Nucleon scattering on major actinides using a dispersive

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Nucleon scattering on major actinides using a dispersive optical model with extended couplings R.

Nucleon scattering on major actinides using a dispersive optical model with extended couplings R. Capote (IAEA/NDS, Vienna), E. Soukhovitskii (JINER, Minsk), J. M. Quesada (Univ. Sevilla), and S. Chiba (Tokyo IT) 14 th INTERNATIONAL CONFERENCE ON NUCLEAR REACTION MECHANISMS 1 14 th Int. Conference on Nuclear Reaction Mechanisms Varenna, Italy, 15 -19 June 2015 Roberto Capote, IAEA Nuclear Data Section e-mail: r. [email protected] org Web: www-nds. iaea. org

Motivation Data q High accuracy requirements were placed on inelastic crosssections 238 U(n, inl)

Motivation Data q High accuracy requirements were placed on inelastic crosssections 238 U(n, inl) in the whole energy range up to 20 Me. V (OECD/NEA WPEC Subgroup 26, NEA, 2008 ). q Changes in PFNS may lead to changes in evaluated inelastic cross sections which are discrepant (cf. INDC(NDS)-0597 (2012)) Physics q Better nuclear structure should be used in reaction calculations for heavy nuclei (beyond rigid-rotor and vibrational models) q Extended multi-band coupling needed with “consistent” coupling (i. e. able to reproduce OM observables for a given CC scheme) 2 14 th Int. Conference on Nuclear Reaction Mechanisms Varenna, Italy, 15 -19 June 2015 Roberto Capote, IAEA Nuclear Data Section e-mail: r. [email protected] org Web: www-nds. iaea. org

Dispersive OMPs SPHERICAL MAGIC NUCLEI, Ca-40, Ca-48, Zr-90, Pb-208, … • R. Lipperheide. Z.

Dispersive OMPs SPHERICAL MAGIC NUCLEI, Ca-40, Ca-48, Zr-90, Pb-208, … • R. Lipperheide. Z. Phys. 202, 58 (1967); G. Passatore, Nucl. Phys. A 95 (1967) 694 • R. Lipperheide and A. K. Schmidt, Nucl. Phys. A 112 (1968) 65 • C. Mahaux and co-workers : 1984 -…; W. Tornow et al (TUNL) • A. Molina, R. C. , et al, PRC 65 (2002) 034616; R. Charity et al, PRC 76 (07) 044314 DEFORMED NUCLEI (Coupled channels, scattering E>0) • A. C. Merchant, P. E. Hodgson and H. R. Schelin. Nucl. Sc. Eng. 111 (1992) 132 • P. Romain and J. P. Delaroche. Proceedings of the Meeting on Nucleon-Nucleus Optical Model up to 200 Me. V, Bruyères-le-Châtel, p. 167 (OECD, Paris, 1997) • A. B. Smith. Ann. Nucl. Energy 28 (2001); 29 (2002); 31 (2004) • E. Soukhovitskii et al, PRC 72 (2005) 024604 ; • R. C. et al, PRC 72 (2005) 064610; J. M. Quesada et al, PRC 76 (2007) 057602 ; • R. C. et al, JNST 45 (2008) 333– 340; • R. C. et al, “RIPL …”, Nucl. Data Sheets 110 (2009) 3107– 3214; • Weili Sun, E. Soukhovitskii, R. C. et al, AIP Conf. Proc. 1235 (2010) 43 -49; • Rui Li et al, PRC 87 (2013) 054611; • J. M. Quesada et al, Nucl. Data Sheets 118 (2014) 270– 272 3 14 th Int. Conference on Nuclear Reaction Mechanisms Varenna, Italy, 15 -19 June 2015 Roberto Capote, IAEA Nuclear Data Section e-mail: r. [email protected] org Web: www-nds. iaea. org

Lane consistent nucleon dispersive OMP Coupling models: Rigid rotor, soft rotor, vibro-rotational model Coupled:

Lane consistent nucleon dispersive OMP Coupling models: Rigid rotor, soft rotor, vibro-rotational model Coupled: levels of the ground state band/excited bands 4 14 th Int. Conference on Nuclear Reaction Mechanisms Varenna, Italy, 15 -19 June 2015 Roberto Capote, IAEA Nuclear Data Section e-mail: r. [email protected] org Web: www-nds. iaea. org

