Transcript Document

Structure of Exotic Nuclei
Witold Nazarewicz (Tennessee)
International School of Nuclear Physics
28th course: Radioactive Beams, Nuclear Dynamics and Astrophysics
Erice, Italy, September 2006
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Introduction: challenges and questions
Microscopic nuclear structure theory
Recent/relevant examples
Summary
Questions that Drive the Field
o
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How do protons and neutrons make stable nuclei and rare isotopes?
What is the origin of simple patterns in complex nuclei?
Physics
What is the equation of state of matter made of nucleons?
of nuclei
What are the heaviest nuclei that can exist?
o When and how did the elements from iron to uranium originate?
o How do stars explode?
Nuclear
astrophysics
o What is the nature of neutron star matter?
o How can our knowledge of nuclei and our ability to produce them
benefit the humankind?
Applications
of nuclei
– Life Sciences, Material Sciences, Nuclear Energy, Security
Effective Field Theory tells us that:
• Short-range (high-k) physics can be integrated out (no need to worry
about explicit inclusion of hard core when dealing with low-k
phenomena)
• Successive two-body scatterings with short-lived high-energy
intermediate states unresolved → must be absorbed into three-body
force
• Power counting can be controlled
• … but the operators have to be renormalized (i.e., consistent with the
power counting)
Weinberg’s Third Law of Progress in Theoretical Physics:
“You may use any degrees of freedom you like to describe
a physical system, but if you use the wrong ones, you’ll be
sorry!”
D. Furnstahl, INT Fall’05
Nuclear Structure: the interaction
Effective-field theory (χPT)
potentials: error bars provided
N3LO: Entem et al., PRC68, 041001 (2003)
Epelbaum, Meissner, et al.
Vlow-k: can it describe low-energy observables?
• Quality two- and three-nucleon interactions
exist
Bogner, Kuo, Schwenk, Phys. Rep. 386, 1 (2003)
• Not uniquely defined (local, nonlocal)
• Soft and hard-core
• The challenge is:
• to understand their origin
• to understand how to use them in nuclei
Bottom-up approaches to nuclear structure
Roadmap
Ab initio
Configuration
interaction
Density
Functional
Theory
Collective and
Algebraic Models
(top-down)
Theoretical
approaches
overlap and
need to be
bridged
Ab Initio Nuclear Structure Theory
(with bare NN+NNN interactions)
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Quantum Monte Carlo (GFMC)
No-Core Shell Model
Coupled-Cluster Techniques
Unitary Model Operator Approach
Faddeev-Yakubovsky
Bloch-Horowitz
…
Input:
12C
13C
16O
The nucleon-based
description works to <0.5 fm
Excellent forces based on the phase shift analysis
EFT based nonlocal chiral NN and NNN potentials
Challenges:
Interaction: NNN
How important is NNNN? See nucl-th/0606017 for 4He estimates
How to extend calculations to heavier systems?
Treatment of weakly-bound and unbound states, and cluster correlations
First applications to reactions in GFMC, NCSM, CCM, …
Diagonalization Shell Model
(medium-mass nuclei reached;dimensions 109!)
Honma, Otsuka et al., PRC69, 034335 (2004)
and ENAM’04
Martinez-Pinedo
ENAM’04
Challenges:
Configuration space
Effective Interactions
Open channels
Towards the Universal Nuclear Energy Density Functional
(non-relativistic, relativistic)
Walter Kohn: Nobel Prize in Chemistry in 1998
0 r   0 r,r    r  ;r  
isoscalar (T=0) density 0  n   p 
1r   1r,r    r  ;r  
isovector (T=1) density 1  n  p 




s0 r    r ;r  '   '
isoscalar spin density
s1r    r  ;r  '   ' 

isovector spin density
 '

 '





i
'  T r,r ' r ' r
2
i
JT r   '   sT r,r ' r ' r
2

T r    ' T r,r ' r ' r
kinetic density

TT r    ' sT r,r ' r ' r
kinetic spin density



jT r  
current density


+CT T  T  j  C sT  TT  J  C
2
T
T
T
Construction of the functional:
E. Perlinska et al.
Phys. Rev. C 69, 014316 (2004)
spin-current tensor density
H T r   CT T2  CTs sT2  CT T T  CTssT sT

