# How is the value of tT^2 calculated for neucleosynthesis

• I
• Buzz Bloom
In summary, the temperature/time relation during the Big Bang nucleosynthesis era can be described by the equation T = (t^2/g*)^(1/4), where t is time in seconds, T is temperature in MeV, and g* is the effective number of particle species. In the standard model, g* is 10.75, taking into account contributions from photons, electron-positron pairs, and neutrino flavors. The value of 0.74 for the nucleosynthesis era is calculated based on this equation. Despite searching for other sources, the information from Wikipedia seems to be the only available material on this topic. There is currently no explanation or reference citation for how this value was determined.
Buzz Bloom
Gold Member
The following quote is from the Wikipedia article
https://en.wikipedia.org/wiki/Big_Bang_nucleosynthesis#Characteristics .
The temperature/time relation in this era can be given by the equation:​

where
t is time in seconds,
T is temperature in MeV, and
g* is the effective number of particle species.
(g* includes contributions of 2 from photons, 7/2 from electron-positron pairs and 7/4 from each neutrino flavor. In the standard model g* is 10.75).​
I would much appreciate seeing a reference citation or an explanation from someone about how the value 0.74 is calculated for the nucleosynthesis era.

By the way, when I searched the internet for this information, all I could find were articles that quoted the same material from Wikipedia.

Last edited:
Hi @Greg Bernhardt:

I think it is time to abandon this thread. I have the impression that there are no PF participants who are able to help me with respect to my question here.

I started a different thread to get help with respect to a different aspect of this thread.
I was pleased to get one useful response, and I am hoping to continue a discussion about that response.

Regards,
Buzz

## 1. How is the value of tT^2 calculated for nucleosynthesis?

The value of tT^2 for nucleosynthesis is calculated using the formula tT^2 = (kB*T)^2 * t, where kB is the Boltzmann constant, T is the temperature, and t is the time. This formula takes into account the temperature and duration of the nucleosynthesis process.

## 2. What is the significance of tT^2 in nucleosynthesis?

tT^2 is used to measure the energy available during nucleosynthesis. It is a critical factor in determining which elements can be formed during this process. Higher values of tT^2 indicate a higher energy environment, which allows for the formation of heavier elements.

## 3. How does tT^2 affect the rate of nucleosynthesis?

The rate of nucleosynthesis is directly influenced by tT^2. Higher values of tT^2 result in a faster rate of nucleosynthesis, as more energy is available for nuclear reactions to occur. This leads to the formation of a greater variety of elements in a shorter amount of time.

## 4. Can the value of tT^2 be measured in a laboratory setting?

Yes, the value of tT^2 can be calculated and measured in a laboratory setting. This can be done by controlling the temperature and duration of a nuclear reaction and using the tT^2 formula to calculate the energy available during the process.

## 5. How does the value of tT^2 change during the course of nucleosynthesis?

The value of tT^2 may change during nucleosynthesis as the temperature and duration of the process change. In general, as the temperature increases, the value of tT^2 also increases, resulting in a higher energy environment and potentially different elements being formed. The value of tT^2 can also decrease as the duration of the process increases, as the energy available may become depleted. This is why the duration of nucleosynthesis is an important factor in the tT^2 calculation.

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