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I NFLUENCE OF P ROJECTILE B REAKUP ON F USION WITH 159 Tb T ARGET

This study investigates the effect of projectile breakup on fusion reactions using stable weakly bound nuclei. The focus is on the reactions involving 6Li, 7Li, and 9Be projectiles, and the 159Tb target. The measurements aim to separate compound nucleus (CF) and incomplete fusion (ICF) events, and also study the effect of deformation on fusion using the well-deformed 159Tb nucleus. Experimental techniques involving characteristic gamma-ray methods are used for precise measurement of fusion cross sections. The results shed light on the reaction mechanisms and the influence of projectile breakup on fusion.

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I NFLUENCE OF P ROJECTILE B REAKUP ON F USION WITH 159 Tb T ARGET

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  1. INFLUENCE OF PROJECTILE BREAKUP ON FUSION WITH 159Tb TARGET MUKESH KUMAR PRADHAN Nuclear Physics Division SAHA INSTITUTEOF NUCLEAR PHYSICS KOLKATA, INDIA

  2. evaporation p n,   fusion n  fission INTRODUCTION Nuclear fusion

  3. Fusion process at energies around the Coulomb barrier To understand reaction mechanisms Study of heavy ion fusion allow to understand the effect of structure of colliding nuclei and transfer reactions (if any)

  4. Reaction involving weakly bound nuclei (e.g.6He,11Be, 11Li, 9Be, 6Li, 7Li) (Breakup threshold energy  0.3 to 2.5 MeV) Breakup process may influence fusion cross sections

  5. Motivation Investigation of effect of breakup of weakly bound nuclei on fusion still far from being well understood special interest --- recent availability of beams of light radioactive (loosely bound) nuclei to understand the structure of halo unstable nuclei  to investigate the effect of their unusual properties (halo/skin, large breakup probability) on the reaction mechanisms • To study reactions of astrophysical interest

  6. Expt. situation  light RIB (produced in secondary reactions)  • low intensity (106 particles/sec) • poor beam energy resolution  Precise measurement of fus is difficult  absence of halo Stable weakly bound nuclei  only the effect of of loose binding (sufficiently low breakup thresholds) Stable beams  intense beams  precise measurement of fus possible (1011-1013 particles/sec) most suitable stable nuclei for these kind of studies :6Li, 7Li , 9Be 6Li 4He + 2H , S =1.47 MeV 7Li 4He + 3H , S= 2.45 MeV 9Be 8Be + n , Sn = 1.67 MeV  n + 4He +4He, S = 1.57 MeV 5He + 4He , S= 2.47 MeV Ref : Phys. Rep. 424 , 1 (2006)

  7. Direct Complete Fusion (DCF) + Sequential CF or CFBU + Incomplete Fusion (ICF) + Non capture breakup (NCBU) + Different processes in reaction involving weakly bound nuclei

  8. Medium & light mass systems Heavy mass systems like 6Li+59Co, 7Li+59Co, 9Be+27Al, 6Li+24Mg, 7Li+24Mg, 6Li+16O, 7Li+12C etc. like 6Li+209Bi, 7Li+209Bi, 9Be+208Pb etc. Chosen to study the mass region A ~ 160-170 ---- Possible to separate CF and ICF events ----- Difficult to separate CF and ICF events No effect of breakup on total fusion (TF) at energies around the Coulomb barrier Suppression of CF at above barrier energies Ref : Phys. Rep. 424 , 1 (2006)

  9. 6Li d  7Li t 2 9Be n 6Li 10B  PRESENT WORK  To investigate the effect of breakup on fusion --- reactions studied with stable weakly bound nuclei --- usually performed using 6Li (S=1.47 MeV), 7Li (S=2.45 MeV)& 9Be projectiles 10B; S=4.5 MeV 11B; S=8.66 MeV Chosentarget 159Tb Fusion measurements 1)Possible to separate CF and ICF events, as the compound nuclei decay predominantly by neutron evaporation channels 11B +159Tb ( Vb= 40.3 MeV) 10B +159Tb ( Vb= 40.7 MeV) 2) 159Tb being well deformed, can also study the effect of deformation on fusion process 7Li +159Tb ( Vb= 26.5 MeV) 6Li +159Tb ( Vb= 26.9 MeV) 3) 159Tb has a 100% abundance

  10. Y xp yn X + P T  CN Z Experimental Techniques for measurement of fus used characteristic –ray method in our measurements to measure the evaporation residues cross sections Suitable when the level-schemes of relevant residual nuclei are well known

