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SYMMETRIES in PHYSICS

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Symmetry and Spontaneous Symmetry Break<strong>in</strong>g<br />

What Did We Learn?<br />

Selected Groups and Symmetries<br />

Spontaneous Symmetry Break<strong>in</strong>g<br />

In the 132 Sn nucleus with 50 protons and 82 neutrons:<br />

... the wave functions do not obey the spherical symmetry ...<br />

They transform under irreducible representations of the SO 3<br />

Calculation shows that the energy eigen-values are degenerate:<br />

(degeneracy equal to 2j+1)<br />

Question: What happens if we cont<strong>in</strong>ue add<strong>in</strong>g nucleons to 132 Sn?<br />

Experiments will show that the result<strong>in</strong>g systems are NOT spherically<br />

symmetric! Strange! - s<strong>in</strong>ce the Hamiltonian of the system obeys<br />

the rotational symmetry exactly!! Let us have closer look...<br />

Jerzy DUDEK<br />

<strong>SYMMETRIES</strong> <strong>in</strong> <strong>PHYSICS</strong>

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