Consequences of Sub-Zeptosecond Lifetimes in Near-Barrier Reaction Dynamics

Mahananda Dasgupta

Department of Nuclear Physics, Australian National University, Canberra

With: K. J. Cook, D.J. Hinde, S. D. Kalkal, D. H. Luong, E.C. Simpson, E. Williams

Collaboration: A. Diaz Torres (Italy), L. Gasques (Brazil), P.R.S. Gomes (Brazil)

ground state

excited quantum states

Many body quantum system

Quantum states 0

+

Not an “elementary”

particle

§  Colliding nuclei in a superposition of quantum states → Distribution of fusion barrier energies

r

V

r

V

Dasso et al., Nucl. Phys. A 405 (1983) 221

Rowley et al., Phys. Lett. B, 254, 25 (1991)

Fusion enhanced for E<VB

VB

E

Ground state

excited states

Quantum states

Well bound nuclei

τ ≥ ps

Weakly bound nuclei

τ ~ zs

Separation/breakup energy

What happens when nuclear

decay lifetimes are similar to the

collision time? (few 10-22 s)

excited states

Quantum states

What happens when nuclear

decay lifetimes are similar to the

collision time? (few 10-22 s)

halos

stable weakly

bound

Weakly bound nuclei

τ ~ zs

Ground state

Separation/breakup energy

Fusion suppression at above barrier energies

Dasgupta et al., PRL 82, 1395 (1999) Dasgupta et al., PRC 70, 024606 (2004)

4He

3H

7Li Weakly-bound

0.80.911.11.21.31.41.5

Fusion of 7Li+209Bi suppressed relative to single-barrier calculation – unlike 18O+198Pt

18O+198Pt7Li+209Bi

216Rn

Q (→α+t) = -2.467 MeV

0.80.70.60.50.40.30.20.10.0

Ec.m./VB(MeV)

σ fus/R

02

7Li+209Bi

σfus = σER+σfis

26% reduction

ProjecFlebreakupintoclusterconsFtuents:

reducescompletefusion

Completefusion

Incompletefusion

Directbreakupintoclustercomponents

(elasFcbreakup,no-capturebreakup)

Completefusionandbreakup

Gasques et al., PRC 79, 034605 (2009)

All measurements at ANU

Fusion from (ER α-decay) + fission

1 – FCF

Reduction of complete fusion

Signorini et. al., EPJ A5, 7 (1999) Tripathi et al., PRL88,172701 (2002) Wu et al., PRC68, 044605 (2003)

Gomes et al.,PRC73,064606 (2006) Rath et al., PRC 79, 051601 (2009)

Dasgupta et al., PRC70 (2004) 024606 Mukherjee et al., PLB636, 91 (2006)

Gasques et al., PRC 79, 034605 (2009) Dasgupta et al., PRC81, 024608 (2010) RIB review: Keeley et al., Prog. Part. Nucl. Phys. Rep. 424, 1 (2007)

Gasques et al., PRC 79, 034605 (2009)

1 – FCF

Is the projectile breakup threshold all that matters?

Reduction of complete fusion

All measurements at ANU

Fusion from (ER α-decay) + fission

InvesFgaFngmechanismscausingbreakup

Completefusion

Incompletefusion

Isthisthecompletepicture?Whatprocessescancausebreakup?Wheredoesbreakupoccur?

Measurementsatsub-barrierenergies:minimizesabsorpFon

Directbreakupintoclustercomponents

(elasFcbreakup,no-capturebreakup)

Beam

Target

BackFront

MeasuringcoincidentchargedfragmentsBALiNarrayMicronSemiconductorDouble-SidedSiliconStripDetectors

“lampshade”configuraFon:backangles“front-back”configuraFon:forwardandbackwardangles115°<θ<170°30°<φ<330°

