Isomer Spectroscopy in Near-Spherical Nuclei Lecture at the ‘School cum Workshop on Yrast and Near-Yrast Spectroscopy’ IIT Roorkee, October 2009 Paddy.

Isomer Spectroscopy in Near-Spherical Nuclei

Lecture at the ‘School cum Workshop on Yrast and

Near-Yrast Spectroscopy’

IIT Roorkee, October 2009

Paddy ReganDepartment of Physics

University of SurreyGuildfordGU2 7XH

Outline• What is an isomer ? • Electromagnetic transition rates.• Weisskopf Single-Particle Estimates• Shell Structure in near spherical nuclei.

– Odd-A singly magic nuclei (e.g., 205Au126)

– Why are E1s ‘naturally’ hindered ?

• Seniority isomers, j2 & jn configurations ?• Near Magic nuclei.

– Limited valence space? Core breaking?

• Magnetic properties: g-factors in seniority isomers.

What is an isomer ?

Why/when do nuclear isomers occur ?(i) large change in spin (‘spin-trap’)(ii) small transition energy between states (seniority isomers) (iii) dramatic change in structure/shape (fission isomers) and/or underlying symmetry (K-isomers)

What information do isomers gives you ? Isomers occur due to single particle structure. For example, transitions are hindered between states with different structures (note, this is not case for seniority isomers).

Metastable (long-lived) nuclear excited state.‘Long-lived’ could mean: ~10-19 seconds, shape isomers in a-cluster resonances or ~1015 years 180Ta 9-→1+ decay.

‘High-spin’ and-decaying isomers just above 208Pb, basicallyas a result of ‘yrast’ (spin) traps..

9/2+

11/2+

(13/2+)99.984% -decay branch, 91% to 13/2+ isomer in 207Pb,7% to 1/2- ground state in 207Pb, Q ~ 9 MeV per decay

0

687

1065

1428 (17/2+)

1462 (25/2+)

211Po

T1/2=25secs

T1/2=0.5 secs

0

115

238

1-

2-

0-

9- 250

T1/2 = 61 min

T1/2 = 25 min- branch =33% branch = 67%

212Bi

212Bi, Z=83, N=129, 9- from vg9/2 x h9/2

Yrastness is what causes these isomers…they simply have ‘nowhere’ to go to (easily).This yrastness is itself caused by high-j intrudersin the nuclear single particle spectrum….

Ex>1MeV, T1/2>1ms (red), T1/2>1hour (black)

From P.M. Walker and G.D. Dracoulis, Nature 399, p35 (1999)

EM Transition Rates

2

22

20 !!12

12Lm

cLL

cLLP

L

Classically, the average power radiated by an EM multipole field is given by

m(L) is the time-varying electric or magnetic multipole moment.is the (circular) frequency of the EM field

dvLmLm iffi *

For a quantized (nuclear) system, the decay probability is determined by the MATRIX ELEMENT of the EM MULTIPOLE OPERATOR, where

i..e, integrated over the nuclear volume.

(see Introductory Nuclear Physics, K.S. Krane (1988) p330).

We can then get the general expression for the probability per unit time forgamma-ray emission, (L) , from:

2

12

20 !!12

121lm

cLL

LLPL fi

L

Note: Transition rates get slower (i.e., longer lifetimes associated with) higher order multipole decays

Weisskopf Single Particle Estimates:

These are ‘yardstick’ estimates for the speed of electromagnetic decays for a given electromagnetic multipole.

They depend on the size of the nucleus (i.e., A) and the energy of the photon (E

2L+1)

They estimates using of the transition rate for spherically symmetricproton orbitals for nuclei of radius r=r0A1/3.

Weisskopf estimates

sp for 1Wu at A~100 and E = 200 keV

M1

2.2ps

M2

4.1s

M3

36 s

M4

43Ms

E1

5.8fs

E2

92 ns

E3

0.2s

E4

66Ms

i.e., lowest multipole decays are favoured….but need to conserve angularmomentum so need at least = Ii-If for decay to be allowed.

Note, for low E and high-l, internal conversion also competes/dominates.

'Near-Yrast' decays

0

500

1000

1500

2000

2500

3000

3500

0 2 4 6 8 10

Spin of decaying state, I

Ex

cit

ati

on

en

erg

y

The EM transition rate depends on E2+1,, the highest energy transitions for the lowest are (generally) favoured. This results in the preferential population of yrast and near-yrast states.

'Near-Yrast' decays

0

500

1000

1500

2000

2500

3000

3500

0 2 4 6 8 10


Ex

cit

ati

on

en

erg

y


'Near-Yrast' decays

0

500

1000

1500

2000

2500

3000

3500

0 2 4 6 8 10


Ex

cit

ati

on

en

erg

y


'Near-Yrast' decays

0

500

1000

1500

2000

2500

3000

3500

0 2 4 6 8 10


Ex

cit

ati

on

en

erg

y


'Near-Yrast' decays

0

500

1000

1500

2000

2500

3000

3500

0 2 4 6 8 10


Ex

cit

ati

on

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erg

y


= gamma-ray between yrast states

'Near-Yrast' decays

0

500

1000

1500

2000

2500

3000

3500

0 2 4 6 8 10


Ex

cit

ati

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y

The EM transition rate depends on E2+1, (for E2 decays E5)

Thus, the highest energy transitions for the lowest are usually favoured. Non-yrast states decay to yrast ones (unless very different , K-isomers

= ray from non-yrast state.

