Chapter 3

Experimental Techniques andMethods

3.1 High spin physics

During past decades nuclear high spin phenomena have been the subject of interest in

both experimental and theoretical points of view. Several new methods were introduced to

study these phenomena. The phenomenon of nuclear rotation was discovered in the early

1950 following pioneering suggestions by Bohr and Mottleson [1, 2]. During the 1960’s

the first experiment with heavy ions initiated by Morinaga and Gujelot including in-beam

γ-ray measurements which provides the way to study nuclei at high angular momentum.

The progress in this new field was made possible by the essential development in

experimental methods of population of high spin states in nuclei. Various nuclear reac-

tion processes were employed to transfer a large amount of angular momentum to final

nuclear state. Such transfer can be expected in nuclear reactions initiated with heavy-ion

projectiles.

3.1.1 Population of high spin states

Fusion evaporation reactions became standard tool to populate high spin states in nuclei.

Different types of nuclear reactions occur when the target is hit by the projectile depending

on incoming energy of the projectile and impact parameter. Figure 3.1 gives a schematic

representation of different kinds of nuclear reactions possible with heavy ion beams based

on impact parameter. If the projectile energy is lower than the Coulomb barrier energy

48

Coulomb ScatteringFormation of Compound Nucleus

Complete Fusion

Impact Parameter

Target Nucleus

Nuclear Field

Projectile

R RT

Rp

Nuclear Scattering

Figure 3.1: Schematic drawing of various kinds of nuclear reaction mechanism possiblewith light projectiles over heavy nucleus.

and impact parameter is large, so that nuclear matter distributions of the projectile and

the target nuclei do not overlap, Coulomb excitation is dominant which refers to purely

electromagnetic excitation of nuclear states. In case of the projectile energy slightly

above the barrier energy with partial overlap of the nuclear matter of the projectile and

the target nuclei, transfer of nucleons is favorable. When the matter distributions overlap

and projectile energy is above the barrier, then the compound nucleus formation becomes

dominant process. Important conditions for formation of the compound nucleus is that

the energy of the projectile must be large enough to overcome Coulomb barrier and the

angular momentum transfer should be small for avoiding fission. The amount of angular

momentum transfer depends on the projectile energy and impact parameter.

For a given projectile and target combination, the coulomb barrier energy is given

by following equation

VCB(MeV ) =1

4πεo

ZpZte2

Ro(Ap1/3 + At

1/3)(3.1)

where Zp, Ap are the atomic number and mass number of projectile and Zt, At are atomic

and mass number for target.

49

The maximum angular momentum transfer (L= R × P) can be estimated from

grazing radius

R = Rtarget + Rprojectile (3.2)

and momentum of the projectile when it hits the target nuclei is

P = 2µ(Ep − V )1/2 (3.3)

where µ is reduced mass of the beam, target system, Ep is energy of the projectile in

center mass frame and V is Coulomb barrier. Therefore maximum angular momentum

transfer is given by

Lmax = 2Rµ(Ep − V )1/2 (3.4)

The grazing radius, reduced mass, energy in center of mass are given below

R = R0(A1/3p + A

1/3t ) (3.5)

µ =Ap ∗ At

Ap + At

(3.6)

ECM =Elab ∗ At

At + Ap

(3.7)

The major advantage of heavy ion fusion reaction is very high angular momentum can

be brought in to the system and the required projectile energy is little more than the

barrier, and beam current required is small typically of the order of nA . With optimum

projectile and target combination, proper choice of beam energy only a few exit channels

are possible.

50

Figure 3.2: A Schematic of decay of compound nucleus.

51

3.1.2 Decay of compound nucleus

The compound nucleus formed in heavy ion fusion reaction has the life time considerably

longer than the transit time of the nucleon through the nucleus. So it forgets history of

formation reaction (how it is formed). Figure 3.2 illustrate decay of compound nucleus

formed in heavy-ion fusion reaction. Statistical model calculation gives life times of the

compound nucleus typically of the order of 10−19 to 10−21 second. The compound nucleus

formed, which is a very hot system can cool down by emission of protons, neutrons,

alpha particles and statistical gamma rays giving rise to various residual nuclei in the exit

channel. The nucleus loses an energy of approximately 8 MeV and only 0.5-2 ~ of angular

momentum in each particle evaporation. The residual nucleus formed thus will still have

a large amount of angular momentum and low excitation energy. When no more energy

left for particle emission then residual nucleus de-excites through emission of stretched

γ rays to reach the ground state. The levels with minimum excitation energy for given

angular momentum is called the yrast states. De-excitation proceeds through these yrast

states to reach the ground state.

Statistical γ-rays from the excited compound nucleus

Far above the yrast line the γ rays, essentially cascade down carrying away large amount

of excitation energy but little angular momentum. These are called quasi-continuum

transitions, because nuclear level density is high and γ-rays are not resolvable. These

statistical γ rays predominantly electric dipole in nature.

Yrast-Like non-statistical γ-ray transitions from the residual nucleus

When yrast line is reached, γ rays cascade from one yrast level to another carrying a

major fraction of angular momentum of excited residual nucleus. These non-statistical

stretched γ-ray transitions will have well defined energies.The yrast-like γ rays can be

either dipole or quadrupole with electric or magnetic character, although a large fraction

are either E2 or M1 type. Besides, in a rotational band, E2 transitions are enhanced over

the other types of γ radiation. Figure 3.3 illustrates the de-excitation paths following

formation of hot compound nucleus.

52

Particle Emission

ray transitions

Fission

(rotational cascades)E2 transitions

Statistical Cascadesof E1 transitions

Exc

itatio

n E

nerg

y(E

)

Nuclear Spin(I)

Entry Lineγ

Figure 3.3: The schematic representation of decay paths of a hot compound nucleusformed in heavy ion fusion reaction.

53

3.2 Pelletron accelerator facilities

The projectiles can be accelerated to high energy with facilities like cyclotrons, linear

accelerators. One of the most commonly used energy augmentation machine is tandem

van de graff linear accelerator, which provides high voltage electric field by transporting

electric charge from ground potential to terminal using an insulating chain. Charged

particle accelerates under influence of this field and acquires an energy equal to the prod-

uct of ion charge and terminal voltage. Negative ions of the required chemical element

are produced through a sputtering process after which an electrostatic field extracts the

ions and injects them into an evacuated tube at ground potential. These negative ions

then accelerate towards positively charged terminal. On reaching the terminal, they are

passed through a thin stripper foil or gas-jet. In this process, several electrons are lost by

these negative ions resulting in their conversion to positive ions. These positive ions are

then accelerated from the positive terminal down to the ground potential. Consequently,

projectiles with velocities up to a few percent of speed of light can be extracted, which

can be allowed to bombard on target material.

