Incomplete fusion studies near Coulomb barrier Pragya Das Indian Institute of Technology Bombay Powai, Mumbai , 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)Introduction 2)Experiment: Measurement of cross-section 3) 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/Nucleon Fails 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 work Cross-section Measurement (Off-line) Experiment (irradiation): Pelletron Accelerator Facility at Tata Institute of Fundamental Research, Mumbai, INDIA Irradiation on 122 Sn, 124 Sn target foils Self-supporting target  2 mg/cm 2 10 B, 11 B beams of energy = 5-7 MeV/Nucleon Off-line singles data collection: Coaxial HPGe detector Absolute efficiency determination: Radioactive source 152 Eu Determination of cross-section: Intensity of  -ray

Data Analysis Nuclei studied:  1/2 > 3 min 128 I (25 m), 126 I (12.9 d), 128 Cs (3.6 m), 123 I (13.2 hr), 124 I (4.2 d), 127 Cs (6.3 h), 122 Sb (2.7 d), 129 Cs (32.1 h), 130 Cs (29.2 m), 126 Sb (19.2 m) Single decay: - decay constant, I - intensity of gamma transition per unit time, N T – number of target nuclei per unit volume, a  - branching intensity,   - absolute efficiency, I b - beam intensity, T – irradiation time, t 1 – start time of data acquisition, t 2 – start time of data acquisition ( 29.21m ) Cs 130 Xe EC (98.4%) 1 +

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

Reaction: 11 B Sn

Sum Rule Model K. 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 projectile like fragment (PLF) Examples of PLF: 4 He, 7 Li, 8 Be.... Complete capture of the projectile (CF) No emission of PLF Probability for the i th reaction channel (partially equilibrated system) ; : Ground state Q- value

Initial Dinuclear systemFinal Dinuclear system Z2iZ2i Z1iZ1i Z2fZ2f Z1fZ1f Captured fragment PLF (Projectile Like Fragment) projectile E beam 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) C 1, C 2 → 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 q c = 0.06 fm -1  ℓ = 2 ħ T = 3 MeV q c = 0.08 fm -1 ℓ max → prescription as given in D. Glass et al., Nucl. Phys. A 237, 429 (1975) ℓ max = 10% increment in the value in OSRM b = 0.3 (C 1 +C 2 ) K = 60 MeV OSRM MSRM

Probability distribution of 11 B Sn reaction T = 3 MeV q c = 0.08 fm -1  ℓ = 1 ħ (2ℓ+1) ℓ E lab (ℓ max ) (MeV) 7 Li 9 Be

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

 Cross-section measurement for the reactions 10, 11 B + 122, 124 Sn 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 ℓ crit  increased the value of ℓ max 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 11 B Sn reaction

Cross-sections of 10 B Sn reaction

Probability distribution of 11 B Sn reaction T = 3 MeV q c = 0.08 fm -1  ℓ = 1 ħ (2ℓ+1) ℓ

Probability distribution of 10 B Sn reaction T = 3 MeV q c = 0.08 fm -1  l = 1 ħ (2ℓ+1) ℓ

Cross-sections of 11 B Sn reaction

Cross-sections of 10 B Sn reaction