dynamics of incomplete fusion in reactions induced by heavy ions

Dynamics of incomplete fusion in reactions induced by heavy

ions

Manoj Kumar Sharma

Department of PhysicsAligarh Muslim University

Aligarh

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1. Introduction

2. Scientific Motivation

3. Experimental details

4. Analysis of the data

5. Conclusions

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a + X Y + b

A nuclear reaction takes place, when an incident ion of sufficient energy (above the Coulomb barrier) interacts with a target nucleus.

Where, a-projectile , X-target

Y-residual nucleus, b-emitted particle

Incident ion

Target nucleus

Residual nucleus

Ejectile

+

Introduction

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Grazing collisionIncomplete fusion and deep inelastic collision

Elastic scattering Direct reactions

Peripheral collisionComplete

fusion

Distant collision

b

b Impact parameter

A pictorial representation of heavy ion reactions

Rutherford Scattering

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In heavy ion reactions, at moderate excitation energies, the dominant processes are;

•Complete Fusion (CF)

•Incomplete Fusion (ICF)

•Pre-equilibrium (PE) emission

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Complete Fusion (CF)Projectile is completely fused with the target nucleus, leading to the formation of an excited composite system that may decay by the emission of n, p, etc., after attaining statistical equilibrium.

65Tb159 73Ta175

8O16

+

Ta174

Hf174

Lu171

n

p

Target Composite system

Projectile

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Incomplete Fusion (ICF)Only a part of the projectile fuses with the target nucleus and the rest of it is going into the beam direction with almost the same velocity as that of incident ion beam.

65Tb159 71Lu171

+

Lu170

Yb170

Er167

n

p

Target Composite system

Residues

Projectile

6C12

16O=12C+

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Some of the important features of ICF……

Higher measured cross-sections than predicted by statistical models,

M. K. Sharma et. at., Phys. Rev. C70 (2004) 044606

65 70 75 80 85 90 95 1000.01

0.1

1

10

100

1000

10000

EXPERIMENTALALICE-91

169Tm(16O,)181Re

(m

b)

Energy (MeV)

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Fractional momentum transfer, in which the residue formed as a result of ICF of projectile travels to a lower range in a given medium.

Incomplete Momentum Transfer

0 100 200 300 400 500 6000

500

1000

1500

2000

2500

EXPERIMENTAL

GAUSSIAN FIT FOR ICF OF 8Be

GAUSSIAN FIT FOR ICF OF 12C GAUSSIAN FIT FOR CF

Yie

ld (

mb

/mg

cm

-2) 169Tm(16O,2pn)175Hf

Cumulative thickness (g/cm2)

M. K. Sharma et. at., Phys. Rev. C70, (2004) 044606

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ICF reactions have attracted attention……..

The threshold for ICF is not well established.

Early studies show occurrence of ICF at higher energies above 10 MeV/nucleon

Recent experimental studies have shown that ICF starts competing with CF even at energies around 5-7 MeV/nucleon i.e, just above the Coulomb barrier.

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Why?.........

Relative contributions of CF and ICF are not well known.

The dynamics of ICF is not well understood at energies around 5-7 MeV/A.

Energy dependence of CF and ICF contributions is not well understood.

No satisfactory theory for ICF is available.

Limited studies are available at <10 MeV/A. HQP_2008_Dubna

In order to answer some of these, measurements of……..

• Excitation functions covering a large range of

energy,

• Recoil range distributions at several energies,

• Angular distributions of the residues,

• Spin distribution of the residues

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12C+27Al39K, Coulomb barrier 24 MeV Beam energy (42 to 82 MeV) 16O+27Al 43Sc, Coulomb barrier 27 MeV Beam energy (55 to 95 MeV) 14N+128Te 142Pr, Coulomb barrier 58 MeV Beam energy (64 to 90 MeV) 16O+130Te 146Nd,Coulomb barrier 53 MeV Beam energy (42 to 82 MeV) 16O+103Rh 119I, Coulomb barrier 48 MeV Beam energy (48 to 90 MeV) 16O+159Tb 175Ta , Coulomb barrier 66 MeV Beam energy (70 to 95 MeV) 16O+169Tm 185Ir, Coulomb barrier 68 MeV Beam energy (70 to 95 MeV)

In the present work, Excitation functions (EFs) for the following systems have been studied;

