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