Detectortelescopegivingp,d,tidenFficaFon

ExperimentalResults:2-DplotsofcoincidentfragmentenergiesE1vs.E2

4He + 4He

3H + 4He

2H + 4He

identified 2H + 4He

Reaction Q-value

D.H. Luong, ANU PhD Thesis

identified 3H + 4He

7Li + 208Pb

Q-valuespectrum–transfer-triggeredbreakup

Luong et al., PRC 88, 034609 (2013) 207Tl*

Luong et al., PRC 88, 034609 (2013)

Structureandthresholds

6.0315 6He+p

7Li

Γ=6.6eVτ~10-16sD.R.Tilleyetal.,Nucl.Phys.A490,3(1988)

0+ 0.000

2+ 3.030

8Be

1+ 0.000

3+ 2.186

6Li

αd 1.474 MeV

3+0.702MeVΓ=24keV Γ=1.5MeV

Long-livedandpromptbreakup

Rmin

α1

α2

ProjecFle

Target

DelayedBreakupDisintegraFonfarfromthetargetfollowingthepopulaFonofalong-livedresonancestate.e.g.8Be0+τ~10-16s

PromptbreakupDisintegraFonnearthedistanceofclosestapproach.DifferentinteracFonbetweeneachfragmentandthetarget.

Delayed≡AsymptoFc

Rminα1

α2ProjecFle

Target

v12

v12

RelaFveenergydistribuFons

•  Narrow resonances cannot affect fusion – long-lifetime •  Assumed that prompt breakup is 50% incoming and 50% outgoing •  Assumed that prompt breakup is 50% incoming and 50% outgoing

PromptdisintegraFon

051015 Erel(MeV)

Luong et al., PLB 695, 105 (2011); PRC 88, 034609 (2013)

8Be0+Associatedwith

8Be2+

Q vs. Erel characterizes all breakup processes

7Li

4He 3H

4He

4He 4He

D.H. Luong et al., Phys. Lett. B695, 105 (2011)

7Li 8Be ↓

7Li

D.H. Luong et al., Phys. Rev. C 88, 034609 (2013)

Luong et al., Phys. Lett. 695, 105 (2011)

n-stripping → 6Li → 4He + 2H

Erel = E*(2.18 MeV ) + Q (-1.5 MeV)

208Pb*

208Pbgs

8Be → 4He + 4He

7Li → 4He + 3H

Erel (MeV)

ü α-d pairs - Q, Erel consistent with n-transfer followed by breakup mostly from 6Li excited state at 2.18 MeV

τ = 3 × 10-20 s

Q vs. Erel characterizes all breakup processes

Breakupfor7Liincidentonmedium-masstargetnuclei

Sunil Kalkal et al, in preparation Sunil Sunil KalkalKalkal et al, in preparation et al, Phys. Rev. C93, 044605 (2016)

•  p-transfer forming 8Be dominates (driven by stability of α; Q ≥ +9 MeV) •  No direct breakup (7Li → α + t) seen for medium mass targets

Wheredoespromptbreakupoccur?

Rmin

α1

α2

P

T

Rmin

α1

α2

P

T

IncomingtrajectoryCaninfluencefusion

OutgoingtrajectoryCannotinfluencefusion(breaksuparerreachingthefusionbarrier)

θ12

Front-backangledetectorconfiguraFonsensiFvetodisintegraFonbeforeRmin

Beam

BreakuplocaFonfromexperimentalobservables

Before Rmin

After Rmin After Rmin Before Rmin

β

0

60

120

180

E.C. Simpson et al., Phys. Rev. C 93, 024605 (2016)

EdSimpson,Talklaterinthissession

BreakuplocaFonfromexperimentalobservables

, recent work, unpublished (2016)

Before Rmin

After Rmin After Rmin Before Rmin

β

0

60

120

180

EffectoflifeFmeinpromptbreakuplocaFon:Sub-barrierbreakupmeasurements

Rmin

α1

α2

P

T

Rmin

α1

α2

P

T

UnboundstatepopulatedImmediatebreakup

Expectdifferencesinopeningangleθ12andrelaFveenergyErel.LargeErelcorrespondtoearlierdisintegraFon

