Isospin mixing E.Farnea INFN Sezione di Padova 1. Isospin - - PowerPoint PPT Presentation

Isospin mixing

E.Farnea

INFN Sezione di Padova

1. Isospin selection rules

• 2. Isospin mixing and forbidden E1 transitions: the 64Ge case
• 3. Spin assignments
• 4. Measurements of linear polarization
• 5. Lifetime measurements
• 6. E1 transitions in mirror nuclei: the 67As-67Se case

Selection rules

Not all electromagnetic transitions are allowed! There are selection rules originated by the structure of the operators inducing the transition, or by the angular momentum coupling between the initial and final state and the emitted photon, for instance: Electromagnetic transitions connecting 00 states are forbidden An electromagnetic transition with multipolarity L can only connect a state with spin Ji to a state with spin |Ji-L|≤Jf ≤Ji+L

Isospin selection rules

Taking a very general expression describing the microscopic current density: 𝑘𝑂 𝑠 = 𝑓𝑞 𝑞𝑞 2𝑁𝑞 𝜀 𝑠 − 𝑠

𝑞 + 𝜀 𝑠

− 𝑠

𝑞

𝑞𝑞 2𝑁𝑞 +

𝑞

𝑑 𝜈𝑞 𝑓ℏ 2𝑁𝑞𝑑 𝛼 × 𝜏𝑞

𝑞

𝜀 𝑠 − 𝑠

𝑞

+ 𝑑 𝜈𝑜 𝑓ℏ 2𝑁𝑞𝑑 𝛼 × 𝜏𝑜

𝑜

𝜀 𝑠 − 𝑠

𝑜

Since the charge can be written as e(1-τ3)/2, the electromagnetic interaction hamiltonian 𝐼(𝑀, 𝑁) = 1 𝑑 𝑘𝑂 𝑠 ∘ 𝐵𝑀𝑁 𝑙𝑠 𝑒𝜐 Naturally divides into two isoscalar and isovector components:

𝐼 𝑀, 𝑁 = 𝐼0 𝑀, 𝑁 + 𝐼1(𝑀, 𝑁)

Isospin selection rules

Calculating the transition amplitude: Γ𝛿(𝑀) = 8𝜌𝑙 𝐾𝑐𝑁𝑐𝑈𝑐𝑈3𝑐 𝐼(𝑀, 𝑁) 𝐾𝑏𝑁𝑏𝑈

𝑏𝑈3𝑏 2 𝑁,𝑁𝑐

And extracting the T3 dependency through the Wigner-Eckhart theorem, it can be «easily» shown that:

Only electromagnetic transitions with ΔT=0, ΔT=±1 are allowed Electromagnetic transitions with ΔT=±1 in conjugate nuclei are identical

Isospin selection rules

In the particular case of the E1 operator, expanding 𝑘𝑂 𝑙𝑠 in power series

• f 𝑙𝑠

and using the long wave approximation, it can be shown that the isoscalar component vanishes. Therefore:

Electromagnetic E1 transitions in conjugate nuclei have the same intensity Electromagnetic E1 transitions in N=Z nuclei are forbidden

In first approximation, in N=Z nuclei, ΔT=0, in other words only the isoscalar term should be considered; this means that:

Isospin mixing

• J. Dobaczewski and I. Hamamoto,

PLB 345 (1995) 181

    

  

Z N T T Z N | | 2 1 

States with different isospin (but same spin and parity) may mix through the Coulomb interaction, making E1 transitions possible also in N=Z nuclei: The amount of the admixture is of the order of a few percent, it is maximum in N=Z nuclei and increases with the atomic number Z up to the heaviest bound N=Z nucleus, 100Sn

64Ge: forbidden transition?

64 32Ge 32

0+ 901.5 2+ 2052.3 4+ 3465.3 (6+) 5179.7 (8+) 2969.3 (3–) 3716.8 (5–) 4245.2 (7–) 5372.4 (9–) 6563.9 (11–) 8006.3 (13–) 6065.0 (2+) 1579.0 2155.2 (4+) 3407.3 (6+) 5175.8 (8+) 2669.9 (3+) 3717.2 (5+) 5025.8 (7+) 901.5 1150.8 1413.0 1714.4 747.5 528.4 1127.2 1191.5 1442.4 576.2 1252.1 1768.5 1047.3 1308.6 1090.9 1819.8 2067.8 677.0 1664.8 1579.0

P.J. Ennis et al.,

• Nucl. Phys. A 535 (1991) 392

64Ge: forbidden transition?

