# Recoil Proton Momentum Spectrum in Neutron Decay

• Waleed Khalid
In summary: Nevermind, I was being stupid, the answer was simple, since I was using a non relativistic conversion I had to multiply with a factor of p/mn

#### Waleed Khalid

I wish to draw the proton momentum spectrum by transforming the energy spectrum of recoil protons. I have calculated the energy spectrum using Nachtmann's spectrum: wp=g1[T]+a*g2[T]
Where:
g1[T]=(1 - x2/σ[T])2 * Sqrt[1 - σ[T]] * (4*(1 + x2/σ[T]) - (4/3*(σ[T] - x2)/σ[T])*(1 - σ[T]));
g2[T]=(1 - x2/σ[T])2 * Sqrt[1 - σ[T]] * (4*(1 + x2/σ[T] - 2*σ[T]) - 4/3*(σ[T] - x2)/σ[T]*(1 - σ[T]));
and σ[T]=1 - 2 * T * mn/(mn-mp)2
and a is the electron neutrino correlation.

To get the momentum spectrum, I am transforming the functions (non relativistically):
TofP[p]=p2/(2*mn)

wmom=wp[TofP[p]]

However this doesn't yield the correct spectrum for the momentum of the recoiled protons, as far as I have gotten it I have to multiply it with p and TofP[p] to get the shape of the correct spectrum (wmom=wp[TofP[p]]*p*TofP[p]). Which doesn't make sense to me, so if anyone can explain I would be highly thankful.

Nevermind, I was being stupid, the answer was simple, since I was using a non relativistic conversion I had to multiply with a factor of p/mn

Waleed Khalid said:
I wish to draw the proton momentum spectrum by transforming the energy spectrum of recoil protons. I have calculated the energy spectrum using Nachtmann's spectrum: wp=g1[T]+a*g2[T]
Where:
g1[T]=(1 - x2/σ[T])2 * Sqrt[1 - σ[T]] * (4*(1 + x2/σ[T]) - (4/3*(σ[T] - x2)/σ[T])*(1 - σ[T]));
g2[T]=(1 - x2/σ[T])2 * Sqrt[1 - σ[T]] * (4*(1 + x2/σ[T] - 2*σ[T]) - 4/3*(σ[T] - x2)/σ[T]*(1 - σ[T]));
and σ[T]=1 - 2 * T * mn/(mn-mp)2
and a is the electron neutrino correlation.

To get the momentum spectrum, I am transforming the functions (non relativistically):
TofP[p]=p2/(2*mn)

wmom=wp[TofP[p]]

However this doesn't yield the correct spectrum for the momentum of the recoiled protons, as far as I have gotten it I have to multiply it with p and TofP[p] to get the shape of the correct spectrum (wmom=wp[TofP[p]]*p*TofP[p]). Which doesn't make sense to me, so if anyone can explain I would be highly thankful.

## What is the Recoil Proton Momentum Spectrum in Neutron Decay?

The Recoil Proton Momentum Spectrum in Neutron Decay is a scientific measurement that describes the distribution of momentum values for protons that are emitted during the decay of a neutron. This spectrum is important in understanding the fundamental properties of subatomic particles and their interactions.

## Why is the Recoil Proton Momentum Spectrum in Neutron Decay studied?

Studying the Recoil Proton Momentum Spectrum in Neutron Decay allows scientists to gain a deeper understanding of the underlying physics and forces that govern the behavior of subatomic particles. This information can also be used to test and refine theories about the fundamental structure of matter.

## How is the Recoil Proton Momentum Spectrum in Neutron Decay measured?

The Recoil Proton Momentum Spectrum in Neutron Decay is measured using specialized detectors and instruments that are designed to detect and record the energy and momentum of the emitted protons. This data is then analyzed and plotted to create the momentum spectrum.

## What factors can affect the Recoil Proton Momentum Spectrum in Neutron Decay?

Several factors can affect the Recoil Proton Momentum Spectrum in Neutron Decay, including the energy of the decaying neutron, the type of decay process (such as beta or alpha decay), and the properties of the surrounding environment (such as temperature and pressure).

## What can the Recoil Proton Momentum Spectrum in Neutron Decay tell us about the decay process?

The shape and characteristics of the Recoil Proton Momentum Spectrum in Neutron Decay can provide valuable information about the decay process itself, including the type of decay and the energies and momenta of the particles involved. This data can also be used to verify the laws of conservation of energy and momentum.