  11. + P T P+T n p Y X g2 g1 COUNTS CHANNEL NUMBER Expt technique for measurement of fusion cross sections by characteristic -ray method FUSION CROSS SECTION (sFUS) SsCH SUM  INDIVIDUAL CHANNEL CROSS SECTION (sCH) correc-tion g.s. g-RAY CROSS SECTION (sg) Ng sg= AREA UNDER A g-RAY PEAK (Ng) egNBNT

  12. Target holder HPGe Detector Clover detector Monitor (Si-SBD) 125o 30o DETECTORS A clover detector (placed at +55o w.r.t beam direction) A HPGe detector (Be-window) (placed at -125o w.r.t beam direction) Two Monitors of Si-SBD (each of thickness 300) as monitor detectors (at angle  30o ) inside the spherical chamber Beam To Faraday cup 30o 159Tb target (1.5 mg/cm2) 55o Monitor (Si-SBD) Diameter of the chamber 20 cm Both in-beam and off-beam decay spectra were taken for each bombarding energy in the energy range 38-72 MeV for beams of 11,10B and 28-43 MeV for 7Li beam covering well below to well above the respective Coulomb barrier in steps of 1 or 2 MeV EXPERIMENTAL DETAILS 11B+159Tb, 10B+159Tb & 7Li+159Tb Beam : 11B (4+,5+), 10B (4+,5+) and 7Li (3+) current : ~ 4-5 nA Target : 159Tb ( self-supporting Tb foil of thickness 1.50  0.07 mg/cm2) Schematic diagram of the experimental arrangement in the 30oS beam line at the 14UD BARC-TIFR Pelletron Accelerator Facility, Mumbai A. Mukherjee, S. Roy, M.K. Pradhan et al, Phys. Lett. B636, 91-95 (2006)

  13. 6Li+159Tb Beam : 6Li (3+) , current : ~ 3-7 nA Target : 159Tb (a self-supporting Tb foil of thickness 1.59  0.08 mg/cm2) DETECTORS A clover detector A HPGe detector (Be-window) (placed at 125o w.r.t beam direction) Two Monitors of Si-SBD (each of thickness 300) as monitor detectors (at angle  30o ) inside the spherical chamber Experimental arrangement at 14UD BARC-TIFR Pelletron Accelerator Facility, TIFR, Mumbai Both in-beam and off-beam decay spectra were taken for each bombarding energy in the energy range 23-39 MeV covering well below to well above the Coulomb barrier (Vb=27 MeV) in steps of 1 or 2 MeV Data Acquisition and offline analysis --- software LAMPS EXPERIMENTALDETAILS M.K. Pradhan et al., Phys. Rev.C 83, 064606 (2011)

  14. Fig. Experimental -ray spectra (clover detector) taken at 125o at two different bombarding energies. Some of the dominant nuclei that are identified to be populated are 163Er, 162Er, 161Er, 160Er corresponding to 2n,3n,4n,5n channels 160Dy, 159Dy, 158Dy,161Ho corresponding to n, 2n 3n d2n channels 160Tb, 158Tb corresponding to 1n stripping & 1n pickup process CF ICF n-transfer

  15. 3n + 167Yb (T1/2= 17.5 m) 4n + 166Yb (T1/2= 56.7 h) 11B + 159Tb [170Yb]* 5n + 165Yb (T1/2= 9.9 m) 6n + 164Yb (T1/2= 75.8 m) 3n + 166Yb (T1/2= 56.7 h) 4n + 165Yb (T1/2= 9.9 m) 10B + 159Tb [169Yb]* 5n + 164Yb (T1/2= 75.8 m) 6n + 163Yb (T1/2= 11.05 m) 3n + 163Er (T1/2= 75 m) 7Li + 159Tb [166Er]* 4n + 162Er (stable) 5n + 161Er (T1/2= 3.21 h) 2n + 163Er (T1/2= 75.0 m) 3n + 162Er (stable) 6Li + 159Tb [165Er]* 4n + 161Er (T1/2= 3.21 h) 5n + 160Er (T1/2= 28.58 h) CF neutron evaporation channels

  16. How to obtain the cross section of product nuclei ? For the even-even residues, like 162Er, measured -ray cross section  (J), for 2+  0+, 4+ 2+, 6+ 4+, 8+  6+, 10+  8+ etc. of the various transitions in the ground state rotational band ; then extrapolating it to J=0+. 162Er For odd-mass nuclei, like 161Er measured the cross section of prompt -rays that feed the ground state; then summing this gamma ray cross sections 161Er

