COMPETITION OF BREAKUP AND DISSIPATIVE PROCESSES

IN 18O (35 MeV/n) + 9Be ( 181Ta ) REACTIONS

AT FORWARD ANGLES

Tatiana Mikhaylova,

JINR, Dubna

 

B. Erdemchimeg 1,2, A.G. Artyukh1,

M. Colonna3, M. di Toro3,

G. Kaminski 1,4, Yu.M. Sereda 1,5,

H.H. Wolter6

1-Joint Institute for Nuclear Research, Dubna, Russia

2- Mongolian National University, Mongolia

3- LNS, INFN, Catania, Italy

4- Institute of Nuclear Physics PAN, Krakow, Poland

5 -Institute for Nuclear Research NAS, Kyiv, Ukraine

6 -University of Munich, Germany

Topics:

• Motivation from experiment

• Transport description

• Evaporation

• Velocity distributions. Residual Fragments

• Break-up component

• Results

Motivation:

loss of energy, friction

exchange of mass

DissipationPeripheral collisions at energies above the Coulomb barrier

(A.G.Arthuk, et al., Nucl.Phys. A701(2002) 96c)

impact parameter b

Aprojectile

Atarget

Afragment

New data in the region between

the Coulomb Barrier and the Fermi Energy

Peripheral reactions at Fermi Energy are expected to be the powerful tool to reach neutron reach

isotopes !

G.A. Souliotis et al, Phys. Rev. Lett., v91 p022701-1(2003)

Structure of primary fragments ,

investigation of reaction mechanism and production of primary

fragments

0.6 0.8 1.0 1.2100

101

102

103

104

105

106

107

N13 N14 N15 N16 N17 N18 N19

v/v0

0.6 0.8 1.0 1.2100

101

102

103

104

105

106

C9 C10 C11 C12 C13 C14 C15 C16 C17 C18

v/v0

Measured: isotope distributions

velocity spectra

Characteristic feature:

peak at beam velocity

asymmetric shape with tail to lower velocities

indication of two-component structure

Try to understand using transport theory!

Results of experiments at COMBAS

spectrometer in FLNR LNR JINR

Then,

the width of distribution is:

2 20

10

( ) ,1

90 /

F P F

P

A A AA

MeV c

P – projectile, F – fragment

Break-up (BU) component, comparison with Goldhaber:

Statistical Model Of Fragmentation Processes

Phys. Lett. V53B (1974) p 306

the underlying picture: suppose nucleons chosen at random should

go off together . What would be the mean square total momentum ?

2

2

( ) ,

9 ,

F P Fn

P

exc

A A Am TA

T MeV E aT

the underlying picture: suppose that the nucleus after excitation

comes to equilibrium at temperature T :

pF 265MeV/c

Û T=15MeV

Tm

Fermi

N

2

pF 265MeV/c

T=?

Tm

Fermi

N

2

<<Fig. 1

Energy spectra of reaction products N, C, B, Be, Li measured in the bombardment

of 208Pb by 16 O ions of 315 MeV at the laboratory angle of 15 ° . The curves are

calculated from eq. (6) as explained in the text. The arrows denoted by VC

, EF

and EP

correspond to the exit-channel Coulomb barrier, the energy predicted for

a fragmentation of the projectile into the observed fragment together with

individual nucleons and α-particles [ 10], and the energy of a product with the

projectile velocity.>>

H. Fuchs and K. Moehring, Rep. Prog. Phys.,1994, v57, p

231

Comparison with similar studies:

Gelbke et al 1977, 16O+208Pb at 27 MeV/u :

cMeV /100800

Lahmer et al, Transfer and fragmentation

reactions of 14N at 60 MeV/u , Z. Phys. A - Atomic Nuclei 337, 425-437

(1990)

Fig. 9.Two-component fits to 13C spectra, measured for 60 MeV/u

14N on various target nuclei

cMeV /610

High energy component also interpreted as direct break-

up.