= ray between yrast states

'Near-Yrast' decays

0

500

1000

1500

2000

2500

3000

3500

0 2 4 6 8 10


Ex

cit

ati

on

en

erg

y





'Near-Yrast' decays

0

500

1000

1500

2000

2500

3000

3500

0 2 4 6 8 10


Ex

cit

ati

on

en

erg

y





'Near-Yrast' decays

0

500

1000

1500

2000

2500

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3500

0 2 4 6 8 10


Ex

cit

ati

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y

Yrast Traps

The yrast 8+ state lies lower in excitation energy than any 6+ state…i.e., would need a ‘negative’ gamma-ray energy to decay to any 6+ state

'Near-Yrast' decays

0

500

1000

1500

2000

2500

3000

3500

0 2 4 6 8 10


Ex

cit

ati

on

en

erg

y

The yrast 8+ state can not decay to ANY 6+.

The lowest order multipole allowed is =4 I=8+ →4+ i.e., an E4 decay.

Yrast Traps

Clusters of levels + Pauli Principle magic numbers, inert cores

Concept of valence nucleons – key to structure. Many-body few-body: each body counts.

Addition of 2 neutrons in a nucleus with 150 can drastically alter structure

Independent Particle Model

• Put nucleons (protons and neutrons separately) into orbits.• Key question – how do we figure out the total angular momentum of a

nucleus with more than one particle? • Put 2j + 1 identical nucleons (fermions) in an orbit with angular momentum

j. Each one MUST go into a different magnetic substate. • Angular momenta add vectorially but projections (m values) add

algebraically. So, total M is sum of m’s

M = j + (j – 1) + (j – 2) + …+ 1/2 + (-1/2) + … + [ - (j – 2)] + [ - (j – 1)] + (-j) = 0

M = 0. So, if the only possible M is 0, then J= 0

Thus, a full shell of nucleons always has total angular momentum 0. This simplifies things.

Podolyak et al., Phys. Lett. B672 (2009) 116

N=126 ; Z=79. Odd, single proton transition; h11/2 → d3/2 state (holes in Z=82 shell).

Selection rule says lowest multipole decay allowed is =11/2 - 3/2 = 4.Change of parity means lowest must transition be M4.

1Wu 907 keV M4 in 205Au has T1/2= 8secs.

‘Pure’ single particle (proton) transition from 11/2- state to 3/2+ state.

(note, decay here is observed following INTERNAL CONVERSION).These competing decays (to gamma emission) are often observed in isomeric decays

More complex nuclei…

• Signatures of nuclear structure help show us which regions of the nuclear chart are explained by ‘single-particle’ excitations

• or deformed regions (see Phil Walker’s lecture).

R(E(4+) / E(2+)) Systematics plot from Burcu Cakirli

e.g., 128Cd, isomeric 440 keV E1 decay.1 Wu 440 keV E1 should have ~4x10-15s; Actually has ~300 ns (i..e hindered by ~108

2

8

20

28

(40)

50

V= SHO + l2.+ l.s.

82

1s1/2

1p3/2

1p1/2

2s1/2

3s1/2

1d5/2

1d3/2

2d3/2

2d5/2

1g7/2

1g9/2

1h11/2

1f7/2

1f5/2

2p3/2

2p1/2

2f7/2

1h9/2

1i13/2Why are E1 s isomeric?

E1s often observed with decay probabilities Of 10-5 →10-8 Wu

E1 single particle decays need to proceed between orbitals which have Delta L=1 and change parity, e.g.,

f7/2 and d5/2

or g9/2 and f7/2

or h11/2 and g9/2

or p3/2 and d5/2

BUT these orbitals are along way from each other in terms of energy in the mean-fieldsingle particle spectrum.

2

8

20

28

(40)

50

V= SHO + l2.+ l.s.

82

1s1/2

1p3/2

1p1/2

2s1/2

3s1/2

1d5/2

1d3/2

2d3/2

2d5/2

1g7/2

1g9/2

1h11/2

1f7/2

1f5/2

2p3/2

2p1/2

2f7/2

1h9/2



f7/2 and d5/2

or g9/2 and f7/2

or h11/2 and g9/2

or p3/2 and d5/2

What about typical 2-particle configs. e.g.,

I=5- from (h11/2)-1 x (s1/2)-1

I=4+ from (d3/2)-1 x (s1/2)-1

2

8

20

28

(40)

50

V= SHO + l2.+ l.s.