  17. Complete Fusion (CF) neutron evaporation channel cross sections

  18. Complete Fusion (CF) cross sections Broda et al., Nucl. Phys. A248, 356 (1975)

  19. 11B: Q= -8.66 MeV 10B: Q= - 4.5 MeV 7Li: Q= -2.45 MeV 6Li: Q= -1.47 MeV For Comparison of CF cross sections --- plotted in reduced scale --- Lower the -breakup threshold of the projectile, larger is the extent of CF suppression --- Higher the –breakup threshold, higher is the bombarding energy where the suppression of CF starts M.K. Pradhan et al., Phys. Rev. C 83, 064606 (2011)

  20. To study the extent of suppression of CF in a theoretical framework Coupled- Channels Code: CCFULL [Ref: Comput. Phys. Commun. 123, 143 (1999)] ● 1-D BPM (one-dimentional barrier penetration model) calculations [In the no coupling limit]

  21. Complete Fusion (CF) cross sections

  22. ● Coupled-Channels (CC) calculations [considering effect of target deformation, 159Tb --- well deformed nucleus] 2= 0.344; 4 =0.062

  23. Complete Fusion (CF) cross sections

  24. Complete Fusion (CF) cross sections

  25. Complete Fusion (CF) cross sections CF Suppression 14% CF Suppression 34% CF Suppression 26%

  26. 161Dy + n +  7Li + 159Tb [162Dy]* +  160Dy + 2n +  159Dy + 3n +  162Ho + n + d t  [163Ho]* + d 161Ho + 2n + d 162Er + 3n +  160Dy + n +  10B + 159Tb [165Er]* +  161Er + 4n +  6Li + 159Tb [161Dy]* +  159Dy + 2n +  158Dy + 3n +   6Li  d [163Ho]* + d 161Ho + 2n + d Channels following Incomplete Fusion (ICF) From the -ray spectra 11B+159Tb, no -lines observed corresponding to ICF

  27. Measured channel cross sections corresponding to ICF events Observed -emitting channel to be the dominant ICF process

  28.  6Li + 159Tb 6Li + 159Tb d d   7Li + 159Tb 7Li + 159Tb t t   10B + 159Tb 10B + 159Tb 6Li 6Li Coulomb barrier argument holds for 6Li and 7Li but not for 10B

  29.  6Li + 159Tb 6Li + 159Tb d d   7Li + 159Tb 7Li + 159Tb t t   10B + 159Tb 10B + 159Tb 6Li 6Li Q= 2.2 MeV Q= +10.2 MeV Q= 3.2 MeV Q= +11.1 MeV Q= 5.2 MeV Q= +4.6 MeV -emitting channel --- favourable ICF process in 10B+159Tb, 7Li+159Tb & 6Li+159Tb --- consistence with Q-value consideration

  30. Summary & Conclusions • Measured CF cross sections for systems 11B,10B,7Li & 6Li+159Tb at energies around respective Coulomb barrier  In sub-barrier energy region, observed enhancement of CF cross sections compared to 1D-BPM calculations ---- explained primarily due to target deformation • At above barrier energies, for the three reactions 10B+159Tb, 7Li+159Tb & 6Li+159Tb, CF cross sections --- suppressed by 145%, 265% and 345% w.r.t. CC calculations respectively --- attributed due to breakup process • Extent of CF suppression at above barrier energy --- correlated with -breakup threshold of the projectiles • The -particle emitting channel --- favoured ICF process for each of the reactions 10B+159Tb, 7Li+159Tb and 6Li+159Tb ---- consistence with Q-value consideration

  31. Prof. S. Roy, SINP Prof. P. Basu, SINP Prof. M. Saha Sarkar, SINP Prof. A. Goswami, SINP Prof. B. Dasmahapatra, SINP Dr. R. Kshetri, SINP Dr. M. Ray, Behala College Dr. P. Roy Chowdhury, SINP Dr. V.V. Parkar, BARC Dr. S. Santra, BARC Dr. K. Ramachandran, BARC Dr. A. Chatterjee, BARC Dr. S. Kailas, BARC Dr. R. Palit, TIFR Dr. I. Mazumdar, TIFR Acknowledgement COLLABORATORS Ph.D. Supervisor:Prof. Anjali Mukherjee, SINP SINP: Saha Institute of Nuclear Physics, Kolkata BARC: Bhabha Atomic Research Centre, Mumbai TIFR: Tata Institute of Fundamental Research, Mumbai

