nuclear isomerism: probes of nuclear structure

Nuclear Isomerism:Probes of Nuclear StructureandTools for the Future

Jennifer Jo ResslerWright Nuclear Structure Laboratory

Yale University

What is nuclear structure?

Nuclear structure is the study of nuclear excited states.

The pattern of excited states gives information on thenucleon-nucleon interaction, which we don’t understand.

atomic structure: study of atomic states created by electronic excitationsnuclear structure: study of nuclear states created by proton

and/or neutron excitations

atomic – nuclear comparisonAtomic

Can be described by a shell model, where electrons fill quantized energy levels.

Can be described by a shell model, where protons and neutrons separately fill quantized energy levels.

Nuclear

n, , m, s parity (-1) n, , m, s parity (-1)

Lowest energy levels have maximum S possible (due to Coulomb) with J = L + S = Σi + Σsi or J = Σji = Σ (i + si)

Lowest energy levels have minimum S possible due to strong force pairing with J = Σji = Σ (i + si)

Energy levels can be calculated by solving theSchrödinger equation using a central potentialdominated by the nuclear Coulomb field.

Energy levels are not easily calculated;nucleons move and interact within aself-created potential.

Spin-orbit coupling is weak Spin-orbit coupling is strongFor 3 electrons in a d orbital:

For 3 nucleons in a d orbital:

Why is the nucleon-nucleon interaction so hard to understand?

Nucleon forces do not vary with distance in a way that can be conveniently described by mathematical formulas!

Even if we could, each nucleon interacts with a few ofit’s neighbors with approximately equal forces –

many body problem

For electrons, consider each electron’s interaction withthe nucleus, then add other electrons as perturbations –

2-body problem

From the Periodic Chart to the Chart of Nuclides

AtPoBiPbTl

2, 8, 20,28, 50,82, 126, …

Magic numbers:

• Fundamental knowledge of the strong force• Formalisms of quantum mechanics (many body system)• Computational modeling and mathematics• Astrophysics• Nuclear medicine• Material science• Defense weapons (simulations)• Etc. (art, forensics, geology, … )

What use is nuclear structure?

Nuclear structure in a nut shell

• The nucleus is a bound system of protons and neutrons.• The nucleus exhibits different shapes and excitations.• Properties are understood on the basis of

single particle and collective motion.• Gamma-rays from the decay of an excited nucleus give information about the arrangement of quantum levels in a nuclear potential well, and the shape of the potential.• The arrangement of excited levels and shape delicately depend

on the nucleon number and angular momentum.

Gamma rays and energy levels

Gamma ray: pure electromagnetic radiationchange in charge distribution: electric momentschange in current: magnetic moments

Emission of a gamma-ray removes Energy Angular momentum, L

one unit L = 1, dipole M1, E1two units L = 2, quadrupole M2, E2

parity: electric (-1)L magnetic (-1)L+1

Selection rule:

|Ji - Jf| ≤ L ≤ |Ji + Jf|

and 0 → 0 transitions are forbidden

only the lowest multipolarities are probable

coincidence

What is an isomer?

nuclear isomer: an excited state that does not decay within ~ps

isomers occur for:• large changes in nuclear spin (>2)

M2, M3, E4 …• small changes in energy• large changes in structure

Isomers decay by electron conversion, gamma emission, particle emission (p, α, β+, β-)

Near closed shells

“spherical structure” : potential is spherically symmetric

ΣH = T + V ( r )i i

H = EΨ Ψi i i

each nucleon moves in an approximately spherical containing potential which represents the average interaction of each nucleon with all other nucleons

(near magic numbers)2, 8, 20,28, 50,82, 126, …

SphericalShell Model

(3p1/2)

(2f5/2)(3p3/2)

1i13/2

2f5/23p3/2

1i13/2

1h9/22f7/2

82π ν

Spherical Shell Model

Spin-orbit splitting brings down high-j states close to low-j states –large change in spin => isomers

These isomers are evidence for the shell structure of nuclei.

