The Atomic NucleusThe Atomic NucleusThe subject of Nuclear Structure is to understand how the Z protons and N neutrons arrange themselves in a bound system and how they react to external fields. Since Z and N vary over a broad range, different features are expected depending on the mass number and on the N/Z ratio.

What is the effective NN interaction?What are the limits of existence for bound nuclei (driplines)?

What is the effective NN interaction?What are the limits of existence for bound nuclei (driplines)?

The Shell ModelThe Shell Model

There is a “surprising” analogy between the description of bound electrons in atoms and bound nucleons in atomic nuclei.

Nuclear Shell Model (M.Mayer et al, 1948-49)

Nuclear Shell Model (M.Mayer et al, 1948-49)

This model is a highly successful one, but the prediction capabilities are somewhat limited when going to nuclei far from stability

Need to “tune” the model parameters collecting information on such nuclei!

Need to “tune” the model parameters collecting information on such nuclei!

Shell structure

Cooper pairing

Collective modes

Nuclear excitationsNuclear excitations

neutrons

protons

rp p

roce

ss

rp p

roce

ss

Crust

pro

cess

es

Crust

pro

cess

es

s-pro

cess

s-pro

cess

s-pro

cess

s-pro

cess

r process

r process

r process

r process

stel

lar bu

rnin

g

stel

lar bu

rnin

gp p

roce

ss

p pro

cess

p pro

cess

p pro

cess

• What is the origin of elements heavier than Iron?• How do stars burn and explode?• What is the structure of a neutron star?

Nova

Time (s)

X-ray burst

331

330

329

328

327

Fre

quen

cy (

Hz )

10 15 20

4U1728-34

T Pyxidis

Neutron star

Nuclear Physics and Stellar Nuclear Physics and Stellar Nucleosynthesis Nucleosynthesis

Stablenuclei

10 ρ0

heavy-ion collisionsheavy-ion collisions

neutron drip-lineneutron drip-line

protonprotondrip-linedrip-line

Nuclei and StarsNuclei and Stars

supernovaesupernovae

Symmetry Energy: Nuclei and Symmetry Energy: Nuclei and StarsStars

Psym(ρ,δ) = ρ2 (∂Esym/ ∂ ρ ) δ2 = ρ0 Esym (ρo) u +1 δ2

u= ρ/ρoEsym (ρ) = Esym (ρo) u

The symmetry energy determines the dynamics of supernovae explosions and the pressure in neutron stars:

Observables (input to the models): Dynamics of heavy-ion collisions at different N/Z ratiosStructure of nuclei far from stability: single-particle and collective properties

How can we perform How can we perform nuclear structure studies?nuclear structure studies?

• In order to study the structure of nuclei, we need to find them in an excited state and to observe the radiation (light particles, electrons, -rays) which they do emit during the de-excitation.

• Excited nuclei can be populated “naturally” by decay of long-lived radioactive nuclei, or by reactions induced by cosmic rays

• Excited nuclei can be populated “artificially” by inducing nuclear reactions in our laboratories, using accelerators

VT ~ 14,5 MV From H to 197Au, E = 30 ÷ 1.5 MeV/A

CW or pulsed

XTU-Tandem

ECR on 350 kV platformSC-RFQs and QWRsVeq ~ 8 MV

PI Injector PIAVE

SC Booster ALPI

68 SC Quarter Wave Resonators (Nb, Nb/Cu)Veq ~ 48 MV, species from 28Si to 197AuInjected by Tandem or PIAVE

TANDEM PIAVE ALPI COMPLEX

Fully operational with noble Gases; ECRIS replacement in Spring 2008

Producing nuclei far from Producing nuclei far from stabilitystability

Using stable beams at energies close to the Coulomb barrier, with a careful choice of the reaction mechanism it is possible to populate nuclei far from stability in different regions of the chart of nuclides

Using stable beams at energies close to the Coulomb barrier, with a careful choice of the reaction mechanism it is possible to populate nuclei far from stability in different regions of the chart of nuclides

Observing nuclei far from Observing nuclei far from stabilitystability

• Following the production of excited, exotic nuclei, there are two basic alternatives, implying quite different experimental problems:– Transport the excited nuclei elsewhere and observe

the (delayed) decays (or chains of decays) off-line– Observe the prompt decays on-line, as they are

produced

Gamma SpectroscopyGamma Spectroscopy

• The observation of the electromagnetic radiation (photons or -rays) emitted by the excited nuclei provides one of the most sensitive tools to investigate the nuclear structure

