Connecting structure and direct reaction modeling

Transcription

1 Connecting structure and direct reaction modeling M. Dupuis, CEA, DAM, DIF, France Perspective on Nuclear Data for the Next Decade /1/214, CEA-TGCC. Collaborators E. Bauge, G. Blanchon, J.-P. Delaroche, G. Haouat, S. Hilaire, F. Lechaftois, S. Péru, N. Pillet, C. Robin, P. Romain, CEA, DAM, DIF, France. T. Kawano, LANL, New Mexico, USA. J. Raynal, CEA Saclay, France. M. Kerveno, P. Dessagne, IPHC, Strasbourg, France. R. Capote, IAEA, Vienna, Austria H. Arellano, University of Chile, Santiago, Chile.

2

3 Nuclear reactions modeling 62 MeV 56 Fe (p,xp) Double differential cross sections

4 Nuclear reactions modeling 62 MeV 56 Fe (p,xp) Double differential cross sections

5 Direct inelastic scattering modeling : phenomenological approach High energy emission : P. Demetriou et al., Nucl. Phys. A 596, 67 (1996) Low energy discrete states excitations : cross sections determined from available measurements (deformation lengths, collective model). Giant resonances : cross sections calculation based on the knowledge of response functions in the continuum which are usually extracted from (e,e ), (h,h ), (h,h f) measurements or from systematics. Pre-equilibrium emission. Depending on the nucleus and the incident energy, the experimental information is not complete and sometimes very scarce: collective response functions for L > 3 and in deformed targets such as actinides.

6 Microscopic model for direct inelastic scattering : spherical targets Nuclear structure model : Random ( Phase Approximation ) ((Q)RPA), D1S interaction Target excitations N = Xpha N pa h Ypha N h a p. ph DWBA calculations : dσ χ dω ( ),N V eff, χ + 2 Optical potentials : U = V eff Transition potentials : U tr = N V eff Folding model with V eff JLM interaction from E. Bauge, J. P. Delaroche, and M. Girod, Phys. Rev. C63, 2467 (21). Haouat (198) JLM RPA Pb(n,n ) 3-1 E= MeV JLM RPA Haouat (198) Kinney (1974) Bainum (1977) Belovikij 13.7 MeV (1972) 1 6 Haouat (198) JLM QRPA Hicks (1994) Cranberg set 1 (1966) Cranberg set 2 (1966) 26 Pb (n,n ), MeV MeV MeV 11.5 dσ/d (mb/str) dσ/d (mb/str) dσ/d (mb/str) 9.5 MeV MeV 28 Pb(n,n ) E= MeV MeV θ c.m. (deg) θ c.m. (deg) θ c.m. (deg)

7 JLM model validation : Rearrangement Transition potential Optical potential: U =V.ρ, ρ = ρ IS = ρ p + ρ n. du Transition potential: U tr = β L dr = du dρ β L dρ dr. Transition density identified to: ρl tr(r)=β L dρ dr. KD : collective model with Koning Delaroche potential (β 3 =.12) MeV 28 Pb(n,n ) 3-1 Central Real JLM Rear 2 JLM Rear 1 JLM Rear KD Rearrangement (Cheon): If V V(ρ) dv(ρ)ρ dρ =V(ρ)+ρ dv(ρ) dρ. Regular term: U tr =V(ρ)ρL tr(r) Rearrangment term: U R tr = ρ dv(ρ) dρ ρ tr L (r) See T. Cheon etal., Nucl. Phys. A437, 31 (1985) : done in (p,p ) 16 O (N=Z). New rearrangement: If V V(ρ p,ρ n ) V(ρ IS,ρ IV ), ρ IV = ρ n ρ p. Regular term: U tr =V(ρ)ρ tr,,is L (r). Rearrangment term 1 (IS): Utr R1 dv = ρ IS Rearrangment term 2 (IV): U R2 tr = ρ IS dv dρ ρ tr,is IS L (r). dρ ρ tr,iv IV L (r). U(r) U(r) r (fm) 25.7 MeV 28 Pb(n,n ) 3-1 Central Imaginary JLM Rear 2 JLM Rear 1 JLM Rear KD r (fm)

8 JLM model validation : Rearrangement Comparison JLM - Collective model Impact of rearrangement : (n,n ) Impact of rearrangement : (p,p ) Pb(n,n ) 3-1 E= MeV 7.5 JLM KD Haouat (198) Kinney (1974) Bainum (1977) Belovikij 13.7 MeV (1972) Pb(n,n ) 3-1 E= MeV 7.5 JLM Rear 2 JLM Rear 1 JLM Rear Haouat (198) Kinney (1974) Bainum (1977) Belovikij 13.7 MeV (1972) Pb (p,p ) 3-1 E= MeV Wagner JLM/RPA rear 2 JLM/RPA rear 1 JLM/RPA rear Stovall (1964) Lewis Scott Kailas (1987) Adams dσ/d (mb/str) dσ/d (mb/str) dσ/d (mb/str) θ c.m. (deg) θ c.m. (deg) θ c.m. (deg)

