david j. dean ornl
DESCRIPTION
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 - PowerPoint PPT PresentationTRANSCRIPT
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
2Neutrino-nucleus interactions
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
3Neutrino-nucleus interactions
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?
4Neutrino-nucleus interactions
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
5Neutrino-nucleus interactions
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
6Neutrino-nucleus interactions
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
7Neutrino-nucleus interactions
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.
8Neutrino-nucleus interactions
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
9Neutrino-nucleus interactions
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
10Neutrino-nucleus interactions
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
11Neutrino-nucleus interactions
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)
12Neutrino-nucleus interactions
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
13Neutrino-nucleus interactions
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
14Neutrino-nucleus interactions
HFB mass tablesHFB mass tables
Stoitsov et al (submitted 2003); Goriely et al, PRC66, 024328 (2002)
15Neutrino-nucleus interactions
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
16Neutrino-nucleus interactions
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.
17Neutrino-nucleus interactions
• 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
18Neutrino-nucleus interactions
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)
19Neutrino-nucleus interactions
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
21Neutrino-nucleus interactions
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)
22Neutrino-nucleus interactions
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
23Neutrino-nucleus interactions
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
24Neutrino-nucleus interactions
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
25Neutrino-nucleus interactions
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)
26Neutrino-nucleus interactions
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.
27Neutrino-nucleus interactions
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.
28Neutrino-nucleus interactions
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)
29Neutrino-nucleus interactions
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
30Neutrino-nucleus interactions
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.
31Neutrino-nucleus interactions
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.)
32Neutrino-nucleus interactions
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
33Neutrino-nucleus interactions
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.
34Neutrino-nucleus interactions
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
35Neutrino-nucleus interactions
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
36Neutrino-nucleus interactions
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
37Neutrino-nucleus interactions
+ 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
38Neutrino-nucleus interactions
Ground states of helium and oxygenGround states of helium and oxygen
39Neutrino-nucleus interactions
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