Quasifission reactions in heavy ion collisions at low energies

A.K. Nasirov1, 2 1Joint Institute for Nuclear Research, 141980 Dubna, Russia2Institute of Nuclear Physics, 100214, Tashkent, Uzbekistan

September 1, 2015 Trento

“Interfacing Structure and Reaction Dynamics in the Synthesis of the Heaviest Nuclei”at the ECT*, Trento, Italy, September 1-4, 2015

Synthesis of superheavy elements in the cold and hot fusion reactions.

2

Quasifission is a binary process producing two reaction products in heavy ion collisions. The basic difference between fusion fission and quasifission is that compound nucleus formation is not achieved in the latter mechanism. Quasifission can be thought of as a bridge between deep-inelastic scattering, where the relative kinetic energy between the fragments can be partially damped, but the mass asymmetry of the entrance channel is mostly preserved, and compound nucleus fission reactions.

Total kinetic energy

Mass distribution

Angular distribution

Fusion-fission Viola systematics with small fluctuations

Gaussian like shape with structure

Mainly isotropic + Anisotropic (L) (L, tK)

Quasifission Viola systematics with large fluctuations

Asymmetric-double gaussian (L, tDNS)

Anisotropic+ isotropic (new) (L, tDNS)

Fast-fission ? ? Mainly isotropic

Comparison of characteristics of reaction fragments

Reaction channels in heavy ion collisions at low energies

5

(Superheavy element)

Complete fusion

(E)

Dependence of the formation of fission-like binary fragments on the orbital angular momentum, L

Fast fission

0 < L < LB 0 < L < Lcap LB < L < Lcap

L=I ω

Mass-energetic distribution of the binary products in heavy ion collisions

Deep inelastic collisionsQuasifission

Fusion-fission

Mechanisms of the reaction following after capture (capture means formation of dinuclear system): Fusion-fission, quasifission and fast-fission.

Progress in study of the quasifission reactionsThe mass distribution of the quasifission products is peaked near the masses of the target and of the

projectile. The fraction of the mass distribution located at symmetry is relatively small.

The fragment kinetic energies are characteristic of the Coulomb repulsion of fission fragments.

The angular distributions are peaked in the vicinity of the grazing angle.

Phys.Rev.Lett. 36, 18 (1976)

Full damped (capture) and partially damped (deep-inelastic collision) events.

diffusion effects on nucleons

angular dependence of energy loss

Mass-angle distribution as function of the beam energy in 63Cu+197Au reaction. C. Ngô et al, Nucl.Phys. A267, 181 (1976).

The increase of the beam energy leads to the shift of the mass distribution of the reaction products to the small angles.

α=M1 t is maximum of the mass distribution as a function of time ;

Γ2 is the square of the width (FWHM) related with diffusion coefficient.

13

Dynamics of complete fusion and a role of the entrance channel in formation of reaction products in heavy ion collisions are questionable or they have different interpretation still now. For example, -- what kind of fusion mechanism makes a main contribution to the formation of compound nucleus: the increase of the neck between interacting nucleus, or multinucleon transfer at relatively restricted neck size, or + ?

The details of angular momentum distribution of dinuclear system and compound nucleus those determine cross sections of evaporation residue, fusion-fission and quasifission products;The theoretical and experimental studies are important in order to clarify the origin of fission events (CN-fission against quasifission), namely, to separate fusion-fission fragments from the quasifission and fast-fission products.

What is questionable in fusion-fission reactions ?

`

II. Quasifission:1) Full momentum transfer;2) Equilibrium of energy distribution and mass distribution;3) Anisotropic and isotropic angular distributions.

III. Compound nucleus formation:1) Full momentum transfer;2) Equilibrium of energy distribution and mass distribution;3) Isotropic angular distributions.

*CNE'L

b

b

b

𝐿=[ 𝑏   x  P   ]Formation of the dinuclear system (Capture reactions)

I. Deep inelastic collisions:1) Partial momentum transfer;2) There is not equilibrium of energy

distribution and mass distribution;3) Anisotropic angular distribution

Beam

Beam

Beam

Interpretation of the mechanism of production radioisotopes with different energy at SHIP

64Ni + 207Pb S. Heinz, V. Comas, F. P. Heßberger,

S. Hofmann, D. Ackermann, et al.Eur. Phys. Jour. A 38, 227 (2008)“Di-nuclear systems studied with the velocity filter SHIP”

Mass – charge and angular distributions of the multinucleon transfer reaction were estimated.

