1. Neutrino-nucleus interactions 1 David J. Dean ORNL Outline I.Overview: general comments a)Comments on nuclear structure b)Neutrino interactions and the nucleus II.Nuclear structure computation and neutrinos III.The inverse reaction: electron capture IV.Conclusions 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

2. Neutrino-nucleus interactions 2 Nuclear structure landscapes protons neutrons 82 50 28 50 82 20 8 2 2 8 126 A=12 A~60 Density Functional Theory self-consistent Mean Field Ab initio few-body calculations r-process rp-process Shell Model The landscape and the models 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 Large-scalecomputing

3. Neutrino-nucleus interactions 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. Neutrino-nucleus interactions 4 Scientific triple point: nuclear structure, nuclear astrophysics, weak interactions 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. We need information on: masses weak decay properties neutrino interactions thermal properties

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

6. Neutrino-nucleus interactions 6 Why is 12 C so ubiquitous? Simplicity! 15.11 1 + 1 12.71 1 + 0 0+00+0 17.33 1 + 1 12 C 12 C* 12 N 12 B 13.36 1 + 1 Other states (T=0): 2 + at 4.44 MeV 0 + at 7.65 0 + at 10.3 M1 Isospin Triplet Only the isovector-axialvector weak currents contribute significantly to both reactions

7. Neutrino-nucleus interactions 7 Brief Formalism (from many papers) weak interaction coupling constant initial, final nuclear energies lepton momentum and energy neutrino energy lepton traces + nuclear matrix elements One-body matrix elements; known Nuclear structure information; needed 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. Neutrino-nucleus interactions 8 Ab initio nuclear structure: Green Function Monte Carlo (ANL/LANL/UIUC) Since 1992: algorithms Variational MC AV18 (2-body) Computing 3-body interaction For A=10, each state takes 1.5 Tflop-hours Indicate the need for 3 (and 4?) body interactions Future prospects: A=12 by 2003/2004 (now) triple alpha burning Reaction aspects NNN studies

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

10. Neutrino-nucleus interactions 10 CD-Bonn AV8’+TM’ Interaction2hw4hw6hw4hwExperiment ( e,e - ) 2.273.23.696.88.9+/-0.3+/-0.9 ( ,  - ) 0.1680.2750.3120.5370.56+/-0.08+/-0.1 m-capture1.462.072.384.436.0+/-0.4 Ab initio results for neutrino-nucleus ( 12 C) cross sections V TNI strongly affects the spin-orbit splitting in nuclei and affects 12 C gs to the T=1,1 + states in mass 12. Results are not completely converged

11. Neutrino-nucleus interactions 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? Saranzin et al., PRL84, 5062 (2000) 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., 12 Be)

12. Neutrino-nucleus interactions 12 S 2n (MeV) 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. Dobaczewsk et al., PRC53, 2809 (1996) Measurements: Masses (shell evolution) Decay properties (continuum) Low-lying spectroscopy Single particle state info

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

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

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

16. Neutrino-nucleus interactions 16 Brief Formalism (from many papers) weak interaction coupling constant initial, final nuclear energies lepton momentum and energy neutrino energy lepton traces + nuclear matrix elements One-body matrix elements; known Nuclear structure information; needed 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. Neutrino-nucleus interactions 17 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 Energy regimes and the SNS E e > 40 MeV E e < 10 MeV Nuclear excitation ambiguous unless  ’s are measured 0 <E nuc < 12 MeV without measuring  ’s

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

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

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

21. Neutrino-nucleus interactions 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. Neutrino-nucleus interactions 22 The role of nuclear structure in supernova

23. Neutrino-nucleus interactions 23 Needed e - Capture Rates 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) Need experimental BGT’s in fp-gds shell nuclei. Experments being planned at MSU

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

25. Neutrino-nucleus interactions 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 systems (Juodagalvis)

26. Neutrino-nucleus interactions 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 -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. Neutrino-nucleus interactions 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. Neutrino-nucleus interactions 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. Neutrino-nucleus interactions 29 Coupled Cluster Theory Correlated Ground-State wave function Correlation operator Reference Slater determinant Energy Amplitude equations 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 Work in progress with Morten Hjorth-Jensen

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

31. Neutrino-nucleus interactions 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. Neutrino-nucleus interactions 32 Terminates at quadruply nested commutators (for H=H 1 +H 2 ) for all T. Method of solution of CC equations Use Baker-Hausdorff Normal order the Hamiltonian Fock operator

33. Neutrino-nucleus interactions 33 T 1 amplitudes from: Method of solution of equations Note T 2 amplitudes also come into the equation.

34. Neutrino-nucleus interactions 34 T 2 amplitudes from: An interesting mess. But solvable…. Nonlinear terms in t2 (4 th order)

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

36. Neutrino-nucleus interactions 36 Correspondence with MBPT 2 nd order 3 rd order

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

38. Neutrino-nucleus interactions 38 Ground states of helium and oxygen

39. Neutrino-nucleus interactions 39 MethodEnergy (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 Triples correction methods (w/ Piotr Piechuch, MSU) He-4 (4 major oscillator shells)