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