SLIDE 1 Towards Microscopic Optical potential from Coupled Cluster
FRIB-Theory Alliance workshop, June 15 2018
- P. Danielewicz
- K. Fossez
- G. Hagen
- G. Jansen
- W. Li
- N. Michel
- W. Nazarewicz
- F. Nunes
- T. Papenbrock
- G. Potel
In collaboration with:
SLIDE 2
structure and reaction channels influence each other Unification of nuclear structure and reactions
Near-threshold effects
Exotic decay modes Taking into account the coupling to the continuum states is essential for the description of drip-lines nuclei.
Nuclei far from stability
0.964 MeV 1.797 MeV 1.867 MeV
4He+2n 5He+n
2
6He
SLIDE 3
transfer reactions probe nuclear response to the addition of nucleon
information about nuclear structure from:
angular differential cross section
absolute value
position
width (in the continuum)
Nuclear structure with transfer reactions
A standard approach to reactions:
spectroscopic factor from structure model cross section from few-body/reaction models
can suffer from inconsistency between the two schemes !
SLIDE 4
Nucleon-Nucleus Optical Potential
SLIDE 5
Nucleon-Nucleus Optical Potential
Phenomenological local potential (A.J Koning, J. P. Delaroche, NPA 2003)
SLIDE 6 energy-dependent/non-local/complex
Feshbach (1958)
SLIDE 7
* all nucleons are active, chiral-EFT n-n, 3n interactions
Microscopic Optical Potential
* Goals: predictive theory for nuclear reactions, reliable/accurate extrapolations for systems far from stability.
(taken from W. Nazarewicz, JPG 2016)
SLIDE 8
Single-particle Green's function
SLIDE 9
Single-particle Green's function
SLIDE 10
Single-particle Green's function
SLIDE 11
Single-particle Green's function Dyson equation
nucleon-nucleus potential
SLIDE 12
Coupled Cluster Theory
Exponential ansatz
1p-1h 2p-2h
1p-1h operator 2p-2h operator
Similarity-transformed Hamiltonian Coupled cluster equations
(G. Hagen, T. Papenbrock, M. Hjorth-Jensen, D. J. Dean, RPP 2014)
SLIDE 13
Coupled Cluster with the Berggren basis
1p-1h 2p-2h
SLIDE 14
Coupled Cluster with the Berggren basis
SLIDE 15 5/2+ 1/2+ 3/2+
PA-CCSD Expt
17O
CC(SD) with N2LOopt : 16O and 17O
SLIDE 16 5/2+ 1/2+ 3/2+
PA-CCSD Expt
17O
CC(SD) with N2LOopt : 16O and 17O
SLIDE 17 5/2+ 1/2+ 3/2+
PA-CCSD Expt
17O
CC(SD) with N2LOopt : 16O and 17O
(J. R, P. Danielewicz, G. Hagen,
- F. Nunes, T. Papenbrock, PRC 2017)
Real part of the (diagonal) neutron S-wave potential @ 10 MeV as a function of the number of Lanczos iterations.
SLIDE 18 Volume integral of the imaginary part
- f the neutron s-wave optical potential
Expt
16O
* calculated optical potential has no absorption below 10 MeV
CC(SD) with N2LOopt : too small absorption
SLIDE 19 Volume integral of the imaginary part
- f the neutron s-wave optical potential
(EOM)-CCSD Expt
16O
* calculated optical potential has no absorption below 10 MeV * absorption can be artificially increased by using finite value for η
CC(SD) with N2LOopt : too small absorption
SLIDE 20 (taken from G. Hagen et al, 2016)
40Ca/48Ca
N2LOsat interaction (A. Ekström et al, 2015) : 2 and 3-body terms
reproduction of binding energies and nuclear radii
SLIDE 21
40Ca(n,n)40Ca
Real part of V(r,r) for the bound states in 41Ca
PA-CCSD Expt
SLIDE 22
40Ca(n,n)40Ca
Real part of V(r,r) for the bound states in 41Ca
PA-CCSD Expt CCSD Expt MeV
SLIDE 23
40Ca(n,n)40Ca @ 5.2 MeV
SLIDE 24
CCSD Expt
48Ca(n,n)48Ca
E=7.81 MeV
SLIDE 25
reaction formalism by G. Potel, F. Nunes, I. Thompson (2015)
Differential cross section for populating the g.s. in 41Ca.
Eexp(7/2-)= -8.36 MeV Epa-ccsd(7/2-)= -7.84 MeV Eexp(5/2-)= -5.78 MeV Epa-ccsd(5/2-) = 1.02 MeV
experiment GF-CC(SD) Differential cross section for populating Jπ=5/2- in 41Ca.
SLIDE 26
Coupled Cluster Green’s function with chiral-EFT nn,3n potentials
Continuum (Berggren) basis
➔ qualitative agreement with data, but overall lack of absorption ➔ preliminary results for (d,p) reactions
Microscopic nucleon-nucleus optical potential
Outlook:
➔ CCSD(T) ➔ Use of the dispersion relation starting with the CCGF potential + perturbation... ➔ other chiral-EFT interaction...