Pelletron accelerator at IUAC

The major Pelletron accelerator available in India is the 15UD Pelletron accelerator in

IUAC, New Delhi. The 15UD Pelletron accelerator at IUAC (Figure 3.4) is a vertical tan-

dem electrostatic accelerator which can deliver beams up to several pnA of current. The

negative ions are produced by the SNICS (source of negative ions by Cesium sputtering)

source placed at top of the accelerator tower, while extraction these negative ions gain

to few keV (250−350-keV) of energy. These negative ions are now attracted towards the

positive terminal where the negative ions are stripped to positive charge state by carbon

foil or gas-jet stripper. These positive ions are further accelerated to ground potential due

to the Coulomb repulsion where the desired ion energy is selected by tuning of analyzer

magnet field and delivered into one of seven different beam lines with the use of switching

magnet.

The energy acquired by these ions

E = (q+1)V + Vinj

54

where q = Charge state of ion after stripping, V= Terminal potential, Vinj = Injector

potential or extraction potential.

3.3 Detection of γ-radiation

The basic aim of γ-ray spectroscopy is to study nuclear structure. In heavy ion fusion

reaction decay of residual nuclei to their ground state usually characterized by the emission

of the cascades of γ-rays. The information about underlying nuclear structure and its

spectroscopic properties can be known by measuring energies, intensities and angular

distribution of these γ-rays. The basic information about spins, parities, multi-polarities

can be obtained by measuring angular correlations, linear polarization etc. With the

advent of present day γ-detector systems like GAMMASPHERE, EUROBALL, INGA,

it is possible to study nuclei up to high angular momentum due to the high efficiency

and resolving power of these powerful detector arrays. The detection efficiency of the

γ-radiation mainly depends on how it interact with the detector material. A detector is

a transducer which converts the incident radiation in to a measurable electrical signal.

3.3.1 Interaction of γ-radiation with matter

Primarily γ-rays in the energy range up to 3 MeV can interact with matter by several

distinct processes. However, three major processes are predominant.

1. Photo electric absorption

2. Compton Scattering

3. Pair production

For energies less than 1.022 MeV pair production is absent and only the Compton

and the photoelectric processes are possible. For energies greater than 1.022 MeV, pair

production is also possible.

Photoelectric effect

In photoelectric effect, incident γ-ray gives up all its energy to an atomic electron, giving

the electron kinetic energy that is slightly less than γ-ray energy due to the energy required

to free the electron from the atom. Thus photo electrons have a very small range of

55

Figure 3.4: Schematic representation of 15UD-Pelletron accelerator at IUAC, New Delhi.

56

energies, dependent only on which atomic orbital they occupied. The ejected electron

will have kinetic energyEk = Eγ - Be

where Eγ is γ-ray energy, Be is the binding energy of the electron in atom. This process

is more desirable for the γ-ray detection since the incident γ-ray deposits all of its energy

in the detector. The photoelectric cross section for interaction of γ-ray of energy Eγ with

atom of atomic number Z is given below. This effect is dominant at low energies (Eγ <

0.3 MeV) [3] can be seen in figure 3.5.

σ ∝ Zn

Eγ5 (3.8)

Compton scattering

The Compton scattering process takes place between incident γ-ray photon and an elec-

tron of an atom in the absorber. In this interaction mechanism, incident photon is de-

flected through an angle θ, with respect to its original direction. Part of the photon energy

is transferred to the electron which is ejected from atom at an angle φ. Compton scat-

tering is an inelastic (in-coherent) process. The photon must overcome electron binding

energy which is a criteria for electron to be ejected. The ejected electron is referred to as

the recoil electron. The process of Compton scattering is shown schematically in figure

3.6. Compton scattering is dominant in the energy range (0.3 < Eγ < 5 MeV). An ex-

pression relating energy transfer and scattering angles can be derived using conservation

of energy and assuming that electrons binding energy is negligible

Eγ′ =

Eγ

1 + Eγ

m0c2(1 − cos θ)

(3.9)

where m0c2 is the rest-mass (511-keV) of the electron. The kinetic energy of electron is

then given as

Ekin = Eγ − Eγ′ =

Eγ

1 + m0c2

Eγ(1−cos θ)

(3.10)

The probability of Compton scattering σ, is roughly proportional to atomic number

Z and inverse of the photon energy Eγ which is given by

σ = CZ

Aρ

1

Eγ

(3.11)

57

Figure 3.5: Absorption cross section for γ-rays in Silicon and Germanium as a functionof energy. Plot is taken from Ref.[4]

58

Figure 3.6: Schematic of Compton scattering phenomenon.

Pair production

Unlike photoelectric absorption and Compton scattering, pair production is a nuclear

interaction process. The incident photon interacts with the electromagnetic field of the

nucleus of atom and an electron-positron pair is created. In order to create electron-

positron pair gamma-ray must have an energy exceeding twice the rest-mass energy of an

electron i.e Eγ ≥ 1.022 keV. The excess energy of the gamma-ray are shared equally as

kinetic energy between electron and positron

Eγ = Ekin + 2m0c2

When energy of positron is reduced to near thermal energies it will interact with

an atomic electron, releasing two 511-keV annihilation photons with opposite directions.

This radiation is referred to as annihilation radiation. The pair production coefficient k,

is roughly proportional to square of the atomic Z number and the natural logarithm of

photon energy.

3.4 Semiconductor detectors

The structure of nuclei can be studied by detecting γ-rays from the de-exciting nuclei.

Basic phenomena of detection of γ-ray is ionization, that the incoming γ-ray gives up part

59

or all of its energy to an electron or positron in detector material. These particles lose their

kinetic energy to other electrons in detector material by scattering which in turn produce

ion-hole pairs. The liberated charge can be collected by either directly with proportional

counter or with semi conductor detectors or indirectly with scintillation detectors. The

proper collection of produced ion-hole pairs by applying suitable voltage across detector

material constitutes the detector signal. The most important property of the detector is

that it should have excellent energy resolution, high detection efficiency, and good timing

characteristics.

Semi conductor detectors, such as Ge or Si(Li), are operated as reverse biased p-n

junction diodes. The reverse bias creates a depletion region, reducing the number of free

charge carriers in the undisturbed crystal. As depletion region is active region in the

detector, bias is set high enough so that entire crystal is depleted, with an operational

gradient of typically a few kilo volts over a few centimeters. The depth of the depletion

region is given by

d = (2ǫV

eN)2

(3.12)

where N is the impurity or dopent concentration and V the bias voltage.