Local densities
and currents
+ pairing…
2
T
J
T
  J
T
T
 2
 3
E tot     0 + H0 r   H1r d r
2m


 sT   jT

Example: Skyrme
Functional
Total ground-state
DFT energy
Nuclear DFT
From Qualitative to Quantitative!
S. Cwiok, P.H. Heenen, W. Nazarewicz
Nature, 433, 705 (2005)
Deformed Mass Table in one day!
• HFB mass formula: m~700keV
• Good agreement for mass differences
UNEDF (SCIDAC-2) will
address this question!
Why is the shell structure changing at extreme isospins?
Interactions
• Isovector (N-Z) effects: search for
missing links
• Poorly-known components of the
effective interaction come into
play
• Long isotopic chains crucial
Interactions
Many-body
Correlations
Configuration interaction
• Mean-field concept questionable for
dripline nuclei
• Asymmetry of proton and neutron
Fermi surfaces gives rise to new
couplings
• Intruders and the islands of inversion
Open
Channels
Open channels
• Nuclei are open quantum systems
• Exotic nuclei have low-energy decay
thresholds
• Coupling to the continuum important
Example: Spin-Orbit and Tensor Force
(among many possibilities)
The origin of SO splitting can be attributed to 2-body SO and tensor forces,
and 3-body force
R.R. Scheerbaum, Phys. Lett. B61, 151 (1976); B63, 381 (1976); Nucl. Phys. A257,
77 (1976); D.W.L. Sprung, Nucl. Phys. A182, 97 (1972); C.W. Wong, Nucl. Phys.
A108, 481 (1968)
The maximum effect is in spin-unsaturated systems
Discussed in the context of mean field models:
Fl. Stancu, et al., Phys. Lett. 68B, 108 (1977); M. Ploszajczak and M.E. Faber, Z.
Phys. A299, 119 (1981); J. Dudek, WN, and T. Werner, Nucl. Phys. A341, 253
(1980); J. Dobaczewski, nucl-th/0604043; Otsuka et al.
and the nuclear shell model:
T. Otsuka et al., Phys. Rev. Lett. 87, 082502 (2001); Phys. Rev. Lett. 95, 232502
(2005)
2, 8, 20
j<
F
j>
Spin-saturated systems
28, 50, 82, 126
j<
F
j>
Spin-unsaturated systems
acts in s and d states of
relative motion
acts in p states
SO densities
(strongly depend on shell filling)
J. Dobaczewski, nucl-th/0604043
J. Dobaczewski,
nucl-th/0604043
Skyrme-DFT
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Additional contributions in deformed nuclei
Particle-number dependent contribution to nuclear binding
It is not trivial to relate theoretical s.p. energies to experiment.
Correlations (including g.s. correlations) are important!
Coupling of nuclear structure and reaction theory
(microscopic treatment of open channels)
Thomas/Ehrman shift
Proton Emitters
ab-initio description
continuum shell model
Real-energy CSM (Hilbert space formalism)
Gamow Shell Model (Rigged Hilbert space)
cluster models
Continuum Shell Model -an old tool!
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U. Fano, Phys. Rev. 124, 1866 (1961)
C. Mahaux and H. Weidenmüller: “Shell Model Approach
to Nuclear Reactions” 1969
H. W. Bartz et al., Nucl. Phys. A275, 111 (1977)
D. Halderson and R.J. Philpott, Nucl. Phys. A345, 141
…
J. Okolowicz, M. Ploszajczak, I. Rotter, Phys. Rep. 374,
271 (2003)
Recent Developments:
SMEC
•K. Bennaceur et al., Nucl. Phys. A651, 289 (1999)
•K. Bennaceur et al., Nucl. Phys. A671, 203 (2000)
•N. Michel et al., Nucl. Phys. A703, 202 (2002)
•Y. Luo et al., nucl-th/0201073
Gamow Shell Model
•N. Michel et al., Phys. Rev. Lett. 89, 042502 (2002)
•N. Michel et al., Phys. Rev. C67, 054311 (2003)
•N. Michel et al., Phys. Rev. C70, 064311 (2004)
•R. Id Betan et al., Phys. Rev. Lett. 89, 042501 (2002)
