It is raining today, nearly all day from the morning. Because there was no lecture to give today, I wanted to take a walk in the hill of Abinger Hammer, where my home is. Yes, there was no lecture today and raining... Theoretical Physicists need a calm and comfortable environment for thinking. Today looked a best day. So, I stayed at home until evening.
There is one thing disturbing my mind recently. It is a relation between symmetry and collectivity. I learned when I was a PhD student that a quantum object with perfect roational symmetry cannot rotate. Therefore, the ground states of the magic nuclei such as 16-O and 208-Pb have zero angular momentum I=0. In many (probably, "most of") textbooks, this is explained by words, and with no mathematics. Well, Dirac said that we need to understand physics without relying on mathematics, and Faraday realized what Dirac said in fact... But, As many other students, it is true that I forced myself to swallow this "well-known" fact as a common sense. However, deep in my heart, there have been something which I cannot digest completely.
I think it is very important to understand (or definte carefully) the term "collectivity". For example, what does the collective wave function mean? In nuclear physics, the particle-plus-rotor model answers this question in a phenomenological manner. So, I decided to use this model to think this problem today.
Out of the window, I saw grey clouds come and go with a great speed. Sometimes, the sound of raindrops was magnified on the roof. Although the problem was hard to solve, I enjoyed this time of thinking under this natural rhythm and melody.
