Prediction,limittation of Shell Model and Comparative Study of Shell Model and Liquid Drop Model

Prediction os shell model

The shell model can predict or explain following properties of nuclei.

i) Stability of closed shell nuclei

ii) It can reproduce the experimentally observed magic numbers.

iii) spin and parity of group state of the nucleus can be determined.

iv) Magnetic moments of nuclei.

v) Phenomenon of nuclear isomerism

vii) \(\beta\) -day

vii) Stripping reactions.

Limitations of shell model

Comparative Study of Shell Model and Liquid Drop Model

The liquid drop model assumes that the nucleons are able to move about within the nucleons like the molecules within the liquid drop.Hence according to this model, a nucleus can be taken as a drop of a liquid and there are very many similarities presented in this model, between a nucleus and a liquid drop. Basically,this model is based upon the similarities between the liquid drop and nucleus.

Despite its similarities assumptions, this model is quite successful to give atomic mass, B.E. accurately to predict \(\alpha\), \(\beta\)+, \(\beta\)- properties and most stable isobars for a given isobaric family against \(\beta\)-decay. To some extent, it can explain the nuclear fission and stability limits against spontaneous fission.

however, this model fails to explain the extra stability of nuclei at the magic numbers, the discontinuities in \(\frac BA\)vs. A curve. It is also can't explain the measured spin-parity,magnetic moments of the nuclei.

The failure of liquid drop model draws the attention of physicists to devise new model named shell model. The new model is similar to Bohr model of electrons in extra-nuclear space. By analogy with closed shell and subshell, it is measured that nucleon from the closed shell and subshell. Evidently, protons and neutrons are not equivalent assumed in liquid drop model, The main difference between shell model and the liquid drop model is that in liquid drop model, It is assumed that the nucleons exert an influence on one another only at close range i.e. they interact strongly only with their immediate neighbours whereas shell model treats the nucleons, individually and it is assumed that the nucleons do not all interact with each other.

The shell model is quite successful to account the magic number and hence the stability of nuclei are explained successfully especially for light nuclei and the discontinuities on \(\frac BA\)vs. A curved is explained. Also, the model is successful in predicting most of the nuclear spin, parity of ground state of nuclei. It also explains the magnetic moment and electric quadrupole moment to some extent through the later one is not so much explained. It can't account for the degree to which many nuclei are non=spherical (ie the observed large electric quadrupole moments of nuclei are not explained by this model). It cannot explain some observed so in parity of heavier nucleon excited nuclei and magnetic moments also, that's why the collective model is devised.

Actually, shell models explain the different characteristics of a nucleus as it explains successfully for lighter nuclei whereas the liquid drop models give the satisfactory result of its predictions on nuclear properties of heavier nuclei.