K 223 Angular Correlation

Transcription

1 K 223 Angular Correlation K Aim of the Experiment The aim of the experiment is to measure the angular correlation of a γ γ cascade. K Required Knowledge Definition of the angular correlation of a γ γ cascade. Explanation of the angular correlation of a hypothetical γ γ cascade. Which quantities enter into the angular correlation coefficients? Perturbation of the angular correlation by hyperfine interaction. What information can one obtain by the measurement of angular correlation - with and without extranuclear perturbation? Design and operation of a scintillation spectrometer; fast-slow coincidence technique; components of the setup (SCA, CFD,...); time resolution of the detector and of the coincidence unit; expected spectrum of 60 Co; Analysis of the experimental data: corrections for solid angle, accidental coincidences and deadjustment; Determination of the angular correlation coefficients by means of least-squaresfit to the data, determination of experimental errors. Decay-scheme of 60 Co (Fig. K 223.2) K Literature Siegbahn Vol. 2: α-,β- and γ-ray Spectroscopy, pp , , , 1695 Melissinos: Experiments in Modern Physics, pp , Riezler/ Kopitzki: Kernphysikalisches Praktikum Schatz/ Weidinger: Nuclear Condensed Matter Physics: Nuclear Methods and Applications, Wiley, 1 st edition (1996), pp , 63-68, Leo: Techniques for Nuclear and Particle Physics Experiments, Springer, 2 nd Rev. edition (1994)

2 Angular Correlation 2 K Assignments The experiment is divided into three parts: 1. Adjustment of the electronics, set-up of the fast-slow-coincidence-circuit with a 60 Co-source. 2. Recording the γ-ray spectrum of the 60 Co-source and adjusting the single channel analyser for the photopeaks of interest. 3. Angular correlation measurement. K Procedure and analysis Adjustment of the electronics Adjustment of the main amplifier In order to obtain a high counting rate the distances between the detectors and the 60 Cosource should be small. Examine the unipolar output of the amplifier with the oscilloscope. The amplifier gain has to be adjusted such that the signals of the high energy γ-rays are not saturated (U max = 9 V ). Plot the shapes of the signals in your report. Adjustment of the Constant Fraction Discriminator (CFD) The slow-output of a CFD is connected to one of the channels of the oscilloscope which is then used as trigger. The unipolar output of the main amplifier is connected to the other channel of the oscilloscope. Trigger the channel of the amplifier signal with the CFD channel. Start with the lowest threshold possible if no signal is observed you will have to increase the threshold. Adjust the threshold of the CFD just above the noise level (bright line at U = 0 V ). The pulse height spectrum of the γ-rays should not be affected. The fast coincidence circuit and the prompt curve The positive outputs of the CFDs are connected to the fast coincidence unit (FC). The slow-outputs are used since they provide the positive signal needed by the FC. The signals are sufficiently fast despite the name. The FCs resolving time should be adjusted to 15 ns (150 scale div.). For lower resolving times the FC will not work properly. Connect the output of the FC with a 50 Ω terminating resistor to one of the counters. Determine the experimental resolving time of the coincidence circuit by using delay cables. Measure and plot the coincidences as a function of the delay time (recording time 40 s). This is the so-called prompt curve. Plot this curve during the experiment. It shows you if you need to delay the output of one of the CFDs.

3 3 Angular Correlation Figure K 223.1: Final setup of the coincidence measurement The slow coincidence circuit The positive outputs of the two SCAs and the FC unit have to be aligned in time. Connect the positive output of the FC unit with one channel of the oscilloscope via the gate & delay generator (D 2 -G 2 ). The output of one SCA is now connected with the other channel of the oscilloscope. The trigger is set to the channel to which the D 2 -G 2 is connected. By means of the time delay potentiometers of the SCA bring the rectangular output signals of the SCA and the D 2 -G 2 to maximum overlap. Do this for the second SCA as well. Measurement of the angular correlation In order to be able to measure an angular correlation, a proper distance between the source and the detectors must be chosen. The choice should be such that the factors for solid angle correction from Siegbahn Vol.2 pp can be applied. Check also Tab. K The crystals geometry is: length 1.0 inch, diameter 1.5 inch. Acquisition of the γ-ray spectra In order to record the spectrum of both NaI(Tl)-detectors connect the outputs of the SCAs to the corresponding counters. Now, with a fixed window width, use the full range of the potentiometers for the lower limit. In order to scan the spectrum the SCA should be operated in the WIN mode. In this mode you have to divide the window width by ten (e.g. a potentiometer setting of 200 scale divisions corresponds to a time gate from x scale units to x + 20 scale divisions.). Useful widths lie between 100 and 200 scale units. Recording time for each window width: 20 s. After the measurement of the spectrum, determine the SCA settings for the measurement of the

4 d [cm] E [MeV] ɛ Q 2 Q Table K 223.1: Photopeak correction factors for 1.5 x 1 crystals. Data taken from [2]. Notice how the efficiency ɛ decreases with the energy of the incident γ-ray. angular correlation. Now use the SCA in the NOR mode and adjust the lower and upper limit with the potentiometers. The photo-peaks of γ 1 and γ 2 should be in the window of each detector. Measurement of the angular dependence of the coincidence rate For angles between 90 and 270 measure the coincidence and the single count rates of each detector in steps of 10 for 400 s each. Measurement of the accidental coincidences For a direct measurement of the accidental coincidences apply maximum delay (all delay cables) to one input of the FC. The acquisition can run overnight in order to acquire a sufficient number of counts. Plot the impulse height spectrum of the amplifier from oscilloscope. Plot the prompt-curve (determine time resolution, and accidental coincidences) Compare the experimental value of the accidental coincidences to the number of accidental coincidences expected from the width of the prompt curve and the single count rates. Plot and describe energy spectrum, show the chosen energy window Accidental coincidences have to be eliminated from the coincidences and a correction for a possible deadjustment of the apparatus has to be applied. The resulting count rates are fitted by a least-squares-fit. Apply the solid angle correction and compare the angular correlation coefficients to the theoretical values for the cascade. Plot the radiation pattern in a polar diagram.

5 Figure K 223.2: Decay scheme of 60 Co, taken from [1] Bibliography [1] R. B. Firestone, Table of Isotopes 8 th edition, (Wiley, New York, 1996) [2] K. Siegbahn, ALPHA-, BETA-, AND GAMMA-RAY SPECTROSKOPY, Vol. 2, North Holland Publishing Company, Amsterdam (1965), p 1695 Best wishes for a successful experiment! Date: July 2014