Calculation of Lamb shift: sign problem

Calculation of Lamb shift

The frequency of the 2S state increases to about a gigahertz above the 2P state (Wiki, Lamb shift entry). So the energy of the 2S state increases with respect to that of the 2P state. The energy is h bar omega multiplied by a correction value integral psi* (1 / m(r) half psi dtau, so the correction value must increase, i..e become greater than 1.

Calculation of Lamb shift: sign problem

To make it clear: If the energy level of 2S becomes less negative valued, the absolute value decreases. Therefore the correction factor of the 2S state becomes smaller than one. Do you agree to this argument?

Horst

Am 25.03.2019 um 15:11 schrieb Myron Evans:

Calculation of Lamb shift: sign problem

OK thanks, I would suggest experimenting to find the m(r) function that gives the experimental result. As long as m(r) becomes one in the Minkowski space, there is freedom of choice, so it can become greater than one. It is encouraging that an exponential m(r) gives the correct result of S being shifted and P not being shifted. There is a rise of about 1000 MHz of the 2S level. This means that the energy level of 2S becomes less negative valued, and the frequency increases. The absolute value of energy increases, so the absolute value of the theoretical result would match the experimental result.

Calculation of Lamb shift: sign problem

Accoring to the diagram of Fig. 1 in UFT429, the Lamb shift affects the
2S1/2 state, not the 2P1/2 state. This is verified by our exponential
m(r) functions. However the absolute value of the energy level shrinks
(because the levels in the diagram are negative). This is in conflict
with the expectation value

integral psi* 1/m(r)^(1/2) psi dtau

which gives values >1 because m(r)<1 near to the centre. The situation
could be remedied by using a m(r)>1, but this would change all our
assumptions we made before.
I appended the diagram with relative energy change of the 2S1/2 state.
The experimental shift has been added. The parameter R is about 0.015
Bohr radii which is about twice the value obtained form s-o coupling in
UFT 429.

Horst

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