Expanded coupling scheme Vibrational-rotational model (even-even nuclides) D. W. Chan et al, PRC 26

Expanded coupling scheme Vibrational-rotational model (even-even nuclides) D. W. Chan et al, PRC 26 (1982) 841; PRC 26 (1982) 861. E. Sheldon. L. E. Beghian, D. W. Chan et al, J. Phys. G: Nucl. Phys. 12, 443 (1986). T. Kawano, N. Fujikawa and Y. Kanda, INDC(JPN)-169 (1993) JENDL-3. 2 Soft (non-axial) rotor (even-even nuclides) Yu. V. Porodzinkij and E. Soukhovitskii, Phys. At. Nuclei 59 (1996) 228 -237 V. M. Maslov et al. , J. Nucl. Sc. Tech. Supl. 2 (2002) 148 -151 CHALLENGE: Derive a dispersive coupled channel potential (Lane consistent) with multiple-band coupling scheme valid for even-even and odd actinides 5 14 th Int. Conference on Nuclear Reaction Mechanisms Varenna, Italy, 15 -19 June 2015 Roberto Capote, IAEA Nuclear Data Section e-mail: r. [email protected] org Web: www-nds. iaea. org

Nuclear shape parameterization Small param. Rigid rotor + dynamical corrections A. Bohr, Mat. Fys.

Nuclear shape parameterization Small param. Rigid rotor + dynamical corrections A. Bohr, Mat. Fys. Medd. Dan. Vid. Selsk. 26, No. 14 (1952): Body-fixed frame aligned with principal axes: b 2, 1=b 2, -1=0; b 2, 2=b 2, -2 => b, g P. O. Lipas and J. P. Davidson, Nucl. Phys. 26, 80 -90 (1961): Octupolar vibrations with even projection better describe low-lying negative parity states b 3, 1=b 3, -1=b 3, 3=b 3, -3=0 => l=3 ; m=0, ± 2 6 14 th Int. Conference on Nuclear Reaction Mechanisms Varenna, Italy, 15 -19 June 2015 Roberto Capote, IAEA Nuclear Data Section e-mail: r. [email protected] org Web: www-nds. iaea. org

Optical model potential 7 14 th Int. Conference on Nuclear Reaction Mechanisms Varenna, Italy,

Optical model potential 7 14 th Int. Conference on Nuclear Reaction Mechanisms Varenna, Italy, 15 -19 June 2015 Roberto Capote, IAEA Nuclear Data Section e-mail: r. [email protected] org Web: www-nds. iaea. org

Even-Even Nucleus DK=m Selection rules: Dnl =0, ± 1 : vibrational rule Intraband transitions:

Even-Even Nucleus DK=m Selection rules: Dnl =0, ± 1 : vibrational rule Intraband transitions: Quadrupolar-GS: Octupolar-GS: 8 14 th Int. Conference on Nuclear Reaction Mechanisms Varenna, Italy, 15 -19 June 2015 Roberto Capote, IAEA Nuclear Data Section e-mail: r. [email protected] org Web: www-nds. iaea. org . . .

Nuclear shape parameterization . . . DK=m Intraband transitions: Interband-transitions: 9 14 th Int.

Nuclear shape parameterization . . . DK=m Intraband transitions: Interband-transitions: 9 14 th Int. Conference on Nuclear Reaction Mechanisms Varenna, Italy, 15 -19 June 2015 Roberto Capote, IAEA Nuclear Data Section e-mail: r. [email protected] org Web: www-nds. iaea. org

235 U Kp=7/2 - Ground state rigid rotor 10 (not coupled bands) Kp=1/2+ DK=3,

235 U Kp=7/2 - Ground state rigid rotor 10 (not coupled bands) Kp=1/2+ DK=3, pp’=-1 <b 33>=0 isomer 14 th Int. Conference on Nuclear Reaction Mechanisms Varenna, Italy, 15 -19 June 2015 Kp=5/2+ DK=1, pp’=-1 <b 31> =0 Kp=5/2+ DK=1, pp’=-1 <b 31>=0 Roberto Capote, IAEA Nuclear Data Section e-mail: r. [email protected] org Web: www-nds. iaea. org