At present, semiconductor detectors are the best for detection of γ-radiation because

of their excellent energy resolution and moderate efficiency. Germanium possesses ideal

electronic characteristics and is most widely used semi conductor material in solid state

detectors. The popular early designs used lithium-drifted germanium [Ge(Li)] as detection

medium. Ge has higher atomic number and has therefore better sensitivity to high-

energy γ-rays. It is also technically possible to manufacture wider intrinsic regions in

Ge than in Si, so that Ge detectors can be used for detection of radiation of a few MeV

energy. Compared to Si, the band gap and the pair creation energy is smaller in Ge,

so that n is higher and also the Fano factor is smaller in Ge (0.08) than in Li (0.1),

which both contribute to give ≈ 27% better energy resolution in Ge. However, narrower

band-gap also increases number of thermally created electron-hole pairs and therefore

the background (dark) current in detector. So Ge detectors should be cooled to liquid

nitrogen temperatures to reduce noise from thermal electrons produced across small band

gap in Ge (0.67 eV) at room temperature. To achieve a depletion region as large as a few

60

Collimator

Target

Ge Crystal

BGO Ge Cryostat

PMTBGO Housing

LN2 Dewar

Figure 3.7: Schematic diagram of HPGe detector.

centimeters with out dielectric breakdown, high purity germanium with impurities on the

order of 109-1012cm3, are typically used.

3.4.1 High-Purity Germanium Detector(HPGe)

In recent years, manufacturers have produced high purity germanium (HPGe) crystals,

essentially eliminating need for lithium doping and simplifying operation of detector. The

n-type coaxial High Purity Germanium (HPGe) detectors have been used for discrete γ-

ray spectroscopy due to its high resolution compared to other detection media. HPGe has

impurity concentrations of around one part in 1012, allowing depletion depths of several

centimeters to be achieved. The n-type material is preferred over p-type because of p-type

is more susceptible to neutron damage. The energy required for producing an electron-

hole pair (at 77 K) is 2.96 eV for Ge and 3.26 eV for Si. Thus an incident γ-ray with an

energy of several hundred keV, produces a large number of such pairs, leading to good

resolution and low statistical fluctuations.

3.4.2 Compton suppression

In γ-ray spectrometry measurements, some photons from the source under investigation

are scattered within the radiation detector itself depositing part of their energy in the

detector and escape. This partial energy deposition leads to Compton associated back-

61

Figure 3.8: Representative γ-ray spectrum of 60Co with and with out Compton-suppression. Spectrum is taken from Ref.[5].

ground representing incomplete energy deposition of incident photons, which leads to the

distortion of the spectrum from actual energy distribution and hence poor peak-to-total

(P/T) ratio. It is possible to detect such (escaping) scattered photons by use of a de-

tector made of a less expensive material such as BGO or NaI surrounding Ge detector.

BGO is preferred over NaI because of its high efficiency and good timing properties. By

correlating events in Ge detector and the surrounding shield (named as Anti Compton

shield-ACS) detector with timing electronics, events counted in ACS detector can be used

to reject simultaneous events in Ge detector (veto signal).

A Compton suppression spectrometer consists of a central Ge-detector surrounded

by a scintillation shield( BGO or NaI). γ-rays from a source outside are collimated before

striking Ge-detectors positioned at right angle to the direction of the beam. Compton

scattered γ-rays from Ge detector can then interact with the surrounding scintillating

material. If resulting signal is above noise level, then it is used to reject recording of any

coincident signal related to Compton event in the Ge-detector. Accordingly, full energy

events should only in principle remain in spectrum of the Ge-detector. However, the

Compton continuum is not completely eliminated since back scattered γ-rays can escape

62

scintillation crystal through the entrance hole of the incident beam. Such γ-rays leave

most of its energy in the Ge-detector and its contribution appears as the Compton of the

spectrum.

3.5 Multi-Detector Arrays

When nucleus is created in excited state by using nuclear reactions or radiation decay,

nucleus is de-excited by emission of cascade of γ-rays. This cascade connects different

energy states with each other. If we use only single detector to detect these γ rays,

we will get the so called singles spectrum which will not give information about the

particular transition of interest as it gives information only about the all the peaks in

the spectrum corresponding to different energy levels. In order to build up level scheme

the de-excitations of nuclei must be time correlated. This can be done by using at least

two γ-ray detectors with condition that, record the data when two detectors detect γ-

ray simultaneously within a specific time-window i.e is double or γ-γ coincidence. By

employing coincidence technique, one can clean up the spectrum, thereby the resolving

power is considerably improved. As number of coincidence fold is increased, one can

get better cleaning of spectrum and will help to identify transitions of weakly populated

states in a nucleus. The major disadvantage is that the count rate is drastically reduced

with the increase of number of folds. The counting rate may be increased with increasing

the target thickness and beam current but these methods in turn causes pileup-of counts.

This drawback can be minimized by increasing the number of detectors. The combination

of several detectors in an array increases the photo-peak efficiency, as well as allowing

coincidence measurements and giving information on angular distributions of the emitted

γ-rays. The present study is carried out using Gamma Detector Array(GDA) at IUAC,

New Delhi.

3.6 Gamma Detector Array (GDA)

Gamma Detector Array is one of the major facility to study nuclear γ-ray spectroscopy

and was established at Inter university Accelerator Center (IUAC) in 1990′s. This facil-

63

Figure 3.9: Schematic view of Gamma Detector Array(GDA).

64

ity contains 12 Compton suppressed n-type High Purity Germanium (HPGe) detectors,

separated in to three groups each consisting of four detectors and are mounted co-axially

in Anti-Compton Shields and making an angle of 45◦, 99◦, 153◦ with respective to the

beam direction and are tilted ±23◦ with respect to the horizontal plane. GDA has a 18

cm diameter, 4 cm height Aluminum scattering chamber equipped with a target ladder

which can accommodate three targets, two view ports and a collimator. The beam can

be viewed on a quartz for proper beam focusing. The beam dump consists of a Ta sheet,

about 2 m downstream from target chamber. This ensures that γ-rays from beam dump

are not viewed directly by Ge detectors. Oil free vacuum is maintained in chamber by a

turbo molecular pump.

