# What is meant by first momentum of energy spectrum (ES)

1. Jul 24, 2010

### Rajini

Hello all,

I wanted to know
what is meant by first momentum of energy spectrum (ES),
second momentum of ES, and also third momentum of ES.
It will be nice with some references, books, etc.

thanks

2. Jul 24, 2010

### K^2

Re: Momemtum

For any function of single variable, f(x), you can find an n-th moment μn using this formula.

$$\mu_n = \int_{-\infty}^{\infty} x^n f(x) dx$$

3. Jul 24, 2010

### AJ Bentley

Re: Momemtum

Never seen that before.
What's the significance of it in relation to a spectrum?

4. Jul 24, 2010

### Dickfore

Re: Momemtum

It's called moment, not momentum. Momentum is a different physical quantity and moment is a statistical function. The energy spectrum is treated like some probability distribution function.

5. Jul 24, 2010

### Rajini

Re: Momemtum

Hi force and k2,
i got some idea from you reply.
Yes it should be moment and not momentum.

6. Jul 24, 2010

### K^2

Re: Momemtum

Provided that spectrum is normalized, that is μ0=1, μ1=<E>, μ2=<E²>, and consequently, ΔE=sqrt(μ21²). I have no idea what the significance of the 3rd moment is.

7. Jul 24, 2010

### Dickfore

Last edited by a moderator: Apr 25, 2017
8. Jul 24, 2010

### K^2

Re: Momemtum

Yes, I'm aware of the name of the 3rd moment. I'm not sure what relevance it has specifically to the energy distribution spectrum. <E> and ΔE have very specific physical consequences. I'm not sure if the same can be said about <E³>.

9. Jul 24, 2010

### Dickfore

Re: Momemtum

So, what is the physical significance of the first and the second moment?

10. Jul 24, 2010

### Rajini

Re: Momemtum

Hi force,
from nis (nuclear inelastic scattering), from 2nd moment of the spectrum you get the mean force constant of the Mössbauer nucleus and from 3rd you get mean square vibrational displacement of the Mössbauer nucleus.
my intention is to ask you all about the general details of these moment formula...
may be some of you for sure know about Lipkin'S sum rule.
tha nks

11. Jul 24, 2010

### K^2

Re: Momemtum

Really?

For starters, <E> is a conserved quantity. ΔE is related to Δt. If this is an energy spectrum of a particle, for example, you just got its mass and half-life.

12. Jul 24, 2010

### Dickfore

Re: Momemtum

Isn't this an oxymoron

13. Jul 24, 2010

### K^2

Re: Momemtum

It's a taxonomy. General details are more specific than detailed generalities, but less specific than plain details.