16.451 Lecture 24: Collective Nuclear Excitations 1

1. Oscillations about spherical equilibrium with characteristic Y(,) pattern:

- occur in even-even nuclei (J = 0+ ground states)

- energy is quantized: En = n ħ where is the characteristic frequency

- shape and frequency depend on the multipole order

- angular momentum and parity are given by: J = , = (-1)

- since excitations are Bosons (integer spin), allowed combinations musthave symmetric total wavefunctions...

= 1

Lowest value of that is observed is the “giant dipole resonance”, = 1:

(neutrons and protons oscillate out of phase – CM remains fixed)

time

protons

neutrons

“Giant Dipole Resonance” in Nuclei: J = 1- “GDR”

• characteristic feature that can be seen in all nuclei

• very short-lived state at high excitation • E1 = ħ1 78 A-1/3 MeV (example below: 197Au, E = 15 MeV)

• 6 MeV (common feature) 10-22 s

• classical analog is an oscillating electric dipole moment – can decay via E1 radiation pattern (signature)

nAuAuAu 196*197197 Electric dipole radiation pattern:

Griffiths, Intro. to Electodynamics:

rr

S ˆsin

~2

2 z

2

= 2

Quadrupole oscillations occur at lower energy: J = 2+

time

• typically, ħ2 ~ 1 MeV in a variety of even-even nuclei

• excitation energy is low, so can expect to see up to several “quadrupole phonons” in the spectrum

• Boson excitations, so require a symmetric wave function under exchange of “particle” (phonon) labels this restricts the total J,

e.g. for two phonons:

onlyJ

Jsymmetric

4,2,0

22

energ

y

0

1 ħ

2 ħ

0+

2+

0+ , 2+ , 4+

Model spectrum

3

Example of vibrational excitations: (Krane Fig. 5.19) 68120

52Te

(E-E ground state)

n=1, = 2, 2+ phonon

n = 2, = 2, J = 0+, 2+, 4+

ħ2

2ħ2

3ħ2 multiple = 2 phononstates, ideally degenerate

(characteristic decay patterns: gamma-rays emitted with “E2” angular distributions, like a quadrupole antenna)

3- state?

E (

MeV

)

0

0.21

0.29

½ +

3/2 +

11/2 -

69121

52Te

contrast, adding one neutron:

4

The 3- state is an octupole phonon, = 3:

= 3 time

• J = 3-

• ħ3 ~ (2-3) ħ2 ~ 2 – 3 MeV

• typically only see one octupole phonon per spectrum

Summary:

• low lying excitations in even-even spherical nuclei have the same characteristic pattern up to a few MeV in excitation energy: 0+ (gs), 2+ (quadrupole phonon), (0+, 2+, 4+) (two phonons), 3- (octupole)

5

2. Quantized Rotations in deformed nuclei:

dm

dmrI

I

LE

2

2

2

Classical rotating object:

Replace L with rotational angular momentum J:

)1(2

)1(||2

2 JJI

EJJJ J

J is quantized; “rotational bands” are spectra characterized by a given value of the moment of inertia, I, and a series of energy levels with J = 1 or 2:

• even-even nucleus: J = (0, 2, 4, 6, 8, 10....) = +

• odd-even deformed nucleus: J = ½ integer, J = 1 within a “band”

moment of inertiasets the scale of theenergy level pattern

allowed J determinea characteristicspacing pattern

6

Example: 176Yb

Quantized energy states of a rotating football!

MeV014.02

)1(2

2

2

I

JJI

EJ

MeV014.02

)1(2

2

2

I

JJI

EJ

J

note: rotations around the symmetry axis are indistinguishable; rotationalangular momentum must be perpendicular to the symmetry axis.

Note -- larger I means smaller energylevel spacing!

7

The moment of inertia gives a measure of the nuclear shape:

z

R()

parameterize the shape, quadrupole moment and moment of inertia assuming constant density football shape:

)16.01(5

3

05.153

4

))(1()(

2

20

ZRQ

R

R

R

R

YRR

ozz

oo

o

If the nucleus rotates like a solid: (rigid body model):

)31.01(5

2 2 oR RMI

If the nucleus rotates like a liquid drop: (rotating fluid model)

2

8

9oF RMI

reality issomewherein between...

8

Evidence of “quasi-fluid” behaviour for rotating nuclei:

spectral analysis:

a plot of E vs J(J+1) should give a straight line with slope ħ2/2I

• confirmed for 174Hf

• but for 158Er, the slope decreases (moment of inertia increases) with increasing J ...

J

Like a rotating fluid:“centrifugal stretching” alongthe symmetry axis occurs forlarger angular momentum!J(J+1)

9

Quadrupole moments and types of excitations across the nuclear chart:

Rare earth region: ~ 0.2 – 0.3, rotational spectra for E-Esingle particle states in adeformed potential for O-E

lighter nuclei:small Q. E-Enuclei havevibrational states

Closed shell nuclei: spherical; O-E nuclei near closed shells aregood “Shell Model”candidates...

10

And FINALLY, a quick word about SNO:

Sudbury Neutrino Observatory: http://www.sno.phy.queensu.ca/

Earth

?

