimento) e granderispetto al numero n di particelle trasferite allora la distribuzioneBINOMIALE puo essere approssimata con una distribuzione diPOISSON cioe:

Pn =< n >n

n!e−<n>

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Trasferimento

Trasferimento di massa

Per nuclei medio pesanti, i.e.40Ca+208Pb e facile avere adisposizione un CENTINAIOmodi diversi di trasferimento.con una probabilita mediap ∼ 0.1

∆M ∼ 10± 4∆E ∼ (5x10 = 50 Mev.

Il TRASFERIMENTO MULTIPLO puo giocare un ruolo moltoimportante nella evoluzione della reazione.

Introduction GRAZING Fusion Applications MNT End

Trasferimento

Trasferimento di massa

Per nuclei medio pesanti, i.e.40Ca+208Pb e facile avere adisposizione un CENTINAIOmodi diversi di trasferimento.con una probabilita mediap ∼ 0.1

∆M ∼ 10± 4∆E ∼ (5x10 = 50 Mev.

Il TRASFERIMENTO MULTIPLO puo giocare un ruolo moltoimportante nella evoluzione della reazione.

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Grazing

Vediamo ora piu in dettaglio il sistema di equazioni accoppiate chedescrive la collisione ed una sua soluzione approssimata.Nell’approssimazione semiclassica l’Hamiltoniana del sistema

H = Ha + HA + Vint(t)

dove l’Hamiltoniana intrinseca del sisema a si scrive:

Ha =∑

i

εia†i ai +

∑λµ

~ωλa†λµaλµ

ed in modo analogo per il sistema A.Notate che gli operatori aλµ sono operatori bosonici, creano unaeccitazione di superfice di energia ~ωλ mentre gli operatori ai

creano un fermione nel livello i = (nljm) di energia εi

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Grazing

Il termine di interazione:

Vint(t) = Vtr (t) + Vin(t) + ∆UaA(t)

doveVtr =

∑(νπ)j ,k

f aka′j (r)a†(ak)a(a′j) + h.c .

Vin =∑λµ

f Aλµ(r)

(a†λµ(A) + aλµ(A)

)+ h.c .

dove f aka′j (r) e il fattore di forma per il trasferimento di unaparticella e f A

λµ(r) e il fattore di forma per la eccitazione dei modisuperficiali L’ultimo termine tiene in conto correzioni per ilpotenziale che descrive il moto relativo.

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Grazing

La funzione d’onda Ψ(t) del sistema puo venire calcolataintroducendo il suo sviluppo in CHANNELS WAVE-FUNCTIONS,soluzioni della equazione di Schrodinger che descrive gli statiasintotici liberi (cioe le autofunzioni di Ha e HA), e quindiriducendo l’equazione di Schrodinger in un sistema di equazioniaccoppiate nelle ampiezze.Qui discuteremo un modo approssimato di soluzione che eappropriato quando ci sono molti canali debolmente popolati.Siamo interessati a calcolare, all’istante t, la distribuzione diprobabilita nelle variabili E ∗

a ,E ∗A,Na,Za,Ma,MA, · · · che descrivono

lo stato del sistema. Questa distribuzione di probabilita e data da:

P(E ∗a ,E ∗

A,Na,Za, · · · ) =< Ψ(t)|δ(Ha−E ∗a ) · · · δ(Za−Za) · · · |Ψ(t) >

Introduction GRAZING Fusion Applications MNT End

Grazing

dove assieme agli operatori Hamiltoniani abbiamo introdotto icorrispondenti operatori per i vari osservabili, quali gli operarorinumero di particelle (per la carica e i neutroni) e momentoangolare. Nel caso degli operatori di carica scriviamo:

Za =∑i ′∈π

a†i ′ai ′ ZA =∑i∈π

a†i ai

ed in modo analogo per gli operatori numero di neutroni. Perquanto riguarda il momento angolare:

Ma =∑

i ′∈π,ν

mi ′a†i ′ai ′ +

∑λ′µ′

µ′a†λ′µ′aλ′µ′

ed in modo analogo per il target-like.

