Transcript Folie 1 - Department

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
New data in the region between
Motivation:
the Coulomb Barrier and the Fermi Energy
Aprojectile
loss of energy, friction
exchange of mass
impact parameter b
Peripheral collisions at energies above the
Coulomb barrier
(A.G.Arthuk, et al., Nucl.Phys. A701(2002)
96c)
Dissipation
Atarget
Afragment
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
7
10
Results of experiments at COMBAS
spectrometer in FLNR LNR JINR
6
10
N13
N14
N15
N16
N17
N18
N19
5
10
4
10
Measured: isotope distributions
velocity spectra
3
10
2
10
1
10
Characteristic feature:
0
10
0.6
1.0
1.2
v/v0
peak at beam velocity
asymmetric shape with tail to
lower velocities
0.8
6
10
C9
C10
C11
C12
C13
C14
C15
C16
C17
C18
5
indication of two-component
structure
10
4
10
3
10
2
Try to understand using transport
theory!
10
1
10
0
10
0.6
0.8
1.0
v/v0
1.2
TFermi 
2
Break-up (BU) component, comparison with Goldhaber:
Statistical Model Of Fragmentation Processes
Phys. Lett. V53B (1974) p 306
mN
pF 265MeV/c
ÛT=15MeV
T=?
the underlying picture: suppose
nucleons chosen at random should go off
together . What would be the mean
square total momentum ?
the underlying picture: suppose that
the nucleus after excitation comes to
equilibrium at temperature T :
Then,
the width of distribution is:

2
0
2
AF ( AP  AF )
AP  1
 0  9 0 M eV / c
1
,

2
 m nT
AF ( AP  AF )
T  9 M eV ,
P – projectile, F – fragment
,
AP
E exc  a T
2
Comparison with similar studies:
Gelbke et al 1977, 16O+208Pb at 27 MeV/u :
<<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.>>
 0  80  100 MeV / c
H. Fuchs and K. Moehring, Rep.
Prog. Phys.,1994, v57, p 231
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
M. Notani et.al.
13C
spectra, measured for 60 MeV/u 14N on
various target nuclei
 0  61 MeV / c
High energy component also
interpreted as direct break-up.
Transport theory: one-body description, BNV approach
time evolution of the one-body phase space density: f(r,p;t)



p 

f  U 
t
m
Vlasov eq.:
mean field:
f
f  I coll  f , 

U(f) = Nuclear Mean Field + Coulomb + Surface + Symmetry terms
Test Particle (TP) representation
(N number of TP per nucleon):
I co ll

 
1
f (r , p, t ) 
NA




  ( r  ri ( t ))  ( p  p i ( t ))
i



p i ( t   t )  p i ( t )   t  r U ( ri , t )



ri ( t   t )  ri ( t )   t p i ( t ) / M
Equations of motion of TP:
2-body
collision term:
p
 f ,  
g
3
3
3
dr
p
dr
p
dr
p 4W 12, 34   f 1 f 2 f 3 f 4  f 1 f 2 f 3 f 4 
2
3

h
W  1 2, 3 4     1 2, 3 4  
 p1 
p2  p3  p 4     1   2   3   4 
Stochastic simulation of collision term: collision of test particles i, j
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
Residual fragments:
Fragment recognition
algorithm:
cut-off density
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
Deflection function (qualitative):
Grazing angle,
Coulomb
rainbow
Deflection angle Q
Impact parameter b
Nuclear
rainbow
attach Coulomb trajectories to
obtain final angles and velocities
Definition of fragments: space integrals over region of density   0 . 1  0
Number of particles
NA 
Space position
Rz 
Velocity
Vi 
Phase space integrals
 


 
d
r
n
(
r
,
t
)

d
r
d
p
f
(
r
, p, t)

 


d
r
n
(
r
,t) z



1
d
r
u
(
r
,
t
)

 i
m


d
r
d
p
  f (r , p, t ) 

d
r


i
1
n(r , t )
( test particles
Z , N , X , Y , Z , PX , PY , PZ
E kin
Nb
 tot 
 b (b
i
k
i 1

