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Background Spin-orbit energy density functional Isovector dependence Sn isotopes
Isovector properties of the nuclear spin-orbitinteraction from the quark-meson coupling model
Ellen McRae
The Australian National University
ellen.mcrae@anu.edu.au
Background
Spin-orbit energy density functional
Isovector dependence
Sn isotopes
Ellen McRae ANU
Isovector spin-orbit from QMC
Background Spin-orbit energy density functional Isovector dependence Sn isotopes
Motivation
I Exotic systemsI Reactions with neutron richI Superheavy elementsI r-process
I Skyrme energy density functional (EDF)I SuccessfulI Phenomenological
I Quark-meson coupling (QMC) modelI Spin-orbit
I Magic numbersI Energy dissipation in collisions
Ellen McRae ANU
Isovector spin-orbit from QMC
Background Spin-orbit energy density functional Isovector dependence Sn isotopes
Spin-orbit energy density functionalI Quark-meson coupling model
[Guichon et al, 1988, 1996, 2006]I Relativistic mean fieldI Quarks couple to mean meson fields (σ, ω, ρ)
HQMCSO =
−1
4M2N
[(Gσ + Gω (2µs − 1)) ρ∇ · J
+
(Gσ2
+Gω2
(2µs − 1) +3Gρ
8(2µv − 1)
) ∑q=n,p
ρq∇ · Jq]
I Free parameters (Gσ, Gω, Gρ and mσ) fixed by nuclear matterproperties
I Skyrme EDF
HSkyrmeSO = −1
2
[W0ρ∇ · J + W ′
0
∑q=n,p
ρq∇ · Jq]
Ellen McRae ANU
Isovector spin-orbit from QMC
Background Spin-orbit energy density functional Isovector dependence Sn isotopes
Isovector dependence
W ′0/W0
1 Standard Skyrme1.86 Modern Skyrme: UNEDF1 [Kortelainen et al, 2012]1.78 QMC
0.1 Standard relativistic mean field (RMF) [Sharma et al, 1995]0.2 QMC without exchange (Fock) terms and µs = µv = 1
Isovec dep. of QMC ≈ UNEDF1
≈ RMF only if both exchange and µ dropped
Ellen McRae ANU
Isovector spin-orbit from QMC
H = −1
2
[W0ρ∇ · J + W ′
0
∑q
ρq∇ · Jq]
Background Spin-orbit energy density functional Isovector dependence Sn isotopes
Sn isotopes
I Hartree-Fock-Bogoliubov calculations: hfbrad[Bennaceur, 2005]
I Compare to experimental g.s. binding energies[Wang et al, 2012] and published UNEDF1 [Erler et al, 2012]
100 110 120 130 140Mass number, A
-4
-3
-2
-1
0
1
2
3
UNEDF1SQMC
Ellen McRae ANU
Isovector spin-orbit from QMC
Background Spin-orbit energy density functional Isovector dependence Sn isotopes
Sn isotopes
∆EB =(W ′
0W0
: 1.78)−(W ′
0W0
: 1)
100 120 140 160Mass number, A
-0.4
-0.2
0
0.2
Bin
din
g e
ner
gy
ch
ang
e (M
eV)
I Isovector dependence of SOterm gives ∆E ∼ 500keV
I Significant for r-processabundances[Mumpower et al, 2016]
Ellen McRae ANU
Isovector spin-orbit from QMC
Background Spin-orbit energy density functional Isovector dependence Sn isotopes
ConclusionsQMC spin-orbit isovector dependence:
I is similar to phenomenological UNEDF1
I should be accounted for in r-process calculations
Ground state masses
Perspectives
I Shell evolution
I Driplines
I Superheavy magic numbersI Time-dependent Hartree-Fock
I Reactions with exotic nucleiI Fusion barriersI TransferI Fission
Ellen McRae ANU
Isovector spin-orbit from QMC
Background Spin-orbit energy density functional Isovector dependence Sn isotopes
References
K. Bennaceur and J. Dobaczewski,2005Comp. Phys. Comm. 168 (2005) 96.
J. Erler et al, 2012Nature 486 (2012) 509.
P.A.M. Guichon, 1988Phys. Lett. B 200 (1988) 235.
P.A.M. Guichon et al, 1996Nucl. Phys. A 601 (1996) 349.
P.A.M. Guichon et al, 2006Nucl. Phys. A 772 (2006) 1.
M. Kortelainen et al, 2012Phys. Rev. C 85 (2012) 024304.
M.R. Mumpower et al, 2016Prog. Part. Nucl. Phys. 86 (2016)86.
M.M. Sharma et al, 1995Phys. Rev. Lett. 74 (1995) 3744.
M. Wang et al, 2012Chin. Phys. C 36 (2012) 1603.
Ellen McRae ANU
Isovector spin-orbit from QMC
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