IMPACT OF NUCLEAR MOMENTS OF INERTIA ON FISSION OBSERVABLES 6th - PowerPoint PPT Presentation

IMPACT OF NUCLEAR MOMENTS OF INERTIA ON FISSION OBSERVABLES 6th Workshop on Nuclear Fission and Spectroscopy of Neutron-Rich Nuclei | Pierre Tamagno – Olivier Litaize CEA/Cadarache MARCH 20-24, 2017 www.cea.fr www.cea.fr 31 MAI 2017 CEA | 10 AVRIL 2012 | PAGE 1

OUTLINE FIFRELIN calculation scheme Role of the moments of inertia and comparison of models for nuclear moments of inertia Impact of shell-structured MoI on fission observables 31 MAI 2017 6th Workshop on Nuclear Fission and Spectroscopy of Neutron-Rich Nuclei | March 20-24, 2017 | PAGE 2

THE FIFRELIN SIMULATION CODE CEA | 10 AVRIL 2012 | PAGE 3 31 MAI 2017

THE FIFRELIN CODE (OUTLINE) Purpose “FIssion Fragment Evaporation Leading to an Investigation of Nuclear data” Provide information on various fission observables as detailed as possible Method Semi-classical simulation of fission decay events by Monte-Carlo sampling of transitions (Hauser-Feshbach) Advantage : many observables, correlation between them Disadvantage : time-consuming for parametric studies Ingredients Phenomenological / Microscopic “sub-"models (level density, strength functions, etc.) Experimental data (fragmentations sampling) Nuclear structure databases (RIPL3) 31 MAI 2017 6th Workshop on Nuclear Fission and Spectroscopy of Neutron-Rich Nuclei | March 20-24, 2017 | PAGE 4

THE FIFRELIN SIMULATION SCHEME* (OVERVIEW) * O. Litaize and O. Serot, Phys Rev C 82 (2010) Select a fissioning isotope Z fiss , A fiss , with excitation energy E* 1. Sample fragments masses and kinetics energies from experimental data 2. � A L , A H KE(A) Y(A) � TKE L , TKE H Sample fragments charges (Gaussian distribution) 3. 2 ( ) Z − Z p 1 − P ( Z ) = c π e c � Z L , Z H Sample fragments angular moments according to a Rayleigh distributions 4. − ( J + 1 / 2) 2 P ( J ) = J + 1 / 2 2 σ 2 e σ 2 1/2 parity sampling � J L , J H , π L , π H Rotational energy E rot L + E rot H is removed from available energy Q and remaining 5. intrinsic energy is distributed according a to temperature-ratio law � (A L ,Z L ) J L, π L , E L * � (A H ,Z H ) J H, π H , E H * | PAGE 5

THE FIFRELIN CODE (CASCADE DECAY) Starting from fragment (A,Z) in state E*,J, π 1. Sampling levels in unknown (continuum) region from level density ρ ( Ε * , J , π ) 2. Experimental levels Additional levels dE dE (from level density sampling) gs A-1 3. Calculating transition width for γ -emission ( γ -strength function) and neutron emission (Optical Model) + level density (again) XL ( E i − E j ) XL ( E i − E j ) 2 L +1 S γ gs y 2 Γ γ i → j = P A 3. ρ ( E i , J i , π i ) X,L Sample transition, scoring, resuming step 1 until GS is reached 4. | PAGE 6 6th Workshop on Nuclear Fission and Spectroscopy of Neutron-Rich Nuclei | March 20-24, 2017

ROLE OF THE MOMENTS OF INERTIA CEA | 10 AVRIL 2012 | PAGE 7 31 MAI 2017

ROLE OF MOMENTS OF INERTIA IN MODEL INITIAL PARAMETERS FIFRELIN adjusted parameters: R T min R T max (temperature law) − ( J + 1 / 2) 2 σ L , σ H Spin cutoff used for sampling initial spin states P ( J ) = J + 1 / 2 2 σ 2 e (identical for all fragmentations) σ 2 k (ratio of moment of inertia to rigid body value) E rot = J ( J + 1) 2 kI rigid r a U σ 2 = I rigid I is not involved only in rotation energy � spherical a ˜ a « However, observations from microscopic level density studies show that the quantity σ 2 /t is not constant, but exhibits marked shell effects similar to the level density parameter a. » (RIPL3, Capote et al. Nuclear Data Sheets (2009) ) Replacing I in spin cutoff expressions must be done with care (don’t double-count � shell effect) 31 MAI 2017 6th Workshop on Nuclear Fission and Spectroscopy of Neutron-Rich Nuclei | March 20-24, 2017 | PAGE 8

