Incomplete fusion studies near Coulomb barrier

Pragya DasIndian Institute of Technology Bombay

Powai, Mumbai 400076, India

Collaborators:1) Bhushan Bhujang (Ph. D. student, IIT Bombay, India),2) R. P. Singh (Inter University Accelerator Center, New Delhi, India)3) R. Tripathi (Bhabha Atomic Research Center, Mumbai, India),

4) B. S. Tomar (Bhabha Atomic Research Center, Mumbai, India).

1) Introduction2) Experiment: Measurement of cross-section3) Theoretical analysis Sum rule Model

(Modification needed)4) Summary

Plan of the talk

Introduction

Importance of Incomplete fusion reaction (ICF):

1) Reaction Mechanism (theoretical):Sum rule model Works well at the beam

energy 10 MeV/NucleonFails in the beam energy range of 5-7 MeV/Nucleon!

2) Scope to produce high angular momentum states (experimental)Nuclei close to -stability line

Our workCross-section Measurement (Off-line)

Experiment (irradiation): Pelletron Accelerator Facility at Tata Institute of Fundamental Research,

Mumbai, INDIA

• Irradiation on 122Sn, 124Sn target foilsSelf-supporting target 2 mg/cm2

• 10B, 11B beams of energy = 5-7 MeV/Nucleon

• Off-line singles data collection: Coaxial HPGe detector

• Absolute efficiency determination: Radioactive source 152Eu

• Determination of cross-section: Intensity of -ray

Data Analysis Nuclei studied: 1/2 > 3 min

128I (25 m), 126I (12.9 d), 128Cs (3.6 m), 123I (13.2 hr), 124I (4.2 d), 127Cs (6.3 h), 122Sb (2.7 d), 129Cs (32.1 h), 130Cs (29.2 m), 126Sb (19.2 m)

Single decay:

- decay constant,I - intensity of gamma transition per unit time,

NT – number of target nuclei per unit volume,a - branching intensity, - absolute efficiency,Ib - beam intensity,T – irradiation time,t1 – start time of data acquisition, t2 – start time of data acquisition

2+

0+ 0.0536.1

0.0 (29.21m)

536.1

130Cs

130Xe

EC (98.4%) 1+

Double decayPeak area (-ray) = P11 + P22

From the straight line fit 1 = (213 3) mb for 128Cs

2 = (9.4 0.8) mb for 128I

2+

0+

1+ 1+

β–EC

128I 128 Cs

442.9

128Xe

24.99 m 3.46 m

12.62% 26.8%

Straight line plot of Area/P2 Vs P1/P2 [ Data points for different t1 , t2 ]

Reaction: 11B + 122Sn

Sum Rule ModelK. Siwek-Wilczyńska et al. Phys. Rev. Lett. 42, 1599 (1979)

J. Wilczyński et al., Phys. Rev. Lett. 45, 606 (1980)Same approach for the

Complete fusion (CF) and Incomplete fusion (ICF) reactions

• Concept of generalized angular momentum Successive “ℓ-windows” with overlaps

• Higher average value of ℓ for the higher mass of the emitted projectilelike fragment (PLF)

Examples of PLF: 4He, 7Li, 8Be . . . .• Complete capture of the projectile (CF)

No emission of PLF• Probability for the ith reaction channel (partially equilibrated system)

; : Ground state Q- value

(i)Qgg

Initial Dinuclear system Final Dinuclear system

Z2i

Z1i

Z2f

Z1f

Capturedfragment

PLF(Projectile LikeFragment)

projectile

Ebeam

Target

Cont…

Coulomb interaction energy due to transfer of charge

Limiting angular momentum

Critical angular momentum

Transmission coefficient

Modified sum rule model (MSRM)b → Impact parameter K → centre of mass energy

Original sum rule model (OSRM)C1 , C2 → half - density radii → surface tension coefficient

Cont…

Centrifugal term

Normalization of probability

All the reaction - channels including CF

Reaction cross-section

Summation runs over the range of partial waves that confines CF and ICF

Cont…

Choice of Parameters

ℓ = 1 ħ

T = 3 MeV qc = 0.06 fm-1

ℓ = 2 ħ

T = 3 MeV qc = 0.08 fm-1

ℓmax → prescription as given in D. Glass et al., Nucl. Phys. A 237, 429 (1975)

ℓmax = 10% increment in the value in OSRMb = 0.3 (C1+C2)K = 60 MeV

OSRM MSRM

Probability distribution of 11B + 122Sn reaction

T = 3 MeVqc = 0.08 fm-1

ℓ = 1 ħ

(2ℓ+1)

ℓ

Elab (ℓmax) (MeV)

7Li9Be

Experiment vs. SRM for 11B + 122Sn

(CFexp) = (129Cs) + (128Cs) + (127Cs)(exp) = (128I) + (126I) + (124I) + (123I)

· Cross-section measurement for the reactions10, 11B + 122, 124Sn at the beam energy 5-7 MeV/nucleon

· Theoretical analysis: Based on Sum rule modelOriginal Sum rule model underestimated the cross-section for -channel

Modified Sum rule model Cross-section near to the experimental value

added the centrifugal barrier term in ℓcrit

increased the value of ℓmax by 10 %

(preliminary theoretical analysis)

In future, check validity of Modified Sum rule model for other reactions as well.

Summary

Thank you !

Backup slides

Cross-sections of 11B + 124Sn reaction

Cross-sections of 10B + 124Sn reaction

Probability distribution of 11B + 124Sn reaction

T = 3 MeVqc = 0.08 fm-1

ℓ = 1 ħ

(2ℓ+1)

ℓ

Probability distribution of 10B + 124Sn reaction

T = 3 MeVqc = 0.08 fm-1

l = 1 ħ

(2ℓ+1)

ℓ

Cross-sections of 11B + 124Sn reaction

Cross-sections of 10B + 124Sn reaction