The role of nuclear shell effects in the yield of the quasifission

products.

Mixing of the distribution of fragment masses versus total kinetic energy

Experimental data from Ref. W.Q. Shen et al (GSI) Phys.Rev.C36, 115 (1987), where two reaction products of deep-inelastic collisions (DIC), quasifission (QF) and fusion-fission (FF) processes are

registered for three reactions at three values of beam energy 5.4, 6.7, 7.5 MeV A.

70ZnDIC

DIC

DIC

FF

FF

QF

QF

DIC

DIC

DIC

QF

QF

QF

18

А – deep inelastic collision productsВ- quasifission products

Z1=20 Z2=82

Mixing products formed in the deep-inelastic collisions and quasifission

Z

Z

G. Fazio et al.,Mod. Phys. Lett. Vol. 20, No. 6 (2005) 391

19

Comparison of theoretical results with the experimental data for the capture, fusion and evaporation residue excitation functions

G. Fazio, et al. Modern Phys. Lett. A 20, No. 6 (2005) 391-405

20

The observed decrease of the quasifission contribution by increase of the collision energy in 48Ca+154Sm reaction. (from paper Knyazheva G.N. et al. Phys. Rev. C 75, 064602(2007).

Evolution of the mass distributioin of quasifission fragments

21

22

TKE=K1+K2

P(M1,M2.TKE)

P(M1,M2)=Σ P(M1,M2.TKE)

<TKE>=Σ TKE P(M1,M2.TKE)

Explanation of the lack of quasifission fragment yields at the expected place of mass distribution in the 48Ca+144Sm reaction

24

Comparison of the capture, fusion-fission and quasifission cross sections obtained in this work with data from experiments

Knyazheva G.N. et al. Phys. Rev. C 2007. Vol. 75. –P. 064602(13).

and evaporation residues

Stefanini A.M. et al. Eur. Phys. J. A –2005. Vol. 23. –P.473

The role of the angular momentum of dinuclear system in competition between complete fusion and quasifission.

The lifetime and rotational angle of the dinuclear system formed in 48Ca+154Sm reaction as a function of the Ec.m. energy.

The overlap of the angular momentum distributions of the fusion-fission and quasifission processes.

Comparison of the potential wells of the nucleus-nucleus interaction for reactions

leading to formation of 220Th.

28

Bqf

Importance of the radial and tangential friction coefficients

A new problem in separation of fusion-fission and the quasifission products in heavy ion collisions when there is overlap their mass and angular distributions.

The partial quasifission excitation function calculated at different values of the collision energy Ec.m. for the 32S + 184W reaction.

The analysis of experimental data deals with the limiting value of angular momentum lCN for complete fusion, as in paper by R.S. Naik et al. Phys. Rev. C 76, 054604 (2007).

• The use of this formula assumes that the quasifission products are not formed in collisions with angular momentum L < LCN.

31

32

The methods of calculation of the capture and fusion cross section in the dinuclear system approach. Main assumptions:

1) the shell effects does not allow to fuse nuclei immediately;2) the hindrance to fusion is determined by the intrinsic fusion barrier

which is determined from the landscape of the potential energy surface of dinuclear system;

3) the interacting nuclei can be deformed and nucleon exchange between them takes place allowing dinuclear system to be transformed

into compound nucleus or to populate shapes corresponding minimal values of the potential energy surface (superdeformed shapes and shapes preceding to quasifission);4) The lifetime τDNS of dinuclear system is determined by its excitation energy and quasifission barrier Bqf.

The evaporation residue cross section (synthesis of superheavy element) is calculated by the well known expression:

σ 𝐸𝑅=∑𝑙=0

𝑙𝑑

(2 𝑙+1¿𝜎 𝑙𝑓𝑢𝑠 (𝐸 , 𝑙 )𝑊 surv ( E ,𝑙 )

𝜎 𝑙𝑓𝑢𝑠 (𝐸 ,𝑙 )=𝜎 𝑙

𝑐𝑎𝑝𝑡𝑢𝑟𝑒 (𝐸 , 𝑙 ) 𝑃CN (𝐸 , 𝑙 )

𝑃 CN (𝐸 ,𝑙 ) is fusion probability which calculated by the methods of dinuclear system concept N.A. Antonenko et al., Phys. Lett. B 319, 425 (1993);Phys. Rev. C 51, 2635 (1995); G. Adamian, N.V. Antonenko, and W. Scheid, Eur. Phys. J. A 41, 235 (2009); A. K. Nasirov et al. Phys. Rev. C 79, 024606 (2009).