 
d
p
p
f
(
r
, p, t)
i

 bi )  k
in boundary )
Isotope Distributions
1,0
Normalized to unity
for each isotope
experimental data,
 < 2.5
0,8
0,6
0,4
0,2
0,0
0.5
absolute
Nt.p.=50
Nt.p.=100
0.4
0.3
0.2
0.1
Z=4
Z=5
Z=6
Z=7
Z=8
0,3
calculation,
b = 7.5-13 fm
0,2
0.0
5
10
A
15
20
18
O+
E / E0
deflection angle –
Ta, 35 MeV / A
0,0
Z=8
1.0
Wilczynski-Plot:
0,1
181
0.8
2
3
4
5 6 7 8 9 10 11 12
number of neutrons N
Z=7
0.6
Z=6
0.4
Z=4
energy loss correlation
0.2
Z=5
0.0
0
10
20
30
angle
More nuclear transfer
More energy loss
Velocity Distributions,
18O
+ 181Ta,
35 AMeV,
O isotopes:
BNV approach
Full solid angle
Velocity Distributions,
QMD approach (A.G. Artukh,
et al., Acta Phys.Pol. 37 (2006)
1875
Q  2 .5
0.3
N=8
N=9
N =10
0.2
0.1
0.0
0.6
0.8
1.0
0.6
0.8
1.0
C Isotopes:
0.02
0.02
N=6
N=7
N=8
N=9
0.01
0.00
0.6
0.8
1.0
0.6
0.8
vfragment / vproj
0.01
1.0
0.00
0
Comparison with the experiment, A.G. Artukh et al,
FLNR, 2001
6
10
13
181
O+ Ta
experiment
5
10
Two components:
18
C
a
4
10
13
Deep inelastic(DIC)+ Break-up(BU)
C
b
15
Velocity distribution peaked at V_projectile
YIELDS
Characteristics of Break-up process (dark red
curve in figure a):
N
BNV
EXP
c
16
O
Gaussian distribution:
d
f  C exp(  ( p  p 0 ) / 2 )
2
2
0,6
The difference between total and break-up curves
,represents DIC (red curves in b,c,d)
and agrees well with our calculations (blue curves).
0,7
0,8
0,9
1,0
vfragment / vproj
1,1
1,2
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
E exc  ( E kin  E pot ) t  0  ( E kin  E pot ) t  freeze  out  E kin
lost . part .
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.
18
18
9
O(35 MeV/n)+ Be
181
O(35 MeV/n )+
Ta
0,1
0,01
0,01
1E-3
1E-3
Relative yields
0,1
4
8
12
SMM, no restrictions
BNV, no restrictions
16
20
0
Afragment
4
8
12
16
20
24
experiment, 
SMM, 
The mass distribution, calculated with the the same angular restrictions as in experiment is too narrow.
* Bondorf J.P.// Phys. Rep. 257
(1995) 133
BNV
XDIC
SMM
18
9
O+ Be
1,0
XDIC
18
9
O+ Be
1,0
0,5
18
181
0,5
O+ Ta
18
1,0
1,0
0,5
0,5
10
12
14
16
18
20
10
12
14
16
181
O+ Ta
18
20
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.
Experiment
 0  60 M eV / c
10
11
12
13
14
15
150
1
16
Be
T  3.8 M eV ,
E exc  27 M eV ,
100
v shift / v 0  0.98
O
N
C
B
50
0
 0  74 M eV / c
150
1
Ta
?
100
T  5.8 M eV ,
O
N
C
B
50
E exc  61 M eV ,
0
10
11
12
13
A
14
15
16
v shift / v 0  0.95
15
2
181
O+ Ta
RDIC/BU
18
3
18
181
O+ Ta
18
9
O+ Be
0,8
0
0,6
BNV
-15
lab
0,4
18
15
9
O+ Be
0,2
0
10
-15
0,5
1,0
b / (R +R2)
1
1,5
Deflection functions:
red lines indicate the angular
restriction of the experiment
12
14
16
AF
Ratio of the yields in the dissipative
and the direct components as a function
of the mass of the fragment.
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
Experimental Description of DIC:
В. В. Волков , Ядерные реакции глубоконеупругих
передач,
Москва, Энергоиздат, 1982
J.Wilczynski, Phys. Lett., 1973, B 47, p 484
U. Schroeder and J.R. Huizinga, Treatise on Heavy-Ion Science
Vol 2, ed. A Bromley, Plenum, New York, p. 113-726 (1984)
Theoretical Description of DIC:
Classical trajectories with Friction (e.g. Gross and Kalinowski)
radial and tangential friction, transport properties
Diabatic Dissipative Dynamics (e.g. Nörenberg)
two-center shell model and avoided Landau-Zener crossings
here: Transport Theory :
early work: M.F.Rivet et al, Phys Lett. B215(1988)55,
reaction Ar +Ag, E/A = 27 MeV
Goldhaber dependance,
results of G. Kaminski
18O
+ 181Ta,
35 Mev/nucl
18O
+ 9Be
35 Mev/nucl
22Ne
+ 9Be
40 Mev/nucl