2p3/21f5/22p1/2

1g9/22d5/21g7/23s1/22d3/21h11/22f7/21h9/21i13/23p3/22f5/23p1/2126

In 82 < N < 126 shell,

odd isotopes;

M213/2+ i13/2

9/2- h9/2

Spherical Shell Model

Coupling between nucleons may also create isomers:

small change in energy => isomers

h9/2 ⊗ f7/2

h9/2 ⊗ i13/211-

different structure => isomers

Non-spherical nuclei“deformed structure”: spherical symmetry is lostto a first approximation, potential is axially symmetric

β2 : measure of extent of deformationspherical β2 = 0large deformation β2 ~ 0.3 – 0.4

oblate (β2 < 0) spherical (β2 = 0) prolate (β2 > 0)

If β2 ~ ± 0.1, Spherical Shell Model states are still observed.

Deformed structures dominate when there are many valence nucleons – i.e. proton AND neutron numbers far from magic

Excited energy levels

even-even Pb isotopes

010002000300040005000

110 115 120 125 130 135

even-even Rn isotopes

110 115 120 125 130

“Spherical” nuclei:

First 2+ state in N=Z Nuclei

020040060080010001200

28 30 32 34 36 38 40 42 44 46

“Deformed” nuclei:

208Pb region

78126124122120118

211Ra209Ra

203Rn202Rn201Rn

Th90 212Th

Z ~ 82, N ~126Near N = 126, Pt (Z=78) and Hg (Z=80) are nearly spherical – but at lower neutron numbers a deformed structureco-exists with the spherical.

95 100 105 110 115 120

Pt experimental data0+2+4+6+8+0+2+4+6+8+

90 95 100 105 110 115 120 125 130

Hg experimental data 0+2+4+6+8+0+2+4+6+8+

90 95 100 105 110 115 120 125

PtHgPbPoRnRa

Moller Nix Swiatecki FRDM

105 110 115 120 125 130

Po experimental data 0+0+2+2+4+4+6+8+

110 115 120 125 130

Rn experimental data0+2+4+4+6+6+8+8+

110 115 120 125 130

Ra experimental data0+2+4+6+8+

100 105 110 115 120 125 130

Calculated and Experimental E(2+)

Po (calc)Po (exp)Rn (calc)Rn (exp)Ra (calc)Ra (exp)

itatio

particle emission

entry region

continuum statistical gamma rays

yrast line

Angular Momentum, I

itatio

projectile target

compound nucleus

Heavy-ion fusion evaporation reaction:π , ν , α

(3- 6 MeV/A)

How are nuclei produced?

• fusion evaporation reactions• deep inelastic reactions• fission fragments• projectile fragmentation

How do we measure γ-rays?Ge semiconductor

- when a γ-ray enters the detector, it disturbs the e- in the Ge crystal and the resulting pulse of charge is proportional to the initial energy of the gamma ray.

Germanium arrays: Gammasphere (LBNL) CLARION (ORNL) YRAST-Ball (WNSL)

YRAST-Ball Up to 13 clover detectors

9 at 90o

4 at 138.5o

2-4 LEPS Currently: 9 clovers and 2 LEPS … ε ≈

ε ≈ 3.9%

YRAST-Ball: Yale-Rochester Arrayfor SpecTroscopy

SASSYER

beam dump

target area

carbon window

beam direction0

1.2 107

0 200 400 600 800 1000

background and contamination Rn x-rays 203Rn 202Rn

200 400 600 800 10000

2 1054 1056 10

51 106

1.2 106

400 450 500 550 600

1.2x106

400 500 600

Energy, keV

Small Angle Separator at Yale for Evaporation Residues

Target area detectors:• YRAST Ball•NYPD• Rutherford detectors• BGO calorimeter• ICEY Ball

Wright Nuclear Structure Laboratory, Yale University

Focal plane detector systems:• Solar cell array • Ge detectors … isomer array• Position sensitive PPAC’s• Silicon-strip detector• MTC, β-decay tagging system• CdZnTe array

SASSYER

delayed γ-rays

prompt γ-rays

Dual study: prompt and delayed

Isomer Decay Tagging

Recoil TOF ~ 800 ns

30Si (148 MeV) + 184W → 210Ra + 4n

Prompt γ-ray spectra

1.2 104

1.4 104

0 200 400 600 800 1000

Energy , keV

200 300 400 500 600 700 800 900

Energy , keV

209,210,211Ra

Ra x-rays

Delayed γ-ray spectra

210Ra0+

6+8+t1/2 = 1.7(2) µs

0 200 400 600 800 1000

Energy, keV

560 580 600 620 640Energy, keV

10coun

54321time (µs)

1.7(2) µs

Correlated spectra

320 400 480 560 640 720 800 880

Energy, keV

210Ra0+

6+8+ t1/2

100 200 300 400 500 600 700 800

Energy, keV

Ra x-rays

11-1112-

518232 307

218635

tentative!