•R. Id Betan et al., Phys. Rev. C67, 014322 (2003)
•G. Hagen et al, Phys. Rev. C71, 044314 (2005)
Other approaches
Resonant (Gamow) states
Also true in many-channel case!
Ê
Gˆ
ˆ
H  e - i Y
Ë
2¯
outgoing
solution
Y (0,k ) = 0, Y (r ,k )ææ
æÆOl (kr)
r Æ•
kn 
2m Ê
Gn ˆ
2 Ëen - i
2¯
complex pole
of the S-matrix
•Humblet and Rosenfeld, Nucl. Phys. 26, 529 (1961)
•Siegert, Phys. Rev. 36, 750 (1939)
•Gamow, Z. Phys. 51, 204 (1928)
One-body basis
Contour is discretized
GSM Hamiltonian matrix
is complex symmetric
J. Rotureau et al., DMRG
Phys. Rev. Lett. 97, 110603 (2006)
Virtual states not included
explicitly in the GSM basis
Michel et al., Phys. Rev. C (2006)
nucl-th/0609016
N. Michel, W.N., M. Ploszajczak, J. Rotureau
Example: Spectroscopic factors and
threshold effects in GSM
One-nucleon radial overlap integral:
One-nucleon radial overlap integral in GSM:
usually approximated by
a WS wave function at
properly adjusted
energy
Spectroscopic factor in GSM:
In contrast to the standard SM, the final result
is independent of the s.p. basis.
In usual applications, only one term remains
Usually extracted from experimental cross section
Prone to errors close to particle thresholds
Threshold anomaly
E.P. Wigner, Phys. Rev. 73, 1002 (1948), the Wigner cusp
G. Breit, Phys. Rev. 107, 923 (1957)
A.I. Baz’, JETP 33, 923 (1957)
R.G. Newton, Phys. Rev. 114, 1611 (1959).
A.I. Baz', Ya.B. Zel'dovich, and A.M. Perelomov, Scattering Reactions and Decay
in Nonrelativistic Quantum Mechanics, Nauka 1966
A.M. Lane, Phys. Lett. 32B, 159 (1970)
S.N. Abramovich, B.Ya. Guzhovskii, and L.M. Lazarev, Part. and Nucl. 23, 305 (1992).
• The threshold is a branching point.
• The threshold effects originate in conservation of the flux.
• If a new channel opens, a redistribution of the flux in other open
channels appears, i.e. a modification of their reaction cross-sections.
• The shape of the cusp depends strongly on the orbital angular
momentum.
Y(b,a)X
X(a,b)Y
Threshold anomaly (cont.)
Studied experimentally and theoretically in various areas of physics:
pion-nucleus scattering
R.K. Adair, Phys. Rev. 111, 632 (1958)
A. Starostin et al., Phys. Rev. C 72, 015205 (2005)
electron-molecule scattering
W. Domcke, J. Phys. B 14, 4889 (1981)
electron-atom scattering
K.F. Scheibner et al., Phys. Rev. A 35, 4869 (1987)
ultracold atom-diatom scattering
R.C. Forrey et al., Phys. Rev. A 58, R2645 (1998)
Low-energy nuclear physics
•charge-exchange reactions
•neutron elastic scattering
•deuteron stripping
The presence of cusp anomaly could provide structural information about
reaction products
Coupling between analog states
in (d,p) and (d,n)
C.F. Moore et al.
Phys. Rev. Lett. 17, 926 (1966)
C.F. Moore et al., Phys. Rev. Lett. 17, 926 (1966)
WS potential depth decreased to
bind 7He. Monopole SGI strength
varied
5He+n
6He
WS potential depth varied
6He+n
7He
Anomalies appear at calculated
thresholds (many-body Smatrix unitary)
Scattering continuum essential
• The non-resonant continuum is important for the spectroscopy of weakly bound nuclei
(energy shifts of excited states, additional binding,…)
• SFs, cross sections, etc., exhibit a non-perturbative and non-analytic behavior (cusp
effects) close to the particle-emission thresholds. These anomalies strongly depend on
orbital angular momentum
• Microscopic CSM (GSM) fully accounts for channel coupling. Thresholds are not
predetermined!