M. Notani et.al.

Vlasov eq.:

mean field: U(f) = Nuclear Mean Field + Coulomb + Surface + Symmetry terms

Transport theory: one-body description, BNV approach

,fIfUfmp

tf

collp

time evolution of the one-body phase space density: f(r,p;t)

Test Particle (TP) representation

(N number of TP per nucleon):))(())((1),,( tpptrr

NAtprf i

ii

Equations of motion of TP:

MtpttrttrtrUttpttp

iii

irii

/)()()(),()()(

2-body collision term: ,collI f

1 2 3 4 1 2 3 412,34 12,34W p p p p

3 3 32 3 4 1 2 3 4 1 2 3 412,34g dr p dr p dr p W f f f f f f f f

h

F. Bertsch, S. Das Gupta , , Phys. Rep.,1988, v160, p 189

V. Baran, M. Colonna, M. Di Toro, Phys. Rep., v 410, 2005, p.335

Stochastic simulation of collision term: collision of test particles i, j

Residual fragments:

Fragment recognition algorithm:

cut-off density

Deflection function (qualitative):

Impact parameter b

Deflection angle Q

Grazing angle, Coulomb

rainbow

Nuclear rainbow

attach Coulomb trajectories to obtain final angles and

velocities

Criterium for the definition of the boundaries of the fragment at freeze-out:

density < 0.1 saturation density

Density contour plots in the reaction 18O(35MeV/n)+181Ta.

Six times (t=0,20,40,60,80,100 fm/c ) are shown

),,(),( tprfpdrdtrnrdNA

ztrnrdRz ),(

),,(),(

11),( tprfppdtrn

rdm

trurdV iii

i

boundaryinparticlestesttprfpdrd )(),,(

Definition of fragments: space integrals over region of density01.0

Number of particles

Space position

Velocity

Phase space integrals

ZYX PPPZYXNZ ,,,,,,,

kinE

kii

N

kitot bbb

b

)( 1

Isotope Distributions

5 10 15 200.0

0.1

0.2

0.3

0.4

0.5

Nt.p.

=100N

t.p.=50

A

calculation, b = 7.5-13 fm

experimental data, < 2.5

Normalized to unity

for each isotope

absolute

2 3 4 5 6 7 8 9 10 11 120,0

0,1

0,2

0,3

0,0

0,2

0,4

0,6

0,8

1,0

Z = 4 Z = 5 Z = 6 Z = 7 Z = 8

number of neutrons N

0 10 20 30

0.0

0.2

0.4

0.6

0.8

1.0

E /

E0

angle

18O + 181Ta, 35 MeV / A

Z = 6

Z = 5

Z = 4

Z = 7

Z = 8Wilczynski-Plot:

More nuclear transfer More energy loss

deflection angle –

energy loss correlation

Velocity Distributions,

BNV approach

Full solid angle05.2Q

O isotopes:18O + 181Ta,

35 AMeV,

0.6 0.8 1.00.0

0.1

0.2

0.3

0.6 0.8 1.0

N = 8 N = 9 N =10

0.00

0.01

0.02

0.6 0.8 1.00.00

0.01

0.02

0.6 0.8 1.0v

fragment / v

proj

N = 6 N = 7 N = 8 N = 9

C Isotopes:

Velocity Distributions,

QMD approach (A.G. Artukh, et al., Acta Phys.Pol. 37

(2006) 1875

Comparison with the experiment, A.G. Artukh et al, FLNR, 2001

Two components:

Deep inelastic(DIC)+ Break-up(BU)

Characteristics of Break-up process (dark red curve in figure a):

Velocity distribution peaked at V_projectile

Gaussian distribution:

The difference between total and break-up curves ,represents DIC (red curves in b,c,d)

and agrees well with our calculations (blue curves).

104

105

106

0,6 0,7 0,8 0,9 1,0 1,1 1,2

YIE

LDS

13C experiment

13C

16O

vfragment

/ vproj

EXP

18O+181Ta

BNV15N

a

d

b

c

2 20exp( ( ) / 2 )f C p p

4 8 12 16 20

1E-3

0,01

0,1

0 4 8 12 16 20 24

1E-3

0,01

0,1

SMM, no restrictions BNV, no restrictions

18O(35 MeV/n )+181Ta

experiment, SMM,

Rel

ativ

e yi

elds

18O(35 MeV/n)+9Be

Afragment

To compare the results of the calculation with the experimental data we attach a statistical evaporation of the excited primary fragments. For this we use the Statistical Multifragmentation Model (SMM), by

Botvina et al. (*). The crucial quantity in this process is the value of excitation energy. Here we use a rough estimate for the excitation energy, where the total excitation energy is given as

. .0( ) ( ) lost part

exc kin pot t kin pot t freeze out kinE E E E E E where the potential energy is calculated from the Bethe and Weizsaecker mass formula], and the excitation energy is divided proportionally between target and projectile-like fragment. A more consistent

evaluation of dissipated energy is under way, calculating the potential energy with BNV.