82

1s1/2

1p3/2

1p1/2

2s1/2

3s1/2

1d5/2

1d3/2

2d3/2

2d5/2

1g7/2

1g9/2

1h11/2

1f7/2

1f5/2

2p3/2

2p1/2

2f7/2

1h9/2



What about typical 2-particle configs. e.g.,

I=5- from mostly (h11/2)-1 x (s1/2)-1

I=4+ from mostly (d3/2)-1 x (s1/2)-1

No E1 ‘allowed’ between such orbitals.

E1 occur due to (very) small fractions of the wavefunction from orbitals in higher shells.

Small overlap wavefunction in multipole Matrix element causes ‘slow’ E1s

2 valence nucleon j2 configurations in magic; magic+-2 nuclei

Seniority (spherical shell residual interaction) Isomers

Geometric Interpretation of the residual

interaction for j2 configuration coupled to Spin J

1

121cos for

cos11111

cos2

121

22112211

2122

21

2

jj

jjJJjjj

jjjjjjjjJJ

therefore

jjjjJ

111 jj 1JJ

Use the cosine rule and recall that the magnitude of the spin vector of spin j = [ j (j+1) ]-1/2

122 jj

interaction gives nice simple geometric rationale for Seniority Isomers from

E ~ -VoFr tan (/2)

for T=1, even J

0

2

4

6

8

180

E(j2J)

90 0

2

468

e.g. J= (h9/2)2 coupled to

0+, 2+, 4+, 6+ and 8+.

interaction gives nice simple geometric rationale

for Seniority Isomers from E ~ -VoFr tan (/2)

for T=1, even J

02

4

68

See e.g., Nuclear structure from a simple perspective, R.F. Casten Chap 4.)

Study the evolution of shell structure as a function of N:Z ratio.

208Pb (Z=82, N=126)

132Sn (Z=50, N=82)

56Ni (Z=28, N=28)

50

82

126

28 (Proton) holes in high-j intruders (f7/2, g9/2 and h11/2) gives rise to ‘seniority isomers’ ‘below’ doubly magic shells.

Expect 8+ and 10+ isomers in 130Cd and 206Hg.

config.) or (i.e.,current of

sign direction/ and state) of mom.

ang. (i.e. loopcurrent of size

reflectsmoment magnetic

x y classicall

AI

g = / I , can use ‘Schmidt model’ to give estimates for what the g-factors should be for pure spherical orbits.

Can measure g directly from ‘twisting’ effect of putting magnetic dipole moment, , in a magnetic field, B. Nucleus precesses with the Larmor frequency, L = gNB

EM Selection Rules and their Effects on Decays

• Allows decays have:

M9 M7, M5, M3, and ; E10 and E8 E6, E4, E2,

torestricted now decays Allowed :nrestrictiofurther a adds This

parity. thechangenot can n transitio thehere thus,

states, final and intialbetween parity conserve toalso Need

. 10 and 7,8,92,3,4,5,6,

of momentumangular carrying

photons with proceed toallowed are

4 to6 from decays e.g.,

II

IIII fifi

e.g., 102Sn52

Why do we only observe the E2 decays ?

Are the other allowed decays present ?

E E2 (1Wu)

M3

(1Wu)

E4

(1Wu)

48

(6+→4+)

112s 782,822 s 2.5E+14s

555 (6+→2+)

66,912s

497

(4+→2+)

0.9ns 61ms 180,692s

1969

(4+→2+)

751ms

102Sn

Conclusion, in general see a cascade of (stretched) E2 decays in near-magic even-even nuclei.

What happens next?

Q. How do you generate higher angular momentum states when the maximum spin that valence space is used up (i.e. j2 coupled to Jmax = (j-1)) ?

A. Break the valence core and excite nucleons across magic number gaps. This costs energy (can be ~3-4 MeV), but can result in large spin increases.

What about core breaking?We can have cases where low-energy (~100 keV) E2 decays competing with high-energy (~4 MeV) E4 transitions across magic shell closures, e.g. 54Fe28.

Z=26; N=28 case. • 2 proton holes in f7/2 shell.• Maximum spin in simple valence space is I=6+. • i.e., (f7/2)-2 configuration coupled to I= 6+

Additional spin requires exciting (pairs) of nucleons across the N or Z=28 shell closures into the f5/2 shell.

E E2 (1Wu)

M3

(1Wu)

E4

(1Wu)146 keV

(10+→8+)

1.01s 613s 20.9E+6s

3578 keV (10+→6+)

6.5ms

Summary• What is an isomer ? • Electromagnetic transition rates.• Weisskopf Single-Particle Estimates• Shell Structure in near spherical nuclei.

– Odd-A singly magic nuclei (e.g., 205Au126)

– Why are E1s ‘naturally’ hindered ?

• Seniority isomers, j2 & jn configurations ?• Near Magic nuclei.

– Limited valence space? Core breaking?

• Magnetic properties: g-factors in seniority isomers.

Isomer Spectroscopy in Near-Spherical Nuclei Lecture at the ‘School cum Workshop on Yrast and Near-Yrast Spectroscopy’ IIT Roorkee, October 2009 Paddy.

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