filipescu@tandem.nipne.ro

1. Study of sub-barrier fission resonances with gamma beams Dan FILIPESCU1, Mihaela SIN2 1) Horia Hulubei - National Institute for Physics and Nuclear Engineering, 2) Bucharest University, Romania filipescu@tandem.nipne.ro

2. Why fission is still a hot topic? No theory or model is able yet to predict all fission observables (fission cross section, post-scission neutron multiplicities and spectra, fission fragments’ properties like mass, charge, total kinetic energy and angular distributions) in a consistent way for all possible fissioning systems in a wide energy range. New nuclear technologies design requires increased accuracy of the fission datarefinements of the fission models and better predictive power. To reach the target accuracies more structural and dynamic features of the fission process must be included in the theoretical models.

3. Why photofission? • Photofission experiments done on available targets may produce additional information to the existing available data from experiments done with neutrons • - differences in compound nucleus states population must be taken into account • Characteristics of ELI-NP Gamma Sorce offer for the first time a viable alternative to the study of sub-barrier fission resonances with neutrons, even below Sn • - very high gamma intensity and excellent energy resolution are required

4. Fission process • Liquid Drop Model • - only the Coulomb (EC) and surface term (ES) depend on deformation • near g.s. ES increases more rapidly than EC decreases – V rises • at larger deformation the situation is reversed – V drops

5. From the initial state to scission The fissioning system shape modifies continuously during the motion from the formation of the initial state (characterized by a small deformation) to the elongated asymmetric pre-scission shape and even scission (where the nuclear system is composed of two touching fragments). Several types of parameterization and sets of deformation (shape) parameters {q} may be required to describe completely the fissionning nucleus in its various stages. potential energy surface – potential energy as function of deformation V({q}) fission path – corresponds to the lowest potential energy when increasing deformation fission barrier – one-dimensional representation of V; V as function of one deformation coordinate (ex. elongation)

6. Fission barrier • - macroscopic models: LDM • – give only a qualitative account of the phenomenon • - microscopic-macroscopic model: LDM + shell correction • – explained a significant number of experimental data • - microscopic models: HFB • – can not provide accurate results for Vf yet, but provide • the trend and are improving

7. Fission barrier Strutinsky’s procedure The value of the shell correction is +, - depending on whether the density of single-particle states at Fermi surface is great or small. Negative corrections for actinides - g.s. - permanent deformation - vicinity of macroscopic saddle point – second well double-humped fission barrier

8. Fission barrier Variation of the shell correction amplitude with changing Z,N together with the variation of the LD potential barrier with changing fissility parameter (EC/2ES) lead to a variation of the fission barrier from nucleus to nucleus: • inner barriers almost constant 5-6 MeV for the main range of actinides; fall rapidly in Th region; • secondary well’s depth around 2 MeV; • outer barriers fall quite strongly from the lighter actinides (6-7 MeV for Th) to the heavier actinides (2-3 MeV for Fm).

9. Fission barrier Early calculations assumed a maximum degree of symmetry of the nuclear shape along the fission path and the theoretical predictions were not in agreement with the experimental barrier heights and the asymmetric mass distribution of the fission fragments. Extensive studies concluded that neutron rich nuclei have axial asymmetry at the inner saddle point and reflection (mass) asymmetry at the outer saddle point. These results have large implications for the barrier heights and for the level densities at the saddle points and explain the mass asymmetry of the fission fragments.

10. Symmetry of inner barrier Shell corrections performed by Pashkevich and subsequent by Howard and Moller prooved that along an isotopic chain exists a mass Atr: - A > Atrinner barrier asymmetry – AAMS (higher inner barr. than the outer one) - A < Atr inner barrier symmetry – ASMS (lower inner barr. than the outer one)

11. Fission barrier The multi-modal fission In Brosa model the mass distribution of the fission fragments can be described considering minimum 3 pre-scission shapes, 3 fission paths which branch from the standard fission path at certain bifurcation points on the potential energy surface. To each of them corresponds a fission mode: symmetric super-long (SL) and asymmetric standard 1 (ST I) and II (ST II). The different barrier characteristics give rise to a separate fission probability along the various fission paths. The corresponding fission probabilities should add up to the total fission probability. The final distributions of the fission fragment properties (mass, charge and TKE) are a superposition of the different distributions stemming from the various fission modes.