64 32Ge 32

0+ 901.5 2+ 2052.3 4+ 3465.3 (6+) 5179.7 (8+) 2969.3 (3–) 3716.8 (5–) 4245.2 (7–) 5372.4 (9–) 6563.9 (11–) 8006.3 (13–) 6065.0 (2+) 1579.0 2155.2 (4+) 3407.3 (6+) 5175.8 (8+) 2669.9 (3+) 3717.2 (5+) 5025.8 (7+) 901.5 1150.8 1413.0 1714.4 747.5 528.4 1127.2 1191.5 1442.4 576.2 1252.1 1768.5 1047.3 1308.6 1090.9 1819.8 2067.8 677.0 1664.8 1579.0

P.J. Ennis et al.,

• Nucl. Phys. A 535 (1991) 392

Intense E1 transition? Forbidden by the isospin selection rules ...

Experiment performed at LNL

32S (125MeV) + 40Ca (1mg/cm2) + 12 mg/cm2 197Au backing

EUROBALL III + n-Wall + ISIS

Laboratori Nazionali di Legnaro

EUROBALL III ISIS n-Wall

Level scheme

64Ge

0+ 902 2+ 2053 4+ 3466 (6+) 5180 (8+) 2970 (3–) 3718 5(–) 4246 7(–) 5373 9(–) 6565 (11–) 8007 (13–) 9628 (15–) 7193 10(+) 8066 12(+) 8914 (14+) (9813) (16+) 1579 1579 528 902 1151 1413 1127 1192 1442 1621 873 848 (899) 747 1714 1820 1665 2068 677

The level scheme constructed using the data from the EUROBALL III experiment does not extend significantly the previously known level

• scheme. On the other hand, it

is confirmed that the 1665keV line is one of the strongest

Need spin and parity assignments to confirm the (tentative) E1 character!!!

Assigning spins/parities

Level with known spin/parity Level with unknown spin/parity The spin/parity of the «top» level (unknown) can be determined, starting from the «bottom» (known) level, by measuring the character of the transition connecting the two levels, or, in other words, the angular momentum carried by the emitted photon

How can we do it in practice? Angular distributions Linear polarization

Angular distributions

In order to measure angular distributions, we need to find a way of populating our nuclei of interest with a well defined distribution of spins This is the case with fusion-evaporation reactions, where the initial angular momentum is orthogonal to the beam direction:

𝑚 = 𝑠 ∧ 𝑞

• Before particle evaporation and photon emission, the

distribution of nuclei has well defined angular momentum and projection of the angular momentum on the beam axis (m=0), namely, they are in an aligned state

• Since the evaporated particles carry at most a few units of

angular momentum, the residual nuclei after evaporation are populated with a distribution of states symmetrically peaked around m=0, with width (alignment) σ

Angular distributions

The angular distribution of photons emitted from an aligned state, having spin I1 and populating a state with spin I2, has quite a simple expression:

𝑋 𝜘 = 𝐵0 + 𝐵2(𝜏, 𝜀, 𝐽1, 𝐽2) ∙ 𝑄2 cosϑ + 𝐵4(𝜏, 𝜀, 𝐽1, 𝐽2) ∙ 𝑄

4 cosϑ

Where A2, A4 are the angular distribution coefficients depending on the spins of the levels and on the multipole mixing ratio δ and P2, P4 are the Legendre polynomials. In principle the angular distribution coefficients should be determined through analysis of singles data. It can be shown that an isotropic gate will not perturb the angular distribution (thus it is possible to make this kind of analysis for weak channels identified through multiple γ coincidences) The finite size of the detectors translates into an «attenuation» of the angular distribution (each detector «sees» a range of angles)

