Transcript Document

Happy Birthday JUSTIPEN!!!
Nuclei as open quantum many-body systems
Witold Nazarewicz (Tennessee)
JUSTIPEN Meeting, RIKEN July 10-11, 2006
Introduction and motivation
Some recent examples
US effort and potential for JUSTIPEN activities
Summary
• Interdisciplinary science
Much interest devoted to the study of small quantum systems that are
coupled to an environment of scattering wave functions (quantum dots,
molecules, clusters, nuclei, hadrons)
• New regime
Weakly bound or unbound states cannot be treated in a Closed
Quantum System formalism. A consistent description of the interplay
between scattering states, resonances, and bound states in the manybody wave function requires an Open Quantum System formulation.
• No escape
Properties of unbound states lying above the particle (or cluster)
threshold directly impact properties of bound states and the continuum
structure.
• Splendid opportunity for theory of exotic nuclei and RNB
experimentation
A unified description of nuclear structure and nuclear reaction aspects
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
Coupling of nuclear structure and reaction theory
ab-initio description
continuum shell model
Real-energy CSM (Hilbert space formalism)
Gamow Shell Model (Rigged Hilbert space)
cluster models
Challenges:
•Treatment of continuum in ab
initio
•How to optimize CSM
configurations spaces?
•Effective forces in CSM
•Multi- channel reaction theory
•Halo nuclei: an ultimate
challenge!
•virtual state
•center of mass
•cross-shell effects
Thomas/Ehrman shift
Proton and Alpha
Emitters
Narrow resonances
A. Arima and S. Yoshida,
Nucl. Phys. A219, 475 (1974)
Non-adiabatic approaches
See references in
A.T. Kruppa and W. Nazarewicz,
Phys. Rev. C69, 054311 (2004)
Fission and Fusion
nuclear collective dynamics
E
fission/fusion
exotic decay
heavy ion coll.
Variety of phenomena:
•symmetry breaking and quantum corrections
•LACM: fission, fusion, coexistence
•phase transitional behavior
•new kinds of deformations
Significant computational resources required:
•Generator Coordinate Method
•Projection techniques
•Imaginary time method (instanton techniques)
•QRPA and related methods
•TDHFB, ATDHF, and related methods
Q0
E
Q
shape
coexistence
Challenges:
•selection of appropriate degrees of freedom
•simultaneous treatment of symmetry
•coupling to continuum in weakly bound systems
•dynamical corrections; fundamental theoretical problems.
•rotational, vibrational, translational
•particle number
•isospin
Q1 Q2 Q
Ab-initio, EFT,…
talk by …)
Barrett
ab-initio description (GFMC, NCSM, Faddeyev,
realistic wave functions and electroweak currents
applications to radiative capture reactions
cluster form factors, spectroscopic factors
EFT description
reactions on deuterium, halo nuclei
Challenges:
• Treatment of continuum in VMC
and GFMC
• NCSM calculations with A=4
projectiles
• Low-energy reactions in NCSM
P. Navratil et al., Phys. Lett. B634, 191 (2006)
EXAMPLES:
K. Nollett, Phys.Rev. C63, 05400 (2001)
P. Navratil, Phys.Rev. C70, 054324 (2004)
P. Navratil, Phys. Rev. C70, 054324 (2004)
Continuum Shell Model -an old tool!
•
•
•
•
•
•
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
NSCL@MSU 2005
•
•
•
How well does nuclear theory describe the energy and spatial structure of the single particle
wave functions?
Can the parameterized N-N force adequately describe the short-range correlations among
the nucleons?
Electron-induced proton knock-out
What is the role of long-range correlations and open channels?
