1 / 39

David J. Dean ORNL

Neutrino detection and nuclear structure research. David J. Dean ORNL. Nothing tends so much to the advancement of knowledge as the application of a new instrument. The native intellectual powers of men in different times are not so much

karah
Télécharger la présentation

David J. Dean ORNL

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Neutrino detection and nuclear structure research David J. Dean ORNL Nothing tends so much to the advancement of knowledge as the application of a new instrument. The native intellectual powers of men in different times are not so much the causes of the different success of their labors, as the peculiar nature of the means and artificial resources in their possession. -- Sir Humphrey Davy • Outline • Overview: general comments • Comments on nuclear structure • Neutrino interactions and the nucleus • Nuclear structure computation and neutrinos • The inverse reaction: electron capture • Conclusions

  2. The landscape and the models 126 82 r-process Large-scale computing protons 50 rp-process 82 28 20 50 Density Functional Theory self-consistent Mean Field 8 28 neutrons 2 20 8 2 A~60 A=12 Ab initio few-body calculations Shell Model Nuclear structure landscapes • Main goals: • Identify/investigate many-body • methods that will extend to RIA • Generate effective interactions • Make reliable predictions • Guide experimental efforts • Pursue interdisciplinary overlaps • (e.g., astro, weak interactions…) • Various approaches to • low-energy nuclear theory: • Coupled-Cluster theory • Shell model Monte Carlo • DMRG/Factorization • Continuum shell models • Scalable parallel shell model • HFB • QRPA • TDHF

  3. Physics issues What understanding do we gain from investigating the nuclear many-body problem? • We will: • understand the evolution of the effective nucleon-nucleon interaction • -- What is the isospin dependence? • -- What is the density dependence? • understand foundations of independent particle motion • -- How does shell structure change with increasing N? • -- What is the role of the continuum in weakly bound nuclei? • understand excitation and decay properties of weakly bound systems • -- Will neutron skins become clustered? • -- What are the soft modes of excitation and core-skin correlations? • understand matter production in the universe • -- What nuclear physics is important for understanding r-process nuclei? • -- What is the role of nuclear science in SN explosion mechanisms?

  4. Scientific triple point: nuclear structure, nuclear astrophysics, weak interactions • We need information on: • masses • weak decay properties • neutrino interactions • thermal properties • Interplay of weak and strong forces • plays a pivotal role in understanding • astrophysics. • Astrophysics has become an important • end-user of nuclear physics. • The three are intertwined.

  5. f l, nl nl i T+1 Neutral current T+1 T=1 T T=1 T T+1 T MT = -T-1 T=1 T-1 MT = -T+1 T T=0 T=1 (T>=1/2) Charged current MT = -T Charged current Some Basics Charged current: Neutral current: All reactions are possible as long as they obey selection rules

  6. 12N 12C* 17.33 1+1 12B 15.11 1+1 13.36 1+1 12.71 1+0 M1 Other states (T=0): 2+ at 4.44 MeV 0+ at 7.65 0+ at 10.3 0+0 12C Why is 12C so ubiquitous? Simplicity! Isospin Triplet Only the isovector-axialvector weak currents contribute significantly to both reactions

  7. Brief Formalism (from many papers) weak interaction coupling constant lepton momentum and energy neutrino energy initial, final nuclear energies lepton traces + nuclear matrix elements Nuclear structure information; needed One-body matrix elements; known If the flux is known, the model dependence involved in determining the one-body density matrix elements represents the uncertainty of the predicted neutrino-nucleus cross sections.

  8. Ab initio nuclear structure: Green Function Monte Carlo (ANL/LANL/UIUC) • Since 1992: • algorithms • Variational MC • AV18 (2-body) • Computing • 3-body interaction • Indicate the need for • 3 (and 4?) body interactions • Future prospects: • A=12 by 2003/2004 (now) • triple alpha burning • Reaction aspects • NNN studies For A=10, each state takes 1.5 Tflop-hours

  9. Predicted neutrino cross sections (from ab initio theory): 12C [Hayes, Navratil, Vary – PRL91, 12502 (2003)] • GFMC effort conclusively demonstrates the need for VTNI • First calculation of neutrino-nucleus scattering in the shell model with VNN + VTNI

  10. Ab initio results for neutrino-nucleus (12C) cross sections CD-Bonn AV8’+TM’ VTNI strongly affects the spin-orbit splitting in nuclei and affects 12Cgs to the T=1,1+ states in mass 12. Results are not completely converged

