Experimental Techniques and Methods

Transcription

1 Chapter 3 Experimental Techniques and Methods 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 reaction 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 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

2 Target Nucleus Nuclear Scattering Projectile R p Impact Parameter R R T Nuclear Field Complete Fusion Coulomb Scattering Formation of Compound Nucleus Figure 3.1: Schematic drawing of various kinds of nuclear reaction mechanism possible with 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 V CB (MeV ) = 1 4πε o Z p Z t e 2 R o (A p 1/3 + A t 1/3 ) (3.1) where Z p, A p are the atomic number and mass number of projectile and Z t, A t are atomic and mass number for target. 49

3 The maximum angular momentum transfer (L= R P) can be estimated from grazing radius R = R target + R projectile (3.2) and momentum of the projectile when it hits the target nuclei is P = 2µ(E p V ) 1/2 (3.3) where µ is reduced mass of the beam, target system, E p is energy of the projectile in center mass frame and V is Coulomb barrier. Therefore maximum angular momentum transfer is given by L max = 2Rµ(E p V ) 1/2 (3.4) The grazing radius, reduced mass, energy in center of mass are given below R = R 0 (A 1/3 p + A 1/3 t ) (3.5) µ = A p A t A p + A t (3.6) E CM = E lab A t A t + A p (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

4 Figure 3.2: A Schematic of decay of compound nucleus. 51

5 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 to 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 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

6 Particle Emission Fission Excitation Energy(E) γ Entry Line ray transitions Statistical Cascades of E1 transitions E2 transitions (rotational cascades) Nuclear Spin(I) Figure 3.3: The schematic representation of decay paths of a hot compound nucleus formed in heavy ion fusion reaction. 53

7 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 product 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 tandem 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 ( 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 + V inj 54

8 where q = Charge state of ion after stripping, V= Terminal potential, V inj = 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 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 MeV pair production is absent and only the Compton and the photoelectric processes are possible. For energies greater than 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

9 Figure 3.4: Schematic representation of 15UD-Pelletron accelerator at IUAC, New Delhi. 56

10 energies, dependent only on which atomic orbital they occupied. The ejected electron will have kinetic energy E k = E γ - B e where E γ is γ-ray energy, B e 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 E γ with atom of atomic number Z is given below. This effect is dominant at low energies (E γ < 0.3 MeV) [3] can be seen in figure 3.5. Compton scattering σ Zn E γ 5 (3.8) The Compton scattering process takes place between incident γ-ray photon and an electron of an atom in the absorber. In this interaction mechanism, incident photon is deflected 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 scattering 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 < E γ < 5 MeV). An expression relating energy transfer and scattering angles can be derived using conservation of energy and assuming that electrons binding energy is negligible E γ = E γ 1 + Eγ m 0 c 2 (1 cos θ) (3.9) where m 0 c 2 is the rest-mass (511-keV) of the electron. The kinetic energy of electron is then given as E kin = E γ E γ = E γ 1 + m 0c 2 E γ(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 = C Z A ρ 1 E γ (3.11) 57

11 Figure 3.5: Absorption cross section for γ-rays in Silicon and Germanium as a function of energy. Plot is taken from Ref.[4] 58

12 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 electronpositron pair gamma-ray must have an energy exceeding twice the rest-mass energy of an electron i.e E γ kev. The excess energy of the gamma-ray are shared equally as kinetic energy between electron and positron E γ = E kin + 2m 0 c 2 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

13 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 where N is the impurity or dopent concentration and V the bias voltage. (3.12) 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 highenergy 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

14 Collimator BGO Ge Cryostat Target LN2 Dewar Ge Crystal BGO Housing PMT Figure 3.7: Schematic diagram of HPGe detector. centimeters with out dielectric breakdown, high purity germanium with impurities on the order of cm 3, are typically used 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 10 12, 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 electronhole 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 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

15 Figure 3.8: Representative γ-ray spectrum of 60 Co with and with out Comptonsuppression. 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 detector 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

16 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

17 64 Figure 3.9: Schematic view of Gamma Detector Array(GDA).

18 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 reduced 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 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

19 66 Figure 3.10: Picture of Gamma Detector Array at IUAC, New Delhi.

20 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 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 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

21 A Bias Ve Raw Ge output Used in Multiplicity filter logic HpGe TFA CFD Delay Gate and Delay gen A B BGO ACS TFA CFD C Y Y Y Bais +Ve To 16 channel disc B To 16 channel TDC C To gate and strecher D Figure 3.11: Block diagram of electronic circuit used for the Compton suppression system in 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

22 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 Master gate acceptance logic for the data acquisition for a valid event when conditions for Compton suppressed E γ -E γ 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 E γ -E γ 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

23 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 ( 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 eventby-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. Availability of ion beams and suitable target materials of required thickness usually limits projectile 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 production 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 production 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 excitation function and optimize beam energy. High intensity known γ transitions of desired 70

24 Ge(1) I/P from Compton Supp.Cir. Ge(12) Ge(1) I/P from Compton Supp.Cir. Ge(12) Ge(1) I/P from Compton Supp.Cir. Ge(12) 16 Chan. Discri. and Latch Time to Digital Converter Gate and Strecher Sync Sync Gate Sum Common Sum Ge Signals (1 12) Fan In Fan Out Amp Amp Trigger List Proce. A X Y ADC Ge(1) ADC Ge(12) N = 1 N > 1 Y B Four Input Coin. Unit C Delayed O/P I/P Run Prompt O/P Busy ADC Multiplexier Delay A Four Input Coin. Unit Y Delay Y TTL NIM TTL NIM ADC Interface B C Interface CAMAC Fan In Fan Out Data Aquisition System Figure 3.12: Block diagram of electronic circuit used for generation of master gate/event. 71