θ12

UnboundstatepopulatedLifeFmedelaysbreakup

Pα1

α2

P

UnboundstatepopulatedImmediatebreakup

UnboundstatepopulatedLifeFmedelaysbreakup

EffectoflifeFmeinpromptbreakuplocaFon:Above-barrierfusionsuppression

Incomplete fusion or no fusion

Fusion T T

§ Breakup measurements made at a range of energies § Probability as a function of distance of closest approach

Rafiei et al., PRC 81, 024601(2010)

A. Diaz-Torres et al, PRL 98, 152701 (2007)

Prompt breakup probabilities at the fusion barrier

Predict above-barrier complete and incomplete fusion

D.J. Hinde et al., PRL 89 (2002) 272701

Experimental results demand advances in models

AbsolutebreakupprobabiliFes

R. Rafiei et al., PRC 81, 024601 (2010)

(surface separation)

K. Cook et al., PRC 93, 064604 (2016)

BreakuplifeFmeandcompletefusionsuppression

K. Cook et al., PRC 93, 064604 (2016)

Reduction of complete fusion

BreakuplifeFmeandcompletefusionsuppression

Reduction of complete fusion

K. Cook et al., PRC 93, 064604 (2016)

Summary and outlook

§  Only breakup before the fusion barrier affects above-barrier fusion

-  new observables can provide information on breakup location

§  What causes suppression of complete fusion? -  thought to be due to breakup of weakly bound projectile

Breakup of projectile-like nucleus following transfer is most probable

Low ZT: all breakup follows transfer

Direct breakup into cluster components

Only significant for high ZT

§  Quantum model needed to match latest experiments that are extremely sensitive to breakup modes and location

-  Lifetime of resonances (even if < zeptosecond) important -  Are lifetimes affected by proximity to target nucleus? -  Final goal – model to understand complete and incomplete fusion

-  suppression only if breakup occurs at short timescales (≤10-21s)

-  fusion suppression not fully explained

Projectile trajectory

Transfer

prob

ability

βvsθ12:asymptoFccalculaFon

0+groundstate(0.092MeV)2+state(3MeV)

CurvesshowcorrelaFonforasymptoFcbreakup

β

α1

α2

β ϑ12

v1

v2

u1

u2

7Li+58Niα+α

Observedpromptbreakupmodes

Contrib

uFon

tonon

-asymptoF

cbreakup

E = 3-4 MeV/u

D.H. Luong et al., PRC 88, 034609 (2013)

7Li6Li

Transfer

BreakupmodesdependonthecombinaFonofprojecFleandtargetnuclei

Transferfollowedbybreakup-amajorcontributortopromptbreakup

α+αα+pα+dα+t

α+pα+d

144Sm207Pb208Pb209Bi

207Pb208Pb209Bi

(Excludeslong-livedresonances)

Direct

TransferDirect

Experimentallyobtainedβvsθ12

0+groundstate2+state

Limitofdetectorcoverage

AsymptoFc

CuttoeliminateelasFcs

7Li+58Niα+α

β

E.C. Simpson et al., Phys. Rev. C 93, 024605 (2016) EdSimpson

Breakupfor7Liincidentonmedium-masstargetnucleiParFcleidenFficaFonbyt.o.f.over11cm(Z=1,2)

•  p-transfer forming 8Be dominates (driven by stability of α; Q ≥ +9 MeV)

7Li + 50Cr, Ebeam =11.7 MeV 7Li + 64Zn, Ebeam =13.6 MeV

8Be → 4He + 4He

6Li → 4He + 2H

5Li → 4He + 1H

•  No direct breakup (7Li → α + t) seen for medium mass targets

SunilKalkal

0

5

OpenquesFons

LimitaFonsofaclassicalmodelofbreakup?

Areresonancewidthscorrectclosetoaheavynucleus?

Mappingfrombelow-barrierbreakuptoabove-barrierfusionandincompletefusion:NeedabsolutebreakupprobabiliFesDetectorsystemefficiency

Key insights to develop predictive models

Prompt breakup –close to target

Transfer-triggered breakup

Focus on breakup close to target