3 Basic nuclear properties-5

Sanjay Kumar Chamoli

Learning Outcomes

From this module students may get to know about the following:

The knowledge of basic nuclear properties.
The importance of nuclear properties.
The experimental ways of determining nuclear properties.

1. Spin

1.1. Directional Correlation Ratio (DCO- ratio) :The information about the DCO ratios is obtained in experiments with multi detector arrays in which the detectors should be placed at different angles with respect to the beam direction. The DCO ratio method is an important tool to infer the spin differences between states observed by the coincidence measurement of the gamma-decay between them.

1.1.1. Importance of DCO ratio : In comparison to the angular distribution, the DCO ratio is advantages in the sense that

– weak transitions can be studied,

– members of multiplets can be analysed and

– no normalisation to the beam charge is necessary

– By use of multidetector arrays the statistical accuracy of the DCO ratios can be increased by analysing many detector combinations .

1.1.2 Calculation of DCO ratio : For most applications the theory of DCO ratios can be simplified with respect to the general directional correlation theory by taking into account the experimental conditions (i) that unpolarized beams are used and (ii) that the detectors are insensitive to the polarization of the -y-rays. Therefore, detectors placed at forward and backward angles with respect to the beam direction can be treated in the same way. The angular correlation of -y-rays emitted from oriented states depends on the spins of the involved levels, the multipolarities and mixing ratios of the -transitions and the m-substate population distribution of the initial state. In the experiment a compound nucleus is produced via fusion evaporation reaction by bombarding a target nucleus with a projectile. The compound nucleus then start decaying by emitting -ray and come to the lower energy state. The -ray from the decaying nucleus are mostly of dipole or quadrupole nature or a mixture of both types. Suppose two detectors 1 and 2, placed at different angles as shown in figure 1, are used to determine the angular correlation of a cascade of two -rays. The detectors are making an angle θ1 and θ2 with the beam direction. The angle between the planes opened by each detector and the beam axis is.

Fig. 1: Geometry of the detector arrangement with the beam as orientation axis.

Fig. 2: The picture of Indian National Gamma Array (INGA) at TIFR, Mumbai.

Fig. 3: DCO Ratio of the transitions belonging to the band gated by 958 keV transition.

The value of RDCO is approximately unity for quadrupole transition and non stretched dipole, the value between 0.4 and 0.6 for stretched dipole and the value between 0.6 and 0.8 implies a mixed transition.

1.1.3 Limitations of DCO ratio method : Though the DCO ratio method is advantageous and therefore preferred over angular distribution measurements method, it has its limitation too. The serious disadvantage is that with this method a spin change of I = ± 1 cannot be distinguished.

2. Parity

The parity of a nuclear state can efficiently be determined by measuring the electric and magnetic nature of de-exciting -rays (Linear polarization). The sign of the measured linear polarization distinguishes electric and magnetic types of gamma-ray transitions. Electric transitions have preferential scattering along the perpendicular direction, while magnetic transitions have scattering along parallel direction. Depending on the energy of -ray, Compton scattering, e– e+ pair production and photoelectric effect can be used for measuring the degree of polarization. The linear polarization along with the angular distribution or DCO ratios measurements can uniquely determine the spins & parities of nuclear states

2.1 Polarization measurement in nuclei : A conventional Compton polarimeter, used to determine the parities of different levels in 155Gd is shown in figure 4. It has one scatterer and two absorbers with 25 segments on the front face of a germanium crystal, each of which acts an individual gamma-ray detector. In this polarimeter, there are three planes and four relevant angles to define the linear polarization of the gamma rays.

Fig. 4: A picture of a conventional Compton polarimeter consisting of one scatterer and two absorbers.

The linear polarization of gamma rays emitted from oriented states formed in nuclear reactions and the angular distribution of the gamma rays are related to each other. For a linear polarized gamma rays, the angular distribution function depends not on their outgoing direction, θ with respect to the beam axis and their electric field direction, ε with respect to the reaction plane. The linear polarization of -rays can be expressed in terms of the angular distribution functions when their electric field is in the reaction plane, W(θ, ε = 00), and when it is perpendicular to the reaction plane, W(θ, ε = 90′). i.e;

2.2 Calculating polarization coefficients theoretically : The polarization coefficients for pure (electric/magnetic) dipole and the (electric) quadrupole transitions in terms of angular distribution parameters a2 and a4 can be derived as:

From the above equations, the maximum value of the polarization in magnitudes at = 90′. Theoretically calculated values of polarization coefficients for pure (electric/ magnetic) dipole and the (electric) quadrupole transitions are listed in table 1.