4+ feeding

200 400 600 800

Energy, keV

210Ra0+

6+8+t1/2 = 1.7(2) µs

prompt γ-ray spectrum

Comparisons to isotones

0.0 0+ 0+ 0+

2+2+2+

2+4+ 4+

4+4+4+

6+8+ 6+

8+ 6+8+

206Po 208Rn 210Ra

473 ns1.7 µs

212 ns

πh9/22

Comparisons to isotopes

2+4+6+8+8+

11-10+

12+14+

6+8+8+10+11-

6+8+10+1111-12-12,13

210Ra 212Ra 214Ra

67 µs11 µs1.7 µs

333 ns

285 ns

230 ns

850 ns

6 protons above Z=82;h9/2

6 h9/22 0+, … 8+

2+(h9/22) 10+, ..

h9/2f7/2 8+

h9/2i13/2 11-

8+ isomer half-life

1.7 µs

473 ns

212 ns

10.9 µs 67 µs

126124122

210Ra 212Ra 214Ra

↑ t1/2 increases

← t1/2 decreasesMore neutron degreesof freedom – lowspin states are not‘pure’ πh9/2

More proton degreesof freedom – 8+ ofπh9/2

2 mixes withπh9/2 x πff/2

(3p1/2)(2f5/2)(3p3/2)1i13/2

2f5/23p3/2

1i13/2

1h9/22f7/2

82π ν

644 ns 910 ns

210Rn 212Rn

350 ns 99 ns

208Po 210Po

Are there other isomers?

Probably.206Po : 9- (νi13/2 x νf5/2) 1.0 µs

(3p1/2)

(2f5/2)(3p3/2)

1i13/2

2f5/23p3/2

1i13/2

1h9/22f7/2

82π ν

πh9/22

isomers in Po and Rn11- (πh9/2 x πi13/2)

Neutron-rich nuclei

large neutron excess – magic numbers no longer magic!

New shell structure –what are the new magic numbers?

Radioactive Ion Beams – (RIA?)

Isomers are excellent probes!

Far from closed shells

Λsymmetry axis

Rotational bands: E α I(I+1)

I + 8I + 9

M1’s

E2’s

Band comprised of two signature partners for even-A (even Z-even N or odd Z-odd N nuclei) favored I = 0, 2, 4, 6 ... unfavored I = 1, 3, 5, 7 ... for odd-A (even Z-odd N or odd Z-even N nuclei) favored I = 1/2, 5/2, 9/2, 13/2 ... unfavored I = 3/2, 7/2, 11/2, 15/2 ...

collective motion =>

I = J + R

rotational bands

E =(1/2I)[ I(I+1) – K2]

Nilsson model

Oblate β2 < 0

Spherical β2 = 0

Prolate β2 > 0

[N nz Λ ]ž ž

[303]7/2

[312]5/2

[321]3/2

[321]1/2[310]1/2

[312]3/2[440]1/2

[431]3/2

[422]5/2

[404]9/2

[413]7/2

[301]3/2[303]5

/2[301]1/2

-0.3 -0.2 -0.1 0.0 +0.1 +0.2 +0.3 +0.4

[431]1/2

Nilsson diagram:

K = Ω1 + Ω2 …

Deformed odd-massA~80 nuclei dominatedby [422]5/2+ and [301]3/2-

configurations:

Z = 39 N = 3979Y 5/2+ 77Sr 5/2+

81Y 5/2+, 3/2- 113 keV

Z = 41 N = 4183Nb 5/2+ 81Zr 3/2-, 5/2+ X keV

79Sr 3/2-, 5/2+ 177 keV

β2 prolate deformation

[404]9/2

[301]3/2

[422]5/2

[440]1/2

[431]3/2

[431]1/2

[413]7/2

0.0 0.1 0.2 0.3 0.4 0.5 0.6

[312]3/2

[303]7/2[310]1/2

[303]5/2[301]1/2

[550]1/2g

Nilsson diagram for A- 80 :

80Y:Z = 39, N = 41

What happens if we combine a deformed odd-proton and odd-neutron?