  11. The role of RIA in determining drip-line properties • RIA will probe the drip line to medium mass • systems. • Shell structures will be far better understood. • Some of these systems exhibit large • shape-coexistence phenomena, indicating • complicated nuclear structure. • Why does one extra proton bind so many • more neutrons? N=20 closure N=28 closure • What to measure for progress • masses (shell structure) • low-lying levels (shape coexistence) • Single particle states (shell structure) • decay widths (e.g., 12Be) Saranzin et al., PRL84, 5062 (2000)

  12. Proton Number 68 62 56 50 44 38 N=80 24 N=82 N=84 20 N=86 16 12 proton drip line 8 4 neutron drip line 0 1.2 1.5 1.8 2.1 2.4 N / Z Evolution of shell structure • Do shell gaps disappear smoothly? • Does the residual interaction affect • the shell gap melting picture? • Continuum scattering acts to • decrease the shell gaps. S2n (MeV) Measurements: Masses (shell evolution) Decay properties (continuum) Low-lying spectroscopy Single particle state info Dobaczewsk et al., PRC53, 2809 (1996)

  13. Mean-field calculations of separation energies RIA limit • Good overall agreement for measured systems • More masses will enable strong constraints on theory

  14. HFB mass tables Stoitsov et al (submitted 2003); Goriely et al, PRC66, 024328 (2002)

  15. Extensions of continuum shell-model approaches Michel et al PRL, 2003 Bennaceur et al., Nucl. Phys. A671, 203 (2000) • Widths of states depend on correct asymptotics. • Level repulsion may be important. • Continuum states affect bound states and visa versa

  16. Brief Formalism (from many papers) weak interaction coupling constant lepton momentum and energy neutrino energy initial, final nuclear energies lepton traces + nuclear matrix elements Nuclear structure information; needed One-body matrix elements; known If the flux is known, the model dependence involved in determining the one-body density matrix elements represents the uncertainty of the predicted neutrino-nucleus cross sections.

  17. Energy regimes and the SNS • Low energy regime (< 10 MeV): • Most important to provide a very detailed description of the nuclear wave • function (via the shell model) for the initial and final states involved. • High energy regime (0.2 - 3 GeV): • Relativistic Fermi gas + particle hole excitations. • Intermediate energy regime: 10 - 200 MeV • Both the details of configuration mixing and particle-hole • excitations play a significant role. Giant resonance regime Ee > 40 MeV Ee < 10 MeV 0 <Enuc < 12 MeV without measuring g’s Nuclear excitation ambiguous unless g’s are measured

  18. Vretenar et al., PLB487, 334 (2000) n p Collective excitations induced by neutrinos: Resonances: ~20 MeV Radial excitations Important property: cross sections obey Thomas-Reiche-Kuhn sum rule: Spin-isospin GDR Typical E1 p n p n Energy of GR’s scale like A-1/3

  19. 15 10 5 0 p n E* E* gs B(GT)/MeV p n Low energy regime: guidance from e-capture on nuclei Koonin, Dean, Langanke, Phys. Rep. 278, 1 (1997) Radha, Dean, Koonin, Langanke, Vogel, Phys. Rev. C56, 3079 (1997)

  20. Systematic data in a given region of the periodic table Langanke, Martinez-Pinedo, Nucl. Phys. A673, 481 (2000)

  21. Model for electron capture on nuclei with N>40, Z<40. • The science: • Electron capture on neutron-rich nuclei during the core collapse of a massive star. • In past supernova simulations, electron capture on nuclei is assumed blocked • beyond the N=40 shell closure. • The model: • Use SMMC results for occupation probabilities at a given temperature (PP+QQ) • Include the occupation numbers as a starting point for RPA calculations. Langanke, Kolbe, Dean, PRC63, 32801R (2001)

  22. The role of nuclear structure in supernova

  23. Needed e- Capture Rates Need experimental BGT’s in fp-gds shell nuclei. Experments being planned at MSU Nuclei with A>120 are present during collapse of the core. • See: Langanke, Martinez-Pinedo, Nucl. Phys. A673, 481 (2000) • Langanke, Kolbe, Dean, PRC63, 032801R (2001) • Langanke et al (PRL, submitted, 2003) (rates calculation) • Hix et al (PRL, almost submitted) (core collapse implications)

  24. Nuclear physics impact: changes in supernova dynamics e-capture on nuclei dominates e-capture on protons Spherical; Newtonian Reduces e-capture in outer region; Increases e-capture in interior region neutrino energies reduced Shock forms deeper, but propagates farther before stalling