235 U Kp=7/2 - (Coupled bands) Kp=3/2+ Kp=7/2+ Kp=3/2 - Ground state rigid rotor

235 U Kp=7/2 - (Coupled bands) Kp=3/2+ Kp=7/2+ Kp=3/2 - Ground state rigid rotor 11 DK=2, pp’=-1 < b 32> non-axial 14 th Int. Conference on Nuclear Reaction Mechanisms Varenna, Italy, 15 -19 June 2015 DK=0, pp’=-1 < b 30> axial DK=2, pp’=+1 < b 22> non-axial Roberto Capote, IAEA Nuclear Data Section e-mail: r. [email protected] org Web: www-nds. iaea. org

239 Pu GS, Kp=1/2+ 12 (coupling scheme) DK=2, pp’=+1 < b 22> non-axial 14

239 Pu GS, Kp=1/2+ 12 (coupling scheme) DK=2, pp’=+1 < b 22> non-axial 14 th Int. Conference on Nuclear Reaction Mechanisms Varenna, Italy, 15 -19 June 2015 DK=3, pp’=-1 DK=0, pp’=-1 < b 33> = 0 < b 30> axial Roberto Capote, IAEA Nuclear Data Section e-mail: r. [email protected] org Web: www-nds. iaea. org

DCC OMP LSQ fit for all “optical“ observables (n, n); (p, p); (p, n)

DCC OMP LSQ fit for all “optical“ observables (n, n); (p, p); (p, n) RIPL 2408 OMP: rigid rotor R. C. , S. Chiba, E. Sh. Soukhovitskii, J. M. Quesada, E. Bauge, Jnst 45 (2008) 333– 340 13 14 th Int. Conference on Nuclear Reaction Mechanisms Varenna, Italy, 15 -19 June 2015 Roberto Capote, IAEA Nuclear Data Section e-mail: r. [email protected] org Web: www-nds. iaea. org

New DCC OMP parameterization 14 14 th Int. Conference on Nuclear Reaction Mechanisms Varenna,

New DCC OMP parameterization 14 14 th Int. Conference on Nuclear Reaction Mechanisms Varenna, Italy, 15 -19 June 2015 Roberto Capote, IAEA Nuclear Data Section e-mail: r. [email protected] org Web: www-nds. iaea. org

15 14 th Int. Conference on Nuclear Reaction Mechanisms Varenna, Italy, 15 -19 June

15 14 th Int. Conference on Nuclear Reaction Mechanisms Varenna, Italy, 15 -19 June 2015 Roberto Capote, IAEA Nuclear Data Section e-mail: r. [email protected] org Web: www-nds. iaea. org

Total cross section differences 16 14 th Int. Conference on Nuclear Reaction Mechanisms Varenna,

Total cross section differences 16 14 th Int. Conference on Nuclear Reaction Mechanisms Varenna, Italy, 15 -19 June 2015 Roberto Capote, IAEA Nuclear Data Section e-mail: r. [email protected] org Web: www-nds. iaea. org

17 14 th Int. Conference on Nuclear Reaction Mechanisms Varenna, Italy, 15 -19 June

17 14 th Int. Conference on Nuclear Reaction Mechanisms Varenna, Italy, 15 -19 June 2015 Roberto Capote, IAEA Nuclear Data Section e-mail: r. [email protected] org Web: www-nds. iaea. org

CONCLUSIONS q New DCC OMP with multiple-band coupling derived for nucleon scattering on actinides:

CONCLUSIONS q New DCC OMP with multiple-band coupling derived for nucleon scattering on actinides: 233, 235, 238 U, 239 Pu, and 232 Th q OMP highlights: ü Based on dispersive relations and Lane consistent. ü Least-squares fit of a regional set of OMP parameters from (n, n), (p, p) & (p, n) IAS. ü CC couplings based on rigid rotor with dynamical corrections with derived selection rules for rotational bands built on vibrational (even-even) or single-particle bandheads (odd nuclei). ü Energy independent geometry. ü Ground state deformations close to those predicted by Nix and Moller (FRDM) 18 14 th Int. Conference on Nuclear Reaction Mechanisms Varenna, Italy, 15 -19 June 2015 Roberto Capote, IAEA Nuclear Data Section e-mail: r. [email protected] org Web: www-nds. iaea. org