Angular Momenta of near-spherical Fission Fragments F. Gönnenwein, University of Tübingen, Germany I.Tsekhanovich, University of Manchester, UK V. Rubchenya, Radium Institute, St. Petersburg, Russia Kazimierz Dolny, Poland September 2006

Deexcitation of Fission Fragments Following scission and relaxation of fragment deformation the „primary“ Fission Fragments are highly excited → n and γ emission PRIMARYY FRAGMENTS Neutron Evaporation SECONDARY FRAGMENTS Statistical Gammas Discrete Gammas Studies of Gammas from Fission yield information on Angular Momentum generated in Fission s s I.Ahmad, W.R.Phillips

Fragment Spin and Gamma Anisotropy With Θ = the (γ, FF) angle A = [W(0°) / W(90°] - 1 ≠ 0 Mostly A > 0 S.Skarsvag 1980 Anisotropy of Gamma emission Interpretation by V. Strutinsky (1960) After scission the Coulomb excitation induces Fragment Spin I leading to W L (θ) = 1 + k L (ħ²I / ΘT)² sin²θ For L = 2: k L = -3/8 → A > 0 Fragment Spin is ⊥ Fission Axis Fragment Spin is linked to Fragment Deformation via Θ

Fragment Spin from Ratio of Isomeric Fragment Yields Isomeric transitions are readily identified In γ-decay chain. Deduce Fragment Spin from feeding of two isomers with different spins, preferably one spin large, the other small. Evaluate spin distribution in a statistical model with Ansatz P(I P ) ~ (2I P + 1) exp[-I P (I P + 1) / B²] with B 2 ≈ Simulate neutron evaporation and emission of statistical gammas to find distribution of spins at entry point to decay of discrete gammas. Calculate feeding of the two spin isomers Compare calculation with experiment and find B and hence I rms of primary spin distribution J.P.Bocquet et al 1979 n statist. γ`s I high I low ground state entry

Angular Momentum from prompt Gamma Spectroscopy 98 Mo P(I) I U(n,f) Y. Abdelrahman I prim Mass J.L.Durell Mass V.A.Kalinin Cf(s,f) <ν><ν> With large Ge-detector arrays measure Level Scheme and Transition Probabilities. Assess the Spin Distribution P(I) at entry points of the discrete level region. With corrections for spin carried away by neutrons and statistical gammas find the average primary spin I prim. 10 Average primary spin I prim (A FF ) as a function of fragment mass suggests a dependence similar to ν(A FF ) which is known to be linked to fragment deformation

Angular Momentum of Fission Fragments: How is it generated ? Bending Model: Coulomb + nuclear forces bring out a potential pocket which aligns deformed fragments on the fission axis. Angular vibrations are excited as zero point oscillations or - in case of finite nuclear temperatures - thermally. J.O.Rasmussen et al 1969 M.Zielinska-Pfabé, K. Dietrich 1974 Pumping Model For constrained alignment of deformed fragments angular momentum Is pumped by motion of nucleons in deformed potential well: Δθ · ΔI ≈ ħ (Heisenberg) I.N.Mikhailov, P.quentin 1999 L-Bonneau et al U(γ,f) adiabatic Mass Mass D.DeFrenne 1984J.L.Durell U(n,f) adiabatic Most data explained as zero-point oscillations of deformed nuclei. Models fail, however, to predict large spins for near-spherical fragments

Aim of experiment Prove the conjecture: large spins of near-spherical fission fragments are not due to zero-point oscillations. Instead, they are due to thermally excited single-particle states How to prove the conjecture Exploit the properties of cold compact fission and cold deformed fission (see foil) Cold deformed fission: the scission configuration has large deformation and no intrinsic excitation energy. For zero-point oscillations spins should be large. For thermally excited sp states spins should be small. Experiment Cold compact fission: the scission configuration has small deformation and no intrinsic excitation energy. Whatever mechanism, spins are expected to be small. Cold compact fission has large E kin while cold deformed fission has small E kin of FFs. Measure ratio of high / low spin population as a function of fragment kinetic energy E kin For Cold Compact Fission : large spins cannot be populated For Cold Deformed Fission: check whether large spins are populated

Cold Compact and Cold Deformed Fission V Coul V Def Deformation Energy V tot Q Cold Deformed Fission: most elongated scission configuration with No Intrinsic Excitation and SMALL TKE Cold Compact Fission: most compact scission configuration with No Intrinsic Excitation and LARGE TKE A. Möller U(n,f) E Kin (LF) / MeV Z o-e effect / % J.Kaufmann 1992 the o-e effect of fragment charge senses the Intrinsic Excitation Free E

Experiment at Lohengrin E/q p/q ΔE + E rest ioni chamber p/q Reactor core target - Experiment performed at the Lohengrin spectrometer of the ILL / Grenoble. - Reaction: 239 Pu(n,f). Spin of compound nucleus 240 Pu*: I = 0 or I = 1ħ. - Lohengrin B- and E-fields are set to select fragments with given mass number A - Fragments are stopped in ionisation chamber positioned in focal plane. - Traveltime of fragments in spectrometer is (1 - 2) μs. - The ionisation chamber is surrounded by a series of Ge-detectors. - Identify charge Z by spectroscopy of gammas hitting the Ge-detectors.

Why study 132 Te? μs 28 μs ● 132 Te has Z = 52 and N =80 and is near-spherical ● From former experiments it is known: Ekin ≈ 9 ħ ● 132 Te is conveniently studied at Lohengrin because it has two isomeric states: one with high spin and a second one with lower spin ● 1) I = 10 + T 1/2 = 3.70(9) μs E = MEV, 2) I = 7 – T 1/2 = 28 μs E =1.925 MeV, ● Note that at Lohengrin only these two isomeric states arrive at the focal plane in an excited state ● The states shown in the level scheme are well understood in the shell model as single particle excitations ● The positive parity states are interpreted as two-neutron hole states ν(h -2 11/2 ) while the negative parity state has probably strong contribution by ν(h -1 11/2, d -1 3/2 )

Spectrum of 132 Te μs 28 μs E kin = 80 MeV Time integration 40 μs The transition 10 + → 8 + is highly converted and not seen as gamma Note the clean gamma-spectrum for FF mass A = → → 7 – 8 + → → – → → 4 + In red: 132 Te In blue: 132 Sn 132Sn The transition 10 + → 7 – is E3 and not observed

Experimental Results μs 28 μs Low members of cascade exhibit as expected no dependence on E kin of fragment E kin / MeV Ratio Cold Deformed Cold Compact Contribution of high spin isomer at high excitation energy drops both at cold compact and cold deformed fission

CONCLUSIONS For the specific example 132 Te it was shown that fragment spin is not generated as zero-point oscillation, instead spin is generated as single-particle excitation However, it is known from experiment that spin of near- spherical fragments from fission exhibit large scatter. Is this due to the different level structure for (e,e), (e,o) and (o,o) nuclei? Experiment will have to tell. LFHF complementary There remains, however, a basic difficulty: A sizable mismatch between the spins of complementary fragments is observed. This points to the existence of large orbital angular momenta: J tot = J LF +J HF +L In semi-classical models the bending mode should, hence, be replaced by the wriggling mode. In a quantum –mechanical model large orbital momenta have been predicted recently

Bending and Wriggling Modes for fissioning nuclei with spin I = 0 Bending Mode I 1 + I 2 = 0 I1I1 I1I1 I2I2 Wriggling Mode I 1 + I 2 + L = 0 I2I2 L fission axis X

to wriggle = godiller