Electromagnetic emission from Oriented Nuclei: Angular distributions

Angular distributions and correlations are only sensitive to the multipolarity L and θ Beam s/J

Some examples

20 40 60 80 100 120 140 160 180

Angle (degrees)

1.6E+06 1.8E+06 2.0E+06 2.2E+06 2.4E+06 2.6E+06 2.8E+06

Intensity

1217 keV 66Ge (4 to 2), gate 521 keV

20 40 60 80 100 120 140 160 180

Angle (degrees)

6.0E+05 6.5E+05 7.0E+05 7.5E+05 8.0E+05 8.5E+05 9.0E+05 9.5E+05 1.0E+06 1.0E+06 1.1E+06

Intensity

1510 keV 66Ge (5 to 4), gate 521 keV

quadrupole transition dipole transition

Symmetric with respect to θ=90° (only even values of the Legendre polynomials allowed)

Angular distribution for the 1665 keV line

20 40 60 80 100 120 140 160 180

Angle (degrees)

4000 5000 6000 7000 8000 9000 10000

Intensity

d  0.089(34) d  3.93(70)

Angular distributions strongly suggest that the observed transition is indeed 54, they are not conclusive, however, concerning the multipole mixing ratio δ

1665 keV 54

Angular distribution for the 1665 keV line

Angular distributions strongly suggest that the observed transition is indeed 54, they are not conclusive, however, concerning the multipole mixing ratio δ

• 90
• 70
• 50
• 30
• 10

10 30 50 70 90

arctg(d)

100 200 300 400 500

c Fixed s/J = 0.386, A0 = 7077

Primary minimum (large δ) Secondary minimum (small δ)

Χ2 analysis

Linear polarization

• γ-rays emitted by oriented nuclei are partially polarized. The polarization

vector is different for E and M transitions

• Compton scattering can be used to measure the degree of polarization through

the dependency with the polarization vector. The Klein-Nishina cross section for linearly polarized γ-rays is the following:

H.D.Hamilton, The electromagnetic interaction in nuclear spectroscopy, North-Holland H.Morinaga and T.Yamazaki, In Beam Gamma-Ray Spectroscopy, North Holland

For stretched transitions with L=1,2 this is maximum at θ=90o

 

     

    ) (cos a ) (cos a ) ( P

2

P P

• n

Polarizati Linear

• f

Degree

2

Legendre angular correlation coefficients

) cos 1 ( c 1 cos sin 2 4

2 2 2 2

                        s

' ' ' ' 2 KN

m E E E E E E E E E r d d

 :angle between the scattering plane and the initial polarization plane

Degree of polarization for a dipole transition as a function of Atanδ. The quadrupole content is:

) 1 (

2 2

d  d  Q

Measurement of the degree of linear polarization

| | | | E

N N 1 ) ( P     

 

N N Q

The scattering probability depends on the polarization plane. Then it is possible to measure the asymmetry

Q is the sensitivity of the polarimeter Stretched E transitions will have positive asymmetry Stretched M transitions will have negative asymmetry

E

 || 

Beam

L.M. Garcia-Raffi et al., NIM A 391 (1997) 461

Measurement of the degree of linear polarization

The degree of linear polarization of the transitions can be measured through the composite Clover detectors of EUROBALL III

𝐵 = 𝑂┴ − 𝑂║ 𝑂┴ + 𝑂║

66Ge 64Ge

0.1 0.2 0.3 0.4 500 1000 1500 2000 2500 3000

Experimental PCO Monte Carlo simulation

Raffi et al. NIM A 391 (97) 461

EUROBALL III Polarization Sensitivity

Energy (keV) Polarization Sensitivity Q

Linear polarization measurement

The observed negative asymmetry is consistent with a strongly mixed 54 transition and with a parity change. The alternative of a non-mixed 54 transition, implying no parity change, is in contrast with the systematics of the mass region.

Transition probability

We have established that the character of the 1665 keV transition is consistent with a 54 decay and with a change of parity. Now the remaining missing information is the strength of the transition, in other words, the transition probability

How can we measure transition probabilities?