Table 1: Theoretically calculated values of polarization coefficients for pure (electric/ magnetic) dipole and the (electric) quadrupole transitions.

Summary : The spin and parity of important nuclear properties. Knowing the spin and parity of a nuclear eigen state can reveal the underlying single particle configurations involved in the formation of that state. Both, the spin and parity of a nuclear state can be determined experimentally. The spin can be obtained by determining the multipole order and the dipole-quadrupole mixing ratio ( ) of the outgoing gamma radiation. To get the two parameters, measuring DCO ratio is better than the angular distribution, accurate measurements need multi-detector array. The parity of a nuclear state can be obtained by measuring the polarization of outgoing gamma rays. It can be concluded that the investigation of DCO ratios allows the determination of spins and dipole-quadrupole mixing ratios.

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References:

Introduction to Nuclear Physics – by Keneth S Krane.
Introductory Nuclear Physics – by Samuel S M Wong.
Nuclear Physics – by R R Roy & B P Nigam.
Handbook of Physics by Condon and Odishaw, TMH NewYork.
Introduction to Nuclear Physics, 2nd Edition, W.N.Cottingham & D.A. Greenwood.
Concept of Nuclear Physics by B L Cohen, McGraw Hill.
Experimental techniques in Nuclear Physics by Dorin N. Poenaru & Walter Greiner
Exotic Nuclear Excitation by S.C. Pancholi
Nuclear spectroscopy Part B, by Fay Ajzenberg- Selove
Theory and Problems of modern Physics (Schaum’s outline Series)
Basic Ideas & Concepts in Nuclear Physics – by K Heyde
The “Particles of Modern Physics” by J. D. Stranathan, Philadephia: Blakiston.
Nuclear Physics by Irving Kaplan, Narosa Publishing House.

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Did you know ?

The spin of nuclei in any state (ground/excited) can be experimentally determined by measuring the angular distribution or the directional correlation (DCO) ratio while the parity can be determined by polarization measurement of de-excited gamma rays.
For spin determination DCO measurement is preferred over angular distribution measurement due to variety of advantages.
For more sensitivity, DCO measurements are done with multi detector arrays.
For parity determination, polarization measurements are done with (linear/circular/elliptical) polarized gamma rays.
The linear polarization of gamma rays emitted from oriented states formed in nuclear reactions has a close relation to the angular distribution of these gamma rays. When gamma rays are linearly polarized, the angular distribution function of gamma rays depends not only on their outgoing direction with respect to the beam axis but also on their electric field direction with respect to the reaction plane, defined by an outgoing gamma ray and the beam axis.
The linear polarization of photons is quantum-mechanically defined as a normalized difference in the number of photons occupying two polarization states.
So, the linear polarization of gamma rays can be expressed in terms of the angular distribution functions when their electric field is in the reaction plane, and when it is perpendicular to the reaction plane,
The polarization has a maximum value in magnitudes at 0 = 90′.
If we determine the polarization of gamma rays experimentally, the spin and the parity will be obtained by comparison with the calculated polarization values.
The method to measure the linear polarization of gamma rays is based on Compton scattering.
In conventional method of polarization measurements of gamma rays, one usually employs a detection geometry in which two absorbers surrounding a scatterer are placed perpendicularly to each other.
Also, one can conveniently measure the linear polarization by arranging the scatterer and absorbers in a way such that the first Compton-scattering plane is perpendicular to the reaction plane while the second Compton-scattering plane matches the reaction plane. For this geometry, the intensity of the Compton-scattered gamma rays counted by absorber 1 and absorber 2 is denoted by N|| and N , respectively.
Each of these intensity is proportional to the differential cross section of Compton scattering and also to the angular distribution function.
Once the sensitivity as a function of the incident gamma-ray energy is known, the linear polarization of the gamma rays can be directly found by using the asymmetry measurement.
As the distance between a scatterer and an absorber is increased, the sensitivity increases because the solid angle decreases; however, the coincidence efficiency gets lower. Thus, the overall quality of a Compton polarimeter depends not only on the sensitivity but also on the coincidence efficiency.

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