• SNO was built over a decade starting in the late 1980’s at a cost of ~ $100M to solve a long-standing problem in the observed deficit of neutrinos coming from the sun.

• A classic radiochemical experiment by Ray Davis et al carried out in a gold mine in South Dakota using the reaction:

had reproducibly detected only about 1/3 of the expected number of neutrinos of solar origin. What was wrong???

eArCl e3737

Prior to SNO, several other solar neutrino experiments were constructed and in operation world wide, e.g. the Kamiokande detector in Japan, SAGE and GALLEXdetectors in Europe ... all had slightly different energy sensitivities and operatedusing different reactions to detect the neutrinos, but all found a discrepancy in thesolar flux!

11

Calculated neutrino flux from fusion reactions in the sun, J. Bahcall et. al

Energy thresholds of various detectors are shown:

12

All detectors, including SNO, show a deficit of electron neutrinos from the sun: 13

SNO – a unique D2O Cerenkov detector that can “see” all neutrino types

4700’ underground in the Creighton nickel mine in Sudbury, Canada, to suppress background from cosmic ray muons, etc:

acrylic vessel holds1000 tonnes of heavywater, D2O that makesan ideal detector forneutrinos.

20” diameter photo-multiplier tubes lookinginward detect Cerenkovlight when a neutrinointeracts in the water

Neutrino candidate event:Cerenkov “ring” on one sideof the detector with nothing entering from the other side.

14

Neutrino detection mechanisms in heavy water:

1. “Charged current” mechanism:

(electron produces Cerenkov light in the water tank)

eppde

2. “Neutral current” mechanism:

resulting neutron can be captured in a salt solution, and resulting -rays, which hit electrons in the water, again produce Cerenkov light that is picked up in the PMT’s

pnd

Ratio of 1 : 2 gives the ratio of electron-type to total neutrinos from the sun!

15

126 seccm1009.005.076.1 CC

12646.043.0

44.043.0 seccm10 09.5

NC

SNO published results: http://www.sno.phy.queensu.ca/sno/publications.html

electron-neutrinos only

all neutrino types

Ratio: 35.0

e

e

Interpretation: • the total number of neutrinos is consistent with expectations from the solar model.

• only electron-type neutrinos are produced in solar fusion reactions

• 2/3 of these must be turning into other neutrino types (, ) before reaching earth!

Significance of the SNO result: first experiment to“see what happened” by measuring all neutrino types

Unavoidable conclusion: neutrinos must have a small butfinite rest mass! (next question: how big is it?)

16

The theory of neutrino mixing gets complicated very quickly, but in a nutshell, the observation of “neutrino oscillations” sets limits on the mass-difference m2

and the mixing angle , e.g. for only two neutrino types, one could write:

21 cossin)0( vvtve

Then as time evolves, with the masses of 1 and 2 being different, the observed“neutrino state” will be a different linear combination of 1 and 2 that depends onthe parameters m2 and sin2 . Combined data from all experiments can be used to place limits on the mixing parameters.... so far, the favoured situation looks like this:

Neutrino masses and mixing: (see, e.g. http://www.sns.ias.edu/~jnb/ ) 17

The SNO result is an incredible achievement for physics and Canada

http://www.nserc.ca/news/2003/p031124.htm

It wasn’t easy! For a few years,the subatomic research communityalmost went broke trying to pay forSNO .... but it was worth it!

SAP visits SNO as chair ofNSERC GSC, 1997 – borrows$3M from NSERC to pay forconstruction cost overrun....

18

Graduate Studies in Physics & Astronomy

Ultrasonic Speckle Pattern

Financial Support:

All students accepted into the Department of Physics and Astronomy receive financial support through scholarships, teaching assistantships and/or research stipends.

For more information, or to receive an application form, contact us by email at physics@umanitoba.ca, or visit our web site at www.physics.umanitoba.ca

• Astronomy and Astrophysics

• Atomic and Molecular Physics

• Condensed Matter and Materials Physics

• Mass Spectrometry of Large Biomolecules

• Precision Atomic Mass Determinations

• Mathematical Physics

• Medical Physics

• Subatomic Physics

think about it!!!!

Canadian Penning Trap Mass Spectrometer at Argonne National Laboratory

The Canadian Penning Trap (CPT) mass spectrometer is installed at the ATLAS facility of the Argonne National Laboratory. Short-lived, unstable nuclides are produced when beams of heavy ions from the ATLAS facility strike a target. The products recoil out of the target and are separated from unwanted contaminations with a gas-filled, split-pole, magnetic separator. Ions of the nuclide selected for study are stopped in helium gas and accumulated in a novel linear RFQ-trap, called the gas cooler. The accumulated ions are transferred to the CPT spectrometer where their masses are determined to an accuracy approaching 1 ppb. With this apparatus we can carry out measurements on a wide variety of nuclides with half-lives greater that 30 ms.

Our program of measurements is aimed at:

improving our knowledge of nuclear masses among nuclei in exotic regions.

obtaining precise mass data that allows tests of the Standard Model and fundamental symmetries.

providing valuable input to astrophysical theories on nucleosynthesis and allow critical tests of the theories of nuclear masses.