Gallagher-Moszkowski rules:K = Ωp + Ωn if Ωp = Λp ± ½ and Ωn = Λn ± ½K = |Ωp - Ωn| if Ωp = Λp ± ½ and Ωn = Λn ± ½

For π[422]5/2+ ⊗ ν[301]3/2- expect 4- ground state, 1- excited state

1- K = 1

80Y rotational bands

D. Bucurescu et al., Z. Phys. A 352, 361 (1995).

80Y isomers

4.7 s isomer19% beta decay81% gamma decay (229 keV)suggested to be M31- 4- decay to ground state

M3 nature confirmed

4.7 µs isomergamma decay (83 keV)suggested to be E1

π [422]5/2+ ⊗ ν [301]3/2 -

J. Döring, H. Schatz, A. Aprahamian et al., PRC 57, 1159 (1998).

A. Piechaczek, E. F. Zganjar et al., PRC 61, 047306 (2000).

C. Chandler, P. H. Regan et al., PRC 61, 044309 (2000).

80Zr beta decay

Beta decay: Gamow-Teller

4-83 keVE14.7 µs 2+

1-83 keVE14.7 µs

80Zr 0+

β+/EC

80Zr 0+

β+/EC

Either scenario feeds the µs isomer…

rp-process nucleosynthesis

32 34 36 38 40 42 44

H. Schatz et al., Phys. Rep. 294, 167 (1998).X-ray burst > 10% reaction flow

Neutron Star

Donor Star(“normal” star)

Accretion Disk

The ModelNeutron stars:1.4 Mo, 10 km radius(average density: ~ 1014 g/cm3)

Typical systems:• accretion rate 10-8/10-10 Mo/yr (0.5-50 kg/s/cm2)• orbital periods 0.01-100 days• orbital separations 0.001-1 AU’s

X-ray burst From H. Schatz, MSU

Astrophysical implications of 80Zr t1/2

40 41 42 43 44

6.85 s

X-ray burst coolswhile 80Zr decays;proton capture on80Y becomes moredifficult.

80Zr set-up

MTC195 MeV 58Ni on 500 µg/cm2 24Mg

Oak Ridge National Laboratory

0+80Zr

83 keV

β+/EC

4.7 µs1+

RMS: Recoil Mass Spectrometer

Oak Ridge National Laboratory, Holifield Heavy Ion Research Facility

Recoil Mass Spectrometer

Momentum Separator (P/Q)

Mass Separator (A/Q)

ED2Q6 Q7

“M/Q separator” or“mass separator”

0 5 10 15 20

Time (s)

80Zr half-life

TAC:Start: scintillator (β)Stop: LOAX (low energy γ)

80Zr t1/2: 4.1(8) s

J. J. Ressler, W. B. Walters, M. Wiescher, A. Aprahamian, et al. Phys. Rev. Lett. 84, 2104 (00).

83 keV

β+/EC

4.7 µs1+

Astrophysical implications of 80Zr t1/2

40 41 42 43 44

X-ray burst remains warmwhile 80Zr decays; protoncapture on 80Y becomespossible.

Does 1- beta decaying isomer play a role?

IDT experiment set-up

85 MeV 28Si on 300 µg/cm2 54FeOak Ridge National Laboratory

delayed γ-rayprompt γ-rays

Isomer Decay Tagging83 keV

Recoil TOF ~ 3.5 µs

t1/2 = 4.7 µs

CLARION: Clover Array for Radioactive ION beams

11 clovers :~ 2.5% efficiency for 1.3 MeV γ-rays

5 at 90o

4 at 132o

2 at 155o

IDT results0

1.5 104

0 50 100 150 200 250 300 350

80Y (pn)

80Sr (2p)

79Sr (2pn)

79Rb (3p)

Energy, keV

3 x 104

0 1000

6 x 1041.5 x 104

1.0 x 104

299334

100 200 300 400 500

Energy, keV

83; 80Y

511; γ−γ

175; 80Rb

78; 80Rb

J. J. Ressler et al., PRC 63, 067303 (01).

143193

238300

83 keV

500 1000

Energy, keV

289 300314

338 431 527538 589 624 814

9511004 1030

E* = 312 keV

But why is this state isomeric?

