1. Determining Reduced Transition Probabilities for 152 ≤ A ≤ 248 Nuclei using Interacting Boson Approximation (IBA-1) Model By
Dr. Sardool Singh Ghumman
Nuclear Science Laboratories
Sant Longowal Institute of Engineering and Technology
(deemed university)
Established by Govt. of India

2. The theoretical B(E2) ratios have been calculated on DF, DR and Krutov models.
A simple method based on the work of Arima and Iachello is used to calculate the reduced transition probabilities within SU(3) limit of IBA-I framework.
The reduced E2 transition probabilities from second excited states of rare-earths and actinide even–even nuclei calculated from experimental energies and intensities from recent data compare better with those calculated on the Krutov model and the SU(3) limit of IBA than the DR and DF models.

3. Nuclear Models
The introduction of nuclear model is an attempt to understand the complicated nature of nuclear interactions and the complex structure of nuclei in a simplified manner.
In general the nuclear models developed up to date to explain, theoretically, the various experimentally observed facts, can be divided into two main categories as; independent particle models (IPM) and strong interaction models (SIM).
In IPM, the nucleons are supposed to move nearly independent of each other in a common nuclear potential e.g., Fermi gas model and shell model.
While in SIM, the nucleons are considered to be strongly coupled to each other inside the bounds of the nucleus e.g. liquid drop and collective models.

4. A model is tested for its validity as to how far it is successful in explaining the experimentally observed facts. In fact, no single model can explain all the properties of nucleus.
For example, the shell model has great success to its credit in predicting spins and parities of the ground and weakly excited states of atomic nuclei, binding energy, islands of isomerism , magic numbers, alpha and beta decay systematics and also the energy levels of odd-A nuclei. According to this model the excitation mechanism involves the change of state of individual nucleons.
Shell Model fails to explain the higher experimental quadrupole moments in many nuclei in the region of closed shells, higher transition probability of low lying states, shifts of magnetic moments from Schmidt lines for nuclei with 150≤A≤190.

5. A large number of collective nuclear models with their limited application to the particular region of the periodic table have been purposed to accept for the above failures of the shell model.
As the nuclear matter is of very high density, the collective motion of all the nucleons thus involves no change in the volume of the nucleus and as such collective motion is only possible for small deformations to the shapes of the nuclei.
All the even-even deformed nuclei with 150≤A≤190 and A>228 show low lying 0+, 2+, 4+……etc. nuclear energy states which can be supposed as a result of collective motions of nuclear matter. The comparison of experimental level energies of these states with the theoretical ones gives us a test of the nuclear model.

6. The transition probabilities : B(E2) ratios
The comparison of experimentally determined gamma ray transition probabilities between nuclear states with the theoretical predictions of nuclear models is one of the most sensitive tools available to investigate the structure of nuclei.
The reduced matrix elements of the multiple operators depend upon the value functions of initial and final nuclear states and hence give information about details of nuclear structure.
The region of even-even nuclei has been tested in terms of these rates for the first 2+ excited states of rotational and ground state bands on the basis of Davydov-Rostovsky (DR) model.
In the present work the B(E2) ratios calculated on the basis of IBA, Krutov, Davydov & Fillipov and Davydov and Rostovsky models have been compared with experimental values.

7. Generation of Spectrum
Krutov described very well the collective motions of the nucleus. According to Krutov, the nucleus is rotating as a whole without being divided into core and external nucleus and the collective motions of the nucleus has been considered as a change of density distribution of the nuclear matter with time. For a nucleus having non-axial equilibrium shape with no coupling between rotation and intrinsic motion; as in a symmetric rotor, the rotation Hamiltonian can be expressed as;

8. E2 Transition Probabilities

9. DF Model: The expressions for B(E2) ratios in units of e2q02/16π,

10. With non-axial rotor model calculations, the two modes of vibrations and rotation of nucleus assumed to not interfere interfere with each other.
However, if this interference is considered then the reduced transition probabilities can be expressed as;

11. Krutov Model
Expressions obtained for Krutov Model are

12. IBA-MODEL
In IBA- Model, the correlated pairs of nucleons are considered as building blocks of collective excitations in nuclei. These correlated pairs of nucleons (similar to Cooper pairs of electron gas) are treated as bosons. In other words the nucleons (Fermions) are coupled to form bosons with angular momenta L = 0, 2 (s and d bosons). The pairs with L values other than 0 and 2 are not included in first approximation. The neutrons and protons get paired to form the neutron bosons and proton bosons respectively, but in first approximation called IBA-I, no distinction is made between the two types of bosons.
However a detail description of the properties of nuclei requires the use of IBA-II in which neutron and proton bosons are treated separately.
But it is still of interest to study the properties of IBA -I especially in view of its relation with the description of collective states in nuclei in terms of shape variables.
For the nuclei in deformed region, Arima and Iachello discussed that the transitions SU(5)-SU(3) and SU(3)-SU(6) from symmetry are possible. The Hamiltonian and E2 operator, having intermediate structure, are used and the transition rates and energies are then calculated numerically.

13. The relations used in the present work i. e
The relations used in the present work i.e., for 2γ → 0g, 2g → 0g transitions are written below:

17. The experimental reduced E2 transition probability ratios were calculated from experimental energies and intensities from the nuclear data sheets using the relation ;

18. RESULTS
The experimental E2 transition probability ratios of 2γ - 2g/ 2γ - 0g transitions along with the theoretical values calculated on IBA, Krutov, DF and DR models are presented in Table.
The reduced E2 transition probabilities from first and second 2+ excited states of rare-earths and actinide even –even nuclei calculated from experimental energies and intensities from recent data compare better with those calculated on the Krutov model and the SU(3) limit of IBA than the DR and DF models.

19. THANKS

20. ARJUN CHAAL