david j. dean ornl

1Neutrino-nucleus interactions

David J. DeanORNL

OutlineI. Overview: general comments

a) Comments on nuclear structureb) Neutrino interactions and the nucleus

II. Nuclear structure computation and neutrinosIII. The inverse reaction: electron captureIV. Conclusions

OutlineI. Overview: general comments

a) Comments on nuclear structureb) Neutrino interactions and the nucleus

II. Nuclear structure computation and neutrinosIII. The inverse reaction: electron captureIV. 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

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


Nuclear structure landscapesp

roto

ns

neutrons

82

50

28

28

50

82

2082

28

20

126

A=12A~60

Density F

unctional T

heory

self-

consistent M

ean Field

Ab initiofew-body

calculations

r-process

rp-p

roce

ss

Shell Model

The landscapeand 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-scaleLarge-scalecomputingcomputing

Large-scaleLarge-scalecomputingcomputing


Physics issues

What understanding do we gain from investigating the nuclearmany-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?

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?


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.

• 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


Some Basics

l

l

AZ

AZAZ

,1

,1,

Charged current:

2

2ZN

M

ZNT

T

T

T

T+1

T-1T

T+1

T

T+1

T=1

T=0T=1 (T>=1/2)

T=1

MT = -T

MT = -T-1MT = -T+1

T=1

Neutral current

Charged current

Charged current

),(, *AZAZNeutral current:

l, l

i

f

l

All reactions are possibleas long as they obey selection rules


Why is 12C so ubiquitous? Simplicity!

15.11 1+1

12.71 1+0

0+0

17.33 1+1

12C

12C*

12N

12B13.36 1+1

e

ee

,

,

Other states (T=0): 2+ at 4.44 MeV 0+ at 7.65 0+ at 10.3

M1

Isospin Triplet

1

1

S

T Only the isovector-axialvector weak currents contribute significantly to both reactions


1

1

22

cos2

MEpEEEEdG

E lllfiCC

Brief Formalism (from many papers)

weak interactioncoupling constant

initial, final nuclear energies

lepton momentumand energy

neutrino energy

pp

pp

l

l cos

lepton traces +nuclear matrix elements

bJ

ajj

i

J

jjfiTJ

f jqjJaaJJqJba

ba ,

iHf W

One-body matrixelements; known

Nuclear structureinformation; 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.


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

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

Indicate the need for 3 (and 4?) body interactions

Future prospects:• A=12 by 2003/2004 (now)• triple alpha burning• Reaction aspects • NNN studies


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


CD-Bonn AV8’+TM’Interaction 2hw 4hw 6hw 4hw Experiment

(e,e-) 2.27 3.2 3.69 6.8 8.9+/-0.3+/-0.9

(,-) 0.168 0.275 0.312 0.537 0.56+/-0.08+/-0.1

m-capture 1.46 2.07 2.38 4.43 6.0+/-0.4

Ab initio results for neutrino-nucleus (12C)cross sections

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


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?

• 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 closureN=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)

What to measure for progress• masses (shell structure)• low-lying levels (shape coexistence)• Single particle states (shell structure)• decay widths (e.g., 12Be)


S2

n (

MeV

)

N / Z

Proton Number

0

4

8

12

16

20

24

384450566268

N=80 N=82 N=84 N=86

1.2 1.5 1.8 2.1 2.4

neutron drip line neutron drip line

pro

ton

dri

p l

ine

pro

ton

dri

p l

ine

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.

• 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

Measurements: Masses (shell evolution) Decay properties (continuum) Low-lying spectroscopy Single particle state info


Mean-field calculations of separation energies

RIA limit

• Good overall agreement for measured systems• More masses will enable strong constraints on theory• Good overall agreement for measured systems• More masses will enable strong constraints on theory


HFB mass tablesHFB mass tables

Stoitsov et al (submitted 2003); Goriely et al, PRC66, 024328 (2002)


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

• 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


1

1

22

cos2

MEpEEEEdG

E lllfiCC

Brief Formalism (from many papers)

weak interactioncoupling constant

initial, final nuclear energies

lepton momentumand energy

neutrino energy

pp

pp

l

l cos

lepton traces +nuclear matrix elements

bJ

ajj

i

J

jjfiTJ

f jqjJaaJJqJba

ba ,

iHf W

One-body matrixelements; known

Nuclear structureinformation; 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.


• 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

Ee > 40 MeVEe < 10 MeV

Nuclear excitationambiguous unless ’s are measured

0 <Enuc < 12 MeVwithout measuring’s


Collective excitations induced by neutrinos: Resonances: ~20 MeV

rkirki 1exp

A

iJi iir

132,1,0''''

Radial excitations

Important property: cross sectionsobey Thomas-Reiche-Kuhn

sum rule:

4

~~)(

2

,13

A

A

NZijjjrf

f Aj

n p n pnp

Typical E1 Spin-isospin GDR

Energy of GR’s scale like A-1/3

Vretenar et al., PLB487, 334 (2000)


Low energy regime: guidance from e-capture on nuclei

271 f251 f

232p212p

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)

ki k

np fij

kninGTB

,

2

12

eZNAZNAe )1,1(),(

20Neutrino-nucleus interactionsLanganke, Martinez-Pinedo, Nucl. Phys. A673, 481 (2000)

Systematic data in a given region of the periodic table


Model for electron capture on nuclei with N>40, Z<40. 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.