𝜎 𝑙𝑐𝑎𝑝𝑡𝑢𝑟𝑒is capture probability, which calculated in different

theoretical models by different way. A. K. Nasirov et al., Nucl. Phys.A759, 342 (2005).K. Kim et al., Phys.Rev. C 91, 064608 (2015).

33

34

2( ) ( )( ) ( ) ( )R

V R RR R R R t R

R R

1 1 2 2( ) ( ) ( ) eff eff

dLR R t R t R R

dt

0 1 1 2 2 ,RL J J J 2 2 2

1 1 2 2

2 2 2R

rot

J J JE

Equations of motion used to find the capture of projectile by target-nucleus

Nucleus-nucleus interaction potential

35

21 21 2

1/2 2 2 22 2 ( ) 2 ( )1 20 2 2 0 2 23

1 1

( , , )

9 3(cos ) (cos )

20 7

C

i ii i i i

i i

Z ZV R e

R

Z Ze R P R P

R

(0) (0) (0) (0) 31 2 1 1 2 2( , , ) ( ) ( )nucl effV R r R f r d r

1( )2 20(0) ( )

2

( ) (1 ( )( , , , , ) 1 exp .

ii oi i ii

i i i i

r R t R Yr R

a

22

1 21 2

( 1)

2 [ ( ]rot

l lV

R J J

36

Hamiltonian for calculation of the transport coefficients of collective motion

1 1 2 2

coll 1 1 2 2 1 2 1 2

micr i i i i

2

coll 1 1 2 2 1 2 1 2

micr

Н H ( ,A , , , , , , , )

Н , , , V (1)

where

PH U ( ,A , , , , , , , ) - for the relative motion of nuclei; (2)

2

ˆ ˆ ˆНP i i T iP P T

P T

i ii i

Z Z A R

n n

Z Z A R

a a a

, ,

( ) ( )

, ,

ˆ ; (3)

ˆ ˆ ˆ ˆ ˆ ˆ ˆ ˆV ( )( ) ( )( )

ˆ ˆ ˆ ˆ( ) ( ) nucleon exchange between nuclei and

particle ho

iT

P T i j j i P T i j j iP T T P P T T PP T P T

i j i j i j i jP P p p T T T TP P P P

i j i ji j i j

T P

i j i j

a for nucleons of nuclei

g R a a a a R a a a a

R a a R a a

( )

le excitations in nuclei; (4)

, and matrix elements of nucleon exchange between nuclei

and particle hole excitations in them caused by meanfield of partner nucleus.P T P T T T

Pi j i j i jg

G.G. Adamian, et al. Phys. Rev. C56 No.2, (1997) p.373-380A.K. Nasirov, Thesis of the Doctor of Science, 2004, Institute of Nuclear Physics, Tashkent

Density dependent effective nucleon-nucleon forces

37

0 1 2 1 2 1 2( ) ' ( ' )efff r C f f g g

The values of the constants of the effective nucleon-nucleon forces from the textbook A.B. Migdal, “Theory of the Finite Fermi-Systems and properties of Atomic Nuclei”, Moscow, Nauka, 1983. The constants of version II were used in our calculations.

( )( ) ( )

(0)ex in ex r

f r f f f

Comparison of the friction coefficients, calculated by different methods

Solid line – G.G. Adamian, et al. PRC 56 (1997) 373

Long dashed --

Short dashed- -

Dotted -

Temperatura= 2 MeV

Temperatura= 1 MeV

Temperatura= 0.5 MeV

By Yamaji et al(microscopic):

S. Yamaji and A. Iwamoto,

Z. Phys. A 313, (1983) 161.

)),()(()),()(()),()((

)),()((),(

where

),(),(),(

******

***)(

*)(**max

ZBZEZBZEZBZE

ZBZEEP

EPEYEP

symDNSqfDNSfusDNS

fusDNSDNS

ZCN

Z

ZDNS

ZCNDNSZDNSCN

sym

Calculation of the competition between complete fusion and quasifission: Pcn(EDNS,L)