9 Pre-equilibrium reaction mechanism Doubly differential (n,n ) or (p,p ) cross sections: Transition amplitude (Born Series) : dσ(k i,k f ) de k dω f de f ( ) E ki E k E N Tfi 2 N T fi = χ ( ) 1 f (k),n V eff +V eff E H +iε V 1 eff +V eff E H +iε V 1 eff E H +iε V eff + χ (+) i (k i ), f ( E ki E k E N ) : spreading functions (damping+escape widths).

10 Pre-equilibrium reaction mechanism Doubly differential cross section (n,n )/(p,p ) Usually at E<2 MeV : reduced to one-step direct process sum of DWBA cross sections. dσ(k i,k f ) de dedω f f ( ) (+) E ki E k E phn χ f (k),n V eff χ ( ) i (k i ), 2 N

11 Microscopic model for direct inelastic scattering off axially deformed targets Calculation with p-h excitations : Interaction fit to match (n,xn) data. underestimates high energy emission [T. Kawano et al., Phys.Rev. C63, 3461 (21)]. Collective (vibrations) states in actinides (low energy and giant resonances) : not well characterized in experiments, usually not included in reactions modeling. Temporary solution used in evaluations : pseudo states = collective states with properties (energy and deformation length) adjusted to fit the observed high energy neutron emission (used in ENDF-BVII, BRC). 238 U (n,xn) Baba (1989) GS rot. band Fis. frag. evap. CN evap. Direct pre-eq. E i =14.1 MeV θ c.m. =6 o QRPA model that describes collective excitations in axially deformed nuclei has been recently develloped in Bruyres and used to describe the excitations spectra in actinides : S.Peru, G.Gosselin, M.Martini, M.Dupuis, S.Hilaire, J.-C.Devaux, Phys.Rev.C 83, (211).

12 Excitation spectrum of a nucleus with a static axial deformation QRPA method : axial deformation, projection K of the total angular momentum on the symmetry axis is a good quantum number, parity is conserved. Target excitations in the intrinsic frame : one phonon excitations. αkπ =Θ + αkπ I = 1 ( 2 ij (KΠ) X αkπ ij η + ip i Ω i η + jp j Ω j ( ) K Y αkπ ij η ipi Ω i η jpj Ω j ) I Target states in the laboratory frame : projection on total angular momentum rotational band for each intrinsic excitation, with angular momenta J K αjmkπ = 2J+1 16π 2 dωdmk J (Ω)R(Ω) αkπ +( ) J+K DM K J (Ω)R(Ω) αkπ

13 Direct inelastic scattering cross section for axially deformed targets Doubly differential cross section : dσ(k i,k f ) dedω f de f ( ) dσ N (k i,k) E ki E k E N N dω Sum over target excitations : = N K Π J K K Π intrinsic excitations, J K rotational band states, dσ N (k i,k) For one excitation : dω need coupling potential U L (r)= V L (r,r )ρ QRPA L (r )r 2 dr (JLM folding model). ρ L (r) : multipole of order L of the QRPA radial transition density between the GS and an intrinsic excitation.

14 QRPA response functions in 238 U Reduce transition probabilities (proton+neutron) B(EJ) ρ I,αKΠ J (r)r J+2 dr 2 (L>2) : provide a measure of excitations collectivity (cross sections magnitude approximately proportional to B(EJ)) QRPA Θ B(E2) (1 4.fm 4 ) J Π =2 + J Π =3 J Π =4 + QRPA (D1S) K = + K =1 + K =2 + B(E3) (1 6.fm 6 ) QRPA (D1S) K = - K =1 - K =2 - K =3 - B(E4) (1 8.fm 8 ) QRPA (D1S) K = + K =1 + K =2 + K =3 + K = E x (MeV) E x (MeV) E x (MeV) 2 quasi-particles : η η HFB B(E2) (1 4.fm 4 ) qp (D1S) K = + K =1 + K =2 + B(E3) (1 6.fm 6 ) qp (D1S) K = - K =1 - K =2 - K =3 - B(E4) (1 8.fm 8 ) qp (D1S) K = + K =1 + K =2 + K =3 + K = E x (MeV) E x (MeV) E x (MeV) Large number of collective excitations at low energy