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)


Gain Radius

Heating

Cooling

-Luminosity

Matter Flow

Proto-NeutronStar

-Spheres

e + n p + e-

e + p n + e+_

e + n p + e-

e + p n + e+_

Shock

The role of nuclear structure in supernova


Needed e- Capture Rates 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 experimentalBGT’s in fp-gds shell nuclei. Expermentsbeing planned at MSU


Nuclear physics impact: changes in supernova dynamics

e-capture on nuclei dominatese-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


Nuclear structure impact on Supernova evolution Neutrino-Nucleus scattering

Nuclear structure impact on Supernova evolution Neutrino-Nucleus scattering

MeV 5.7E

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

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)


Conclusions and PerspectivesConclusions 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.


From applications to development:Coupled Cluster Theory

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.


A short historyA short history

Formal introduction:1958: Coester, Nucl. Phys. 7, 4211960: Coester and Kummel, Nucl. Phys. 17, 477

Introduction into Chemistry (late 60’s):1971: Cizek and Paldus, Int. J. Quantum Chem. 5, 359Numerical implementations1978: Pople et al., Int. J. Quantum Chem Symp, 14, 5451978: Bartlett and Purvis, Int. J. Quantum Chem 14, 561

Initial nuclear calculations (1970’s):1978: Kummel, Luhrmann, Zabolitzky, Phys. Rep. 36, 1 and refs. therein1980-90s: 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 interactionsUseful References

Crawford and Schaefer, Reviews in Computational Chemistry, 14, 336 (2000)Bartlett, Ann. Rev. Phys. Chem. 32, 359 (1981)


Coupled Cluster TheoryCoupled Cluster Theory

TexpCorrelated Ground-State

wave functionCorrelation

operatorReference Slater

determinant

321 TTTT

f

f

f

f

abij

ijbaabij

ai

iaai

aaaatT

aatT

2

1

THTE exp)exp(

0exp)exp( THTabij

EnergyEnergy

Amplitude equationsAmplitude 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-JensenWork in progress with Morten Hjorth-Jensen


Choice of model space and the G-matrixChoice of model space and the G-matrix

Q-Space

P-Space

Fermi

Fermi

+…

=

+

h

p

G

ph intermediatestates

CC-phh

p

)~(~1

)~(0

QGQQH

QVG

aitab

ijtWe also include folded diagrams: eliminates orreduces -dependence.


Tests of numerical convergenceTests of numerical convergence

pqrs

rsqppq

qposc aaaarsGpqaaqTpH4

1

Numerical parameters:

• Oscillator energy• G-starting energy• size of P space

Numerical parameters:• Oscillator energy• G-starting energy• size of P space

FD ,~

Standard 1 body + 2 body Hamiltoniansderived from Chiral Lagrangians (EFT)interactions supplied by R. Machleidt (Idaho).(Also implemented CD-Bonn and others.)

Standard 1 body + 2 body Hamiltoniansderived from Chiral Lagrangians (EFT)interactions supplied by R. Machleidt (Idaho).(Also implemented CD-Bonn and others.)


2122

1121

,,,,2

1

,,2

1,,)exp()exp(

TTHTTH

TTHTHTHHTHT

Terminates at quadruply nested commutators(for H=H1+H2) for all T.

Method of solution of CC equationsMethod of solution of CC equations

Use Baker-HausdorffUse Baker-Hausdorff

Normal order the HamiltonianNormal order the Hamiltonian

ijiosc

pqrsrsqp

pqqppq ijijiTiaaaarspqaafH ||

2

1||

4

1

i

oscpq qipiqTpf ||00 H

Fock operator


T1 amplitudes from:T1 amplitudes from: 0exp)exp( THTai

Method of solution of equationsMethod of solution of equations

Note T2 amplitudes also come into the equation.


T2 amplitudes from:T2 amplitudes from: 0exp)exp( THTabij

An interesting mess. But solvable….An interesting mess. But solvable….

Nonlinear terms in t2(4th order)

)()()()( jifijfijfijP


On first iteration, assume that all t’s on the RHS of aboveequations are zero. Then:

Iterative SolutionIterative Solution

abij

abij

aiai

ai

Dijabt

Dft

||

Insert into the RHS and obtain new amplitudes

Continue until convergence


Correspondence with MBPTCorrespondence with MBPT

jiba

abij

ijababij

tijabE

Dijabt

)1(

)1(

2

2nd order

jiba

abij

kc

acik

cd

cdij

kl

abkl

abij

tijabE

tcjkbabPijPtcdab

tijklt

)2(

)1()()()1(2

1

)1(2

1)2(

3

3rd order


+ 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

jiba

abij

Q

klcd

cdjl

abik

klcd

bdkl

acij

klcd

abkl

cdij

klcd

dblj

acik

abij

NtijabE

ttcdklijPttcdklabP

ttcdklttcdklabPijPNt

);3(

)1()1()(2

1)1()1()(

2

1

)1()1(4

1)1()1()()(

2

1;3

4

A few more diagramsA few more diagrams


Ground states of helium and oxygenGround states of helium and oxygen


Method Energy (MeV)--------------------------------------------------------CCSD -23.607315CR-CCSD[T],I -24.4818CR-CCSD[T],II -24.5011CR-CCSD[T(M3)],I -25.362CR-CCSD[T(M3)],II -25.377FULL CI -24.92

Triples correction methods (w/ Piotr Piechuch, MSU)He-4 (4 major oscillator shells)

]2[

3212

121 2

11 TTTTTTI

]2[

33

1212

121 6

1

2

11 TTTTTTTII

david j. dean ornl

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