1-83 keVE14.7 µs

4-M3 229 keV

324 731

β2 prolate deformation

[404]9/2

[301]3/2

[422]5/2

[440]1/2

[431]3/2

[431]1/2

[413]7/2

0.0 0.1 0.2 0.3 0.4 0.5 0.6

[312]3/2

[303]7/2[310]1/2

[303]5/2[301]1/2

[550]1/2g

Nilsson diagram for A 80 :

2+:π [422]5/2+ ⊗ ν [431]1/2+

Compare with N=4179Sr ½+ band : similar moment of inertia – very deformed

=> 2+ state may be a shape isomer

1- is not ‘pure’ : [413]7/2+ ⊗ [303]5/2-, [422]5/2+ ⊗ [312]3/2-, [431]3/2+ ⊗ [301]3/2-, [431]3/2+ ⊗ [303]5/2-, [431]1/2+ ⊗ [301]3/2-

K-isomers

high-K

Expect K-isomers in regions wherehigh-Ω orbitals of deformed nuclei are near the Fermi surface

178HfK = 00+

K = 88+

K = 1616+

1.1 MeV

2.4 MeV

64% ν[514]7/2- x ν[624]9/2+

36% π[404]7/2+ x π[514]9/2-

ν[514]7/2- x ν[624]9/2+

x π[404]7/2+ x π[514]9/2-

K-isomers

Z = 74, N = 104 Ta/Hf region A ~ 180near stabilitylong-lived isomers (sec – years)

Z = 66, N = 104 Dy, A ~ 170neutron driplineunstable beams

Z = 66, N = 74 A ~ 130, 140proton driplineµs isomers – IDT

Heavy elements – No (Z = 102) and Z=110 have been reported

A~170-190

YbLuHfTaWReOs

100 105 110

proton rich

neutron rich

Need:unstable beams (N>Z) oralternative production mode(not fusion evaporation)

Non-structure interestsAstrophysics: most elements are produced in neutron-capture processes

s-process : proceeds via successive neutron captures and beta decays

slow neutron capture rate;Rcapture << Rbeta

r-process : proceeds via successive neutron captures and beta decays

fast neutron capture rate;Rcapture > Rbeta

Yb 104 105 106176Lu

3.7 hours

4 x 1010 years

Non-structure interests

Potential energy source: controlled triggering of isomer decay

2.4 MeV, t½ = 31 years 40 ± 20 keV

observed: Phys. Rev. Lett. 82, 695 (1999).refuted: Phys. Rev. Lett. 87, 072503 (2001).

γ-ray lasers: 43,44,45,46Sc, 58Co, 57Fe, 63Ni, 65,67Zn, 74Ga, 69,73,75,77Ge, 76As, 77,79Se, 77,79,83Kr, 83Rb,90,92Nb, 99Mo, 105Ru, 100,105Rh, 107Pd, 103,107,109,110,111,116,118,120Ag, 116,119In, 109Cd, 115Sn,118,120,122,126Sb, 120,122I, 125Xe, 134,140Cs, 137,138La, 140Nd, 141,152,154Eu, 153,157Gd, 157,169,171Er,165,167Tm, 172,173,177Lu, 173,175Hf, 177,181,183Ta, 179,180Re, 181Os, 187Pt, 189Au, 207,209,210Po,206Bi, 243Cm

Bio-engines??

Chart of Nuclides

Z Neutron rich nuclei: very l i t t le known!

Exotic proton rich nuclei

Summary of isomer studies presented

Spherical – 210Raprobe: spherical structuretool: correlate states across the µs-isomer

Deformed – 80Yprobe: deformed structuretool: 80Zr beta decay

and to correlate states across the µs-isomer

Understanding why certain states are isomeric is important!

THANKS!

Is a recoil/mass separator necessary?

Not always –beam

YRASTBall and target chamber

90Zr foil and BGO detectors

200 280 360 440 520

delayedprompt*.00075

counts

Energy (keV)

Other techniques

a) thick target experiments -- recoil is stopped

-- short-lived (ns) isomers

b) beam pulsing-- beam on/off regularly-- short-lived isomers

c) Moving tape collector

d) fission => isomers

beamtarget

Comparisons to isotopes

2+4+6+8+8+

11-10+

12+14+

6+8+8+10+11-

2+4+4+

6+8+10+1111-12-12,13

210Ra 212Ra 214Ra

67 µs11 µs2.2 µs

333 ns

285 ns

230 ns

850 ns

6 protons above Z=82;h9/2

6 h9/22 0+, … 8+

2+(h9/22) 10+, ..

h9/2f7/2 8+

h9/2i13/2 11-

7000600050004000300020001000time (ns)

t1/2 = 456

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