Moment of Inertia 2 I/ ¯ h 100 200 300 0 *Moller et al., Atomic Data and Nuclear Data Tables, 59 (1995) Ti-42 Ti-48 Fe-60 Ni-56 Cranking (Inglis-Belyaev) model using FRDM* microscopic model Irrotational flow Rigid body Ni-58 Ni-62 I crank Zn-62 I irrot I rigid Exp Zn-68 Zn-70 Ge-70 Se-74 Sr-88 INERTIA CLASSICAL AND SEMI-CLASSICAL MOMENTS OF Zr-92 Mo-92 Mo-96 Ru-96 Cd-106 Cd-110 Cd-112 I rigid = 2 Sn-116 Sn-122 Te-110 Te-120 Te-122 Te-124 I irrot = 9 Te-128 Xe-120 6th Workshop on Nuclear Fission and Spectroscopy of Neutron-Rich Nuclei | March 20-24, 2017 Xe-122 Xe-124 Xe-126 Xe-134 fragments” “fission Ba-122 Ba-124 Ba-126 5 MR 2 (1 + 0 . 31 β 2 + 0 . 44 β 2 Ba-128 Quasi-particle energy and level occupations from BCS equations Ba-130 Ba-134 Ba-136 Ce-126 8 π AMR 2 β 2 Ce-128 Ce-130 Ce-132 Ce-140 Ce-142 Ce-152 Nd-134 Nd-142 Single-particle wave-functions from FRDM Nd-144 Nd-152 Nd-154 Nd-156 Sm-142 Sm-154 Sm-156 Gd-154 Gd-156 Gd-158 Gd-160 2 Gd-164 Dy-156 Dy-158 Dy-160 Dy-162 Dy-164 Dy-166 Er-162 Er-164 Er-166 Er-168 Er-170 Yb-164 Yb-166 Yb-168 Yb-170 rare-earths Yb-172 Yb-174 Yb-176 Yb-178 Hf-170 Hf-172 Hf-174 Hf-176 2 + ... ) Hf-178 Hf-180 Hf-182 W-176 W-178 W-180 W-182 W-184 I irrot ⌧ I rigid W-186 Th-224 Th-226 Th-228 Th-230 Th-232 Th-234 U-230 actinides U-232 U-234 U-236 U-238 U-240 Pu-236 | PAGE 9 Pu-238 Pu-240 Pu-242 Pu-244 Pu-246 Cm-242 Cm-244 Cm-246 Cm-248 Cf-248 Cf-250 Cf-252 Fm-254

IMPACT ON FISSION OBSERVABLES Only rotational energy modified, Cranking used with k=2, Application to 252 Cf(sf) CEA | 10 AVRIL 2012 | PAGE 10 31 MAI 2017

SAW TOOTH 31 MAI 2017 6th Workshop on Nuclear Fission and Spectroscopy of Neutron-Rich Nuclei | March 20-24, 2017 | PAGE 11

AVERAGE NEUTRON ENERGY IN CM 31 MAI 2017 6th Workshop on Nuclear Fission and Spectroscopy of Neutron-Rich Nuclei | March 20-24, 2017 | PAGE 12

AVERAGE NEUTRON ENERGY IN CM rigid cranking rigid Stronger Z -dependency in the A =120-140 and A=85-95 regions for the cranking than the rigid body cranking 31 MAI 2017 CEA | 10 AVRIL 2012 | PAGE 13

GAMMA SPECTRUM (1/2) 31 MAI 2017 CEA | 10 AVRIL 2012 | PAGE 14

GAMMA SPECTRUM (2/2) 31 MAI 2017 CEA | 10 AVRIL 2012 | PAGE 15

CONCLUSIONS The moment of inertia is involved in many aspect in de-excitation models. The shell structure bared by the cranking-based moments of inertia can significantly impact fission observables. Effect on spin cutoffs must be investigated with care as remaining parameters used in systematics have been obtained with rigid-body models. 6th Workshop on Nuclear Fission and Spectroscopy of Neutron-Rich Nuclei | March 20-24, 2017 | PAGE 16

I rigid = 2 5 MR 2 (1 + 0 . 31 β 2 + 0 . 44 β 2 2 + ... ) Thank you for your attention Commissariat à l’énergie atomique et aux énergies alternatives DEN Centre de Saclay | 91191 Gif-sur-Yvette Cedex DER T. +33 (0)1 XX XX XX XX | F. +33 (0)1 XX XX XX XX SPRC Etablissement public à caractère industriel et commercial | RCS Paris B 775 685 019