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Grazing

Per calcolare la probalita P(E ∗a , · · · ) non risolviamo il sistema di

canali accoppiati ma calcoliamo prima la FUNZIONECARATTERISTICA che e definita:

Z (βa, βA, ξa, ξA, · · · ) =< Ψ(t)|e i Haβa+i HAβa+i Naξa+···|Ψ(t) >

dove i βa, · · · sono dei parametri.Si procede in questo modo, in quanto la funzione caratteristica epiu facile da calcolare e possiede interessnti proprieta. Laprobabilita e allora data attraverso una semplice trasformata diFourie cioe:

P(E ∗a ,E ∗

A, · · · ) =

∫ +∞

−∞dβadβA · · ·Z (βa, βA, · · · )e−iE∗a βa−iE∗Aβa−···

Introduction GRAZING Fusion Applications MNT End

Grazing

Siccome molte volte non siamo interessati ad avere la espressioneesplicita della probabilita P(E ∗

a ,E ∗A, · · · ) ma piuttosto ci

accontentiamo di conosce i valori medi e le deviazioni standarddelle varie varuabili E ∗

a ,E ∗A, · · · che definiscono lo stato finale

queste possono essere dedotte direttamente dalla funzionecaratteristica.Infatti si ha:

< E ∗a >=

1

i

d

dβalnZ (βa, · · · )

∣∣∣∣∣βa=0

e per la deviazione standard:

σ2E∗a

= − d2

dβ2a

lnZ (βa, · · · )

∣∣∣∣∣βa=0

Introduction GRAZING Fusion Applications MNT End

Grazing

Il calcolo della funzione caratteristica e molto tedioso, per cui milimitero a suggerire i diversi steps ed a mettere in evidenza leapprossimazioni che si fanno.E conveniente lavorare nella rappresentazione di interazione. Allorasi scrive:

|Ψ(t) >= T ei~

R t−∞ V (t′)dt′ |0 >

dove T e il time-ordering operator e V (t) e l’interazione nellarappresentazione di interazione, cioe:

V (t) = e i(Ha+HA)tV (t)e−i(Ha+HA)t

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Grazing

l’interazione e somma di tre termini Vin, Vtr e ∆UaA. Seassumiano che le eccitazione collettive sono INDIPENDENTI daltrasferimento possiamo scrivere:

T e−i~

R t−∞ V (t′)dt′ = T e−

i~

R t−∞ Vtr (t′)dt′T e−

i~

R t−∞ Vin(t

′)dt′ · · ·

Mentre il termine inelastico puo essere calcolato esattamente, iltermine di trasferimento viene calcolato fino al secondo ordine, cioescrivendo:

T e−i~

R t−∞ Vtr (t′)dt′ = e

− i

~R t−∞ Vtr (t′)dt′− 1

2~2

R t−∞ dt′

R t′−∞ dt′′[V (t′),V (t′′)]

Per quanto riguarda il terzo termine della interazione, esso nonpone particolari problemi, in quanto e un c-number.

Introduction GRAZING Fusion Applications MNT End

Grazing

Riassumendo voglio ricordare che i risultati di questo modello sonodeterminati dai ben noti:• fattori di forma

- transferimento di un nucleone fjk(R(t))- excitatione collectiva dei modi inelastic. fλµ(R(t))

(il traferimento multiplo visto in approssimazione sequenziale)• energie di legame• densita dei livelli media

Il moto relativo e calcolato usanto il ben noto potenziale diAkyuz-Winther. Ricordiamoci che questo e influenzato dallaeccitazione dei modi superficiali. Tutti i modi (trasferimento ecollettivi sono considerati indipendenti.

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Grazing

Riassumendo voglio ricordare che i risultati di questo modello sonodeterminati dai ben noti:• fattori di forma

- transferimento di un nucleone fjk(R(t))- excitatione collectiva dei modi inelastic. fλµ(R(t))

(il traferimento multiplo visto in approssimazione sequenziale)• energie di legame• densita dei livelli media

Il moto relativo e calcolato usanto il ben noto potenziale diAkyuz-Winther. Ricordiamoci che questo e influenzato dallaeccitazione dei modi superficiali. Tutti i modi (trasferimento ecollettivi sono considerati indipendenti.

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Grazing

Consideriamo la collisione del 40Ca su 120Sn ad una energiasuperiore alla barriera Coulombiana (15%):

Si vede chiaramente che le probalita di trasferimento su ciascuncanale sono abbastanza piccole per cui l’overcounting non eeccessivo.

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GRAZING: cosa puo calcolare

GRAZING calculates how the reaction cross section is sharedamong the different final mass partitions up to the ORBITING:

GRAZING

Beyond the ORBITING only the capture probability can beestimated.

Introduction GRAZING Fusion Applications MNT End

GRAZING: cosa puo calcolare

GRAZING calculates how the reaction cross section is sharedamong the different final mass partitions up to the ORBITING:

GRAZING

70 %

Beyond the ORBITING only the capture probability can beestimated.

Introduction GRAZING Fusion Applications MNT End

GRAZING: cosa puo calcolare

GRAZING calculates how the reaction cross section is sharedamong the different final mass partitions up to the ORBITING:

GRAZING

70 %

Beyond the ORBITING only the capture probability can beestimated.