• The emission of -rays is a well understood process from the theoretical point of view, hence the smallest effects can provide valuable information on the nuclear structure

• Contrary to the detection of particles, high resolution is possible

DetectorsDetectors

• A detector is an object translating the arrival of a radiation quantum into a (measurable) electric signal which can be:– generated outside of the active volume of the detector

(eg scintillators coupled to photomultiplier tubes)– generated inside of the active volume of the detector (eg

semiconductor detectors)

Current modeCurrent mode

I

Dete

ctor

A possible mode of operation consists in measuring the average current produced within the detector.

This mode of operation is not much used in spectroscopy since there is no information on the energy of the individual radiation quanta, only on their rate.

Pulse modePulse modeHere the information on energy and time of arrival of the individual quanta is preserved.

Typically, the charge flowing at the detector electrodes is collected by a preamplifier, which we can approximate by a RC circuit.

RC small compared to the charge collection time: the output signal is basically the same as the current signal:

V(t)=R i(t)

RC large compared to the charge collection time: the output signal rises as the current signal and decays exponentially with time constant RC. Its amplitude V=Q/C is proportional to the energy if C is constant.

SpectraSpectra

The usual way to visualize the response of a detector is a differential spectrum, namely a histogram in which each channel content is the number of events with amplitude within the “bin”. The integral version is not as widely used.

Differential Integral

When monochromatic radiation hits a detector, one expects that the response of the detector is always the same, in other words, that a peak appears in the differential spectrum.

The resolution R is defined as the ratio between the peak full width at half maximum (FWHM) and its position, R=FWHM/H0, but conventionally the values of FWHM and energy can be provided. For gaussian peaks, the statistical limit is:

ResolutionResolution

N

FR 35.2

NR

35.2

where N is the peak area. In practice the resolution can be better than such a limit and the Fano factor F<1 is introduced:

EfficiencyEfficiency

• The absolute efficiency is defined as the ratio between the number of detected and emitted quanta

• The intrinsic efficiency is defined as the ratio between the number of detected quanta and the number of quanta hitting the detector

• These two quantities are related by geometrical factors

• The peak efficiencies (absolute and intrinsic) are defined in a similar way

Interaction of radiation with Interaction of radiation with mattermatter

• As a rule of thumb:– Charged particles (electrons, protons) release their

energy in a gradual and continuous way– Neutral particles (neutrons, photons) release their

energy through “catastrophic events” changing their energy and/or nature in a radical way

Photon Interaction MechanismsPhoton Interaction Mechanisms

~ 100 keV ~1 MeV ~ 10 MeV -ray energy

Photoelectric Compton Scattering Pair Production

cosθ1cm

E1

EE

20

γ

γγ'

A photon can interact with an atom,releasing an electron with energy:

Ee=E-Eb

where Eb is the electron binding energy. The ionised atom can then rearrange its electrons, emitting X-rays which are typically reabsorbed. In first approximation, the cross section for photoelectric absorption is:

Photoelectric AbsorptionPhotoelectric Absorption

54,5.3

nE

zn

Shell effects, however, are typically quite evident.

Compton ScatteringCompton Scattering

cos11 2

cm

EE

E

e

00 eE

Compton scattering is the elastic scattering of a photon on an electron. For a free electron, the energy of the scattered photon depends on the scattering angle :

2

2

21

2

cmE

cmEEE

e

ee

221 cmE

EEEE

eeC

The energy of the scattered electron in the extreme cases, , is:

From which we obtain the gap between the photon energy and the maximum electron energy (which for large values of E is approximately 256 keV):

Compton ScatteringCompton Scattering

cos11cos1

cos11

2

cos1

cos11

1

d

d2

2222

2erz

The angular distribution of the scattered photon is described by the Klein-Nishina formula:

where =E/mec2 and re is the classical electron radius.For photon energies larger than a few hundred keVs the angular distribution is highly anisotropical and peaked to small forward angles. It strongly decreases with the increasing photon energy.