Nuclear Lifetimes

Gt =

Excited nuclear states with a width Γ «survive» for a lifetime τ such that: If τ>10-22 s the width becomes smaller than the separation between

• states. One can write:

where M is the operator for the decay and ψi, ψf are the wavefunctions

• f the initial and final states. If more decay modes are concurrent:

Nuclear lifetimes  transition probabilities

= reduced transition probability τ = lifetime, = gamma ray energy B is given in units of efmL µNfmL–1

Transition Probabilities

Nuclear Lifetimes

A collection of N0 nuclei produced at time t-0 will decay with lifetime τ according to the (exponential) law: Where the transition probability (decay rate) is given by: And it is related to the half- life through:

Feeding of Excited States – Lifetimes

tM . . . ti t t1 M M-1 i . . . i-1 2 1 N0

The observed (apparent) lifetime of a state depends on the lifetime(s) of the state(s) feeding it. The Bateman equations of radioactive decay hold: where Ni(t) is the population of level i at time t, assuming:

Feeding of Excited States – Lifetimes

t t1 2 1 N0

Feeding of Excited States – Lifetimes

The observed (apparent) lifetime of a state depends on the lifetime(s) of the state(s) feeding it. The Bateman equations of radioactive decay hold: where Ni(t) is the population of level i at time t. If there is a sidefeeding the initial population(s) do not vanish:

tM . . . ti tSF(i-1) tSFi tSF(M1) t t1 tSF1 tSF M i . . . i-1 2 1 N0

Feeding of Excited States – Lifetimes

The Bateman equation is not a single equation but a method for setting up a differential equations describing the decay of the chain of interest as a function of time based on the decay rates and the initial population of the states

tM . . . ti tSF(i-1) tSFi tSF(M1) t t1 tSF1 tSF M i . . . i-1 2 1 N0

Feeding of Excited States – Lifetimes

The Bateman equation is not a single equation but a method for setting up a differential equations describing the decay of the chain of interest as a function of time based on the decay rates and the initial population of the states

tM . . . ti tSF(i-1) tSFi tSF(M1) t t1 tSF1 tSF M i . . . i-1 2 1 N0 In case of fusion–evaporation reactions there is large side feeding from unresolved states in the continuum with unknown

• lifetimes. The feeding times from such

states are usually much shorter than the in band decay times

Feeding of Excited States – Lifetimes

The Bateman equation is not a single equation but a method for setting up a differential equations describing the decay of the chain of interest as a function of time based on the decay rates and the initial population of the states

tM . . . ti tSF(i-1) tSFi tSF(M1) t t1 tSF1 tSF M i . . . i-1 2 1 N0 In case of fusion–evaporation reactions there is large side feeding from unresolved states in the continuum with unknown

• lifetimes. The feeding times from such

states are usually much shorter than the in band decay times

Side feeding effects on the lifetime measurements can be avoided by using coincidence sets on transitions above the state of interest

Feeding of Excited States – Lifetimes

t t1 2 1 N0 N1

NFR Coulex Indirect Methods Direct Methods t (s) 10-18 10-15 10-12 10-9 FEST Electronic DSAM RDDS RFD RSAM GRID

GRID: Gamma ray induced Doppler broadening DSAM: Doppler shift attenuation method RFD: Recoil straggling method RDDS: Recoil distance Doppler shift method RSAM: Recoil shadow anisotropy method FEST: Fast electronic scintillation method NFR: Nuclear resonance fluorescence Coulex: Coulomb excitation cross section

Techniques for Lifetime Measurement

Direct Methods

• determine directly τ

Indirect Methods

• determine the width Γ

Irradiation and Counting

Lifetimes ~ sec – min

• sample irradiated to produce isomeric state
• transport sample to a low–background area (tape transport)
• counting decays with a Ge detector

39Ca produced in REXTRAP

at ISOLDE

B.Blank et al., EPJ A44 (2010)363

radioactive ions

detection

• b

gas counter

• g

germanium GSI tape system

Irradiation and Counting: FEST

• Poor Ge time resolution limit τ > several ns
• LaBr3 detectors excellent time resolution

(<400ps)