25 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 necessary 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 radioactive sources 152 Eu, 133 Ba, 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 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 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 133 Ba, 152 Eu and 60 Co 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 152 Eu. A slight non linearity for large pulse height can be corrected by higher order calibrations like quadratic or polynomial calibration. Energy calibration 72

26 Figure 3.13: Block diagram showing various data-analysis steps followed in constructing final level scheme for nuclei of interest. 73

27 of each detector was represented by a quadratic function of channel number, i.e., E = ax 2 + 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 Efficiency calibration The efficiency calibration is needed for detector as detection efficiency changes as a function 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 measuring the energies and corresponding photo peak area, the energy dependence of the photo peak efficiency can be directly determined. Standard radioactive sources 152 Eu and 133 Ba 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, E γ = exp[a 0 + A 1 ln(e γ ) + A 2 ln(e γ ) 2 + A 3 ln(e γ ) 3 + A 4 ln(e γ ) 4 ] (3.13) Gain matching After obtaining the accurate calibration of data is to ensure that the data from each detector 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 152 Eu 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

28 10.00 Realtive Efficiency Energy (kev) 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 152 Eu from the two detectors are matched to common 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 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 correlation 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

29 ADC-10-S 6.0K 4.0K Counts 2.0K 0 ADC-11-S 6.0K 4.0K 2.0K Channel Number Figure 3.15: Comparison of energy spectra of detectors 10 and 11 before gain match (top) and after gain match (bottom). 76

30 of raw data. To create a two-dimensional γ-γ matrix, each event is unfolded into pairs of two energies (E γ x, E γ y) and the bins corresponding to E γ x and E γ 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 E γ -E γ 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 E γ - E γ symmetric matrix, which was created using data from all the detectors 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 symmetrized to make two energy axis equivalent. This was done by adding its transpose to itself. E sym = 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 (θ 1 ) on one axis, and data of other group of detectors at an angle (θ 2 ) on other axis. These events are stored into a separate matrix, called DCO matrix, with θ 1 detectors on one axis while the θ 2 detectors on the other axis. This DCO matrix is 77

31 Figure 3.16: Shows typical two dimensional γ - γ matrix. Figure 3.17: Projection of events on an axis of a matrix. 78

32 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 E x and E y. 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 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 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

33 Figure 3.18: The total projection spectra without (top) and with background subtraction (bottom). 80

34 E7 E4 E6 E3 E8 E5 E2 E1 E9 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 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 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 If the gate is set on E7 transition, then corresponding projected spectrum (shown in 81

35 E9 E2 E6 E8 E3 E5 Gate on E1 E7 E4 Counts E1 E2 E9 E6 E8 E5 Gate on E7 Channel Number(Energy) Figure 3.20: Example of gated spectra gated on E1 and E7 with reference to the example level scheme shown in Fig

36 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 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 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 As first step calculate the intensities of γ 1 and γ 2 by measuring the area and efficiency of them from singles spectrum. Now project a gated spectrum by gating on ground state transition (γ 1 ) whose intensity is assumed as 100%. From this gated spectra measure the intensity of γ 2. Using these values calculate the normalization factor is given by 83

37 Figure 3.21: Typical gated spectra on γ transitions 840 kev,1109 kev and 1134 kev of 70 Ge. 84

38 γ 4 γ 3 γ 2 γ 1 Figure 3.22: An illustrative level sequence to demonstrate the measurement of intensity. N = ( I γ 12 I γ2 )( I γ ) (3.14) Where I γ1, I γ2 are intensities of γ 1 and γ 2 from singles spectra. I γ12 is the intensity of γ 2 in the gated spectrum of γ 1. Now the relative intensities of remaining transitions can be obtained by I γ2 = I γ 12 N, I γ 3 = I γ 13 N, I γ 4 = I γ 14...and so on. The errors include the uncertainty of fit and background N subtraction 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

39 J ll L, L 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 J i =L+J f π=π i.π f 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 2 λ -pole(e λ) radiation : π i π f = (-1) λ Magnetic 2 λ -pole(m λ) radiation : π i π f = (-1) λ+1 A transition with mixed multipolarity (usually, λ = 1 and 2) has a multipole mixing ratio δ defined as δ 2 = 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 J π, 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 transition (for example) which 86

40 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 J π 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, multipolarities, and transition intensities is given by angular correlation function, w(θ): w(θ) = a k P k (cosθ) where coefficients a k depend on spins and multipolarities of the γ-transitions involved, and P k (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 a k 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) =a 0 + a 2 P 2 (cosθ) For a pure stretched quadrupole transition( L = 2 and I = 2 ) the angular distribution is a fourth order polynomial in terms of cosine θ and can be expressed as w(θ) =a 0 + a 2 P 2 (cosθ) + a 4 P 4 (cosθ) the peaking of m state distribution about m = 0 results in a pure dipole transition having the normalized coefficient A 2 = a 2 /a 0 less than 0 and a pure quadrupole transition having a 2 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 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