40 Nasirov A.K. et al. Nuclear Physics A 759 (2005) 342–369

Fazio G. et al, Modern Phys. Lett. A 20 (2005) p.391

2Z 3,..., 2,Zfor

),,()(

),,(),,(),,(

tot

*)()(

*1

)(1

*1

)(1

*

tEY

tEYtEYtEYt

ZZqfZZZ

ZZZZZZZZ

Nucleon transfer coefficients for evolution of the charge asymmetry of dinuclear system

41

ttW

tWtntngt

TzPz

tt

TP

TzPzTPPTPT

TPTPZ

TzPzTzPz

Zz

ZzZZZZ

Zz

Zz

)-(cose 2.-e+1()(

)-()())(1)((

1

)2(-)2(-

2)()(

2

,

)(

ii / G.G. Adamian, et al. Phys. Rev. C53, (1996) p.871-879

R.V. Jolos et al., Eur. Phys. J. A 8, 115–124 (2000)

A new problem in separation of fusion-fission and the quasifission products in heavy ion collisions when there is overlap their mass and angular distributions.

The partial quasifission excitation function calculated at different values of the collision energy Ec.m. for the 32S + 184W reaction.

Comparison of the partial fusion cross sections of the 40Ar+180Hf and 82Se+138Ba reactions leading to the same compound nucleus 220Th

K. Kim et al. Phys.Rev.C 91, 064608 (2015)

(a)(b)

(d)(c)

Fusion hindrance increases by increasing the orbital angular momentum.

• F

44

Dependence of the driving potential and quasifission barrier on the angular momentum of dinuclear system formed in reactions leading to formation of compound nucleus 216Th. PHYSICAL REVIEW C 72, 064614 (2005)

Udr = B1 + B2 - (BCN + VCN (L ))

+ V (A, Z, ß1 , α1 ; ß2 , α2 ; R,L)

212

21

2

]([2

)1()()(

JJR

llRVRVV NCoul

45

Calculation of the life time of dinuclear system

46

Collective enhancement of level density of DNS

Description of the observed angular anisotropy of the fissionlike products.

Estimation of the quasifission contribution in the observed angular anisotropy of the fissionlike products.

A.K. Nasirov, et al. Eur. Phys. J. A 34, 325–339 (2007)

B. John, S.K. Kataria,Phys.Rev.C 57, 1337 (1998)

B.B. Back et al, Phys. Rev.Lett. 50, 818 (1983)

Statistical calculation of the anisotropy of the angular distribution

𝐴≈1+⟨ 𝑙2 ⟩𝑖ℏ2

4 ⟨𝜏𝑒𝑓𝑓 𝑇 ⟩

A.K. Nasirov, et al. Eur. Phys. J. A 34, 325–339 (2007)

50

Partial fusion cross section as a function of the orientation of axial symmetry axis reactants

Nasirov A.K. et al.

The role of orientation of nuclei

symmetry axis in fusion dynamics,

Nucl. Phys. A 759 (2005) 342

52

Dependence of the driving potential (а) and quasifission barrier (b) on the mutual orientations of the axial symmetry axes of nuclei

A.K. Nasirov, et al.Nucl. Phys. A 759 (2005) 342

Conclusions1. One of version of the dinuclear system model is being developed to study entrance

channel dynamics of heavy ion collisions at the near Coulomb barrier energies. 2. Dynamics of the macroscopic and microscopic degrees of freedom can be calculated by

analysis of the coupling term connecting them. As a result we find transport coefficients for the relative motion.

3. Method developed by us allows to calculate partial and total cross sections of the capture and fusion of colliding nuclei, as well as decay of the formed dinuclear system

(quasifisson).

4. The angular momentum distribution of the compound nucleus is used by the advanced statistical code to calculate the evaporation residue cross sections, particularly, the cross sections synthesis of superheavy nuclei.

5. The anisotropy in the angular distribution of the fusion-fission and quasifission fragments can be is studied by analyzing the angular-momentum distributions of the dinuclear system and compound nucleus which are formed after capture and complete fusion, respectively.