Nuclear Physics: Semi empirical mass formula for ever?
One of the pioneering models (~1930) of nuclear physics is the well known liquid drop model, also called the semi-empirical mass formula, or Bethe -Weizsäcker formula. Since its inception, this model has undergone 3 main improvements with the introduction of the nuclear deformation (deformed nuclei), the introduction of pairing and the introduction of the shell correction due to the magic numbers. At present there are powerful versions of this model for evaluating the binding energy with appreciable precision (that can "compete and even beat" more elaborated models) .
The question is the following: how, with the progress (both experimental and theoretical) of current nuclear physics (such as the standard model, the Quantum ChromoDynamics (QCD) theory, the Higgs Boson, the BCS model, the HARTREE-FOCK BOGOLIUBOV (HFB) model, the relativistic mean field theory , the interacting bosons model (IBM), the Nuclear Shell Model, etc ...) it is amazing to find that such an old and simple model still has always its place among these so elaborated and so complicated new theories?
Normally, such a rudimentary model should not resist the new "armada of theoretical tools" in the nuclear theory. This old and simple model remains a formidable efficiency concerning the nuclear binding energy, fission barriers and many other questions. Why?
Dear Mr Alvioli,
I will try to answer your remarks, one by one, methodically, in due course (today and tomorrow).
You put Newton's mechanics on the same level as the Bethe-Weizsaker formula by saying that the new concepts of nuclear physics do not invalidate the semi-empirical formula. I will ask you a simple question: "Have you only noticed that in the ballistic trajectory of a projectile, Newton's mechanics does not use any adjustment (fit) and obtains the exact solution with the desired precision? Moreover it is true when you say that relativistic mechanics does not invalidate Newtonian mechanics. However, when a model gives perfect results, it becomes a theory. There is a difference between a model and a well-established theory (using a minimum of postulates). I think that we should not confuse a model with a well-established theory. The liquid drop model is just an image of fluid mechanics "transposed" to nuclear physics with a mixture of ingredients.
Dear Mr Alvioli,
In response to your remark:
"I'm not sure all of the topics you mentioned are relevant to the question, but still."
I have stated a lot of "things" (which however are all related to nuclear physics) which are somewhat "distant" from the question for the simple reason that nuclear physics (by the number of its aspects) does not seem unified.
Maybe we need a new J. C. Maxwell of nuclear physics.
In fact nuclear physics (nuclear structure) is characterized by collective aspects and particle aspects (individual aspect). Hence the use of collective models and particle models. It is rather difficult to find a fundamental model which describes the 2 aspects simultaneously.
In my opinion, the semi-empirical mass formula in its most sophisticated versions (such as that of the FRDM: https://arxiv.org/abs/1508.06294) derives its strength from the mixing of a collective model (liquid drop) and of quantum corrections (pairing and shell effects) representing the particle aspect.
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