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
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Witold Nazarewicz (Tennessee)
JUSTIPEN Meeting, RIKEN July 10-11, 2006
Introduction and motivation
Some recent examples
US effort and potential for JUSTIPEN activities
(medium-mass nuclei reached;dimensions 109!)
Honma, Otsuka et al., PRC69, 034335 (2004)
A. Arima and S. Yoshida,
Nucl. Phys. A219, 475 (1974)
See references in
A.T. Kruppa and W. Nazarewicz,
Phys. Rev. C69, 054311 (2004)
heavy ion coll.
Fission and Fusion
nuclear collective dynamics
talk by Barrett
K. Nollett, Phys.Rev. C63, 05400 (2001)
P. Navratil, Phys.Rev. C70, 054324 (2004)
P. Navratil, Phys. Rev. C70, 054324 (2004)
P. Navratil et al., Phys. Lett. B634, 191 (2006)
Also true in many-channel case!
of the S-matrix
Contour is discretized
GSM Hamiltonian matrix
is complex symmetric
One-nucleon radial overlap integral:
One-nucleon radial overlap integral in GSM:
usually approximated by
a WS wave function at
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
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).
in (d,p) and (d,n)
C.F. Moore et al.
Phys. Rev. Lett. 17, 926 (1966)
J. Rotureau et al., DMRG
The GSM Hamiltonian
For the O-isotopes:
zero surface delta interaction
For the He-isotopes: finite-range surface Gaussian interaction
WS potential depth decreased to bind 7He. Monopole SGI strength varied
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)
talk by Ogata channels
talk by Nakatsukasa
Kyoto (vis. prof.)
Coupling of nuclear structure and reaction theory
(microscopic treatment of open channels)
Current US effort (RIATG)
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
Resonance states, properties channels
Can one calculate G with sufficient accuracy?
For narrow resonances,
Resonant states, properties channels
Humblet and Rosenfeld: Nucl. Phys. 26, 529 (1961)
S can be taken as a sphere of radius R:
Also true in many-channel case!
“Spin-orbit splitting” in GSM channels
Influence of configuration mixing and continuum coupling