• Ge–(LaBr3–LaBr3) coincidences

the slope yields directly the lifetime

V.Werner et al., J. of Physics312(2011)092062 169Tm(12C,7n)174Re  174W*

Methods Based on the Doppler Effect

Doppler shift lifetime measurement methods:

• Recoil Distance Doppler Shift (RDDS) 1 ps – 1 ns
• Doppler Shift Attenuation Method (DSAM) 100 fs – 1 ps
• Fractional Doppler Shift Method 5 fs – 50 fs

The relativistic Doppler shift formula: When β<<1, as in the case for instance of fusion-evaporation reactions, reduces to: It is therefore possible to distinguish between photons emitted in-flight

• r at rest, based on the observed energies, and viceversa it is possible to

deduce the recoil velocity from the energy difference between the «stopped» and the «in-flight» photons:

Recoil Distance Doppler Shift (RDDS) Method

• thin target ~500 µm/cm2 (movable)
• thick stopper (‘plunger’ foil) usually in Au
• recoils decay in–flight over a distance x
• recoils decay as stopped in the stopper
• both stopped and in–flight emitted gamma

rays are detected

• sh: shifted component
• u: unshifted component

Det.

q

Measure the difference of intensity

• f the two components as a function
• f the target–to–stopper distance

Recoil Distance Doppler Shift Method

122Ba P.G.Bizzeti et al., PRC 82 (2010)054311

GASP+Köln plunger

Recoil Distance Doppler Shift (RDDS) Method

Stop flight

Det.

q

Decay curve

W.Scmitz et a., PLB 303(1993)230

The intensity of the in-flight and stopped components is: The ratio of the unshifted component to the total intensity: Depends on the lifetime τ.

Recoil Distance Doppler Shift (RDDS) Method

Stop flight

• precision of the distance ~0.1 µm
• target–to–stopper distance measured as

a capacitance between the 2 plates

• well stretched target and stopper and

good parallelism

• distance scale transformed in time scale

from average velocity

• in complex level schemes the result is

altered by

• multiple exponential decay

components

• feeding from states above with

comparable lifetimes

• use Bateman for the feeding of the

states and make a global fit of the level scheme

• doesn’t work for unknown feeding

Det.

q

Differential Decay Curve Method

Coincident Differential Decay Curve Method gate from above – eliminates the problems of unknown feeding – selects the feeding path of the states B A B – A coincidence has 3 components (gate set on B): it is not possible Reformulating the Bateman equations in terms of the observed unshifted intensity for different target-to-stopper distances: Where bij are the branching ratios for the feeding transitions

Coincident DDCM

Gating from above on B (A is measured):

• gate on (s+u)  eliminates background & side feeding
• gate on u  direct lifetime measurement with no need of solving

the Bateman equation

122Ba

Doppler Shift Attenuation Method (DSAM)

v(t) from Monte Carlo simulation with stopping power

• thin target ~500 µm/cm2
• target backing of a high Z stopper

material (Au/Pb/Ta)

• recoils decay in–flight while stopping

in the target

• lineshape depends on the nuclear

lifetime

Doppler Shift Attenuation Method (DSAM)

v(t) from Monte Carlo simulation with stopping power

• DSAM applies when the lifetime is of the
• rder of the slowing down time of the

recoils in the target (10–13 – 10–12 s)

• analysis of the gamma ray lineshapes as a

function of the detection angle to determine the nuclear lifetime

• the lineshape will depend on the velocity
• f the recoil (from v0 to 0) when the

gamma ray was emitted

• the centroid of the lineshape is a

measure of the average recoil velocity

• the centroid is expressed usually in

terms of Doppler Shift Attenuation Factor

Doppler Shift Attenuation Method (DSAM)

v(t) from Monte Carlo simulation with stopping power

• v(t) is determined based on the stopping

powers

• stopping powers:
• electronic stopping
• nuclear stopping (scattering of the

nucleus) – Monte Carlo simulations of the recoil velocity profiles

• the lineshape dN/dE can be directly related to

the nuclear lifetime

• a knowledge of the velocity distribution dv/dt

allows for the calculation of the lineshape for a given τ

• the accuracy of the method is limited by the
• inaccuracy of the stopping power

models (10 – 15% systematic error)