Continuum ComptonContinuum Compton

e

e

e

e

e EEE

E

Ef

Ef

E

N

2

2

2

1

11

2

1

d

d

The spectrum of the scattered electrons can be deduced from the Klein-Nishina formula:

e

eee EE

E

E

cmEf

2

1where:

Since the actual energy deposition is performed by the electrons, photons interacting via Compton scattering will produce a continuum spectrum as shown here. Corrections are needed since electrons are not free, rather bound in materials, producing a smoothening of the actual spectrum (Compton profile)

1332 keV photons

Compton shoulder

Pair productionPair production

Photons with energy larger than 2mec2 can materialize (in the Coulomb field of a nucleus) in an electron-positron pair with total kinetic energy E-2mec2.Electron and positron subsequently release their energy in the medium; the positron eventually annihilates releasing two 511 keV photons. 1. The threshold for this process is 1.022 MeV

2. This process dominates at high photon energies (E > 10 MeV)

3. This process depends approximately on the square of the atomic number of the medium.

Cross Sections in NaI(Tl)Cross Sections in NaI(Tl)NaI(Tl)

Energy (MeV)

Cro

ss S

ect

ion

Atomic shell K

Pairprod.

Comptonscatt.

Photoelectricabs.

Cross Sections in Cross Sections in GermaniumGermanium

Compton scatt.

(10 keV) ~ 55 m (100 keV) ~ 0.3 cm (200 keV) ~ 1.1 cm

(500 keV) ~ 2.3 cm (1 MeV) ~ 3.3 cm

Mean free path(E) = MA/(NAV.) . 1/E

Photoelectric

Pairprod.

Response functionResponse function

• The response function is the differential spectrum obtained with a detector when hit by monochromatic radiation

• We can consider some schematic cases:– Large detectors– Small detectors– Intermediate size detectors

““Large” detectorsLarge” detectors

In the ideal case of a very large detector (with respect to the mean free path of the radiation), the incoming radiation is fully absorbed.Since it is not possible to discriminate the time at which the individual interaction points are produced, the detector is only sensitive to the total energy deposition.

““Large” detectorsLarge” detectors

The response function of a “large” detector is very simple and it includes only a full-energy peak (which in most practical cases can be treated as a photopeak).

Ideal Ge sphere, 1 m diametre.3 MeV photons

Some devices (Total Absorption Spectrometers) are a good implementation of this limit!

Some devices (Total Absorption Spectrometers) are a good implementation of this limit!

Lucrecia TAS at GSI

Full-energy peak

““Small” detectorsSmall” detectors

In this case there is a high probability that the incoming photons are only partially absorbed.In the response function, besides the full-energy peak, one can identify a continuum generated by photons which underwent Compton scattering and, if the photon energy is larger than 1.022 MeV, peaks due to the missed detection of one or both the annihilation photons (single and double escape peaks).

Compton continuum

full-energy peak

Double escape peak

E=1.33MeV

E=3MeV

Intermediate size detectorsIntermediate size detectors

Compton continuum

Full-energy peak

Double-escape peak

Single-escape peak

The situation is qualitatively similar to the case of “small” detectors, although in practice also other components can be identified, due for instance to the environmental background (eg 40K), to the bremsstrahlung radiation, to the X-rays characteristic of the material surrounding the detector and a peak of approximately 250 keV due to the back scattering of the incoming photons.

HPGe detector used with the GASP array

In-beam In-beam -ray -ray spectroscopyspectroscopy

Our goal is to extract new valuable information on the nuclear structure through the -rays emitted following

nuclear reactions

Problems: complex spectra!

Many lines lie close in energy and the

“interesting” channels are typically the weak

ones ...

152Dy

What we want … What we get …

The nucleus is always full of surprises

Instrumentation advances New Science

New tools for new New tools for new phenomenaphenomena

From Sodium Iodideto Germanium detectors

104Ag and 106 Ag

With high-resolution devices the nuclear world seems quite

different!

Continuous effort to consistently improve

our detectors and their response function

Spectroscopic history of Spectroscopic history of 156156DyDy

The “spectroscopic history” of 156Dy is a

notable example of how the progress with the

acceleration and detection techniques leads to better insight

on the nuclear structure.