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27Al(12C,n)34Cl, 27Al(12C,23p)28Mg, 27Al(12C,32pn)24Na, 27Al(16O,2n)34Cl, 27Al(16O,33p)28Mg, 27Al(16O,33pn)27Mg,

27Al(16O,42pn)24Na, 27Al(16O,43p)24Ne, 128Te(16O,4n)138Pr, 128Te(16O,5n)137Pr, 128Te(16O,p4n)137Ce, 128Te(16O, 5n)133La, 128Te(16O, 6n)132La, 128Te(16O, 2pn)135La, 128Te(16O, 22pn)131I, 128Te(16O, 3)130I, 103Rh(16O,pn)117Te, 103Rh(16O,p2n)116Te,

103Rh(16O,p3n)115Te, 103Rh(16O,p4n)114Te, 103Rh(16O,2n)117Sb,

103Rh(16O,2pn)116Sb, 103Rh(16O,2p2n)115Sb, 103Rh(16O,p4n)110Sn, 103Rh(16O,2)111In, 103Rh(16O,2n)110In, 103Rh(16O,22n)109In, 103Rh(16O,23n)108In, 103Rh(16O,3n)106Ag, 103Rh(16O,33n)104Ag, 103Rh(16O,34n)103Ag, 159Tb(16O,3n)172Ta, 159Tb(16O,4n)171Ta, 159Tb(16O,5n)170Ta, 159Tb(16O,p3n)171Lu, 159Tb(16O,p4n)170Lu, 159Tb(16O,)172Hf, 159Tb(16O,n)170Hf, 159Tb(16O,2n)169Hf, 159Tb(16O,3n)168Hf, 159Tb(16O,4n)167Hf, 159Tb(16O,p3n)167Lu, 159Tb(16O,2n)166Tm, 159Tb(16O,22n)165Tm, 169Tm(16O,3n)182Ir, 169Tm(16O,4n)181Ir, 169Tm(16O,p2n)182Os, 169Tm(16O,p3n)181Os, 169Tm(16O,)181Re, 169Tm(16O,2n)179Re, 169Tm(16O,3n)178Re, 169Tm(16O,4n)177Re, 169Tm(16O,p3n)177W, 169Tm(16O,2pn)178Ta, 169Tm(16O,3pn)177Hf 169Tm(16O,2p3n)172Hf ,169Tm(16O,3n)172Lu

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The experiments have been carried out using the Pelletron accelerator facility of the Inter University Accelerator Facilities (IUAC) (Formerly known as NSC), New Delhi, INDIA.

Samples preparation:

27Al (Rolling Method)

103Rh (Rolling Method)

128,130Te (Vacuum evaporation)

159Tb (Rolling Method)

169Tm (Vacuum evaporation)

Methodology adopted

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Thickness measurements

The thickness of each target was determined by the -transmission method.

27Al 2.00 mg/cm2

103Rh 1.80 mg/cm2

128Te (66%) 0.90 mg/cm2

130Te (68%) 1.00 mg/cm2

159Tb 1.80 mg/cm2

169Tm 0.50 mg/cm2

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Incident beam

Al-Catcher foil/Energy degreder

Target

A typical stack arrangement for the measurement of EFs

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Irradiation

The irradiations were carried out in the General Purpose Scattering Chamber (GPSC) having in-vacuum transfer facility.

A typical experimental set up for the measurement of EFs

Incident beam

Target

Catcher

Fara

day c

up

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General Purpose Scattering Chamber

ITF

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Inside view of GPSC

Lower armUpper arm

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The delay time between stop the irradiation and beginning of the counting may be minimized.

Target may be replaced without disturbing the vacuum inside the chamber.

Invacuum Transfer Facility

Pirani gauge

Valve-I

Valve-II

Port for rotary pump

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Post Irradiation Analysis

The samples were taken out from the scattering chamber and activities induced in the samples were analyzed using HPGe detector.

The detector was pre-calibrated using various standard sources i.e., 22Na, 60Co, 133Ba, 137Cs, 152 Eu etc.,

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A typical geometry dependent efficiency curves for various source detector distances as a function of -ray energy is shown.