Introduction GRAZING Fusion Applications MNT End

ORBITING: from order to chaos

For energies close to EB , thetravelling time in the insidepocket τin is important for theevolution of the reaction.

Not all the trajectories thatreach the inner pocket lead tocapture.

IMPORTANCE OF iWVol(r)

Of course the dynamics of the inner pocket isrelevant only if the absorption is not to strong.Notice that most of the coupled-channelcodes impose the incoming-wave boundaryconditions at the pocket location.

Introduction GRAZING Fusion Applications MNT End

ORBITING: from order to chaos

For energies close to EB , thetravelling time in the insidepocket τin is important for theevolution of the reaction.

Not all the trajectories thatreach the inner pocket lead tocapture.

IMPORTANCE OF iWVol(r)

Of course the dynamics of the inner pocket isrelevant only if the absorption is not to strong.Notice that most of the coupled-channelcodes impose the incoming-wave boundaryconditions at the pocket location.

Introduction GRAZING Fusion Applications MNT End

ORBITING: from order to chaos

For energies close to EB , thetravelling time in the insidepocket τin is important for theevolution of the reaction.

Not all the trajectories thatreach the inner pocket lead tocapture.

IMPORTANCE OF iWVol(r)

Of course the dynamics of the inner pocket isrelevant only if the absorption is not to strong.Notice that most of the coupled-channelcodes impose the incoming-wave boundaryconditions at the pocket location.

Introduction GRAZING Fusion Applications MNT End

Fusion cross section

In a Potential Model if T`(E ) is thetransmission probability through thepotential barrier (Hill-Wheelerformula) the Fusion cross sectionis:

σ(E ) = π~2

2µE

∑`(2` + 1)T`(E )

Notice: it assumes that all theflux reaching the inner pocketlead to the formation of thecompound nucleus (Fusion).

Introduction GRAZING Fusion Applications MNT End

Fusion cross section

By using the inverse parabolic approximation:

T`(E ) =1

1 + exp[2π(Ec − E )/~ωc ]ωc =

√− 1

maA

∂2Ueff

∂r2

one obtains the well known: WONG formula

σ(E ) =R

2

c~ωo

Eln

1 + exp

[2π

~ωo(E − Ec)

]

Rc ∼ RB with RB the Coulomb barrier for ` = 0.

Introduction GRAZING Fusion Applications MNT End

Fusion cross section

E Ec (sharp cut-off model T` = 1; ` < `c):

σ(E ) = πR2c

[1− UaA(Rc)

E

]

E Ec the total reaction cross section behaves:

σ(E ) =R

2

c~ωo

Eexp

[2π

~ωo(E − Ec)

]

This potential model underestimate the cross section for energiesbelow the Coulomb barrier.

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Couplings - Barrier distribution

H. Esbensen (1981) - In thepresence of couplings the barrier VB

is not well defined, one should heretalks about barrier distributionD(VB) and calculate fusion via:

σ(E ) =

∫ ∞

0σ(E ,VB)D(VB)dVB

By using the ZPM approximation hewas able to estimate the contributionof the surface modes to the fusioncross section.

Introduction GRAZING Fusion Applications MNT End

Couplings - Barrier distribution

Rowley, Satchler and Stelson(1991) suggested that the barrierdistribution can be obtained directlyfrom the experimental excitationfunction by:

D(E ) =d2

dE2Eσ(E )

This barrier distribution coincidewith the one provided by thecouplings to reaction channels ifthe eigenvalues of the couplingHamiltonian are energyindependent

Introduction GRAZING Fusion Applications MNT End

Couplings - Barrier distribution

Timmer et al. (1995) extractedbarrier-distribution from thequasi-elastic cross section (sum ofelastic, inelastic and transferchannels) by using:

Dqe(E ) = − d

dE

[σqe(E ,Ω)

σRuth

]

Barrier Distribution

The barrier distribution is a fingerprint of the reaction thatcharacterize the important channel couplings. It retainsstructures representative of the eighenchannel barriers(eighenvalues of the coupling Hamiltonian)

Introduction GRAZING Fusion Applications MNT End

Couplings - Barrier distribution

Timmer et al. (1995) extractedbarrier-distribution from thequasi-elastic cross section (sum ofelastic, inelastic and transferchannels) by using:

Dqe(E ) = − d

dE

[σqe(E ,Ω)

σRuth

]Barrier Distribution

The barrier distribution is a fingerprint of the reaction thatcharacterize the important channel couplings. It retainsstructures representative of the eighenchannel barriers(eighenvalues of the coupling Hamiltonian)

