Angular Momentum of Spherical Fission Fragments F Gnnenwein

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 10 -15 s - 10 -14 s Statistical Gammas Discrete Gammas I. Ahmad, W. R. Phillips Studies of Gammas from Fission yield information on Angular Momentum generated in Fission

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

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(IP) ~ (2 IP + 1) exp[-IP(IP + 1) / B²] with B 2 ≈ <IP 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 Irms of primary spin distribution J. P. Bocquet et al 1979

Angular Momentum from prompt Gamma Spectroscopy Level Scheme and Transition Probabilities P(I) With large Ge-detector arrays both the can be determined. This allows to assess the Spin Distribution P(I) at the entry points of 98 Mo the discrete level region. With corrections for spin carried away by neutrons and statistical gammas find the average primary spin Iprim. 2 Y. Abdelrahman 1987 Iprim Results obtained for the 235 U(n, f) average primary spin Iprim 7 as a function of fragment mass suggest a similar dependence 4 80 on mass as the one knwon for 120 Mass J. L. Durell 1997 10 I 160 the average neutron multiplicity linked to fragment deformation 4 <ν> 10 6 252 Cf(s, f) 2 0 80 120 Mass V. A. Kalinin 2002 160

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. J. O. Rasmussen et al 1969 Angular vibrations are excited as zero point oscillations or M. Zielinska-Pfabé, K. Dietrich 1974 - in case of finite nuclear temperatures - thermally. Pumping Model For constrained alignment of deformed fragments I. N. Mikhailov, P. quentin 1999 angular momentum Is pumped by motion of nucleons in L-Bonneau et al. 2005 deformed potential well: Bending model fails <Iprim> 12 to predict large spin 8 for near-spherical 4 magic fragments 80 120 Mass J. L. Durell 1997 160 (Heisenberg) 12 <Iprim> 235 U(n, f) Δθ · ΔI ≈ ħ adiabatic 8 4 238 U(γ, f) 84 108 132 Mass 156 D. De. Frenne 1984

Why study 132 Te? . 3 7 μs 10+ 8+ ● 132 Te has Z = 52 and N =80 and is doubly near-magic ● From former experiments it is known: < I >Ekin ≈ 9 ħ ● 132 Te is conveniently studied at Lohengrin because it has 28 μs - two isomeric states: 7 6+ 4+ one with high spin and a second one with lower spin ● 2+ 1) I = 10+ T 1/2 = 3. 70(9) μs E = 2. 723 MEV, 2) I = 7 – T 1/2 = 28 μs E =1. 925 Me. V, ● 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 0+ ● The positive parity states are interpreted as two-neutron hole states ν(h-211/2) while the negative parity state has probably strong contribution by ν(h-111/2, d-13/2)

Experiment at Lohengrin - 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 =132. - 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. ΔE + Erest ioni chamber Reactor core p/q E/q target p/q

Cold Compact and Cold Deformed Fission Q Cold Compact Fission: most compact scission Energy Free E Vtot VCoul Cold Deformed Fission: VDef most elongated scission configuration with No Intrinsic Excitation Deformation fragment charge senses the Intrinsic Excitation 232 U(n, f) Z o-e effect / % the o-e effect of 85 A. Möller 1996 95 105 EKin (LF) / Me. V J. Kaufmann 1992

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 Ratio 697 / 974 1. 5 0. 04 (4 → 2) / (2 → 0) 0. 5 60 0. 08 (8 → 7) + (8 → 6) Σ (6 → 4 → 2 → 0) 80 60 Ekin/Me. V Cold Deformed 80 Ekin/ Me. V Cold Compact Cold Deformed Cold Compact

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 235 U(n, f) ● There remains, however, a basic difficulty: the sizable mismatch between the spins of light and heavy fragments calls for large Iprim <LF> orbital angular momenta. It means that in the semiclassical models the bending mode should be replaced by the wriggling mode. 90 <HF> 120 mass 150

Bending and Wriggling Modes for fissioning nuclei with spin I = 0 I 1 I 2 Bending Mode I 1 + I 2 = 0 I 1 L Wriggling Mode I 2 I 1 + I 2 + L = 0

to wriggle = godiller