0 200 400 600 800 1000 1200 1400 16000.000

0.005

0.010

0.015

0.020

0.025

0.030

0.035

0.040

0 200 400 600 800 1000 1200 1400 16000.000

0.005

0.010

0.015

0.020

0.025

0.030

0.035

0 200 400 600 800 1000 1200 1400 16000.000

0.005

0.010

0.015

0.020

0.025

0.030

0 200 400 600 800 1000 1200 1400 16000.000

0.005

0.010

0.015

0.020

0.025

Eff

icie

ncy

Energy (keV)

(a)2 cm

(c)

(b)3 cm

Eff

icie

ncy

Energy (keV)

4 cm

Eff

icie

ncy

Energy (keV)

(d)5 cm

Eff

icie

ncy

Energy (keV)

M. K. Sharma et. al., Nucl. Phys. A 776, 2006 (84)

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The observed -rays spectrum for 16O+27Al and 16O+159Tb systems

M. K. Sharma et al., Phys. Rev. C70 (2004)044604

5800 5850 5900 5950 6000 6050 6100 6150 6200101

102

103

1700 1750 1800 1850 1900 1950 2000 2050 2100

102

103

600 650 700 750 800 850 900 950 1000102

103

104

105

Channel No

c

1308 keV

24Na

b

Co

un

ts

400 keV

28Mg

a

146.2 keV

34mCl

M. K. Sharma et. al., Phys. Rev. C75 (2007)044608

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M. K. Sharma et al., Nucl. Phys. A776 (2006)84

The observed -rays spectrum for 16O+159Tb system at 95 MeV

0 500 1000 1500 2000 2500 3000 3500 4000 4500 5000100

1000

10000

100000

Cou

nts

Channel No.

1072

keV

(16

O,p

4n)

620

keV

(16

O,4

n)

16O+159Tb at 95 MeV

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The intensity of these -rays are used to measure the reaction cross-section using following formulation.

where, A is the total observed counts during the accumulation time t3 of the induced activity of decay constant ,No the number of target nuclei irradiated for time t1 with a particle beam of flux , t2 the time lapse between the stop of irradiation and the start of counting, the branching ratio of the characteristic -ray and Gthe geometry dependent efficiency of the detector. The factor [1-exp (t1)] takes care of the decay of evaporation residue during the irradiation and is typically known as the saturation correction.

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Analysis of the excitation functions has been done using three different computer codes,

CASCADE PACE2 ALICE-91Compound nucleus

Compound nucleus

Compound nucleus as well as PE emission

Hauser-Feshbach Theory

Monte Carlo Simulations

Weisskopf-Ewing model for CN calculations,

Hybrid model for PE-emission.

None of these codes take in account ICF contribution

Analysis

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M. K. Sharma et al., Phys. Rev. C70 (2004) 044606

Experimentally measured and theoretically calculated EFs HQP_2008_Dubna

The residues 171Hf which may be formed via the reaction 159Tb(16O,p3n) and may also be formed by the + decay of higher charge isobar precursor 171Ta produced via the reaction 159Tb(16O,4n). As such, the measured activity of residues 171Hf has contribution from precursor decay also.

+16O 159Tb 175Ta

171Ta

171Hf

+4n

p3n

70 75 80 85 90 95 100 1051

10

100

1000

Fig. 2

CUMULATIVE YIELD INDEPENDENT YIELD CASCADE PACE2ALICE-91

159Tb(16O,p3n)171Hf

(m

b)

Energy (MeV)

M. K. Sharma et. al., Nucl. Phys. A 776 (2006) 86

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Experimentally measured and theoretically calculated EFs

M. K. Sharma et. al., Nucl. Phys. A 776 (2006)83

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65 70 75 80 85 90 95 100 1050.1

1

10

100159Tb(16O, 3n)172Ta

EXPERIMENTAL CASCADE PACE2 ALICE-91

(m

b)

Energy (MeV)

At higher energies, the calculation of EFs done with code ALICE-91 gives significant contribution from PE-emission also.


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M. K. Sharma et. al., Nucl. Phys. A 776 (2006)83

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Experimentally measured EFs

M. K. Sharma et. al.,

Nucl. Phys. A 776 (2006)83 Phys. Rev C 77 (2008)014607

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From the analysis of the excitation functions, enhancement of the cross-sections in comparison to theoretical calculations done using statistical model codes, may be attributed to ICF processes.