• unknown side feeding of the states

Doppler Shift Attenuation Method (DSAM)

v(t) from Monte Carlo simulation with stopping power

Steps for the simulation of the lineshapes

• simulate the slowing down history of

the recoils in the backing; provides v(t) and θR(t)

• calculate the Doppler shift observed

at the angle θg as a function of time

• calculate the population N(t) of the

state by solving the Bateman equation

• simulate the energy spectrum in a

gamma ray detector from N(t)

• compare with the experimental

lineshape and minimize χ2

Doppler Shift Attenuation Method (DSAM)

0+ 2+ 850 4+ 2384 6+ 4325 8+ 6360 10+ 7381 8+ 6493 6+ 4872 4+ 3585 4396 3– 5137 5– 12+ 6820 849.5 1534.5 1941.0 2035.3 1021.4 8 8 8 . 5 2 1 6 7 . 6 1620.8 2488.0 1286.7 2735.0 2753.0 740.6 3546.3 1 5 5 3 130 +

• T1/2=45.9 sec

52Fe

Gate from below

Fractional Doppler Shift

• in the case of superdeformed bands with large Qt lifetimes are very short

(<100 fs)

• gamma ray emission occurs before significant slowing down of the recoils

 large Doppler shift with angle and no significant lineshape

• use of F(t) for the analysis of the centroids shift

48Ti (@214 MeV)+ 100Mo  144Gd

target 100Mo 1 mg/cm2 on Au 10 mg/cm2 GASP – configuration I

Fractional Doppler Shift

• in the case of superdeformed bands with large Qt lifetimes are very short

(<100 fs)

• gamma ray emission occurs before significant slowing down of the recoils

 large Doppler shift with angle and no significant lineshape

• use of F(t) for the analysis of the centroids shift

Centroid shift

The experiment in Strasbourg

32S (137.5MeV) + 40Ca (1mg/cm2)

EUROBALL IV + plunger (+ EUCLIDES)

IReS Strasbourg

Lifetimes

100 300 500 700 900 1100 1300 10-1 100 101 102

Ip=7- Eg=528 keV t=43.1+2.9 ps Distance (mm) Intensity

• 2.5

Ip=5- Eg=1665 keV t=24.4 +3.5 ps

100 300 500 700 900 1100 1300

Distance (mm)

100 101 102 103

Intensity

• 2.9

Fit of the ‘’unshifted’’ component only. Considering the experimental branching ratios:

B(E1, 1665 keV) = (2.26±1.25)·10-7 W.u. B(M2, 1665 keV) = 5.7±3.0 W.u. B(E2, 747 keV) = 1.0±0.5 W.u.

Comparison of 64Ge and 66Ge

0+ 0+ 957.0 2+ 2173.7 4+ 902 2+ 2053 4+ 2798.3 3– 3684.2 5– 4205.7 7– 5493.7 9– 2970 3(–) 3718 5– 4246 7– 5373 9– 528 1127 902 1151 747 2068 1665 521.5 1288.0 957.0 1216.7 885.9 1841.3 1510.5

66Ge 64Ge

B(E1) = 2.5 (0.9) 10-7 W.u. B(E1) = 3.7(6) 10-6 W.u.

Could we exploit the similarities between the decay schemes of 64Ge and 66Ge to obtain information on the amount of isospin mixing in 64Ge?

Comparison of 64Ge and 66Ge

Assuming complete similarity between the nuclear wave functions in 64Ge and

66Ge (with 2 particles or 2 holes difference), we can write:

𝐵 = 64, 𝐾, 𝑈, 𝑈

3 = 0 = (𝐵 = 66, 𝐾, 𝑈 + 1) ⊗ (ℎ2, 𝐾 = 0, 𝑈 = 1) 𝐾, 𝑈,𝑈 3 = 0

Considering the mixing between states with different isospin in 64Ge, one finds:

