Angular Momentum of Spherical Fission Fragments F. Gönnenwein University of Tübingen In collaboration with V. Rubchenya and I.Tsekhanovich Saclay May 12,2006

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

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) / B ² ] 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

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 both the Level Scheme and Transition Probabilities can be determined. This allows to assess the Spin Distribution P(I) at the 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 Results obtained for the average primary spin I prim as a function of fragment mass suggest a similar dependence on mass as the one knwon for the average neutron multiplicity 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) Bending model fails to predict large spin for near-spherical magic fragments

Why study 132 Te? μs 28 μs ● 132 Te has Z = 52 and N =80 and is doubly near-magic ● 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 )

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 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 = 52 of Te by spectroscopy of gammas hitting the Ge-detectors.

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 Cold Compact Fission: most compact scission configuration with No Intrinsic Excitation 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

Experimental Method and Results Aim of the experiment: prove that large spins of near-spherical fission fragments are not due to a deformation dependent mechanism of spin generation Method: measure spin as a function of fragment kinetic energy pushing the energies into the regions of both cold compact and cold deformed fission. In particular, in cold deformed fission fragments are stronlgy deformed but carry no intrinsic excitation. Are spins found large or not? How to proceed: the size of spin is assessed from measuring the ratio of populations for high spin / low spin. To this purpose intensities of gamma-lines properly chosen are compared. 132 Te 697 / 974 (4 → 2) / (2 → 0) Cold Deformed Cold Compact Ratio E kin / MeV (8 → 7) + (8 → 6) Σ (6 → 4 → 2 → 0)

Conclusions ● Corroborated by experiment the suggestion is that large fragment spins observed for near-spherical nuclei are due to single particle excitations. The experiment was performed for 132 Te having two proton particles and two neutron holes outside of the closed shells with Z = 50 and N = 82, respectively. For these nuclei the shell model predicts that nucleon orbits being paired in the ground state become aligned at rather low excitation energies. Only in cold fission, both compact and deformed, these states are running out of energy for their population. ● It should be interesting to study with the method exploited here more systematically the angular momentum of near-spherical nuclei with even and odd numbers of particles and holes outside of closed shells. Pronounced fluctuations are expected ● There remains, however, a basic difficulty: the sizable mismatch between the spins of light and heavy fragments calls for large orbital angular momenta. It means that in the semiclassical models the bending mode should be replaced by the wriggling mode. 235 U(n,f) mass I prim

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

to wriggle = godiller