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. WollersheimGSI

1

2

Pair transfer as a function of spin

Spectroscopic quantities

Intrinsic quantities pair transfer amplitude

Parameters IAaaIA ,,2 0

IAaaIA ,,2 0 2;2(,,2 IIEBAIQAI

0aa Q

40Ar238U

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), 276I.Peter,W.von Oertzen et al., Eur.Phys. J.A16(2003),509

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

),,(

zyxR

V

En(λ,ω)

ω

λ

Φ 0

CΦ 1

Φ 1=eiγ Φ0

E2(λ,ω)

E1(λ,ω)

Φ1= -Φ0

chemical potential λ, angular velocity ω, pairing gap Δ

Berry's Phase and the Backbending Effect

gJ

gsssiJ

<A

+2,

J/(a

+a+

) l=0/

A,J

>

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

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

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 ΔEmin. 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 i13/2

levels for the nucleus 166Yb and 170Hf are given on the abscissa.Y. Sun et al, Z. Phys. A339 (1991) 51

172,174Yb on 206Pb 174,176Hf on 206Pb

The calculation show the diabolic effect for 206Pb on 174Hf. This calculation assumes 174Hf transfers to 172Hf. The symbol o’s are non diabolic case and Δ’s are diabolic cases.

L F Canto et al PRC 47,2836(1993).

yrast-states yrare-states

174Hf(206Pb,208Pb)172Hf

2n-transfer probability as a function of spin

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 SetupBeam: 174,176Hf and 172,174Yb, Target : 206Pb (500μg/cm2 thick),

Experimental Setup & Beam time request

Beam: 174,176Hf and 172,174Yb, Target : 206Pb (500μg/cm2 thick),

Beam Energy: 5-8 MeV/A .

Beam Current: 109 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.

Beam Time Request

Two ExperimentsEach experiment: 30 Shifts

Total : 60 Shifts.

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

Thanks