  32. Thank You

  33. where with fm MeV fm-1 To study the extent of suppression of CF in a theoretical framework Coupled- Channels Code: CCFULL [Ref: Comput. Phys. Commun. 123, 143 (1999)] CCFULL do not consider the effect of breakup of projectiles Bare potential: Woods-Saxon parameterization of Akyüz-Winther (AW) potential [Ref: R.A. Broglia, A. Winther, Heavy Ion Reactions, Vol.1] Calculations with shallow potentials --- lead oscillations of transmission coefficients --- to minimize, potential well chosen to be deeper

  34. Vb Rs Vb1 R1 Vb2 R2 Effect of target deformation Target (Z2,A2) Projectile (Z1,A1) Coulomb barrier for two inert spherical nuclei Vb= Z1Z2e2/ Rs = Z1Z2e2/ rs(A11/3+A21/3) R1< Rs So, Vb1 > Vb R2> Rs So, Vb2 < Vb Considering all possible orientation of target nuclei --- give rise to a distribution of barriers – some with lower heights & some with higher heights

  35. A + B [C]*  -ray cross section,  = N / ( NB NT) N  area under the –ray peak   absolute efficiency of the -ray detector at the corresponding energy NB  no. of beam particles/sec NT  no. of target nuclei /cm2  =0 E A + B [C]*      0 D   -decay  =0 E in-beam method [when the residual nuclei stable or have very long half-lives (several hours to years )] off-beam method [when the residual nuclei are -active]

  36. 3/2 0.0 T1/2=3.21 hr 363.6 keV; I()=0.056 573.8 keV; I()=0.037 528.0 keV; I()=0.39 726.8 keV; I()=0.84 826.6 keV; I()=64 16168Er93 66% EC:100% 826.6 463.2 298.6 252.7 99.6 0.0 16167Ho94 Cross sections were also obtained by off-beam method by following respective radioactive decay Cross sections obtained by both in-beam & off-beam method agreed well within the limits of uncertainty ------ showing that the g.s. corrections for these nuclei were very small Also the cross sections obtained using the data from the clover detector agreed very well with those obtained from the HPGe detector

  37. Interaction potential between two colliding nuclei Target (ZT, AT) = Coulomb(VC) + Nuclear(VN) + Centrifugal (Vcent) Projectile (ZP, AP) r • VC( r) = ( 3RC2 – r2)ZPZTe2 / 2RC3 for r  RC =ZPZTe2/ r for r  RC RC = ro(AP1/3 + AT1/3), ro the radius parameter •VN( r)  -V0 / [1+exp(r-R0)/a] ---Woods-Saxon form •Vcent( r) = ħ2l(l+1)/ 2r2 Vb : fusion barrier Rb : fusion radius

  38. For Light system Complete Fusion (CF) pn  6Li 16O 20Ne 22Na Incomplete Fusion (ICF)  6Li 16O 20Ne  d Total Fusion (TF) = CF+ICF

  39. Complete Fusion (CF) 213Rn 2n  3n 212Rn 6Li 209Bi 215Rn Incomplete Fusion (ICF) 2n 209Po  6Li 3n 209Bi 208Po 211Po d  For Heavy system

  40. Simplest model of Fusion: One-dimensional Barrier Penetration Model (1-D BPM) interacting nuclei—inert spherical objects radial separation --- only degree of freedom quantum mechanical tunneling using WKB method Ref: Phys. Rev. Lett. 31, 766 (1973); Rep. Prog. Phys. 51, 1047 (1988) Fusion of light nuclei: systems systems systems 6Li+16O fus (mb) systems systems Ref: Nucl. Phys. A. 645, 13 (1999)

  41. Fusion of heavy nuclei: Effect of target deformation Effect of +ve Q-value transfer reaction E/Vb E/Vb Sub-barrier fusion enhancement Experimental evidence --- fusion near barrier --- strongly influenced by intrinsic degrees of freedom, e.g. deformation, collective excitation, transfer of nucleons Ref: Annu. Rev. Nucl. Part. Sci. 48, 401 (1998)

  42. Ref: Dasso et al, Nucl. Phys. A 405 (1983) 381; Rep. Prog. Phys. 51 (1988) 1047 Coupled Channels Model Coupling of elastic or entrance channel to internal degrees of freedom (inelastic and transfer channels) gives rise to a distribution of barriers --- some lower and some higher than original single barrier coupling Vb Enhances fusion at below barrier energies

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