  25. Nuclear structure impact on Supernova evolution Neutrino-Nucleus scattering • Example: • Sampaio, Langanke, Martinez-Pinedo, Dean, • Phys. Lett. B529, 19 (2002). • -- cross section from shell model GT0 strength calculation. • -- low-energy neutrinos can upscatter from thermally • excited states during collapse •  Increases neutrino energy, lowers entropy Underway: systematic study in Z<40, N>40 systems (Juodagalvis)

  26. Conclusions and Perspectives • For a given nucleus measure (make a campaign): • Gamow-Teller strength distributions from np-reactions (SIBs) • e-A reaction cross sections in the lab (e.g., Darmstadt) • Use S(U4) to understand the expected n-A response. • Make data cuts to obtain low-energy information • The quantum many-body problem requires significant effort. • Progress is being made, but ab inito theory is best done in light • to medium-mass nuclei (new ideas may allow us to move to Fe). • Models in heavier nuclei can be constrained by data, but • these models often have less predictive power. • The future • Nuclear science requires measurements.

  27. From applications to development: Coupled Cluster Theory • Some interesting features of CCM: • Fully microscopic • Size extensive: • only linked diagrams enter • Size consistent: • the energy of two non-interacting • fragments computed separately is the same as that • computed for both fragments simultaneously • Capable of systematic improvement • Not variational; in many cases behaves variationally • Amenable to parallel computing Computational chemistry: 100’s of publications in 2002 (Science Citation Index) for applications and developments.

  28. A short history • Formal introduction: • 1958: Coester, Nucl. Phys. 7, 421 • 1960: Coester and Kummel, Nucl. Phys. 17, 477 • Introduction into Chemistry (late 60’s): • 1971: Cizek and Paldus, Int. J. Quantum Chem. 5, 359 • Numerical implementations • 1978: Pople et al., Int. J. Quantum Chem Symp, 14, 545 • 1978: Bartlett and Purvis, Int. J. Quantum Chem 14, 561 • Initial nuclear calculations (1970’s): • 1978: Kummel, Luhrmann, Zabolitzky, Phys. Rep. 36, 1 and refs. therein • 1980-90s: Bishop’s group. Coordinate space. • Few applications in nuclei, explodes in chemistry and molecular sciences. • Hard-core interactions; computer power; unclear interactions • Nuclear physics reintroduction: • 1999: Heisenberg and Mihiala, Phys. Rev. C59, 1440; PRL84, 1403 (2000) • Three nuclei; JJ coupled scheme; bare interactions • Useful References • Crawford and Schaefer, Reviews in Computational Chemistry, 14, 336 (2000) • Bartlett, Ann. Rev. Phys. Chem. 32, 359 (1981)

  29. Coupled Cluster Theory Correlation operator Correlated Ground-State wave function Reference Slater determinant Energy • With all T’s the spectrum of H is the • same as the spectrum of the • similarity transformed H; formally valid • In practice E closely approximates a • variational theory when T is truncated Amplitude equations Work in progress with Morten Hjorth-Jensen

  30. = + +… h G h CC-ph p p Choice of model space and the G-matrix Q-Space P-Space ph intermediate states We also include folded diagrams: eliminates or reduces w-dependence.

  31. Tests of numerical convergence • Numerical parameters: • Oscillator energy • G-starting energy • size of P space Standard 1 body + 2 body Hamiltonians derived from Chiral Lagrangians (EFT) interactions supplied by R. Machleidt (Idaho). (Also implemented CD-Bonn and others.)

  32. Method of solution of CC equations Use Baker-Hausdorff Terminates at quadruply nested commutators (for H=H1+H2) for all T. Normal order the Hamiltonian Fock operator

  33. Method of solution of equations T1 amplitudes from: Note T2 amplitudes also come into the equation.

  34. T2 amplitudes from: Nonlinear terms in t2 (4th order) An interesting mess. But solvable….

  35. Iterative Solution On first iteration, assume that all t’s on the RHS of above equations are zero. Then: Insert into the RHS and obtain new amplitudes Continue until convergence

  36. 2nd order 3rd order Correspondence with MBPT

  37. A few more diagrams + all diagrams of this kind (11 more) 4th order [replace t(2) and repeat above 3rd order calculation] + all diagrams of this kind (6 more) 4th order

  38. Ground states of helium and oxygen

  39. Triples correction methods (w/ Piotr Piechuch, MSU) He-4 (4 major oscillator shells) Method Energy (MeV) -------------------------------------------------------- CCSD -23.607315 CR-CCSD[T],I -24.4818 CR-CCSD[T],II -24.5011 CR-CCSD[T(M3)],I -25.362 CR-CCSD[T(M3)],II -25.377 FULL CI -24.92

More Related