Introduction GRAZING Fusion Applications MNT End

Fusion and GRAZING

Tunneling effects are introduced in thesemiclassical description by using theWKB expression of the transmissioncoefficient

T`(E ) = exp

−2

~

∫ rN

rC

√2µ

[U(`, r)− E

]

where rC and rN , for the given ` and E ,are the classical turning points(Coulomb and nuclear).NB. The couplings to the surface modesmodify the actual position rB of thebarrier B

Introduction GRAZING Fusion Applications MNT End

Fusion and GRAZING

From the system of coupled equationswe can calculate at each instant t, theprobability for the system to have agiven excitation energy or equivalently agiven energy in the relative motion(distribution of barriers). Thus thecalculation of the transmissioncoefficient

T`(E ) =

∫ +∞

−∞P(Er )T`(E − Er )dEr

NB - The distribution of barriers isenergy dependent

ω −→(ω − µΦo

)

Introduction GRAZING Fusion Applications MNT End

Fusion and GRAZING

Introduction GRAZING Fusion Applications MNT End

Fusion and GRAZING

Introduction GRAZING Fusion Applications MNT End

High Energy

Heavy-Ion Fusion Reactions: Open Questions

Very low energies E << EB

The fusion excitation functionis not exponential (Wong)

High energies E > EB

Do we need a long-rangenuclear potential or otherreaction channels suppressfusion?It is possible to use the SAMEpotential for fusion andquasi-elastic reactions ?

Introduction GRAZING Fusion Applications MNT End

High Energy

Heavy-Ion Fusion Reactions: Open Questions

Very low energies E << EB

The fusion excitation functionis not exponential (Wong)

High energies E > EB

Do we need a long-rangenuclear potential or otherreaction channels suppressfusion?It is possible to use the SAMEpotential for fusion andquasi-elastic reactions ?

Introduction GRAZING Fusion Applications MNT End

High Energy

Heavy-Ion Fusion Reactions: Open Questions

Very low energies E << EB

The fusion excitation functionis not exponential (Wong)

High energies E > EB

Do we need a long-rangenuclear potential or otherreaction channels suppressfusion?It is possible to use the SAMEpotential for fusion andquasi-elastic reactions ?

Introduction GRAZING Fusion Applications MNT End

High Energy

To keep in mind

Almost all the models of heavy-ion reactions conform to thefollowing paradigm: they must provide a good description of

The elastic scattering to gain information on the ion-ionpotential

Inelastic and transfer channels to gain information on thecoupling-matrix elements

The 58Ni +124 Sn and 16O +208 Pb are among the few systemswhere for several bombarding energies we have measurments for:

elastic, inelastic and transfer

fusion (ER)

fission and deep-inelastic (incomplete fission)

Introduction GRAZING Fusion Applications MNT End

High Energy

To keep in mind

Almost all the models of heavy-ion reactions conform to thefollowing paradigm: they must provide a good description of

The elastic scattering to gain information on the ion-ionpotential

Inelastic and transfer channels to gain information on thecoupling-matrix elements

The 58Ni +124 Sn and 16O +208 Pb are among the few systemswhere for several bombarding energies we have measurments for:

elastic, inelastic and transfer

fusion (ER)

fission and deep-inelastic (incomplete fission)

Introduction GRAZING Fusion Applications MNT End

NiSn

58Ni +124 Sn System

Introduction GRAZING Fusion Applications MNT End

NiSn

58Ni +124 Sn System

Introduction GRAZING Fusion Applications MNT End

NiSn

58Ni +124 Sn System

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NiSn

58Ni +124 Sn System

Multi-neutron transfer

Introduction GRAZING Fusion Applications MNT End

NiSn

58Ni +124 Sn System

Multi-neutron transfer

Fission+ER+DIC

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NiSn

58Ni +124 Sn System

Multi-neutron transferFission+ER+DIC

Introduction GRAZING Fusion Applications MNT End

OPb

16O +208 Pb System

Introduction GRAZING Fusion Applications MNT End

OPb

16O +208 Pb System

Introduction GRAZING Fusion Applications MNT End

OPb

16O +208 Pb System

DIC collisions (quasi-fission, incomplete fusion,...)are the most likely candidates to explain the HINDRANCE

to FUSION at the higher energies

Introduction GRAZING Fusion Applications MNT End

OPb

16O +208 Pb System

DIC collisions (quasi-fission, incomplete fusion,...)are the most likely candidates to explain the HINDRANCE

to FUSION at the higher energies

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Some Phenomenology of MNT

Introduction GRAZING Fusion Applications MNT End

Some Phenomenology of MNT

The system does not reach charge equilibration. Thepopulation in the (N,Z) plane is dictated by the Qopt

For each transferred neutron the cross section drops by aconstant factor (∼3.5) (sequential transfer)

Introduction GRAZING Fusion Applications MNT End

Some Phenomenology of MNT

The ONE-neutron transfer channel is much larger than theONE-proton transfer channel

The pure TWO-proton transfer is as large as the ONE-protontransfer (pair-transfer mode ?)

