14th Internat. Conf. Nucl. Reaction Mechanisms, Varenna, 19th June 2015 1 PRE-EQUILIBRIUM (EXCITON) MODEL AND THE HEAVY-ION REACTIONS WITH CLUSTER EMISSION

14th Internat. Conf. Nucl. Reaction Mechanisms, Varenna, 19th June 2015

1

PRE-EQUILIBRIUM (EXCITON) MODELAND THE HEAVY-ION REACTIONS

WITH CLUSTER EMISSION

E. BětákInst. of Physics, Slovak Acad. Sci., Bratislava,

Slovakia([email protected])

J. CsehATOMKI, Debrecen, Hungary

mailto:[email protected]

14th Internat. Conf. Nucl. Reaction Mechanisms, Varenna, 19th June 2015 2

1. Motivation2. Consistency of the exciton model – master eq.

approach3. Coalescence and Iwamoto-Harada model for cluster

emission in its density formulation4. Extensions of the Iwamoto-Harada model5. Cluster emission with angular momentum

variables6. Cluster emission from heavy-ion collisions


MOTIVATION

Candidates for hyperdefomed nuclei are expected to be formed (relatively easily) in (light) heavy-ion reactions at not too high energy (say, incident energy of few tens or as a maximum few hundreds of MeV).

Some combinations of colliding ions have been suggested.

The question is, which energies seem to be favourable for their creation.

We aim to get some hints for this process, and illustrate it on the 20Ne + 20Ne -> 36 Ar (plus something: α, 2n+2p, n+p+d, …)

The production cross section serves as the main indiucator. Therefore we applied statistical pre-equilibrium model with additions suitable to this aim.


CONSISTENCY OF THE EXCITON MODEL - MASTER EQUATIONS APPROACH

Master equations are capable to describe the whole process in time from the very creation of the composite system through its equilibration up to the decay of compound nucleus within a single formalism, not mixing various approaches.

Using the density-dependent formulation of the so-called Iwamoto-Harada model (Dobes and Betak, 5 years before I+H) for cluster emission, pick-up as well as knock-out can be included. Obviously, one pays for the single approach with the lost of majority details, like details of the structures in spectra, but the cross sections describe the average trends rather satisfactorilly.

A technical handicap remains: the set of master

equations is huge, but we have a suitable algorithm to solve it.


5 5

COALESCENCE MODEL FOR CLUSTER EMISSION

Kalbach (Cline, Kalbach-Cline, Kalbach-Walker), Ribanský & Obložinský

Emision rate (nucleons):

Coalescence clusters:

)(),,(

),,1()(

12),,( *

32pR

Ehp

UhpsEn xxINVxx

xx

cx

x

xxxxx

xxINVxx

xx

cx g

BppR

Ehp

UhppsEn

),0,()(

),,(

),,()(

12),,( *

32


coalescence IH model IHB model knock-out

COALESCENCE (IWAMOTO-HARADA) MODEL FOR CLUSTER EMISSION IN ITS DENSITY FORMULATION

Generalized (coalescence + pickup) Iwamoto & Harada, Dobeš & Běták, Bisplinghoff

EMISSION RATE PROPORTIONAL to the CLUSTER FORMATION PROBABILITY

SINGLE-CLUSTER DENSITY INVERSELY PROPORTIONAL to the CLUSTER FORMATION PROBABILITY

12*

1*

11

* ),,0(),0,(),,(

),0,(),,(

*

dpppEhpp

BpUhpp

x

p

p

E

B

xxxx

x

xx

THEREFORE the result is PARAMETERLESS !

7

Bisplinghoff

Pickup limited by the binding energy of nucleons in the cluster (i.e. about 28 MeV for alphas and 2 MeV for deuterons)

Now Limitation due to binding energy for all clusters

Only low-exciton configurations with pickup (CN limit!)

Thermal “blurring” considered

Admixture allowed for all potential well (Heisenberg uncertainty relation)

Possibility of knockout (initial stage only) for alphas

E

dU0

),0,1(),4,0(


8

14th Internat. Conf. Nucl. Reaction Mechanisms, Varenna, 19th June

2015 9

Calculations without spin (old)

a) deuterons


Bb) alphas

14th Internat. Conf. Nucl. Reaction Mechanisms, Varenna, 19th June

2015 11

c) α-knockout admixtures from the fit to the data


Cluster emissionCluster emission withwith

angular momentumangular momentumvariablesvariables

Spin variables:

Coupling of nucleons to form a coalescence or pickup cluster may be – in a very rough approximation – considered included in the formation probability.

Therefore, no additional couplings appear in the emission rates and the only place affected by the angular momentum are different transition coefficients and via competitions to other (nucleon,γ) channels.

Exception: knock-out – α-particle is not formed during reaction, but it is already present in the target nucleus.




15

Primary nucleon, deuteron, alpha and gamma energy spectra (gammas with cascades) from 197Au+p at 62 MeV

14

th In

tern

at. C

on

f. Nu

cl. Reactio

n M

ech

an

isms, V

are

nn

a,

19

th Ju

ne 2

01

5

16

HEAVY IONS – INITIAL CONFIGURATION(without spin variables today)

Cindro et al.:

for lower energies,

where


)(

)(08.038.009.0

arg

arg0

projt

projt

proj AA

AA

A

n

proj

Ccm

A

VE

HEAVY IONS – CLUSTER BREAKUPKalbach Walker, www-nds.iaea.org/fendl3/docs/dBreakupRCM2.pdf

where the normalizatoion factor is only weakly sensitive to the projectile.

We use this as very rough initial approximation.


18

MeV

EEMeV

E

Dinc

inc

bu

14exp1[

170exp

)(2/1

20


P r e l i m i n a r y

20 Ne + 20 Ne

CONCLUSIONS Clusterization itself parameterless Effective only at initial stages, what enables proper equilibrium

(compound nucleus) limit Thermal blurring of nucleons allowed Pickup (IHB) generalized to all types of clusters For strongly bound ejectiles knockout possible: Included angular momentum, but the couplings of nucleons to form a

cluster are hidden in cluster formation probability Introduction of spin variables enhances the cluster emission compared

to spin-independent case. (It plays similar role as deformation according to Blann & Komoto)

All calculations presented here are just with default parameters (level densities, inverse c.s., transition matrix element).

Possibility to indicate various contributing mechanisms leading to the same (nearly equilibrated) composite system, and to select the most suitable conditions for structure studies, like existence of hyperdeformed nucli.

Further effort: heavy ions, cluster emission, pre-equilibrium with some elements of direct reactions and spin variables tgogether within one formalism


20

Thank you


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14th Internat. Conf. Nucl. Reaction Mechanisms, Varenna, 19th June 2015 1 PRE-EQUILIBRIUM (EXCITON) MODEL AND THE HEAVY-ION REACTIONS WITH CLUSTER EMISSION