To enquire about opportunities for summer research assistants, graduate students and post-doctoral fellows please contact:

Dr. Kumar S. SharmaDepartment of Physics and AstronomyUniversity of ManitobaWinnipeg, Manitoba, Canada R3T 2N2

sharma@physics.umanitoba.ca

1 m

Schematic view of the CPT spectrometer and related apparatus.

(K.S. Sharma)

(J. Birchall, W.R. Falk, S.A. Page, W.T.H. van Oers)

The subatomic physics group has a vigorous research program based at leading accelerator facilities. We are interested in fundamental symmetry properties of the weak and strong interactions, and how these affect nucleon structure.

At Jefferson Laboratory (USA), we play a leading role in two major experiments that involve measurements of tiny parity- (mirror symmetry) violating asymmetries in electron-proton scattering:

The `G0’ experiment, currently underway, will measure parity-violating asymmetries at a range of momentum transfers to map out the role that strange quarks play in the proton’s electromagnetic structure.

The `Qweak’ experiment will measure the forward scattering asymmetry at very small momentum transfer as a precision test of the electroweak mixing angle sin2W -- any deviation from the Standard Model prediction is a sensitive probe of additional force carriers and thus indicates new physics.

At Los Alamos National Laboratory (USA), we make use of the world’s highest intensity pulsed cold neutron beam to make a definitive measurement of parity violation in the fundamental process n+p d+, which will settle a long standing controversy regarding the pion exchange component of the weak nuclear force.

We have openings for graduate students as well as summer undergraduate research projects!Students have the opportunity to travel and interact with top ranking scientists from around the world through participation in these leading international collaborations.

Contact Dr. S.Page (spage@cc.umanitoba.ca) for more information!

Fundamental Symmetries and Nucleon Structure

The Qweak Experiment at Jefferson Lab: A Search for Physics Beyond the Standard Model

(J. Birchall, W..R. Falk, S.A. Page, W.T.H. van Oers)

A major new initiative, the `Qweak’ experiment, is under rapid development at Jefferson Laboratory. Qweak will measure the proton’s weak charge -- a basic property, like its electric charge and mass, which determines how a proton responds to the weak interaction. We will infer the proton’s weak charge from measurements of parity violating electron-proton scattering at very small momentum transfer; electrons scattered at small angles will be deflected into very sensitive detectors by a large magnetic spectrometer that is being constructed by our group. By providing a first precision measurement of this important property, the Qweak experiment will also provide a stringent test of the Standard Model that describes the fundamental interactions on a microscopic scale. Our new experiment has the potential to

make the first really high precision test of the running of the weak coupling constant to low energy. If a discrepancy with theory is found, Qweak could be one of the first experiments to provide convincing evidence that there are additional elementary force carriers beyond what we know today. Theorists have shown that the Qweak experiment should be able to infer the possible existence of hitherto unobserved force carriers up to the impressively high mass scale of 4.7 TeV, which is currently beyond the reach of direct experimental tests. Positions are currently available for graduate students who would to participate in this exciting endeavour.

Contact: Dr. S. Page: spage@cc.umanitoba.ca

Fundamental symmetries with trapped ultra-cold atoms and ions

We are a new group at the U. of Manitoba, establishing a research programme in laser- cooling and trapping of francium at the ISAC radioactive beam facility at TRIUMF, Vancouver

Goal: study electroweak interaction and search for physics beyond the Standard Model by performing very precise laser-spectroscopic experiments

contact: Gerald Gwinner, Dept. of Physics, Univ. of Manitoba, (204) 474-9856, gwinner@physics.umanitoba.ca, www.physics.umanitoba.ca/people/faculty/gwinner.html

The squared Weinberg-angle, a key observable in electro- weak physics, as a function of the interaction energy

Schematic of a magneto-optic trap (MOT) to capture Fr atoms produced in a nuclear reaction at ISAC into a millimeter-sized ball of 107 atoms cooled to 100 micro-Kelvin.

We are looking for graduate students interested in this combination of fundamental physics and table-top laser spectroscopy

at low energies, atomic parity nonconservation experiments areunique in probing the Standard Model

(G. Gwinner)

The TITAN ion trap facility at ISAC (G. Gwinner)

contact: Gerald Gwinner, Dept. of Physics, Univ. of Manitoba, (204) 474-9856, gwinner@physics.umanitoba.ca, www.physics.umanitoba.ca/people/faculty/gwinner.html

projects:

1. a electron-cooler trap to pre- cool highly-charged ions before injection into the pre- cision trap

2. design of a Penning ion trap to perform measurements of the electron’s bound-state g- factor to test QED and nuc- lear structure

We collaborate with a group at TRIUMF (J. Dilling et al.) on the realization of an ion trap system mounted on-line at the TRIUMF ISAC radioactive beam facility, which will be unique in the world.

Physics goals: measure extremely precisely masses of unstable nuclei -- this information is crucial to our understanding of stellar nucleosynthesis (nuclear astrophysics) and weak interaction experiments.