Get Complete Project Material File(s) Now! »

**Introduction**

The simplest view of the atomic nuclei is that they are composed of neutrons and protons, collectively called nucleons. Theoretical and experimental studies of nuclei revealed that the nucleons constituting them, are not distributed uniformly inside a nucleus. These studies proved the presence of \clusters » of nucleons in the nucleus, and the participation of such clusters in nuclear reactions. The concept of clustering is quite sophisticated and the denition of this will emerge later. Of all such clusters, the one formed by two protons and two neutrons is the most ubiquitous because of its high symmetry and binding energy. As is well known, this is referred to as the -particle, although its properties inside a nucleus may not be the same as that of a free -particle, owing to the action of the surrounding nucleons.

Some nuclei can spontaneously emit the -particles. This phenomenon was discovered at the very beginning of the nuclear era and is known as the -decay. There is a renewed interest in -decay partly due to an increase of the role played by -decay in the spectroscopy of unstable nuclei [1], which is primarily motivated by the connected question involving clustering of nucleons in nuclei [2] and partly due to \exotic » decay modes discovered in 1984 [3], which is decay via the spontaneous emission of heavier clusters, such as 14C, 20O, 24Ne, etc.

**Microscopic Approach with Optical Model**

Another simple microscopic decay theory (MAOM) was developed in [64], by extending the basic formalism of [49] which unies the advantages of the shell-model description of nuclei involved with the optical model for the emitted cluster. This microscopic description of the decay needs to know two sets of basic states: the states jKi of the initial system and the scattering states jC

Ei describing the relative motion in the nal channel.

**Density Dependent and -nucleus Potential**

Although, the above description for generalized DFM had an undisputed success for heavy ions reactions with the parameters given in Tables 4.2 and 4.3, we use in our study the work of Chaudhuri [72], which is well suited for -nucleus interactions as it accounts for the higher order exchange eects and the Pauli blocking correctly. In that work the M3Y-Reid eective nucleon-nucleon interaction supplemented by a density-dependent term was used. The resultant model (called DDM3Y) gave a consistent picture of elastic scattering.

For the density-independent part, the direct term of Eq. (4.3) and the delta simulated form of the exchange term Eq. (4.8) were used. This is known as a zero-range pseudopotential

1 Introduction

2 Basic Equations and Conservation Laws

I Review of -decay theories

3 Decay theories

3.1 Phenomelogical models

3.1.1 Gamow Model

3.1.2 Preformed Cluster Model .

3.2 Microscopic Models .

3.2.1 Self-Consistent Microscopic Approach .

3.2.2 Microscopic Approach with Optical Model

3.2.3 Microscopic description and Superasymmetric Fission Model

II Our calculations

4 Methods of Calculation

4.1 The Double Folding Model .

4.1.1 Formalism of the DFM .

4.1.2 Density Dependent and -nucleus Potential

4.1.3 Charge and Nucleon Density Distributions

4.2 Decay Widths

4.2.1 Method A: Quasi-bound state wavefunction approach

4.2.2 Method B: SAFM and DFM

4.2.3 Method C: QCA and DFM .

4.3 Model parameters

5 Results: Analysis and Discussion

5.1 Method A: Numerical results

5.2 Method B and C: Numerical results

5.2.1 Method B: SAFM and DFM

5.2.2 Method C: PCM and DFM

5.3 Comparison of the Methods

6 Conclusions

GET THE COMPLETE PROJECT

A MICROSCOPIC DESCRIPTION OF NUCLEAR ALPHA DECAY