# A surprise result using Helmann-type potential

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• ftr
In summary, the conversation discusses the Helmann type potential, which combines the Yukawa and Coulomb potentials and is used in physics. It is noted that the value of "a" in the equation can be interpreted as a length rather than an exchange mass for the force. By using e^2=3 and various values for "a", it is observed that the curves converge to a value of .000272287. This value is found to be close to the proton-electron mass ratio and can also be used to calculate the electron mass. The system is also found to be scale invariant and the possibility of obtaining the potential from first principles is discussed. However, it is noted that the chosen value of 11000 for r is arbitrary
ftr

\begin{align}
V(r,a)=\frac{e^2}{r}-\frac{e^2}{r}exp(\frac{-r}{a})
\end{align}

The above equation is called Helmann type potential which is a combination of Yukawa and coulomb potential. It is used to solve many problems in physics, for example
https://arxiv.org/pdf/1307.2983.pdf

But I noticed a remarkable property, which could be just some coincidence. Now, with Yukawa potential we typically interpret "a" in above equation as the exchange mass for the force. However here we interpret "a" just as length for inverse of two masses that INTERACT with each other.

if we use e^2=3 and use several values for "a"(the horizontal column in Exel sheet) and plot against distance, we see something strange. It seems that all the curves converge to a value of .000272287.

I used 300,700,1300,1711 for the shown plot. but you can use any such numbers. Also I have calculated for 1836 as an info only.

so if we multiply .000272287 by 2 and take the inverse we get 1836.2977 which is close to the proton-electron mass ratio. Or in another way, the electron mass can be taken to be .000272287*2=0.0005445

Now we figure which r,a will give us 1 which is the mass of the proton compared to the electron mass.
by inspection I find a nice solution(although others exist) r=3.8, a=3.8 that gives the potential to be
.499 and multiply that by 2 you get almost 1
If we take 1836.1526 to be the electron reduced Compton wave and see the value of 3.8 by comparison
we have 3.86159e-13*3.8/1836.1527= .7991738 e-15

which is very close to proton radius

The system is also remarkable in that it is scale invariant

I don't know what all that means. but I wonder if it is possible to get this potential from first principle at least.

You can use this to do and verify all calculations

3/r-(3/r)*EXP(-1*r/a)
http://m.wolframalpha.com/

Last edited:
The curves go to zero. If you evaluate them at a large r/a ratios, then you just get approximately 3/r. For r=11000, this gives 3/11000, if you invert it and divide it by 2 you get 11000/6 = 1833. That is close to the electron to proton mass ratio. So what? The number 11000 is completely arbitrary. Pick r=6000 and the same calculation gives 1000. Pick r=6000 pi and the same calculation gives 1000 pi.

jim mcnamara
mfb said:
The curves go to zero. If you evaluate them at a large r/a ratios, then you just get approximately 3/r. For r=11000, this gives 3/11000, if you invert it and divide it by 2 you get 11000/6 = 1833. That is close to the electron to proton mass ratio. So what? The number 11000 is completely arbitrary. Pick r=6000 and the same calculation gives 1000. Pick r=6000 pi and the same calculation gives 1000 pi.

Yes, it is somewhat arbitrary. However, given the fact if you zoom that 11000 is the START of "good" convergence and it coincides with an interesting number it seems to be saying something, coupled to the proton results.

But yes, there must be a way to confirm that position independently. I think I know how to get to it approximately, but unfortunately I am not feeling well now , maybe a bit later.

11000 is not the start of "good convergence". It is the point where the diagram with your chosen values doesn't show differences any more. Zoom in or take a=10000 and it will show differences. Consider a smaller range for a and you'll get curves that are very close together earlier. There is absolutely nothing special about 11000, and we don't do numerology here. I closed the thread.

DrClaude

## 1. What is a Helmann-type potential?

A Helmann-type potential is a mathematical model commonly used in theoretical chemistry to describe the energy landscape of a molecule or chemical system. It takes into account both the kinetic and potential energy of the system, allowing for more accurate predictions of molecular behavior.

## 2. How is a surprise result defined in the context of Helmann-type potential?

A surprise result in this context refers to a finding that is unexpected or goes against previously established theories or predictions. In other words, it is a result that deviates from what was initially anticipated based on the use of Helmann-type potential.

## 3. Can you provide an example of a surprise result using Helmann-type potential?

One example of a surprise result using Helmann-type potential is the discovery of a new stable isomer of a molecule that was previously thought to be unstable. This unexpected finding was made possible by the more accurate energy landscape provided by the use of Helmann-type potential.

## 4. What are the advantages of using Helmann-type potential in scientific research?

Using Helmann-type potential can lead to more accurate and reliable predictions of molecular behavior, as it takes into account both kinetic and potential energy. This can help researchers better understand and explain experimental results, and potentially uncover new and unexpected phenomena.

## 5. Are there any limitations or drawbacks to using Helmann-type potential?

One limitation of using Helmann-type potential is that it requires a significant amount of computational power and time to calculate. Additionally, the accuracy of the results is dependent on the quality of the input parameters and assumptions made in the model. Therefore, it is important for researchers to carefully validate and interpret the results obtained using Helmann-type potential.

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