15 Analysis of MeV (n,xn) 238 U spectra 11.8 MeV 238 θ c.m. =3 o U(n,xn) θ =3 θ =6 θ =12 Miura (1999) Miura (1999) Miura (1999) GS band GS band GS band Fission CN Direct 11.8 MeV 238 θ c.m. =6 o U(n,xn) Fission CN Direct 11.8 MeV 238 θ c.m. =12 o U(n,xn) Fission CN Direct 11.8 MeV Baba (1989) GS band 14.1 MeV 238 θ c.m. =3 o U(n,xn) Fission CN Direct MeV 238 θ c.m. =6 o U(n,xn) Baba (1989) GS band Fission CN Direct Baba (1989) GS band 14.1 MeV 238 θ c.m. =12 o U(n,xn) Fission CN Direct 14.1 MeV MeV 238 θ c.m. =3 o U(n,xn) Baba (1989) GS band Fission CN Direct 18 MeV 238 θ c.m. =6 o U(n,xn) Baba (1989) GS band Fission CN Direct 18 MeV 238 θ c.m. =12 o U(n,xn) Baba (1989) GS band Fission CN Direct 18. MeV

16 Comparison to previous more phenomenological calculations Kawano one-step direct : 14.1 MeV 238 θ c.m. =6 o U(n,xn) Baba (1989) GS band Fission CN MSC Direct Microscopic model with QRPA : 14.1 MeV 238 θ c.m. =6 o U(n,xn) Baba (1989) GS band Fission CN Direct MeV 238 θ c.m. =12 o U(n,xn) Baba (1989) GS band Fission CN MSC Direct MeV 238 θ c.m. =12 o U(n,xn) Baba (1989) GS band Fission CN Direct High energy cross section (E f >1 MeV): rather good. Clearly underestimated at E f 6-1 MeV = TUL calculations in EMPIRE: fit the (n,xn) data well. = What is missing?

17 Non-natural parity excitations d 2 σ/d de (mb/mev/sr) 14.1 MeV 28 Pb (n,xn) θ c.m. = 6 o n.n.p J 6 8 MeV 28 Pb (p,p ) to n.n.p. (DWBA Melbourne g-matrix) E out (MeV) Contribution of non-natural partity (n.n.p.) excitations (π =( ) L+1 ): up to 2% of the emission cross section. Transition not-possible within the JLM convolution model ( S =1). Adjust a new interaction for folding models with missing terms (start from gmatrix or effective interaction from Nuclear Structure approach). Low cost-short term solution : level densities folded with averaged cross-sections.

18 Two-step process to two-phonons states Two-steps process Second order transition amplitude to two-bosons states: T fi =T (1) fi + χ ( ) f (k),n 1,N 2 V eff 1 E H +iε V eff χ (+) i (k i ), N 1,N 2 =Θ + N 1 Θ + N 2 : two bosons state. Two-step: already included in TUL-EMPIRE model = need to carefully compare the components of the two models

19 Perspective : two-step process d 2 σ/d de (mb/mev/sr) 14.1 MeV 28 Pb (n,xn) Elastic Evaporation One Step Direct θ c.m. = 6 o 14.1 MeV 238 U (n,xn) Baba (1989) 14.1 MeV 238 θ c.m. =6 o U(n,xn) GS band Fission CN Direct E out (MeV) Level Density (MeV -1 ) Pb One phonon Two phonons Excitation energy (MeV) Level Density (MeV -1 ) U One phonon Two phonons Excitation energy (MeV)

20 (n,xnγ) cross sections Impact new direc inelastic xs on (n,n γ) xs.

21 Reaction mechanisms for (n,n γ)

22 Residual nucleus spin distribution in 238 U Direct inelastic scattering 238 U (n,n ) : hypothesis : equilibration to a compound nucleus with excitation energy E, spin-parity J,Π. Spin distribution : Exciton model used in TALYS (for E <2 MeV): R(J)= (2J+1)2 (J )2 2πσ 3 e 2σ σ =.72A Results form QRPA inelastic scattering model : R(J,E in )= σ J(E in ) J σ J (E in ), σ J(E in ) : cross section summed over all states of spin J. Normalized spin distributions (%) Excitons QRPA E in =6 MeV J (h units) Normalized spin distributions (%) Excitons QRPA E in =12 MeV J (h units) Normalized spin distributions (%) Excitons QRPA E in =18 MeV J (h units)

23 238 U (n,n γ) cross sections for transitions in the GS rotational band σ(e) mb σ(e) mb Fiotades (24) Excitons QRPA E γ =13,5 kev E in MeV Fiotades (24) Hutcheson (29) Excitons QRPA E γ =158,8 kev E in MeV Collaborations IPHC (Strasbourg)-CEA/DAM-IFIN : (n,n γ) 238 U et 232 Th. σ(e) mb σ(e) mb Fiotades (24) Hutcheson (29) Bacquias (213) Excitons QRPA E γ =21,9 kev E in MeV E γ =257,8 kev Fiotades (24) Bacquias (213) Excitons QRPA E in MeV

