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

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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

SLIDE 1

www.cea.fr www.cea.fr

IMPACT OF NUCLEAR MOMENTS OF INERTIA ON FISSION OBSERVABLES

MARCH 20-24, 2017

6th Workshop on Nuclear Fission and Spectroscopy

f Neutron-Rich Nuclei

| Pierre Tamagno – Olivier Litaize CEA/Cadarache

31 MAI 2017 | PAGE 1 CEA | 10 AVRIL 2012

SLIDE 2

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 | PAGE 2 6th Workshop on Nuclear Fission and Spectroscopy of Neutron-Rich Nuclei | March 20-24, 2017

SLIDE 3

THE FIFRELIN SIMULATION CODE

31 MAI 2017 | PAGE 3 CEA | 10 AVRIL 2012

SLIDE 4

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 | PAGE 4 6th Workshop on Nuclear Fission and Spectroscopy of Neutron-Rich Nuclei | March 20-24, 2017

SLIDE 5

1. Select a fissioning isotope Zfiss, Afiss, with excitation energy E*

2. Sample fragments masses and kinetics energies from experimental data

3. Sample fragments charges (Gaussian distribution)

4. Sample fragments angular moments according to a Rayleigh distributions 1/2 parity sampling

5. Rotational energy Erot

L + Erot H is removed from available energy Q and remaining

intrinsic energy is distributed according a to temperature-ratio law

| PAGE 5

THE FIFRELIN SIMULATION SCHEME* (OVERVIEW)

* O. Litaize and O. Serot, Phys Rev C 82 (2010)

P(Z) = 1 cπ e

− Z −Z p

( )

ZL, ZH

P(J) = J + 1/2 σ2 e

−(J + 1/2)2

2σ2

JL, JH, πL, πH Y(A) KE(A) AL, AH TKEL, TKEH (AL,ZL) JL, πL, EL* (AH,ZH) JH, πH, EH*

SLIDE 6

1. Starting from fragment (A,Z) in state E*,J,π

2. Sampling levels in unknown (continuum) region from level density ρ(Ε*,J,π)

3. Calculating transition width for γ-emission (γ-strength function)

and neutron emission (Optical Model) + level density (again) 3. 4.

Sample transition, scoring, resuming step 1 until GS is reached

| PAGE 6

Experimental levels Additional levels (from level density sampling)

dE

A

gs

THE FIFRELIN CODE (CASCADE DECAY)

dE

A-1

gs

Γγi→j = P

X,L

y2

XL(Ei − Ej)2L+1 Sγ XL(Ei − Ej)

ρ(Ei, Ji, πi)

6th Workshop on Nuclear Fission and Spectroscopy of Neutron-Rich Nuclei | March 20-24, 2017

SLIDE 7

ROLE OF THE MOMENTS OF INERTIA

31 MAI 2017 | PAGE 7 CEA | 10 AVRIL 2012

SLIDE 8

ROLE OF MOMENTS OF INERTIA IN MODEL INITIAL PARAMETERS

31 MAI 2017 | PAGE 8

FIFRELIN adjusted parameters: RT

min RT max (temperature law)

σL, σH Spin cutoff used for sampling initial spin states (identical for all fragmentations) k (ratio of moment of inertia to rigid body value)

I is not involved only in rotation energy

« However, observations from microscopic level density studies show that the quantity σ2/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)

Erot = J(J + 1) 2kIrigid

P(J) = J + 1/2 σ2 e

−(J + 1/2)2

2σ2

σ2 = Irigid

spherical

a ˜ a r U a

6th Workshop on Nuclear Fission and Spectroscopy of Neutron-Rich Nuclei | March 20-24, 2017

SLIDE 9

CLASSICAL AND SEMI-CLASSICAL MOMENTS OF INERTIA

Rigid body Irrotational flow Cranking (Inglis-Belyaev) model using FRDM* microscopic model *Moller et al., Atomic Data and Nuclear Data Tables, 59 (1995)

| PAGE 9

Irigid = 2 5MR2(1 + 0.31β2 + 0.44β2

2 + ...)

Iirrot = 9 8π AMR2β2

2

Iirrot ⌧ Irigid

Ti-42 Ti-48 Fe-60 Ni-56 Ni-58 Ni-62 Zn-62 Zn-68 Zn-70 Ge-70 Se-74 Sr-88 Zr-92 Mo-92 Mo-96 Ru-96 Cd-106 Cd-110 Cd-112 Sn-116 Sn-122 Te-110 Te-120 Te-122 Te-124 Te-128 Xe-120 Xe-122 Xe-124 Xe-126 Xe-134 Ba-122 Ba-124 Ba-126 Ba-128 Ba-130 Ba-134 Ba-136 Ce-126 Ce-128 Ce-130 Ce-132 Ce-140 Ce-142 Ce-152 Nd-134 Nd-142 Nd-144 Nd-152 Nd-154 Nd-156 Sm-142 Sm-154 Sm-156 Gd-154 Gd-156 Gd-158 Gd-160 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 Yb-172 Yb-174 Yb-176 Yb-178 Hf-170 Hf-172 Hf-174 Hf-176 Hf-178 Hf-180 Hf-182 W-176 W-178 W-180 W-182 W-184 W-186 Th-224 Th-226 Th-228 Th-230 Th-232 Th-234 U-230 U-232 U-234 U-236 U-238 U-240 Pu-236 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

