1. No category

Nuclearphysicsand
theUnifiedNuclearModel
ofAageBohrandBenMo9elson
1975
-Theclassicalview:theliquiddropmodel
-Thequantumview:theindependent
parEcle(shell)model
-Reconcilingthetwoviews
-CollecEvemoEon:rotaEons&vibraEons
-  Someongoingnewstuff
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Rutherfordsca9ering(1911)
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Nucleardensityandradius
- Densityapprox: 2.1017kg/m3
-Numberdensityapprox:0.15nucleons/fm3
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Nuclearradius:
Volume:
NB:Nuclearsizescaleswithnumberof
cons4tuents:
LIKEADROPOFLIQUID!
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BindingEnergypr.Nucleon
Moststable
FUSION
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FISSION
• 
Semiempiricalmassformulabasedon
theliquiddropassumpEon:
• 
• 
Volume(bulk):
• 
Coulombrepulsion:
• 
Symmetryenergy:
• 
PairingcorrecEon:
Surfacereducesbinding:
JensJørgenGaardhøje.NuclearPhysics.
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NielsBohr’sCompoundNucleusmodel
(1936)
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ShellstructureandMagicNumbers
• 
• 
ParEcularstabiliEesatparEclenumbers:
2,8,20,28,50,82,126….
areobserved.
Thesenumberarecalledthemagicnumbers
andsuggestthatanatomicnucleushasa
shellstructureliketheatom
• 
=>TrytosolvetheproblemusingacentralpotenEal(eventhoughnucleardensityprofiledoes
notsuggestthatthiswillwork).
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EnergylevelsobtainedbysolvingSchrödingerequaEon
WavefuncionsareanEsymmetricfor
fermionicsystems
RadialequaEon
WhatpotenEalVtouse?
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Woods-SaxonpotenEal
Sincenucleondensityisconstantin
nuclearinterior:
TrywithpotenEalwithflatcentralpart.
ρ
R r
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VWS+VslreproducesMagicNumbers
Needspin-orbit
couplingterm
Leveldegeneracyis
(2j+1)
Mayer,Jensen,…
1949
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WhydoestheShellModelwork?
p’
p
pi’
pi
pF
Sca9eringsonlyallowed
iffinalstatesare
outsideFERMIsphere
Momentumandenergy
conservaEon
f
1
Sca9eringissupressed
insidethenucleusdue
toPauliBlocking
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2
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E/EF
10
But,shellmodeldoesNOTexplainlow-lying2+states
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CollecEveexcitaEonsinvolveallthenucleonsin
coherentmoEon
Bohr,Mo9elson,Rainwater1953
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VibraEonalstatesin120Te
seeninexperiment
V
r
+
-
+
-
3phononstates
+
2phononstates
IfthevibraEonis
harmonicthestatesare
equidistant
(cf.Harmonicoscillator)
1phononstate
G.S.
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RotaEonalspectrum
γ
γ
γ
γ
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RotaEonalenergy
=--->spectrumofrotaEonalstates
Rigidclassicalrotor:
RigidQMrotor:
Jisthemomentofiner-a
Reflection symmetry ψ(-r)= ψ(r)=>onlystateswithposiEveparityareallowed
=>onlyEVENvaluesoftherotaEonalangularmomentum
E
=>
=>
Obtain
moment
ofinerEaJ
I
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MomentofinerEaofnuclei
J
Rigidbodylimit
Backbend:breakofa
pairofnucleonsdue
toCoriolisforce
I
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CoriolisanE-pairing
Fcoriolis=2mvxω
ω
+j
+mj
+j
+j
+j
-mj
-j
-j
CoriolisforcesinarotaEngnucleuscanbreakapairofnucleons
movinginEmereversedorbits
andalignthesingleparEcleangularmomentaalongtherotaEonaxis
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Nilssonshellmodelfordeformednuclei
Use3-Dimdeformedharmonicoscillatorpoten4al
withaxialsymmetry,spinorbitandl2terms
=>solvetheSchrödingerequaEontogetnuclear
energylevels.
SvenGösta
Nilsson.
DeformaEon=>J=l+sisnolongeragoodQ.N.!
àDegeneracyofJstatesislised.
⇒ Labelsinglenucleonstatesby:
⇒ N=n3+n┴ ;
⇒  Λ (component of l on symmetry axis) and
⇒  Ω (component of j on symmetry axis)
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Nilssonstates
NewShell
Closures(=
magic
numbers)for
deformed
nuclei
Shellclosures
(=magic
numbers)for
spherical
nuclei
Predictlarge
deformaEonfor
N=86,f.ex.
nucleus152Dy
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SuperdeformaEon
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SEARCHFORSUPERHEAVYELEMENTS
Predictedislandofstabilityat
Z≈110-120andN≈175-185
Z=109-118
Longestlived
istheheaviest
isotope=>
Probably
morestable
cansEllbe
found.
Z=115
recently
announced
(2013)
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JensJørgenGaardhøje.NuclearPhysics.
Dubnium
105Db(29hrs)
Seaborgium
106Sg(1.9mn)
Bohrium
107Bh(61s)
Hassium
108Hs162(12mn)
DoublyMagic?
Copernicium
112Cn(4.2mn)
UnunocEum
118Uuo(0.89
ms)
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11Li
Nucleifarfromstability:
HaloNuclei
Weakly
bound
neutrons
=>
neutron
halo
PhysicsnearDRIPLINEofrelevancefor
AstrophysicalreacEons(s&sprocess)
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ProposedAcceleratordrivenfissionsystem:Myrrha(Belgium)
AcceleratordrivenFusion
&
TransmutaEonofexisEng
Nuclearwaste
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QuarkGluonPlasma(QGP)
ThestateoftheUniverseuptothefirstmicrosecond.
CollecEveeffects=>Fluidquarksoup
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