156Dy

Neutron rich heavy nuclei (N/Z → 2)• Large neutron skins (r-r→ 1fm)• New coherent excitation modes• Shell quenching

132+xSn

Nuclei at the neutron drip line (Z→25)• Very large proton-neutron asymmetries• Resonant excitation modes• Neutron Decay

Nuclear shapes• Exotic shapes and isomers • Coexistence and transitions

Shell structure in nuclei• Structure of doubly magic nuclei • Changes in the (effective) interactions

48Ni100Sn

78Ni

Proton drip line and N=Z nuclei• Spectroscopy beyond the drip line• Proton-neutron pairing• Isospin symmetry

Transfermium nucleiShape coexistence

Challenges inChallenges in Nuclear Structure Nuclear Structure

Neutron-rich beams

Physics with radioactive Physics with radioactive beamsbeams

Nuclei under extreme Nuclei under extreme conditionsconditions

Eexc

J

N- ZN+Z

Neutro

n-proton ratio

Angular momentum (Deformation)

Coupling withcontinuum

Binding energy

Angular momentum

Isosp

in

Excitation energy

Nuclei under extreme Nuclei under extreme conditionsconditions

With state-of-the-art experiments we try to study nuclei under “extreme” conditions in order to collect valuable information to refine the theoretical description and our knowledge of the nuclear interaction

Isospin: N/Z ratios much larger (or smaller) than the stability line

Spin: highly rotating nuclei

Temperature: “hot” nuclei

Isospin: N/Z ratios much larger (or smaller) than the stability line

Spin: highly rotating nuclei

Temperature: “hot” nuclei

The quest for the spin frontier was a major driving force in the development of modern instrumentation

The world of High-SpinThe world of High-Spin

Producing fast rotating Producing fast rotating nucleinuclei

Following the development of accelerators for heavy ions, it became

possible to populate nuclei at high spin

The stability of a nucleus under rotation can be estimated using the liquid-drop model. At low frequencies the shape of a rotating drop is oblate, at higher frequency it becomes prolate (Jacobi transition)

Quantum rotorsQuantum rotors

12

IIEI J

Only a non-spherical quantum object can rotate (around an

axis different than the symmetry axis)

Here J is the moment of inertia. In case of axially symmetric rotors I

can only assume even values because of the symmetry for

reflection.

JJ

22

2

2

864

II

III EEIEEE

Regularly spaced transitions!Regularly spaced transitions!

Moments of inertiaMoments of inertia

I

E

d

d

Defining the rotation frequency as:

There are two possible expressions for the moment of inertia:

1

2

)1(

d

d

I

EI

I

J

11

2

2

2

)2(

d

d1

d

d

II

E

J

Kinematical: requires knowledge of spin

Dynamical: requires knowledge of spin

differences

Moments of inertiaMoments of inertia

The two definitions of moment of inertia coincide only for rigid rotors (energy strictly proportional to

I2)

Can we really consider the nucleus a good rigid rotor?Can we really consider the nucleus a good rigid rotor?

AlignmentsAlignments

Rather than rotating the nucleus as a whole, another possibility to generate angular momentum is to align the orbital angular momenta of individual nucleons in high-l orbitals (rotation around a symmetry axis)

This process can continue up to the full alignment of all nucleons, producing a band terminating state

BackbendingBackbendingWhen the rotational frequency is high enough, a pair of nucleons can break (align) with a sudden change in the moment of intertia. The regular sequence of transitions is interrupted.

This is known as backbending from the characteristic behaviour of the moment of inertia vs rotational frequency plot.

DeformationDeformation

How deformed can a nucleus be?

Increasing the deformation costs energy and eventually the Coulomb repulsion will cause the nucleus to fission.

In particular cases, due to shell effects, a second minimum at large deformation develops, in which (weak) rotational structures can be built How can we enhance these

structures experimentally?How can we enhance these structures experimentally?

RidgesRidgesUsing at least two detectors in coincidence, weak rotational structures can be enhanced by looking “sideways” at the coincidence matrix, which should result in a “ridge” structure.

Superdeformed bandsSuperdeformed bands

With the appropriate tools, it was possible to observe discrete transitions from long (20 transitions or more) and weak (populated with a cross section lower than 10-4 of the total cross section) rotational structures.