Anti-Compton shields (ACS) made up of Bismuth Germinate crystals (BGO) are

used to reject Compton scattered events thereby Compton background considerably re-

duced in Ge spectrum. The ACS shields of symmetric design are mounted onto two

rigid mechanical structures, on either side of beam line. These structures are mounted

on two trolleys moving on a guide rail to allow positioning of detectors. Each of these

ACS consists of eight optically separated 15 cm long BGO crystals which are coupled to

a photomultiplier tube. In front end of the BGO shield, suitably shaped NaI(Tl) crystal

is optically coupled to detect low energy back scattered γ-rays from Ge detector. The

direct hit of the γ-rays from the reaction can be avoided with the collimator made of

lead or tungsten, placed in front cone of ACS. The peak to total efficiency for each of the

unsuppressed HPGe detector is ≈ 17% and with suppression it becomes ≈50%. Figure

3.9 depicts the view of GDA.

3.6.1 Electronics for GDA

The electronics setup designed for GDA at IUAC has been sectioned in to three logical

circuit groups are

1. Compton Suppression system in Gamma Detector Array.

2. BGO multiplicity filter system to get the γ ray multiplicity information.

3. A master gate (indicates a valid event selection) is generated if two or more Ge

detectors are in coincidence.

65

Figure 3.10: Picture of Gamma Detector Array at IUAC, New Delhi.

66

The primary aim of this electronics setup facilitates to acquire data in singles and

in multi parameter mode, through a CAMAC interface. The block diagrams shown in

figure 3.11 and 3.12 are the electronics setup’s used to record the following information

in LIST mode:

¥ Energy information from individual HPGe detectors at various angles in singles

with or without multiplicity gate.

¥ Energy and timing information from all HPGe detectors in event mode.

¥ Hit pattern of all the HPGe and BGO detectors. The Hit pattern signifies the

number of coincidence fold recorded for the particular event.

3.6.2 Compton suppression and pile-up rejection

The γ-rays that deposit part of the energy in Ge crystals are rejected using the signal form

the Anti-Compton Shields surrounding HPGe detector. The block diagram of the logic

circuit designed for Compton suppression and pile-up rejection is shown in figure 3.11.

The energy signal from a detector is amplified with help of amplifier whose output signal

is fed to an ADC. The Compton suppression is done with timing signals from the Ge and

ACS. The timing signal from Ge crystal is amplified by the timing filter amplifier (TFA)

which is fed to a constant fraction discriminator (CFD) to get TTL output pulse having

width of 20 ns. The threshold of the CFD is set to just above noise level (≈20 keV) to

accept pulses whose output >20 keV. The time signal from ACS is also processed by TFA

and CFD (threshold ≈ 30 keV), which gives output pulse having width of 300 ns. A delay

is introduced for time matching of the signals from Ge crystal and ACS. The Ge logic

pulse (input A) and the ACS logic pulse (input B) are fed to a 4 input fast coincidence unit

(ORTEC CO4010). To achieve Compton suppression, anti-coincidence logic is established

between the two pulses. A common problem in nuclear spectroscopy is pulse pile-up caused

by non-zero response time of detection between two-events. The fact, the pulses from a

radiation detector are randomly spaced in time can lead to interfering effects between

pulses when counting rates are high. These effects are generally called pile-up and can be

minimized by making the total width of the pulses as small as possible. To achieve this,

a part of Ge logic pulse (signal A) is delayed by 50 ns and stretched to width of 10 µs

67

HpGe

BGO−ACS

Bais +Ve

Bias −Ve

TFA

TFA

CFD

CFD

DelayGate and

Delay gen

A B

C

Y Y Y

B

C

D

To 16 channel disc

To 16 channel TDC

To gate and strecher

A

Raw Ge output Used in Multiplicity−filter logic

Figure 3.11: Block diagram of electronic circuit used for the Compton suppression systemin GDA.

and then fed back to the coincidence unit in anti-coincidence. This makes sure that after

accepting a Compton suppressed signal, the coincidence unit blocks off any other signal

which overlap within a time period of 10 µs. The coincidence module (CO4010) generates

logic output which is Compton suppressed termed as Ge.ACS. The NIM outputs from

the CO4010 now sent to 16 channel discriminator latch for γ-γ coincidence selection and

a 16 channel time to digital converter to acquire the time spectra of Ge detectors. The

TTL outputs from CO4010 is used to gate individual HPGe energy ADC after proper

delay and adjustment of pulse width.

68

3.6.3 Generation of master gate and data acquisition

The logic for generation of master gate and data acquisition system is shown in the

figure 3.12. Master gate acceptance logic for the data acquisition for a valid event when

conditions for Compton suppressed Eγ-Eγ coincidence. The Master gate unit uses the

signals (Ge.ACS) from Compton suppressed logic unit (C04010). These signals are fed to

a 16 channel discriminator latch (Philips 7106) generates a SUM output which indicates

number of detectors having valid data. The other output delivers a 16-bit word, called

hit pattern which identities the fired detectors when a pulse is applied at SYNC input.

The SUM output is fanned out into two pulses which are fed to two CFDs (711). The

thresholds of these CFDs are set, such that one of them gives an output pulse even if

only one Ge detector is fired (N ≥ 1) while the other gives an output pulse when the

number of Ge detectors fired is greater than one (N > 1). In order to establish two fold

Eγ-Eγ condition, a fast coincidence unit (ORTEC CO4010) is used having three inputs

A, B, and C. Inputs A and B are the N >1 pulse and N ≥ 1 pulse (delayed by ≈200 ns),

respectively, while input C is delivered by OR logic of RUN and BUSY outputs of the

Event Handler module. An anti-coincidence of input A with inputs B and C is demanded.

The purpose of delayed N ≥1 pulse (input B) is to reset output pulse of CO4010 after a

fixed time while function of the input C is to block output if an event is currently being

processed. The output of this CO4010 coincidence unit qualifies MASTER GATE as it

signals that there is a two or more fold Ge event. Outputs from this unit are used (a)

COMMON ’stop’ to signals of 16 channel TDC (b) INPUT of event handler to signal the

start of acquisition.

After generation of master gate, final task to be completed is acquisition of the data

in list-mode. The data that is to be acquired in the events is (1) Timing information

of Ge detectors which are fired given by the 16 channel TDC. (2) The hit pattern, i.e.,

identifies detectors which are fired is given by the 16 channel discriminator latch.(3) The

energies of the gamma-rays detected which are obtained by amplifying the Ge energy

signals processed by spectroscopy amplifiers (ORTEC 572) and feeding the outputs gated

ADCs . The outputs of ADCs are given to ADC multiplexers which deliver the digital

69

data to ADC interface module.