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Some Phenomenology of MNT

EVAPORATION may strongly influence the isotopicdistribution of the final fragments, these are indeed producedquite HOT (at high excitation energies)

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Isotopic distribution

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Isotopic distribution

1pt

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Isotopic distribution

1pt

1pt+2pt

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Isotopic distribution

1pt

1pt+2pt

+Evap.

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Angular distribution and QE

Nuclear Potential

From Grazing we extract theimaginary potential iWtr (r) tocalculate with a quantalcoupled-channels calculationelastic and inelastic scattering.

Introduction GRAZING Fusion Applications MNT End

Angular distribution and QE

Nuclear Potential

From Grazing we extract theimaginary potential iWtr (r) tocalculate with a quantalcoupled-channels calculationelastic and inelastic scattering.

Introduction GRAZING Fusion Applications MNT End

PRISMA+CLARA

Introduction GRAZING Fusion Applications MNT End

PRISMA+CLARA

Introduction GRAZING Fusion Applications MNT End

PRISMA+CLARA

Introduction GRAZING Fusion Applications MNT End

PRISMA+CLARA

Introduction GRAZING Fusion Applications MNT End

PRISMA+CLARA

Introduction GRAZING Fusion Applications MNT End

PRISMA+CLARA

Doppler Correction

V

V

V

b

B

a

a A B

b

γ

γ

PRISMA

CLARA

CLARA

Introduction GRAZING Fusion Applications MNT End

PRISMA+CLARA

Doppler Correction

V

V

V

b

B

a

a A B

b

γ

γ

PRISMA

CLARA

CLARA

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PRISMA+CLARA

Exci

tatio

n en

ergy

Angular Momentum (I)

rel F

yras

t

V << V

V ~ Vrel F

Fusion Reaction

Introduction GRAZING Fusion Applications MNT End

PRISMA+CLARA

Exci

tatio

n en

ergy

Angular Momentum (I)

rel F

yras

t

V << V

V ~ Vrel F

Fusion Reaction

Introduction GRAZING Fusion Applications MNT End

PRISMA+CLARA

Exci

tatio

n en

ergy

Angular Momentum (I)

rel F

yras

t

V << V

V ~ Vrel F

Fusion Reaction

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PRISMA+CLARA

2+

2+

3−

3+

0+

9/2+

1/2+

11/2−

ZrZr Nb9695 97

0

1

2

3

E [

MeV

]

5/2−

5/2+ 0+ 9/2+

1/2−

5/2−

(7/2+,5/2+)

Introduction GRAZING Fusion Applications MNT End

PRISMA+CLARA

2+

2+

3−

3+

0+

9/2+

1/2+

11/2−

ZrZr Nb9695 97

0

1

2

3

E [

MeV

]

5/2−

5/2+ 0+ 9/2+

1/2−

5/2−

(7/2+,5/2+)

Introduction GRAZING Fusion Applications MNT End

To de End

Nuclear degrees of freedom (collision time τ =√

a/ro)

• INELASTIC fin(r) ∼ e−r/ain ain = 0.65 fm(few channels but strong)• low lying: mass (D) large NON adiabatic

force (C) small coupled-channels• high lying: mass (D) small adiabatic

force (C) large

• TRANSFER ftr (r) ∼ e−r/atr a1tr = 1.2 fm a2

tr = 0.6 fm(many channels but weak)

play an important role in: energy dissipation (friction),Imaginary (iW ) and polarization (∆V ) potentials< n >= Np Eloss = ∆E < n >

Introduction GRAZING Fusion Applications MNT End

To de End

Nuclear degrees of freedom (collision time τ =√

a/ro)

• INELASTIC fin(r) ∼ e−r/ain ain = 0.65 fm(few channels but strong)• low lying: mass (D) large NON adiabatic

force (C) small coupled-channels• high lying: mass (D) small adiabatic

force (C) large

• TRANSFER ftr (r) ∼ e−r/atr a1tr = 1.2 fm a2

tr = 0.6 fm(many channels but weak)

play an important role in: energy dissipation (friction),Imaginary (iW ) and polarization (∆V ) potentials< n >= Np Eloss = ∆E < n >