Following reactions have been found to have significant contribution from ICF27Al(16O,2n)34Cl, 27Al(16O,33p)28Mg, 27Al(16O,33pn)27Mg, 27Al(16O,42pn)24Na, 27Al(16O,43p)24Ne, 128Te(16O, 5n)133La, 128Te(16O, 6n)132La, 128Te(16O, 2pn)135La, 128Te(16O, 22pn)131I, 128Te(16O, 3)130I, 103Rh(16O,2p2n)115Sb,

103Rh(16O,p4n)110Sn, 103Rh(16O,2)111In, 103Rh(16O,2n)110In, 103Rh(16O,22n)109In, 103Rh(16O,23n)108In, 103Rh(16O,3n)106Ag, 103Rh(16O,33n)104Ag, 103Rh(16O,34n)103Ag, 159Tb(16O,)172Hf, 159Tb(16O,n)170Hf, 159Tb(16O,2n)169Hf, 159Tb(16O,3n)168Hf, 159Tb(16O,4n)167Hf,

159Tb(16O,p3n)167Lu, 159Tb(16O,2n)166Tm, 159Tb(16O,22n)165Tm, 169Tm(16O,)181Re, 169Tm(16O,2n)179Re, 169Tm(16O,3n)178Re, 169Tm(16O,4n)177Re, 169Tm(16O,p3n)177W, 169Tm(16O,2pn)178Ta, 169Tm(16O,3pn)177Hf 169Tm(16O,2p3n)172Hf ,169Tm(16O,3n)172Lu

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FICF increases with increase in beam energy

The Contribution of ICF has been deduced by subtracting the cross-section of CF from total cross-sections.

Phys. Rev C 77 (2008)014607

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Mass asymmetry dependence of ICF fraction

• ICF is observed in competition with CF in energy range presently studied.

• In present systems ICF is found to increase with beam energy.

• SCF is found to be large in more mass asymmetric systems as compared to mass symmetric system.

•It may however, be pointed out that the results shown here may not be conclusive and more experimental data for a large number of systems may be required to get detailed information about the suppression of CF over ICF.

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Recoil Range Distributions• The measurement of RRD is based on the linear

momentum transfer of the projectile to the target nucleus.

• In CF reactions, the linear momentum is completely transferred to the target nucleus, thus the residues formed by CF may be trapped at a larger distance in the stopping medium.

• While in case of ICF reactions, partial transfer of projectile momentum takes place thus the residues may be trapped at a shorter distance in the stopping medium . HQP_2008_Dubna

Thin Al -catcher foils

Experimental Set-up for Recoil Range Distribution measurements

Target foil

Incident Beam

Recoiling Nucleus

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In the present work, following systems have been used to measure RRD of the residues.

16O + 159Tb 175Ta ( 92 MeV )

16O + 169Tm 185Ir ( 76, 81 & 87 MeV )

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100 200 300 400 500 6000

200

400

600

800

1000

1200

Yie

ld (/

mg

/cm

2 )

Cummulative thickness (g/cm2)

Experimental

159Tb(16O,4n)171Ta

0 100 200 300 400 500 600 7000

50

100

150

200

250

300

Yie

ld (/

mg

/cm

2 )


Experimental

159Tb(16O,p3n)171Hf

0 100 200 300 400 500 600 7000

500

1000

1500

2000

2500

3000

Yie

ld (/

mg

/cm

2 )


Experimental

159Tb(16O,2p2n)171Lu

0 100 200 300 400 500 600 7000

1000

2000

3000

4000

Yie

ld (/

mg

/cm

2 )


Experimental

159Tb(16O,p4n)170Hf


Experimental measured Recoil Range Distribution for 16O+159Tb @ 92 MeV HQP_2008_Dubna

0 100 200 300 400 500 6000

20

40

60

80

Yie

ld (/

mg

/cm

2 )


159Tb(

16O,2n)

170Lu

0 100 200 300 400 500 600 700

0

20

40

60

80

100

120

140

Yie

ld (/

mg

/cm

2 )


159Tb(

16O,n)

168Tm

0 100 200 300 400 500 600-10

0

10

20

30

40

Yie

ld (/

mg/

cm2 )


159Tb(

16O,2n)

165Tm

0 100 200 300 400 500 600 700

500

1000

1500

2000

2500

3000Y

ield

(/

mg

/cm

2 )


159Tb(

16O,n)

170Lu


Experimental measured Recoil Range Distribution HQP_2008_Dubna

Experimental measured Recoil Range Distribution for 16O+169Tm @ 95 MeV HQP_2008_Dubna

0 100 200 300 400 500 6000

1000

2000

3000

4000

5000

6000

7000

8000


Y

ield

(m

b/m

g c

m-2)

169Tm(16O,2p2n)181Re

EXPERIMENTAL GAUSSIAN FIT FOR ICF GAUSSIAN FIT FOR CF

The experimentally measured RRD has been fitted with Gaussian peaks.