The above mentioned information from corresponding modules are ensured by a

Event Handler Module. This module is fed by Master gate signal as its input. The prompt

output from this module is used to gate the individual ADCs, after being ‘AND’ed with the

individual Ge.ACS signal. This ensures that gate is not opened for ADCs having no data.

Simultaneously the Event Handler Module produces a BUSY signal which inhibits module

to process any further Master gates till it gets a CLEAR signal. After giving sufficient

time (≈80-100 µs) to the ADCs for conversion, the Event handler generates an output

(delayed o/p) which is used to trigger the List Processor to read all ADC information and

clear buffers. Next, List Processor clears BUSY signal from Event Handler and system

is ready to accept subsequent event. Finally, the valid coincidences are recorded event-

by-event using online CAMAC (Computer Automated Measurement And Control) based

data acquisition system CANDLE [25] developed at IUAC.

3.7 Data analysis procedure

The experiments aimed to study spectroscopic properties of nuclei using multi-detector

arrays usually involve various steps before and after the experiment. Once the physics

problem is selected, one has to decide suitable reaction to populate desired nucleus. Avail-

ability of ion beams and suitable target materials of required thickness usually limits pro-

jectile and target combinations. In case of high spin structure studies, the beam energy

must be above the Coulomb barrier for projectile and target combination, at which pro-

duction cross section of the nucleus of interest and magnitude of angular momentum is

optimum. Higher energy of projectiles also results in higher input of angular momentum

and shifts the spin distribution of final nucleus to higher spin values. Theoretically pro-

duction cross section can be obtained for a reaction using statistical model codes PACE

and CASCADE. The beam energy is further corrected for energy loss in target material

and excess energy required to populate high spin states of nuclei. During the experiment

singles data is collected for certain time intervals at different beam energies to get exci-

tation function and optimize beam energy. High intensity known γ transitions of desired

70

Fan Out

Fan In

N > 1

N = 1

YY

C

A

Coin. Unit

Four Input

YC

BA

YX

Delay

Delay

Prompt

Delayed

TTL NIM

TTL NIM

Fan In

Data A

quisition System

AD

C

CA

MA

C

Interface

Interface

MultiplexierA

DC

O/P

O/P Busy

Run

Fan Out

Four Input

Coin. Unit

B

Ge S

ignals(1−

12)

Amp

Amp

ADC

Ge(1)ADC

Gate

Sync

Common

Sum

Tim

e to Digital C

onverter16 C

han. Discri. and Latch

Gate and S

trecher

Sync

Sum

Ge(12)

Ge(12)

Ge(12)

Ge(12)

Ge(1)

Ge(1)

Ge(1)

I/P from

Com

pton−S

upp.Cir.

I/P from

Com

pton−S

upp.Cir.

I/P from

Com

pton−S

upp.Cir.

Trigger

List Proce.

I/P

Figure 3.12: Block diagram of electronic circuit used for generation of master gate/event.

71

nucleus is used as reference for preliminary identification of transitions of desired nucleus

in the singles energy spectrum. Final beam energy is decided based on the yields measured

from singles energy spectra collected at different beam energies.

After optimizing the beam energy, the data is collected in list-mode which is nec-

essary for construction of level scheme. Data is collected in event mode and later sorted

offline. After in-beam experiment, singles data is also collected with standard radioac-

tive sources 152Eu,133Ba, placed at target position. These singles data utilized for energy

calibration and efficiency correction of the detectors.

Data collected during experiment is of large volume typically in the order of 109.

The volume of the data sets depends on number of detectors, number of detected γ

rays. Therefore, organization of raw data is of great importance to permit fast access for

further analysis. The treatment of data can be divided into two main steps, pre-sorting

and compression. Pre-sorting includes energy calibration, gain-matching and efficiency

correction and setting time gate. In experiments, various steps are involved in processing

collected data before getting actual information about nuclear properties like γ intensities,

nature of transitions, parity etc, which are necessary to establish level scheme of the nuclei

of interest. Figure 3.13 is a schematic representation of data analysis procedure followed

in the present study.

3.7.1 Energy calibration of γ spectrum

The energy calibration for each HPGe detector is to be performed as first step of analysis.

Correlation between the channel and the energy has to be established using the data from

the standard radioactive sources. This is done by using standard radioactive sources 133Ba,

152Eu and 60Co which covers wide energy range from 80-keV to 1408-keV. Calibration with

sources of known energies allows us to correlate the channel number with actual γ-ray

energy. The resulted spectrum is expressed the γ-frequency (counts) as a function of

γ-ray energy (channel number). The initial two point linear calibration is performed

by visually identifying two prominent peaks from the spectrum with reference to known

strong transition of 152Eu. A slight non linearity for large pulse height can be corrected

by higher order calibrations like quadratic or polynomial calibration. Energy calibration

72

Figure 3.13: Block diagram showing various data-analysis steps followed in constructingfinal level scheme for nuclei of interest.

73

of each detector was represented by a quadratic function of channel number, i.e., E =

aX2 + bX + c, where X is the channel number. The quadratic fit generally provides

energy calibration with an accuracy of 0.1 keV within the energy range 0-2 MeV. Several

spectrum analysis packages are available for automatic energy calibration.

3.7.2 Efficiency calibration

The efficiency calibration is needed for detector as detection efficiency changes as a func-

tion of γ-ray energy. The absolute photo peak efficiency of a detector is defined as a

ratio of counts in the photo peak to number of photons emitted by the source in that

counting time. Detector efficiency can be determined by using a standard radioactive

sources emitting γ-rays of various energies whose relative intensities are known. By mea-

suring the energies and corresponding photo peak area, the energy dependence of the

photo peak efficiency can be directly determined. Standard radioactive sources 152Eu and

133Ba were used for this purpose. These sources were put at target position for accurate

determination of photo peak efficiency for actual in-beam data. The measured values are

useful in determining the relative intensities of observed γ-rays, The experimental relative

efficiency values of detector was fitted with the function,

Eγ = exp[A0 + A1ln(Eγ) + A2ln(Eγ)2 + A3ln(Eγ)

3 + A4ln(Eγ)4] (3.13)

3.7.3 Gain matching

After obtaining the accurate calibration of data is to ensure that the data from each detec-

tor should have constant energy dispersion, that the energy of the γ-ray required to have

a definite relation with the channel number, therefore the data is independent of identity

of detector. This is achieved by multiplying channel number with a suitable constant to

achieve gain-matching, usually 0.5 or 1 keV/Channel. Figure 3.15 (bottom) shows the

energy spectrum of 152Eu before gain matching of calibrated data. It shows that 778,

867, 964-keV transitions occurs at different channel numbers for detector 10 and detector

11. If such data from individual detectors are added to get a single energy spectrum, will

result in multiple peaks or broadening of peaks, resulting in loss of actual information of

74

400 800 1200 1600

5.00

10.00

Energy (keV)

Rea

ltive

Effi

cien

cy

0

Figure 3.14: The photo peak efficiency curve for GDA.

the γ-ray. This discrepancy is removed by doing proper gain matching. Analysis package

CANDLE [25] developed at IUAC was used for gain matching of individual detectors.