12. Fission barrier The triple-humped fission barrier (Th anomaly) In the thorium region, the second hump appears just under the maximum predicted by the liquid drop model, therefore its exact shape is very sensible to the shell effects. It was demonstrated that a shell effect of second-order would split the outer barrier giving rise to a third very shallow well. A triple-humped barrier for the actinides in thorium region, allowing the existence of hyper-deformed undamped class III vibrational states could explain the disagreement between the calculated and experimental inner barrier height and also the structure in the fission cross section of non-fissile Th, Pa and light U isotopes.

13. Fission barrier - description • parabolicbarriers • numerical barriers • Static fission barriers extracted from full 3-dimensional HFB energy • surfaces as function of quadrupole deformation

14. Fission barrier - description • parabolic barriers humps only described by decoupled parabolas entire fission path described by smoothly joined parabolas It is customary to assume that the mass tensor it is diagonal in the deformation space coord. system and all diagonal elements are equal to a constant which is very important for the fission barrier parameterization and for the transmission coefficient calculation.

15. Fission barriers Transition states, class I, II, …states

16. Fission barriers Transition states, class I, II, …states • transition states – excited states at saddle points • class I (II,III) states – states of the nucleus with deformation corresponding • to first (second, third) well

17. Fission barriers Transition states, class I, II, …states

18. Fission barriers Transition states - discrete Quantum structure of the fission channels is important for accurate descriptions of fission cross sections at the sub-barrier and near-barrier energies; it depends on the nuclear shape asymmetry and the odd-even nucleus type. Mirror-asymmetric even-even nuclei have ground-state rotational band levels with Kπ = 0+, J = 0, 2, 4... - that unify with the octupole band levels Kπ = 0−, J = 1, 3, 5... in the common rotational band. Additional unification arises for axial asymmetric shapes and levels of the γ-vibrational band with Kπ = 2+, J = 2, 4... The quantum number of the corresponding rotational bands for odd and odd-odd nuclei are estimated in accordance with the angular momentum addition rules for unpaired particles and the corresponding rotational bands. -continuum Consistent treatment of all reaction channels would require for the transition state densities the same formulation used for the normal states, adapted to consider the deformation and collective enhancement specific for each saddle point.

19. Fission barrier - description • numerical barriers - Static fission barriers extracted from full 3-dimensional HFB energy surfaces as function of quadrupole deformation - Global microscopic nuclear level densities within the HFB plus combinatorial method.

20. Initial state • neutron (γ, p, α…) induced fission: • • CN states populated directly or after gamma-decay - (n,f) • • states in residual nuclei - (n,n’f), (n,2nf), (n,3nf)

21. Initial state • neutron induced fission: fertile and fissile nuclei • gamma-ray induced fission: no such classification

22. Fissionin CN statistical model The fission cross section: - cross section of the initial state formation - fission probability  - entrance channel ’ -outgoing competing channels E - energy of the incident particle inducing fission Jπ - spin, parity of the CN state

23. Efi ħωi Transmission coefficients • parabolic barrier Hill-Wheeler formula for the transmission coefficient through a parabolic barrier:

24. Transmission coefficients • non-parabolic barrier The coefficients Ti are expressed in the first-order WKB approximation in terms of the momentum integrals for the humps:

25. Transmission coefficients - decoupled humps Nhhumps

26. Transmission coefficients – entire barrier WKB approximation N. Fröman, P. O. Fröman; JWKB Approximation, North-Holland, Amsterdam (1965)

27. Fission mechanisms Hamiltonian of a fissionable nucleus: H=Hβ+Hi+Hiβ Hβdescribes the fission degree of freedom Hidescribes the other collective and intrinsic degree of freedom Hiβaccounts for the coupling between the fission mode and other degrees of freedom. Wave functions of the total Hamiltonian: Below the inner barrier the vibrational states |β n> may be classified as class I and class II vibrations depending on whether the amplitude is greater in the ground state (I) or secondary minimum (II). The compound states |c> of the system may be classified as class I and class II, according to the type of vibrational states dominating in the expansion. The interaction term Hiβ leads both to a coupling between the vibrational and intrinsic degrees of freedom (the vibrational damping) and between class I and class II states.