𝑗, 𝐾 = 𝛾𝑗 𝐾, 𝑈 = 0 + 𝛽𝑗 𝐾, 𝑈 = 1 𝑔, 𝐾′ = 𝛾𝑔 𝐾′, 𝑈 = 0 + 𝛽𝑔 𝐾′, 𝑈 = 1

With standard angular momentum coupling techniques and exploiting the fact that for small values of 𝛽𝑗, 𝛽𝑔 one can approximate 𝛾𝑗=𝛾𝑔=1:

(𝑗, 𝐾 ℳ 1 (𝐹1) 𝑔, 𝐾′)(64𝐻𝑓) = (𝛽𝑗 − 𝛽𝑔) ∙ 2 3 (𝑗, 𝐾 ℳ 1 (𝐹1) 𝑔, 𝐾′)(66𝐻𝑓)

Therefore, the minimum value of isospin mixing in 64Ge is such that:

𝐶(𝐹1, 𝐾 → 𝐾′, 64Ge)= 8 3 𝛽2𝐶(𝐹1, 𝐾 → 𝐾′, 66Ge)

𝜷𝟑 = 𝟑. 𝟔%+𝟐. 𝟏% −𝟏. 𝟖%

E1 transitions in 67As and 67Se

In mirror nuclei 67As34 and 67Se33 (Tz = ±½) two pairs of analogue transitions 9/2+ → 7/2- are

• bserved

The E1 transition amplitude is expected to be the same (neglecting interpherences between the isovector term and the «residual» effects of the isoscalar term, which vanishes exactly only in the long wave approximation):

( )

2

; ) 1 ( ) 1 ( ; 2 1 ) 1 (

z i i IV IS z i i z

T T J E E T T J T E B M  M   

E1 transitions in 67As and 67Se

In mirror nuclei 67As34 and 67Se33 (Tz = ±½) two pairs of analogue transitions 9/2+ → 7/2- are

• bserved

The E1 transition amplitude is expected to be the same (neglecting interpherences between the isovector term and the «residual» effects of the isoscalar term, which vanishes exactly only in the long wave approximation):

( )

2

; ) 1 ( ) 1 ( ; 2 1 ) 1 (

z i i IV IS z i i z

T T J E E T T J T E B M  M   

The experiment at ANL

• Fusion-evaporation reaction

32S+40Ca (@90MeV), (α,p) and

(α,n) channels

• Gammasphere + Microball +

Neutron Shell, ATLAS accelerator of the Argonne National Laboratory

• Gold backing to stop the

recoils

• Lifetimes extracted with the

“centroid shift’’, technique, verified with known reference transitions

67As and 67Se: relative centroid shifts

67As and 67Se: relative centroid shifts

Multipole mixing ratio

Multipolarities were measured using the ADO ratios (Angular Distribution from Oriented States) normalized to ‘’known’’ transitions: Experimental ADO ratios (normalized to a known E2 transition), compared with the theoretical values.

Energy (KeV) B(E1) (10-6 wu) B(E1) (10-6 wu) Energy (KeV) 717 0.4(4) 1.4(4) 725 303 <1.4(9) 8.3(2.4) 319

Experimental B(E1)

67Se 67As

In both nuclei the measured values are consistent with a large ratio between the isoscalar and the isovector contributions:

IS/IV~ 0.35(20)

The expected effect, however, is small and not compatible with the experimental findings: IS/IV ~ 10-4

Induced isoscalar term

A non vanishing isoscalar contribution could originate from the terms which are normally neglected in the long wave approximation, such as those with high order in 𝑙𝑠

• r the magnetic ones.

The mixing between the two 7/2- levels could influence the E1 transition amplitude, which in first approximation is a single particle transition g9/2- f7/2. The sign of this effect would be opposite in the two nuclei.

Coherent increase?

A coherent mixing with several high-energy states (giant resonances) could induce large effects. For instance, the isovector component of the Coulomb interaction could be approximated with: Where the second term is the isovector monopole operator: The mixing of the considered states with the isovector giant monopole states (IVGMR) would lead to IS/IV~0.25

Bini et al., Lett. Nuovo Cimento 41 (1984) 191 Colo et al., Phys. Rev. C 52 (1995) R1175 Bizzeti, Proceedings of the Workshop on Exotic Nuclei at the Proton Dripline, Camerino, 2001