The areas under the two peaks have been computed.

The relative contributions of the CF and ICF processes are obtained by dividing the area of the individual peak by the total area.

16O+169Tm185Ir* 181Re+2p2n(CF 355%)

12C +169Tm181Re* + + (ICF 655%)

M. K. Sharma et. al., Phys. Rev. C 70 (2004) 044606

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0 100 200 300 400 500 6000

500

1000

1500

2000

2500

Gaussian fit to the recoil range distribution

EXPERIMENTAL


GAUSSIAN FIT FOR ICF OF 12C GAUSSIAN FIT FOR CF

Y

ield

(m

b/m

g c

m-2)

169Tm(16O,2pn)175Hf


16O+169Tm185Ir* 176Hf+2pn CF 255%

12C +169Tm181Re* 176Hf + pn ICF of 12C 455%

8Be +169Tm178Ta* 176Hf + pn ICF of 8 Be 305%

Manoj Kumar Sharma et. al., Phys. Rev. C70 (2004)044606

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0 50 100 150 200 2500

100

200

300

400

500

600

EXPERIMENTAL GAUSSIAN FIT FOR ICF OF particle


Yi

eld

(mb/

mg

cm-2

)

169Tm(

16O,3n)

172Lu



ICF of 8 Be 745%

ICF of 265%


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0 50 100 150 200 250 3000

100

200

300

400

500

600

700

800


Y

ield

(m

b/m

g c

m-2)

169Tm(16O,32n)171Lu

EXPERIMENTAL GAUSSIAN FIT FOR ICF OF PARTICLE



ICF of 8 Be 285%

ICF of 72 5%


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0 100 200 300 400 500 600 7000

500

1000

1500

2000

2500

3000

Yie

ld (/

mg/

cm2 )


159Tb(16O,n)170Lu

0 50 100 150 200 250 300 350 400

0

20

40

60

80

100

120

140

160

180

200

Yie

ld (

/m

g/cm

2 )


159Tb(16O,n)162HO

0 100 200 300 400 500 600 700

0

50

100

150

Yiel

d (

/m

g/cm

2 )


159Tb(16O,n)166Tm

0 100 200 300 400 500 600 700

0

20

40

60

80

Yie

ld (/

mg

/cm

2 )


159Tb(16O,2n)169Lu


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The experimentally measured RRD has been fitted with Gaussian peaks.The areas under the two peaks have been computed. The relative contributions of the CF and ICF processes are obtained by dividing the area of the individual peak by the total area.

30 % CF70 % ICF


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The experimentally measured RRD

45 % CF

27% ICF

28% ICF


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The experimentally measured RRD

15 % ICF49 % ICF36 % ICF


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Angular Angular distribution of distribution of

residuesresidues

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Stack of annular Al-catchers with concentric holes

Experimental set up for the measurement of Angular distribution of residues

169Tm Target(Thickness 47.24g/cm2)

16O7+

6.5cm

Aluminium backing (thickness

1.1mg/cm2 ) 1.8 cm

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The observed -rays spectrum for 16O+27Al system at 85 MeV for angular distribution of residues

M. K. Sharma et. al., Phys. Rev. C 75 (2007)044608

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Measured angular distribution for reactions 27Al(16O,2n)34Cl

M. K. Sharma et. al., Phys. Rev. C 75 (2007)044608

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0 1000 2000 3000 4000 5000 6000 700010-3

10-2

10-1

100

101

10-3

10-2

10-1

100

101

10-3

10-2

10-1

100

101

102

E=

51

1 k

eV

E=

36

5.6

ke

V

E=

36

0.7

ke

V 210-300

Channel number

E=

36

5.6

ke

V

E=

51

1 k

eV

E=

36

0.7

ke

V

130-210

Co

un

ts p

er

sec

E=

89

1.1

ke

V

E=

76

4.2

ke

V

E=

18

0.2

ke

V

E=

23

8.7

ke

V

E=

27

3.1

ke

V

E=

12

6.9

ke

V

E=511 keV 00-130

The observed -rays spectrum for 16O+169Tm system at 81 MeV for angular distribution of residues

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Angular distribution of residue 181Re at 81 MeV

HQP_2008_Dubna

Angular distribution of several residues in 16O+169Tm at 81 MeV

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• The enhancement of experimentally measured cross-sections for alpha emission channels over their theoretical predictions have been attributed to the fact that these residues are not only formed by the complete fusion but also through incomplete fusion.

