1. Search for diabolic pair transfer at higher angular momentum states by using heavy-ion induced reaction Dr. Samit Kr. Mandal Department of Physics & Astrophysics Delhi University Spokesperson H. J. Wollersheim GSI

2. Pair transfer as a function of spin Spectroscopic quantities Intrinsic quantities pair transfer amplitude Parameters 40 Ar 238 U

3. Nuclear Josephson Effects: Enhanced transfer of nucleon pairs between two superfluid heavy nuclei in a cold reaction correspond to a super-current. alternating current JE : Strong coupling situation Flux oscillation in particular mass partition Characteristic dependences on incident energy or reaction angle Transfer probability values larger than 0.5 direct super current JE : Weak coupling situation Enhanced transfer of several nucleon pairs Transfer probability values less than 0.5 G.Eckert et al. Z.Phys. A343 (1992), 276 I.Peter,W.von Oertzen et al., Eur.Phys. J.A16(2003),509

4. Berry Phase, Diabolic Pair Transfer A quantum phase effect arising in systems that undergo a slow, cyclic evolution. Parallel transport of vector along surface of sphere. In this figure both vectors stay tangential to curved surface at all times. A phase of 90 o is introduced. A diabolical point, where two energy surfaces touch and a closed path on the lower surface encircling this point

5. Berry's Phase, Diabolic Pair Transfer Berry's phase is a simple mathematical fact. Berry considers a Hamiltonian, which depends on external parameters Examples: (a) Nilsson Model R=β (b) Cranked Shell Model R=(λ,Δ,ω) A diabolical point, where two energy surfaces touch and a closed path on the lower surface encircling this point V En(λ,ω)En(λ,ω) ω λ Φ 0 C Φ 1 Φ 1 =e iγ Φ 0 E2(λ,ω)E2(λ,ω) E1(λ,ω)E1(λ,ω) Φ 1 = -Φ 0 chemical potential λ, angular velocity ω, pairing gap Δ

6. Berry's Phase and the Backbending Effect J(ђ) Two different paths around a diabolic point The oscillating behavior of the pair transfer matrix element has a close analogy to the oscillating behavior of the electric current in Superconducting Quantum Interference Devices as a function of the magnetic field, the DC-Josephson effect

7. Berry's Phase in Nuclear Physics Full horizontal arrow indicates pair transfer matrix elements with positive sign and dashed arrows indicate those with negative sign. K quantum number for j=13/2 is shown.  open problem for experimentalist Pair transfer matrix

8. Calculated yields for yrast states (including feeding from yrare states) compared to data.  -ray yields are arbitrarily normalized to the calculation at the 6 + to 4 + state. No clear evidence for diabolical pair transfer observed within the sensitivity range of the experiment No other experiments was reported in the literature !! 206 Pb( 156 Gd, 158 Gd) 204 Pb [nondiabolic case] 206 Pb( 156 Gd, 154 Gd) 208 Pb [presumed diabolic case] K. G. Helmer et al PRC 48,1879(1993).

9. Proposed Systems: The Hf and Yb-chain : The interaction strength in the level crossing between the ground state band and the s-band characterized by the minimal distance between the yrast band and the first excited band ΔE min. Connected lines correspond to minimal distances for the angular momenta I= 10-16ħ. Full dot symbols indicate the even mass Yb-isotopes. The position of the deformed single-particle energies of the v i 13/2 levels for the nucleus 166 Yb and 170 Hf are given on the abscissa. Y. Sun et al, Z. Phys. A339 (1991) 51 172,174 Yb on 206 Pb 174,176 Hf on 206 Pb

10. The calculation show the diabolic effect for 206 Pb on 174 Hf. This calculation assumes 174 Hf transfers to 172 Hf. The symbol o’s are non diabolic case and Δ’s are diabolic cases. L F Canto et al PRC 47,2836(1993). yrast-statesyrare-states 174 Hf( 206 Pb, 208 Pb) 172 Hf 2n-transfer probability as a function of spin

11.  The experiment will be performed at X7 beam line  The ion beam from UNILAC facility.  Annular proportional counter for particle detection  Cluster Ge–detector from EUROBALL and segmented Super Clover will be used for gamma-ray detection Experimental Setup Beam: 174,176 Hf and 172,174 Yb, Target : 206 Pb (500μg/cm 2 thick),

12. Experimental Setup & Beam time request Beam: 174,176 Hf and 172,174 Yb, Target : 206 Pb (500μg/cm 2 thick), Beam Energy: 5-8 MeV/A. Beam Current: 10 9 pps. Estimated cross-sect ion (Coupled Channels Calculations- FRESCO)~ 1 μb for excited state of interest Yield ~ 200 counts/hr. Gamma detection efficiency ~ 4% For each isotope, shifts required = 14 shifts. Setting up detectors & particle-γ coincidence = 2 shifts. Total shift require : 30 for each experiment with two isotopes 50% of duty cycle of accelerator has been taken into account.

13. Beam Time Request Two Experiments Each experiment: 30 Shifts Total : 60 Shifts.

14. Collaborators : Sunil Kalkal, Mansi Saxsena Department of Physics & Astrophysics, University of Delhi, India & Punita Verma Kalindi College, University of Delhi, India & Jürgen Gerl, Magdalena Gorska, Henning Schaffner,Ivan Kojouharov, Jurek Grebosz, R. Hoischen Gesellschaft für Schwerionenforschung, Darmstad, Germany

15. Thanks