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Incomplete fusion studies near Coulomb barrier
Pragya DasIndian Institute of Technology Bombay
Powai, Mumbai 400076, India
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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).
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1) Introduction2) Experiment: Measurement of cross-section3) Theoretical analysis Sum rule Model
(Modification needed)4) Summary
Plan of the talk
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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
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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
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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+
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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 ]
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Reaction: 11B + 122Sn
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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
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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
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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
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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…
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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
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Probability distribution of 11B + 122Sn reaction
T = 3 MeVqc = 0.08 fm-1
ℓ = 1 ħ
(2ℓ+1)
ℓ
Elab (ℓmax) (MeV)
7Li9Be
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Experiment vs. SRM for 11B + 122Sn
(CFexp) = (129Cs) + (128Cs) + (127Cs)(exp) = (128I) + (126I) + (124I) + (123I)
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· 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
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Thank you !
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Backup slides
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Cross-sections of 11B + 124Sn reaction
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Cross-sections of 10B + 124Sn reaction
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Probability distribution of 11B + 124Sn reaction
T = 3 MeVqc = 0.08 fm-1
ℓ = 1 ħ
(2ℓ+1)
ℓ
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Probability distribution of 10B + 124Sn reaction
T = 3 MeVqc = 0.08 fm-1
l = 1 ħ
(2ℓ+1)
ℓ
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Cross-sections of 11B + 124Sn reaction
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Cross-sections of 10B + 124Sn reaction