• The analysis of RRD and ADs have clearly indicated the significant contribution of ICF.

• Relative contributions of CF and ICF processes have been separated out.

• Attempt has been made to separate out energy dependence of CF and ICF.

Conclusions

HQP_2008_Dubna

List of Publications in International Journals during 2004-07

1. Influence of incomplete fusion on incomplete fusion; observation of a large incomplete fusion fraction at E 5-7 MeV/nucleon: Pushpendra P. Singh, B. P. Singh, Manoj Kumar Sharma, Unnati, Devendra P. Singh, Rakesh Kumar, K.S. Golda, and R. Prasad, Phys. Rev. C. 77 (2008) 014607

2. Production of fission-like events after complete and in-complete fusion of 16O projectile with 159Tb and 169Tm at E/A~6 MeV: Pushpendra P. Singh, B. P. Singh, Bhavna Sharma, Unnati, Manoj Kumar Sharma, H. D. Bhardwaj, Rakesh Kumar, K. S. Golda and R. Prasad. International Journal of Modern Physics E Vol 17, No. 1 (2000) 1-18

3. Reaction mechanism in the 16O+27Al system: Measurement and analysis of excitation functions and angular distribution: Manoj Kumar Sharma, Unnati, Devendra P. Singh, Pushpendra P. Singh, H. D. Bhardwaj, and R. Prasad: Phys. Rev. C. 75 (2007) 064608

4. A study of pre-equilibrium emission of neutrons in 93Nb(,xn) reaction: Manoj Kumar Sharma, H.D. Bhardwaj, Unnati, Pushpendra P. Singh, B.P. Singh and R. Prasad: European Journal of Physics A 31 (2007) 43.

5. Observation of complete and incomplete-fusion components in 159Tb, 169Tm(16O,x) reactions: Measurement and analysis of forward recoil ranges at E/A 5-6 MeV: Pushpendra P. Singh, Manoj Kumar Sharma, Unnati, Devendra P. Singh, Rakesh Kumar, K.S. Golda, B. P. Singh and R. Prasad, Eur. Phys. J. A 34 (2007) 29.

6. A study of the reaction occurring in 16O+159Tb system below7 MeV/nucleon energies: Excitation Functions and Recoil Range Distributions: Manoj Kumar Sharma, Unnati, B.P. Singh, H.D. Bhardwaj, Rakesh Kumar, K. S. Golda and R.Prasad: Nuclear Physics A 776 (2006) 83.

7. A study of pre-equilibrium emission in some proton and alpha induced reactions: B.P. Singh, Manoj Kumar Sharma, M. M. Musthafa, H.D. Bhardwaj and R.Prasad, Nuclear Instrument and Methods A 562 (2006) 717.

HQP_2008_Dubna

8 A study of excitation functions for some residues produced in the system 14N+128Te in energy range 64-90 MeV: Unnati, Manoj Kumar Sharma, B.P. Singh, Sunita Gupta, H.D. Bhardwaj, R.Prasad and A. K. Sinha: International Journal of Modern Physics E 14 (2005) 775.

9 Measurement and analysis of cross-sections for (p,n) reactions in 51V and 113In: M.M. Musthafa, Manoj Kumar Sharma, B.P. Singh, and R.Prasad Applied Radiation and Isotopes, 62 (2005) 1419

10 A study of complete and incomplete fusion in 16O+169Tm system: Excitation Functions and Recoil Range Distributions: Manoj Kumar Sharma, Unnati, B. K. Sharma, B.P. Singh, H. D. Bhardwaj, Rakesh Kumar, K. S. Golda and R.Prasad: Phy. Rev. C. Vo. 70. (2004) 044606

HQP_2008_Dubna

List of Collaborators :-

1. Prof. R. Prasad AMU2. Dr. B. P. Singh AMU3. Ms. Unnati AMU4. Mr. Pushpendra P. Singh AMU5. Mr. Devendra P. Singh AMU6. Dr. H.D. Bhardwaj Unnao7. Dr. R. K. Bhaumik IUAC8. Mr. Rakesh Kumar IUAC9. Ms. K.S. Golda IUAC

HQP_2008_Dubna

HQP_2008_Dubna

dynamics of incomplete fusion in reactions induced by heavy ions

Documents

coulomb barrier

mev beam energy

icf contributions

dynamics of icf

incident ion beam

beam direction

occurrence of icf

result of icf