100 200 300 Moment of Inertia 2I/¯ h Icrank Irigid Iirrot Exp

Quasi-particle energy and level occupations from BCS equations Single-particle wave-functions from FRDM

actinides rare-earths “fission fragments”

6th Workshop on Nuclear Fission and Spectroscopy of Neutron-Rich Nuclei | March 20-24, 2017

SLIDE 10

IMPACT ON FISSION OBSERVABLES

Only rotational energy modified, Cranking used with k=2, Application to 252Cf(sf)

31 MAI 2017 | PAGE 10 CEA | 10 AVRIL 2012

SLIDE 11

SAW TOOTH

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

SLIDE 12

AVERAGE NEUTRON ENERGY IN CM

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

SLIDE 13

AVERAGE NEUTRON ENERGY IN CM

31 MAI 2017 | PAGE 13 CEA | 10 AVRIL 2012

rigid cranking Stronger Z-dependency in the A=120-140 and A=85-95 regions for the cranking than the rigid body rigid cranking

SLIDE 14

GAMMA SPECTRUM (1/2)

31 MAI 2017 | PAGE 14 CEA | 10 AVRIL 2012

SLIDE 15

GAMMA SPECTRUM (2/2)

31 MAI 2017 | PAGE 15 CEA | 10 AVRIL 2012

SLIDE 16

CONCLUSIONS

| PAGE 16

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

SLIDE 17

DEN DER SPRC

Commissariat à l’énergie atomique et aux énergies alternatives Centre de Saclay | 91191 Gif-sur-Yvette Cedex

T. +33 (0)1 XX XX XX XX | F. +33 (0)1 XX XX XX XX

Etablissement public à caractère industriel et commercial | RCS Paris B 775 685 019

IMPACT OF NUCLEAR MOMENTS OF INERTIA ON FISSION OBSERVABLES

MARCH 20-24, 2017

6th Workshop on Nuclear Fission and Spectroscopy

| Pierre Tamagno – Olivier Litaize CEA/Cadarache

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

THE FIFRELIN SIMULATION CODE

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)

1.

Select a fissioning isotope Zfiss, Afiss, with excitation energy E*

2.

Sample fragments masses and kinetics energies from experimental data

3.

Sample fragments charges (Gaussian distribution)

4.

Sample fragments angular moments according to a Rayleigh distributions 1/2 parity sampling

5.

Rotational energy Erot

intrinsic energy is distributed according a to temperature-ratio law

THE FIFRELIN SIMULATION SCHEME* (OVERVIEW)

P(Z) = 1 cπ e

( )

ZL, ZH

P(J) = J + 1/2 σ2 e

2σ2

JL, JH, πL, πH Y(A) KE(A) AL, AH TKEL, TKEH (AL,ZL) JL, πL, EL* (AH,ZH) JH, πH, EH*

1.

Starting from fragment (A,Z) in state E*,J,π

2.

Sampling levels in unknown (continuum) region from level density ρ(Ε*,J,π)

and neutron emission (Optical Model) + level density (again) 3. 4.

Sample transition, scoring, resuming step 1 until GS is reached

dE

A

gs

THE FIFRELIN CODE (CASCADE DECAY)

dE

A-1

gs

Γγi→j = P

X,L

y2

XL(Ei − Ej)2L+1 Sγ XL(Ei − Ej)

ρ(Ei, Ji, πi)

ROLE OF THE MOMENTS OF INERTIA

ROLE OF MOMENTS OF INERTIA IN MODEL INITIAL PARAMETERS

FIFRELIN adjusted parameters: RT

σL, σH Spin cutoff used for sampling initial spin states (identical for all fragmentations) k (ratio of moment of inertia to rigid body value)

« However, observations from microscopic level density studies show that the quantity σ2/t is not constant, but exhibits marked shell effects similar to the level density parameter a. » (RIPL3, Capote et al. Nuclear Data Sheets (2009) )

shell effect)

Erot = J(J + 1) 2kIrigid

P(J) = J + 1/2 σ2 e

2σ2

σ2 = Irigid

a ˜ a r U a

CLASSICAL AND SEMI-CLASSICAL MOMENTS OF INERTIA

Rigid body Irrotational flow Cranking (Inglis-Belyaev) model using FRDM* microscopic model *Moller et al., Atomic Data and Nuclear Data Tables, 59 (1995)

Irigid = 2 5MR2(1 + 0.31β2 + 0.44β2

2 + ...)

Iirrot = 9 8π AMR2β2

2

Iirrot ⌧ Irigid

Quasi-particle energy and level occupations from BCS equations Single-particle wave-functions from FRDM

actinides rare-earths “fission fragments”

IMPACT ON FISSION OBSERVABLES

Only rotational energy modified, Cranking used with k=2, Application to 252Cf(sf)

SAW TOOTH

AVERAGE NEUTRON ENERGY IN CM

AVERAGE NEUTRON ENERGY IN CM

rigid cranking Stronger Z-dependency in the A=120-140 and A=85-95 regions for the cranking than the rigid body rigid cranking

GAMMA SPECTRUM (1/2)

GAMMA SPECTRUM (2/2)

CONCLUSIONS

Irigid = 2 5MR2(1 + 0.31β2 + 0.44β2

2 + ...)

Thank you for your attention