Spectroscopic factors 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 CQS 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 significant 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)
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
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)
N. Michel et al., GSM
nucl-th/0601055
J. Rotureau et al., DMRG
nucl-th/0603021
The GSM Hamiltonian
For the O-isotopes:
zero surface delta interaction
For the He-isotopes: finite-range surface Gaussian interaction
non-perturbative
behavior
scattering
continuum
essential
WS potential depth decreased to bind 7He. Monopole SGI strength varied
WS potential depth varied
•The new paradigm is born: shell-model treatment of open
channels
•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 particleemission thresholds. These anomalies strongly depend on
orbital angular momentum
The continuum in reaction theory
CDCC
Spectroscopic information
comes from reactions
Experiments with exotic nuclei will
require a firm understanding of
reaction theory in order to
interpret the meaning of the data
Parallel momentum distributions for nucleon
removal from 15C + 9Be
J. Tostevin PRC66, 024607 (2002)
Why is the shell structure changing at extreme isospins?
Interactions
Many-body
Correlations
Open
Channels
Coupling of nuclear structure and reaction theory
(microscopic treatment of open channels)
Current US effort (RIATG)
• Ab initio reaction theory
•
LLNL (Navratil, …), Arizona (Bertulani, Barrett,…), ANL (Nollett, …)…
• CDCC
•
talk by Ogata
Nunes (MSU), Thompson (LLNL), Mukhamedzhanov (Texas A&M)…
• Continuum Shell Model
•
Michel, Nazarewicz, Rotureau (ORNL), Volya (FSU), Zelevinsky (MSU).…
Kyoto (postdoc)
• Narrow resonances (proton emitters, SF)
•
Esbensen (ANL), Nunes (MSU), Mukhamedzhanov (Texas A&M), Nazarewicz (ORNL)
• Fission
•
LANL, LLNL, ORNL, Seattle
• Fusion
•
talk by Nakatsukasa
Balantekin (Wisconsin), Oberacker, Umar (Vanderbilt)
• Continuum QRPA
•
Kyoto (vis. prof.)
Bertsch (Seattle), Engel (UNC), Nazarewicz, Stoitsov (ORNL), Shlomo (Texas A&M),
Conclusions
Tying nuclear structure directly to nuclear reactions within a
coherent framework applicable throughout the nuclear landscape
is an important goal. For light nuclei, ab-initio methods hold the
promise of direct calculation of low-energy scattering
processes, including those important in nuclear astrophysics, and
tests of fundamental symmetries. In nuclear structure for
heavier nuclei, the continuum shell model and modern mean-field
theories allow for the consistent treatment of open channels,
thus linking the description of bound and unbound nuclear states
and direct reactions. On the reaction side, better treatment of
nuclear structure aspects is equally crucial. The battleground in
this task is the newly opening territory of weakly bound nuclei
where the structure and reaction aspects are interwoven and
where interpretation of future data will require advances in
understanding of the reaction mechanism.
(NSAC Nuclear Theory Report)
JUSTIPEN will play important role!
Gamow states of finite potential
V  Vn  VLS  VCoul
120Sn
Unbound
states
Discrete
(bound)
states
eF
n
0
eF
p
Resonance states, properties
i Ê
Gˆ ¸
Ï
(t ) = expÌ - t e - i ðY (r ,k)
2 ¯ý
Ó Ë
G ¸
Ï
F (t ) F (0) = expÌ t ð Y (r ,k) Y(r ,k)
Ó 2 ý
T1/ 2 = ln 2 ,
G
= 6.58³10- 22 MeV ³sec
Can one calculate G with sufficient accuracy?
22
Ts.p.  310 sec  3babysec.
For narrow resonances,
explicit time
propagation difficult!
Resonant states, properties
Humblet and Rosenfeld: Nucl. Phys. 26, 529 (1961)
 j dS  GÚ d r
3
j
(
2mi
S
V
)
Y *—Y - Y —Y * ,
r = Y *Y
S can be taken as a sphere of radius R:
G
R2 Újr dW
3
Úr d r
VR
Also true in many-channel case!
j -
G
Ê
Žr
r = 0 —j +
= 0ˆ
Ë
¯
Žt
“Spin-orbit splitting” in GSM
Influence of configuration mixing and continuum coupling
S1n(6He)=0