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Incomplete fusion studies near Coulomb barrier

Incomplete fusion studies near Coulomb barrier. Pragya Das Indian Institute of Technology Bombay Powai , Mumbai 400076, India. Collaborators:. Bhushan Bhujang ( Ph. D. student, IIT Bombay, India ) , R. P. Singh ( Inter University Accelerator Center, New Delhi, India )

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Incomplete fusion studies near Coulomb barrier

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  1. Incomplete fusion studies near Coulomb barrier Pragya Das Indian Institute of Technology Bombay Powai, Mumbai 400076, India

  2. Collaborators: BhushanBhujang(Ph. D. student, IIT Bombay, India), R. P. Singh (Inter University Accelerator Center, New Delhi, India) R. Tripathi(Bhabha Atomic Research Center, Mumbai, India), B. S. Tomar(Bhabha Atomic Research Center, Mumbai, India).

  3. Plan of the talk 1) Introduction 2) Experiment: Measurement of cross-section 3) Theoretical analysis Sum rule Model (Modification needed) 4) Summary

  4. Introduction Importance of Incomplete fusion reaction (ICF): • Reaction Mechanism (theoretical): Sum rule model  Works well at the beam energy  10 MeV/Nucleon Fails in the beam energy range of 5-7 MeV/Nucleon! • Scope to produce high angular momentum states (experimental) Nuclei close to -stability line

  5. Our workCross-section Measurement (Off-line) Experiment (irradiation): Pelletron Accelerator Facility at Tata Institute of Fundamental Research, Mumbai, INDIA • Irradiation on 122Sn, 124Sn target foils Self-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

  6. 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 130Cs 0.0 (29.21m) EC (98.4%) 2+ 536.1 536.1 0.0 0+ 130Xe 1+

  7. Double decay Peak area (-ray) = P11 + P22 From the straight line fit 1 = (213  3) mbfor 128Cs 2 = (9.4  0.8) mbfor 128I Straight line plot of Area/P2 Vs P1/P2 128I 128 Cs [ Data points for different t1 , t2 ] 1+ 1+ β– EC 24.99 m 3.46 m 2+ 12.62% 442.9 26.8% 0+ 128Xe

  8. Reaction: 11B + 122Sn

  9. Sum Rule ModelK. Siwek-Wilczyńska et al. Phys. Rev. Lett. 42, 1599 (1979)J. Wilczyńskiet 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 projectile like 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

  10.  Coulomb interaction energy due to transfer of charge Ebeam projectile Target Cont… Z1f Z1i PLF (Projectile Like Fragment) Z2i Z2f Captured fragment Initial Dinuclear system Final Dinuclear system

  11. Cont… Limiting angular momentum Critical angular momentum Original sum rule model (OSRM) C1 , C2 → half - density radii  → surface tension coefficient Modified sum rule model (MSRM) b → Impact parameter K → centre of mass energy Centrifugal term Transmission coefficient

  12. Normalization of probability Cont… All the reaction - channels including CF Reaction cross-section Summation runs over the range of partial waves that confines CF and ICF

  13. Choice of Parameters OSRM T = 3 MeV qc = 0.08 fm-1 T = 3 MeV qc = 0.06 fm-1 ℓ = 2 ħ MSRM ℓmax = 10% increment in the value in OSRM b = 0.3 (C1+C2) K = 60 MeV ℓmax→ prescription as given in D. Glass et al., Nucl. Phys. A 237, 429 (1975) ℓ = 1 ħ

  14. Probability distribution of 11B + 122Sn reaction Elab (ℓmax) (MeV) T = 3 MeV qc = 0.08 fm-1 ℓ = 1 ħ (2ℓ+1) 7Li 9Be ℓ

  15. Experiment vs. SRM for 11B + 122Sn (CFexp) =  (129Cs) +  (128Cs) +  (127Cs) (exp) =  (128I) +  (126I) +  (124I) +  (123I)

  16. Summary • Cross-section measurement for the reactions 10, 11B + 122, 124Sn at the beam energy 5-7 MeV/nucleon • Theoretical analysis: Based on Sum rule model Original 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 ℓmaxby 10 % (preliminary theoretical analysis)  In future, check validity of Modified Sum rule model for other reactions as well.

  17. Thank you !

  18. Backup slides

  19. Cross-sections of 11B + 124Sn reaction

  20. Cross-sections of 10B + 124Sn reaction

  21. Probability distribution of 11B + 124Sn reaction T = 3 MeV qc = 0.08 fm-1 ℓ = 1 ħ (2ℓ+1) ℓ

  22. Probability distribution of 10B + 124Sn reaction T = 3 MeV qc = 0.08 fm-1 l = 1 ħ (2ℓ+1) ℓ

  23. Cross-sections of 11B + 124Sn reaction

  24. Cross-sections of 10B + 124Sn reaction

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