24 Discussion (n,2n) Cross Sections (barn) n,2n ENDF/B-VII BRC σ (mb) Frehaut (198) 238 Frehaut set 2 (198) U (n,2n) Konno (1993) Raics (199) Kornilov (198) Veeser (1978) Filatenkov (199) Karius (1979) Excitons QRPA Cross Sections (barn) Am(n,2n) 24 Am TALYS ENDF/BVII ENDF/BVI.8 JENDL n Pu Neutron Energy (MeV) E (MeV) Neutron Energy (MeV) Exp. data: similar (n,2n) slope for 238 U and 241 Am. Microscopic calculation of direct inelastic scattering: does not change 238 U (n,2n) slope. Perspectives : Same calculation in progress for 239 Pu, but we expect similar results that in 238 U : = could other reaction mecanisms explain the (n,2n) slope in 239 Pu? = New (n,2n) data interpretation in 239 Pu?

25 Light targets : multiparticle-multihole (mpmh) configurations method Nuclear excitations : sum of ph,1p1h, 2p2h... mpmh type excitations on a correlated GS. Nuclear structure observables : first results in limited configurations space (sd-shell) B(E2) [e 2 fm 4 ] 8 Si isotopes Exp. Eq. 1 Eqs A F(q) Full self-consistency Si 2 F C,th 2 F C,th x 2.5 Y. Horikawa (1971) S. W. Brain (1977) G. C. Li (1974) S. Yen (1983) q (fm -1 ) Nucleon induced reactions : DWBA calculations with mpmh wave-functions = complementary test of nuclear sturcture. dσ/d (mb/str) DWBA with Melbourne g-matrix Full self-consistency 65 MeV 28 Si (p,p ), σ th σ th x 2 Kato (1985) θ c.m. (deg) (p,p ) cross-section display the same behavior as for (e,e ). Calculation in larger space (not limited to sd-shell) and a new effective interaction (extended Gogny force : tensor, finite range everywhere) = expected reliable nuclear struture input for direct reaction models for nucleon scattering on light nuclei (ex : 16 O). Mpmh worker : N. Pillet, C. Robin, D. Peña, J. Lebloas Refs.: J. LeBloas et al. Phys.Rev.C 89, 1136 (214), N. Pillet et al. Phys.Rev.C 85, (212), C. Robin : PhD manuscript (214).

26 Conclusions and future work Microscopic models for nucleon inelastic scattering off spherical or axially deformed nuclei One phonon excitations predicted form (Q)RPA calculation (D1S interaction). Observed high energy neutron emission is well reproduced (pour E in <2 MeV). QRPA low energy collective states explain the pseudo states origin. No arbitrary distinction between direct inelastic scattering and pre-equilibrium emission. Improve the description of 238 U (n,n γ) reactions for 238 U. Discrepancy between predictions and data at lower emission energy in 238 U and 232 Th : highlight the needs to introduce other reaction mechanisms such as two-step process. In progress Analysis of (n,xn) and (n,xnγ) to 232 Th, 239 Pu et 241 Am (weak coupling approximation for odd nuclei). 239 Pu (n,2n) cross section extracted from (n,2nγ) data : new analysis with microscopic direct reaction modeling. Comparison of QRPA response functions used in the TUL model and the present model (R. Capote).

27 Future work Non natural parity excitations for axially deformed targets: enlight the need of a better effective interaction at low energy. Fit new effective interaction to low energy from g-matrix, problem of non-locality. Calculation of second order with two phonons excitations. Millions of transition to consider : approximations needed. Use D1S-QRPA response functions in TUL-like model. Fit deformation parameters from collective model analysis, use them in the secon order calculation. Whithin ten years... Coupled channel calculations with QRPA transition densities including interband coupling. Extension of RPA-OMP (G. Blanchon) to direct inelastic scattering. Coupled channel with non-local potentials : mandatory if we want to use fully microscopic potentials. Use of mpmh wave functions for reactions on light nuclei. Introduce progresses in microscopic nuclear reaction models in global nuclear reaction codes (TALYS, EMPIRE...) to improve (step by step) nuclear data evaluation.

28 THANK YOU FOR YOUR ATTENTION Collaborators E. Bauge, G. Blanchon, J.-P. Delaroche, G. Haouat, S. Hilaire, F. Lechaftois, S. Péru, N. Pillet, C. Robin, P. Romain, CEA, DAM, DIF, France. T. Kawano, LANL, New Mexico, USA. J. Raynal, CEA Saclay, France. M. Kerveno, P. Dessagne, IPHC, Strasbourg, France. R. Capote, IAEA, Vienna, Austria H. Arellano, University of Chile, Santiago, Chile.