* Bondorf J.P.// Phys. Rep. 257 (1995) 133

The mass distribution, calculated with the the same angular restrictions as in experiment is too narrow.

0,5

1,0

10 12 14 16 18 200,5

1,0

XDIC18O+9Be

18O+181Ta

we show the dependence of the centroidsof the dissipative velocity distribution XDIC

before (BNV) and after (SMM) evaporation for the calculations without and

with angular restriction compared to the experiment.

Several symbols for one mass correspond to different elements.

Experiment - blue squares.

Calculation without angular restriction - green circles.

Calculation with angular restriction - red stars.

For BNV the description is rather good,

for SMM there are considerable deviations.

These last values are preliminary and may be due to insufficient sampling of the reaction.

Comparing the results of BNV and SMM calculations one can see that the fragments corresponding to the same mass number A has larger velocity in

the SMM plot than in BNV one. This is due to the fact that they are produced by evaporation of the heavier fragment that had larger mass in BNV plot.

0,5

1,0

10 12 14 16 18 200,5

1,0

XDIC 18O+9Be

18O+181Ta

SMMBNV

10 60 /MeV c

Experiment

10 11 12 13 14 15 16

10 11 12 13 14 15 160

50

100

150 Ta?

O N C B

A

0

50

100

150 Be

O N C B

0

3.8 ,27 ,

/ 0.98exc

shift

T MeVE MeVv v

10 74 /MeV c

0

5.8 ,61 ,

/ 0.95exc

shift

T MeVE MeVv v

10 12 14 16

0,2

0,4

0,6

0,8 18O+181Ta 18O+9Be

AF

RD

IC/B

U

Ratio of the yields in the dissipative and the direct

components as a function of the mass of the fragment.

0,5 1,0 1,5

-15

0

15

-15

0

15

18O+9Be

lab

b / (R1+R2)

18O+181Ta32

BNV

Deflection functions:

red lines indicate the angular restriction of

the experiment

The relative yield of the dissipative over the direct contributions is much

smaller for the Ta target. This can be understood from the deflection

function, which shows that for Ta only a small range of impact parameters

contributes to the dissipative process.

Conclusions:

1. The study of heavy ion collisions in the Fermi energy regime gives the opportunity to learn about equilibration

processes in low-energy heavy ion collisions and to provide estimates of yields of exotic nuclei.

2. We studied such reactions with a transport description, including secondary evaporation of the excited

primary fragments.

3. We find, that the dissipative part of the observed yield is qualitatively described by the calculations: the

velocity distributions are in reasonable agreement, while the isotope distributions are still too narrow with

the present simple estimate of the excitation energy.

4. The direct components follows the behaviour of the Goldhaber model, but it would be desirable, to have a

more microscopis theory for this.

5. The relative ratio of the two contribution can be understood qualitatively from the deflections functions

Thank you for attention

Incomplete fusion model: M. Veselsky, Nucl. Phys. A 705 (2002) 193

Application to 22Ne + 9B experiment: G.Kaminsky, et al. (NUFRA2007 conference, Antalya, Turkey, 2007)

partly also shift to lower velocities

В. В. Волков , Ядерные реакции глубоконеупругих передач,

Москва, Энергоиздат, 1982

U. Schroeder and J.R. Huizinga, Treatise on Heavy-Ion Science

Vol 2, ed. A Bromley, Plenum, New York, p. 113-726 (1984)

J.Wilczynski, Phys. Lett., 1973, B 47, p 484

Experimental Description of DIC:

Theoretical Description of DIC:

Classical trajectories with Friction (e.g. Gross and Kalinowski)

radial and tangential friction, transport properties

here: Transport Theory :

early work: M.F.Rivet et al, Phys Lett. B215(1988)55,

reaction Ar +Ag, E/A = 27 MeV

Diabatic Dissipative Dynamics (e.g. Nörenberg)

two-center shell model and avoided Landau-Zener crossings

Goldhaber dependance,

results of G. Kaminski

18O + 181Ta,

35 Mev/nucl

18O + 9Be

35 Mev/nucl

22Ne + 9Be

40 Mev/nucl