Timofeyuk, Blokhintsev, Tostevin, Phys. Rev. C68, 021601 (2003)
Non-Borromean two-neutron halos
NSCL@MSU 2005
Example: Surface Symmetry Energy
Microscopic LDM and Droplet Model Coefficients: PRC 73, 014309 (2006)
Collective potential V(q)
Presence of shell effects in
metastable minima seems to be
under control.
Important data needed to fix
the deformability of the NEDF:
• absolute energies of SD states
• absolute energies of HD states
Advantages:
• large elongations
• weak mixing with ND structures
Different
deformabilities!
theory (DFT)
experiment
Er
spherical
systems
Pb
deformed
systems
Ra
U
octupole
collectivity
Average value:
symmetry energy
Shell
closure
deformed
systems
Stoitsov, Nazarewicz + Cakirli, Casten
Example: High-spin intruder states
S2n
S2p
Brown & Sherrill, MSU
Intruder states in the sdpf nuclei
G. Stoitcheva et al.,
Phys. Rev. C73, 061304(R) (2006)
f7/2
28
20
d3/2
deformed
structures
intruder
states
Zdunczuk et al.,Phys.Rev. C71 (2005) 024305
•Excellent examples of single-particle configurations
•Weak configuration mixing
•Spin polarization!
•Experimental data available
P. Bednarczyk et al.,
Acta Phys. Pol. B32, 747 (2001)
45Sc
spdf space
1p-1h cross-shell
Antoine
Bansal, French, Phys. Lett. 11, 145 (1964); Zamick, Phys. lett. 19, 580 (1965)
sd
fp
sd
fp
Crucial for the island
of inversion around
32Mg!
ESM-EEXP (MeV)
the isospin-dependent contribution to the excitation energy of a 1p-1h state
SM
SM’
SM’’
0.4
0.2
0
-0.2
-0.4
42Ca
40Ca
42Sc
44Ca
44Sc
43Sc
44Ti
45Sc
46Ti
45Ti
47V
46V
Pandya transformation on the cross shell ME
What are the limits of atoms and nuclei?
Do very long-lived superheavy nuclei exist?
What are their physical and chemical properties?
How to get there?
HRIBF 2005
T. Nakatsukasa et al., Nucl. Phys. A573, 333 (1994)
spin-flip
Z-rich nuclei:
Collective M1 strength
Enhanced in deformed
N=Z nuclei
Probes T=1 physics
(g9/2)2 excitation
Collective or single-particle?
Skin effect? Threshold effect?
LAND-FRS
Energy differential electromagnetic
dissociation cross section
Deduced photo-neutron
cross section.
IS
IV
130Sn
132Sn
140Sn
J. Terasaki, J. Engel,
nucl-th//0603021
SKM*+QRPA+HFB
Conclusions
A comprehensive description of nuclei and their reactions is coming
Exotic nuclei are essential in this quest: they provide missing links
Discussed:
•Origin of shell structure changes
•Many-body GSM treatment of structure and reactions
•Surface-dependence of the symmetry energy (masses, deformed
states)
•Learning about cross-shell physics from intruder states
•The superheavies: how to get there?
•Quest for collective exotica
THE END
COULOMB SHIFT
Coulomb:
on
off
Brandolini et al., PRC66, 021302 (2002)
0.10
deformed g.s
and spherical Imax
E([f7/2]n) [MeV]
SLy4
0.05
0
-0.05
42Ca 43Sc
polarization of
strong field
~500keV
SkO
0.15
(C)
(W. Satula et. al)
dEC=EHF - EHF [MeV]
Relative Coulomb shift
6.5
45Sc
46Ti
44Ca 44Sc 45Ti
40Ca 44Ti
47V
42Sc
46V
Absolute Coulomb shift
of terminating state
50Cr
SkO
SLy4
6.0
5.5
5.0
4.5
Coulomb:
SkO
46Ti
on
off
SLy4
on
off
The Nuclear Many-Body Problem
Energy, Distance, Complexity
few
body
heavy
nuclei
quarks
gluons
vacuum
quark-gluon
soup
QCD
nucleon
QCD
few body systems many body systems
free NN force
effective NN force
Spectroscopy of open systems: proton emitters
Non-adiabatic theory:
B.Barmore et al., Phys.Rev. C62, 054315 (2000)
A.T. Kruppa and WN, Phys. Rev. C69, 054311 (2004)
(e.g., the local central force)