The top spectrum in figure 3.15 depicts the situation after gain match process. In which

γ-rays of energy 778, 867, 964-keV in 152Eu from the two detectors are matched to com-

mon channels (displayed in energy units). After gain matching of energy ADCs are done,

the delay between all the TAC combinations are matched to correct for small differences

in cable length and electronic timing and to obtain a total γ-γ TAC between pairs of all

detectors. This γ-γ TAC will be useful in selecting time gate. Usually prompt time gates

are preferred if only the prompt γ-ray sequences are of interest in the decay scheme of

nucleus under study. The prompt time gate is also useful to discard γ-transitions from

levels under isomeric states and to reduce random coincidences.

3.7.4 γ-γ matrices

Construction of level scheme is based on coincidence relation between de-exciting γ-rays

from excited states. Using conventional γ-γ coincidence technique one can establish corre-

lation between γ-transitions from different excited states of nucleus of interest. To do this

coincidence analysis, data has to be sorted in to γ-γ matrices after proper gain-matching

75

Channel Number

Co

un

ts

2521 2636 2751 2866 2981 3096 3211 3326

0

2.0K

4.0K

6.0K

0

2.0K

4.0K

6.0K

ADC-10-S

ADC-11-S

Figure 3.15: Comparison of energy spectra of detectors 10 and 11 before gain match (top)and after gain match (bottom).

76

of raw data.

To create a two-dimensional γ-γ matrix, each event is unfolded into pairs of two

energies (Eγx, Eγ

y) and the bins corresponding to Eγx and Eγ

y are incremented on the x- and

y-axis, respectively. In present work two dimensional γ-γ matrices were constructed using

software packages CANDLE [25] and INGASORT [26]. In Eγ-Eγ matrix, the coincidence

information of γ-rays is arranged as an event in two dimensional histogram. Two axes of

the histogram represents the energy of the detected γ-rays, and the 1-D projection over

this 2-D histogram will give energy information and number of pairs of γ-transitions which

are in coincidence to each other. Higher fold dimensional arrays of data such as three and

higher dimensional, usually referred as Cube and Hyper cube can also be generated from

higher fold coincidence data.

In the present work, two separate matrices were constructed, in order to establish

level scheme of the nuclei of interest and to obtain the multipolarities of γ-transitions.

The first one is Eγ - Eγ symmetric matrix, which was created using data from all the de-

tectors with out keeping identity of individual detectors. Events which contain higher fold

γ-coincidences were unfolded into two-fold events before incrementing 2-D matrix. The

matrix has dimensions of 4096 x 4096 channels with energy dispersion 0.5 keV/channel

and it covers the energy range upto 2 MeV. With large number of gamma detectors in

4π geometry, the isotropic detection of γ-ray is assumed. The purpose of this matrix is

to analyze coincidence relationship between γ-transitions, hence further matrix is sym-

metrized to make two energy axis equivalent. This was done by adding its transpose to

itself.Esym = E (x, y) + E (y, x)

The second type of matrix constructed is angle dependent matrix, which is also

called asymmetric matrix and is necessary for analysis of angular correlation information.

This asymmetric matrix is made depending on angles of the detectors in array. This

matrix is created by taking one group of detectors contain energy coincidences between

them at an angle (θ1) on one axis, and data of other group of detectors at an angle (θ2)

on other axis. These events are stored into a separate matrix, called DCO matrix, with

θ1 detectors on one axis while the θ2 detectors on the other axis. This DCO matrix is

77

Figure 3.16: Shows typical two dimensional γ - γ matrix.

Figure 3.17: Projection of events on an axis of a matrix.

78

used to obtain information about the γ-ray multipolarities.

3.8 Analysis of coincidence data

Each matrix element (x, y) in generated matrix corresponds to number of coincidences

between detected γ-rays with energy Ex and Ey. These recorded coincidence events are

in three combination’s contains photo peak events in both sets of detectors, or Compton

events in one set of the detector and the photo peak events in other sets of detectors, or

Compton events in both sets of detectors. Out of these combinations of recorded data,

only photo peak - photo peak events gives full energy information and the remaining

combination’s of recorded data has to be removed from the data. This process is known

as background subtraction. Figure 3.18 is a representative of projection spectra depicts

the situation before and after background subtraction.

3.8.1 Total projection

In case of symmetric matrix, the total projection spectra on both x-axis and y-axis are

identical. The total projection spectrum on x axis is obtained by summing counts in all

y channels corresponds to each x channel, which is named as total x-projection. The

y-projection of matrix is also obtained in similar fashion. The total area under these

spectra gives number of events stored in the matrix. These total projection spectra are

generally used for the preliminary identification of γ-transitions belonging to all the nuclei

produced in the experiment. Figure 3.18 shows an example of total projection spectra in

which γ-rays belonging to strong reaction channels are labeled.

3.8.2 Construction of level scheme

The total projection spectrum contains γ-rays from different reaction channels, therefore

proper gating is required to isolate the set of correlated γ-rays belonging to the nucleus of

interest. Coincidence spectrum is obtained by selecting a narrow energy window (gated γ)

on one axis and projecting the one dimensional spectra (1-D) spectrum on the other axis.

This projected 1-D spectra usually shows γ-transitions which are in coincidence with gated

γ-transition. From this spectra one can identify new γ-transitions which are in coincidence

79

Figure 3.18: The total projection spectra without (top) and with background subtraction(bottom).

80

E1

E2

E3

E4

E8

E9

E5

E6

E7

Figure 3.19: Sample level scheme for illustrating the coincidence relationship.

with the gated γ-ray and belongs to nucleus of interest. Now we have to verify these new

transitions (by projecting gates on them), whether they are in coincidence with known

transitions of the nucleus of interest. In this way the new γ-transitions belonging to the

nucleus of interest can be identified.