28. Fission mechanisms class I states class II states complete damping complete damping medium damping no (low) damping

29. Fission mechanisms • Models for fission coefficient calculation • conventional approach – complete damping of vibrational class I and II (III) • - doorway-state model – the elements of the coupling matrix are calculated • - optical model for fission – the absorption out of fission mode is • described by an imaginary potential

30. Fission mechanisms – optical model for fission The coupling between the vibrational and non-vibrational class II (III) states makes possible for the nucleus to use the excitation energy to excite other degrees of freedom and this is interpreted as a loss, an absorption out from the flux initially destinated to fission. This absorption is described by an imaginary potential in the second well. Complex potential - real part: 3 (5) parabolas smoothly joined - imaginary part:

31. Fission mechanisms within optical model for fission Transmission through the complex double-humped barrier • direct - via the vibrational states • indirect - reemission after absorption in the isomeric well E*

32. Fission coefficients within optical model for fission Double-humped barrier Tdir, Tabs are derived in WKB approximation for complex potential

33. Transmission coefficients

34. Fission coefficients within optical model for fission Double-humped barrier Full K-mixing: Based on these relations, a recursive method was developed to describe transmission through triple- and n-humped barriers.

35. Transmission through multi-humped barriers Graphic representation of the recursive method used to calculate some of the direct and absorption coefficients for a four-humps barrier. The transmission coefficients entering the calculations are represented by dashed arrows and the derived coefficients are represented by full arrows.

36. Transmission through multi-humped barriers The evolution of the flux absorbed in the second and third wells. Each time new contributions are accumulated to the flux undergoing fission and to the one absorbed in the first well. The shape changing between the second and third wells continues till the fractions initially absorbed in these wells are exhausted. M. Sin, R. Capote, Phys.Rev.C 77, 054601 (2008)

37. Fission coefficient

39. σ(b) 231Pa(n,f) σ(b) 233U(n,f) σ(b) 238U(n,f) E (MeV) E (MeV) Very good descriptive power EMPIRE calculations performed by Mihaela SIN – Bucharest University

40. Fission coefficient

41. 232Th(n,f) Triple humped barr.

42. Fission coefficient

43. n,  234Pa 1.2 m; 6.8 h  234U 2.4 105 y n, 3n  n, f n,  n, 2n n,  233Th 22 min  233Pa 27 d  233U 1.6 105 y n, f  n, f n,  n, 2n n, 2n n,  232Th 1.4 1010 y 232Pa 1.3 d  232U 69 y n, 3n  n, f  n, f n, 2n n,  n, xn 231Th 26 h  231Pa 3 104 y  n, f n,  n, 2n 230Th 7.5 104 y 230Pa 17 d   n, f Th-U fuel cycle - Protactinium effect - Possible use in ADS hybrid systems

44. n + 233Pa f  234Pa p  f   f n 233Th 230Ac d p  p  f  n n 233Pa p  f   n f 232Th 229Ac d p  p  f  n n 232Pa p  f   f n 231Th 228Ac d p  p  f  n n 231Pa p  f   f n 230Th 227Ac d p  p  f  n n 230Pa p  f  n 229Th d p  f  n 229Pa p  f  n 228Th p  f  n 228Pa p  n Primary and secondary chains for n + 233Pa reaction up to 50 MeV

45. G.Vlăducă, F.J.Hambsch, A.Tudora, S.Oberstedt, F.Tovesson, D.Filipescu Nucl. Phys. A 740(2004)3 Fission cross section 233Pa(n,f)

46. Gamma-ray strength functions • Gamma transmission coefficient: • Closed forms for the E1 strength functions • Standard Lorentzian model (SLO) • Kadmenskij-Markushev-Furman model (KMF) • Enhanced Generalized Lorentzian model (EGLO) • Hybrid model (GH) • Generalized Fermi Liquid model (GFL) • Modified Lorentzian model (MLO) Normalization:

47. Study of gamma capture resonances Porter-Thomas (=1) widths distribution • Gamma-ray strength functions normalization • Level density parameterization check and tuning • Statistical model hypothesis check Wigner spacing distribution

48. EXFOR Empire EXFOR Empire ENDF-VII.1 JENDL/PD TENDL-2011 U-238(g,abs) EXFOR Empire EXFOR Empire ENDF-VII.1 JENDL/PD TENDL-2011 U-238 photo-reaction cross sections: experimental data, evaluations, preliminary calculations U-238(g,f) U-238(g,f) U-238(g,non)

49. EXFOR Empire ENDF-VII.1 TENDL-2011 U-238(g,2n) U-238(g,n) U-238(g,*) EXFOR Empire (g,abs) (g,f) (g,g) (g,n) (g,2n) U-238 photo-reaction cross sections: experimental data, evaluations, preliminary calculations

50. EXFOR Empire ENDF-VII.1 JENDL/PD TENDL-2011 U-238(g,non)