These bands were called superdeformed because the deformation corresponded to extremely elongated shapes (2:1 ratio in the ellipsoid axes)

Linking transitionsLinking transitions

In most cases, the SD bandhead is “floating” and only J(2) can be determined.

Only in a few cases the linking transition(s) between normal deformed and superdeformed states could be observed.

These cases are obviously very important since a direct comparison between theory and experiment is possible.

Observing discrete SD Observing discrete SD structuresstructures

In our quest to observe discrete superdeformed (or hyperdeformed) structures, the experimental problem is the following:

put into evidence long sequences of -rays, produced at a level 10-4 of the total cross section, in a limited amount of time

Channel selectionChannel selection

• In order to select a specific reaction channel, multiple coincidences can be used– Each nucleus has characteristic sequences of -rays– More nuclei can have transitions with similar

energies but– The probability of having (long) sequences of

gammas with similar energies in different nuclei is much lower!

• Detecting more gammas in coincidence and putting conditions on the detected energies, only the channel of interest will survive (ideally, of course!)

Doppler broadeningDoppler broadening• In most cases of interest, the nuclei we are studying emit the

radiation in flight at relativistic velocities. The detected energies will therefore be different than the intrinsic energies because of the Doppler effect.

• The Doppler shift of the photon energies cannot be fully recovered because of the finite solid angle covered by the detector(s), translating into an indetermination on the direction of the photons

• The final effect is a broadening of the Doppler-corrected line, thus affecting the performance of the detector(s)

• It should be noticed that in some cases the effect is relatively small (for instance, fusion-evaporation between medium-mass nuclei with emission of neutrons), while in other cases, such as multinucleon transfer, due to the characteristics of the reaction mechanism, the effect is not negligible.

• Additional detectors to recover the intrinsic energy resolution can be very useful

Efficiency vs. ResolutionEfficiency vs. Resolution

With a source at rest, the intrinsic resolution of the detector can be

reached; efficiency decreases with the increasing detector-source

distance.

With a moving source, due to the Doppler effect, also the effective energy resolution depends on the

detector-source distance

Small dLarge d

Large Small

High Low

Poor FWHMGood FWHM

Efficiency vs. GranularityEfficiency vs. Granularity

Photopeak efficiency is essential to collect enough statistics (in a limited amount of time)

Granularity is also essential to avoid summing effects and to obtain the required selectivity through high-fold coincidences

Basic idea: the regular pattern survives the coincidence, the (uncorrelated) background is smeared everywhere

Compton suppressionCompton suppression

The cross section for Compton scattering in germanium implies quite a large continuous

background in the resulting spectra

Concept of anti-Compton shield to reduce such background and increase the P/T ratio

P/T~30%

P/T~50%

Resolving powerResolving power

We need objective criteria to compare the performance of different arrangements of

detectors!

Concept of Resolving Power

Resolving powerResolving power

The performance of our array will depend:• On the effective energy resolution

(narrower peaks will stand out on the background)

• On the P/T ratio (only peaks are “interesting”)

• On the photopeak efficiency (we don’t have infinite time at our disposal to perform our measurements)

Resolving powerResolving powerDefining the resolving power as:

T

P

E

SER

F

B

P RN

N

Where SE is the separation of lines in the rotational structure and E is the effective energy resolution, the peak-to-background ratio, observing at fold F, will be:

Premium in improving the overall response function (large P/T, good energy resolution)

EfficiencyEfficiencyEfficiency does not influence the way peaks stand out of the background. On the other hand, fixing the collection time, the area of peaks will depend on the efficiency:

FA

Premium in improving the overall photopeak efficiency

Operating pointOperating pointThe fraction of the total cross section that can be effectively detected in a fixed time depends both on the resolving power and on the detection efficiency: F

FR

The intersection of the two curves fixes the optimal operating point for the array

Array Sensitivity and Resolving Array Sensitivity and Resolving powerpower

Resolving power R:

T

P

E

EER

'

)FWHM(

Sensitivity :

R P

Capability to resolve a -ray

Minimum fraction of TOTAL

observable

With ancillary devices:

ationmindiscri

ancillaryP FR

Ancillary devicesAncillary devices

A very effective way of improving the NP/NB ratio without increasing the observational fold is to reduce the value of NB through auxiliary (ancillary) devices.

These detector could also improve the resolving power by improving the effective energy resolution.