To illustrate idea of coincidence method, a hypothetical level scheme was drawn

in figure 3.19. As gate is set on particular γ-transition, gated spectrum will contain

γ-transitions that occur in the decay path. Figure 3.20 is a representative projection

spectrum gated on E1 with respective to level scheme shown in figure 3.19. The gate on

E1 will project spectrum contains all remaining transition from E2 to E9 except E1. It is

to be noted that the gating energy (E1) will not appear in the gated spectrum. Therefore

it is clear that E1 is in coincidence with all transitions in level scheme shown in figure

3.19. If the gate is set on E7 transition, then corresponding projected spectrum (shown in

81

E6

E8

E8

Gate on E7

E1E2

E2

E3

E4

E7

E5

E5

E9

E9

Channel Number(Energy)

Cou

nts

Gate on E1

E6

Figure 3.20: Example of gated spectra gated on E1 and E7 with reference to the examplelevel scheme shown in Fig.3.19.

82

figure 3.20) contain all transitions except E3 and E4, since E7 is not in coincidence with

E3 and E4. In this way the coincidence relation between various γ-rays can be confirmed.

The placement of these γ-rays in a cascade are generally depends on their intensity. In

figure 3.19 the transition E4 has high intensity which is placed at the bottom of the level

scheme and the remaining transitions are placed above it in assuming as the intensity of

γ-transitions decreasing as we go to high excitation levels. The number of counts under

the particular photo-peak is also an estimate of intensity of γ-transition.

As discussed above, most important step involved in building the level scheme is

to identify set of new γ-transitions belonging to nucleus of interest using multiple gated

spectra. An example of such a gated spectra of present experimental work with γ-gates

is shown in figure 3.21. It is clear from the figure that intense transitions 1039-, 1113-,

1143-keV are in coincidence with each other in all gated spectra representing transitions

belonging to same cascade. Once correlation between coincident γ-rays of a particular

nucleus are identified then their ordering in a cascade can be done by measuring the

relative intensity of each γ-transition.

3.8.3 Intensity measurement of γ-rays

Measurement of intensities of γ-transitions will be useful for the placement of γ-rays in

level scheme. In order to calculate intensities of γ-transitions both singles and coincidence

spectra were used. The γ-rays intensity was obtained from area under the γ-peak corrected

for detection efficiency. After individual intensities are obtained, they are normalized using

intensity values of the low lying transitions in the total projection spectrum. Generally the

lowest ground state transition is used for normalization, whose intensity is assumed usually

be 100%, thereby relative intensities of remaining γ-transitions are obtained. However this

basic method has to be modified if one looks at the gated spectrum. In order to have

a feel of the technique of measuring intensity, an arbitrary level scheme is given in 3.22.

As first step calculate the intensities of γ1 and γ2 by measuring the area and efficiency of

them from singles spectrum. Now project a gated spectrum by gating on ground state

transition (γ1) whose intensity is assumed as 100%. From this gated spectra measure the

intensity of γ2. Using these values calculate the normalization factor is given by

83

Figure 3.21: Typical gated spectra on γ transitions 840 keV,1109 keV and 1134 keV of70Ge.

84

γ2

γ1

γ3

γ4

Figure 3.22: An illustrative level sequence to demonstrate the measurement of intensity.

N = (Iγ12

Iγ2

)(Iγ1

100) (3.14)

Where Iγ1, Iγ2

are intensities of γ1 and γ2 from singles spectra. Iγ12is the intensity

of γ2 in the gated spectrum of γ1.

Now the relative intensities of remaining transitions can be obtained by Iγ2=

Iγ12

N, Iγ3

=Iγ13

N, Iγ4

=Iγ14

N......and so on. The errors include the uncertainty of fit and background

subtraction.

3.8.4 Angular correlations and spin assignments

Spin of excited nuclear levels populated in fusion evaporation reaction can be determined

by measuring angular distribution of γ-ray transitions. Angular correlation techniques are

powerful means of determining the spins and multipolarities involved in decay of a given

nucleus. Theory of these methods were discussed in detail in Ref [9, 10, 11]. The excited

nuclear states populated in fusion-evaporation reactions decay to lower-lying states with

85

ll

0

2

J

+

+

Ll

,L

Figure 3.23: Illustration of measuring multipolarities of γ-transitions.

emission of photons that carry an angular momentum L(eigenvalue λ, component µ) and

parity π following the conservation laws

Ji=L+Jf

π=πi.πf

where λ is multipolarity of the γ-transition. In general, for a given multipolarity λ there

are two kinds of radiations observed, namely electric and magnetic which are defined as

follows.

Electric 2λ-pole(E λ) radiation : πiπf = (-1)λ

Magnetic 2λ-pole(M λ) radiation : πiπf = (-1)λ+1

A transition with mixed multipolarity (usually, λ = 1 and 2) has a multipole mixing

ratio δ defined as

δ2=T (λ′)T (λ)

where λ′ =λ + 1 (usually) and T refers to the partial transition probabilities.

If we are interested in measuring the spin and multipolarity of a higher lying state

illustrated by the transition as given in figure 3.23

To determine Jπ, L, L′ and δ, then, we need to find a way to create an unequal

population of magnetic substates in our given decay. In beta decay, one can do this by

observing another transition in cascade, immediately below the transition of interest. By

gating on gamma ray events corresponding to 2+1 → 0+

1 transition (for example) which

86

occurred in a given detector, at a given angle, we have just defined our quantization

axis (in contrast to in-beam experiments, where the beam axis is the quantization axis).

In defining a quantization axis by picking our first detector, we have ensured that the

number of events corresponding to gamma decays from a subsequent transition Jπ → 2+1

transition in the second detector will be related to the spin and multipolarity of the initial

state and subsequent transition.

The angular correlation function describing the relationship between spins, multi-

polarities, and transition intensities is given by angular correlation function, w(θ):

w(θ) = akPk(cosθ)

where coefficients ak depend on spins and multipolarities of the γ-transitions involved,

and Pk(cosθ) are Legendre polynomials and θ is angle of detection with respect to beam

axis. By measuring the intensity of gamma ray distributions as a function of angle and

fitting w(θ), the expansion coefficients ak can be obtained. For a pure stretched dipole

transition (L = 1 and ∆I = 1), angular distribution is a second order polynomial in terms

of cosine θ and can be expressed as

w(θ) =a0 + a2P2(cosθ)

For a pure stretched quadrupole transition( L = 2 and ∆I = 2 ) the angular distri-

bution is a fourth order polynomial in terms of cosine θ and can be expressed as

w(θ) =a0 + a2P2(cosθ) + a4P4(cosθ)

the peaking of m state distribution about m = 0 results in a pure dipole transition having

the normalized coefficient A2 = a2/a0 less than 0 and a pure quadrupole transition having

a2 greater than 0. So by Measuring angular distribution of a particular γ-ray it is possible

to distinguish between γ-rays from quadrupole or dipole transitions.

3.8.5 Directional correlation of oriented states(DCO)

The DCO ratios were used to distinguish between quadrupole and dipole transitions. The

multipolarity of γ-rays emitted from aligned states can be determined by measuring DCO

ratios. Theory of the DCO has been extensively discussed in Ref [12, 13, 14]. These

87

Figure 3.24: Intensity distribution for quadrupole and dipole transitions as a function ofangle with respect to the beam direction. Figure is taken from Ref.[15].

DCO ratios can be extracted from angular correlation measurements which generally

requires coincidence data, since singles energy spectra are very complex by containing

many overlapping lines from different reaction channels populated in heavy-ion reactions.

Moreover Doppler broadening of photo-peaks complicates spectrum further.

Angular correlation studies depends on spin of level, multipolarity, mixing ratio of

γ-transitions and the m-substate population distribution of the initial state. Generally

in fusion evaporation reactions initial spins of populated nuclei are aligned in a plane

orthogonal to beam axis. Therefore decayed γ-rays have anisotropic angular distribution

of their yields. Assume two successive gamma rays γ1 and γ2 are emitted from an aligned

state and observed at angles θ1 and θ2, respectively, with respect to the beam axis, z ,

with the angle φ, where φ is the angle between the two planes defined by the direction

of the emitted γ rays and the z axis. Then the intensity can be calculated from [16] the

following expression:

w(θ1,θ2,φ) = N Σλ,λ1,λ2Bλ1

(I1)Aλ1,λ2

λ (γ1) Aλ2(γ2) Hλ,λ1,λ2

Bλ(θ1, θ2, φ)

where N is a normalization factor, Bλ1describes alignment of the state with respect to

the z axis, coefficients A contain physical parameters, such as spins of states involved,

88

θ1

θ2

γ2

γ1

Z

Detector

Det

ecto

r

φBeam axis

Figure 3.25: Geometry of detectors arrangement and the directional correlation of twosuccessive γ-rays γ1 and γ2 emitted from oriented states.

89

multipolarities, and mixing ratios of γ-transitions and Hλ,λ1,λ2Bλ(θ1, θ2, φ) is the angular

function. The indices λ are even integers. Figure 3.24 shows the intensity distribution

for quadrupole and dipole transitions as a function of angle with respect to the beam

direction. This anisotropic angular distribution of γ rays can be used for determination

of DCO ratio.

The DCO ratio is defined as

RDCO =w(θ2, θ1, φ)

w(θ1, θ2, φ)(3.15)

To determine the experimental DCO ratio, a two dimensional angle dependent ma-

trix is constructed for spin assignment and to find nature of the γ-transitions with events

recorded at an angle θ1 (close to 90◦) taken as one axis and those recorded at θ2 (forward

or backward) taken as the other axis.

The experimental DCO ratio can than be defined as, the ratio of the intensity Iγ

of a measured transition at θ1 when gated on a reference γ-ray at θ2 to the intensity of

a measured transition at θ2 when gated on a reference γ-ray at θ1( where the reference

γ-ray is of known multipolarity ).

RDCO =Intensity of γ1 observed at θ1 gated on γ2 at θ2

Intensity of γ1 observed at θ2 gated on γ2 at θ1

(3.16)

For different multipolarities, the angular distributions are different and the DCO

ratio is either less than or greater than 1, depending on the gated and measured γ-ray

multipolarities. Usually this ratio turns out to be ≈ 1 for stretched quadrupole transitions

and it is ≈ 0.5 for pure dipole transitions when the gating transitions is quadrupole.

Where as if the gating transition is dipole, this ratio is nearly equal to 2 for quadrupole

transitions(∆ J = 2) and ≈ 1.2 for dipole transitions(∆ J = 1).

But pure non-stretched dipole (∆J = 0) transitions are indistinguishable from

quadrupole transitions solely on the basis of DCO data. However, states populated in

fusion evaporation reactions decay strongly along the yrast line by ∆J 6=0 transitions.

Hence γ-rays for which the RDCO values are close to unity for gates on E2 transitions, are

most likely to be quadrupole in nature. An additional advantage of DCO ratio method

is that since both the sets of data are collected simultaneously, systematic errors coming

90

from counting time, efficiency are insignificant. For highest sensitivity, the ideal detectors

positions would be 90◦ and either of 0◦ or 180◦. Figure 3.25 is a schematic representation

of geometry of detectors arrangement and the directional correlation of two successive

gamma rays γ1 and γ2 emitted from oriented states.

An illustrative example of angle gated DCO correlation spectra is presented in figure

3.26. The spectra shown in the figure are obtained by gating on known quadrupole

transition 1039 keV of 70Ge at forward (45◦) and middle (99◦) angles. The calculated

RDCO values closely equal to 1 for 1113, 1134, 1143, 1252 and 1262 keV, which are

established as quadrupole transitions. Whereas the the RDCO ≈ 0.6 for known dipole

transitions 250 and 288 keV. The details of the obtained intensities, multipolarites and

DCO ratios in the present study are discussed and summarized in chapter 4 and chapter

5.

3.9 Summary

In summary, the present chapter presents the various experimental techniques adopted

to study in-beam gamma spectroscopy. The basic methods of interaction of gamma rays

with matter are discussed. The experimental setup Gamma Detector Array (GDA) for

the study of nuclear structure physics at Inter University Accelerator Center(IUAC) is

discussed in detail. Electronics setup for γ-γ coincidences, Compton suppression asso-

ciated with GDA are explained. Thereafter various steps in proceeding the experiment,

data analysis methods for matrix formation, intensity and efficiency correction are ex-

plained at length. Finally the level scheme construction, relative intensity calculations

and assignment of spin and parities through angular correlation techniques are discussed.

91

Energy(keV)

Co

un

ts

1090 1140 12401190 0

128

256

384

512

640

768

896Gate on 1039(at 99 )

Gate on 1039(at 45 )o

o

1113

1134

1143

1252 12

62

E2

E2

E2

E2E2

Energy(keV)

Cou

nts

325175 225 275 0

128

256

384

512

640

768

896

Gate on 1039 at 45 o

oGate on 1039 at 99

288

250

M1

M1

Figure 3.26: Typical angle gated DCO correlation spectra showing the difference betweenquadrupole and dipole transitions in 70Ge. The gating transition 1039 keV is quadrupolein nature.

92

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