Gamma Definition and 685 Threads

Hello, In our course of complex analysis we proved that the gamma function, \Gamma(z) = \int_0^\infty t^{z-1} e^{-t} \mathrm d t for 0 < Re(z), is analytical. We did this by defining f_{\epsilon,R}(z) = \int_\epsilon^R t^{z-1} e^{-t} \mathrm d t about which we can prove that it is analytical...

Here are some recent papers on attempts to detect dark matter directly or indirectly: a solar system test with a possible positive result: http://arxiv.org/abs/1001.1697 direct detection, with seemingly contradictory results: http://arxiv.org/abs/1106.1066 via gamma-ray astronomy...

In Zee's Quantum Field theory book he writes \begin{align}\gamma^0 &= \begin{bmatrix}I & 0 \\ 0 & -I\end{bmatrix}=I \otimes \tau_3 \\ \gamma^i &= \begin{bmatrix}0 & \sigma^i \\ \sigma^i & 0\end{bmatrix}=\sigma^i \otimes \tau_2 \\ \gamma^5 &=\begin{bmatrix}0 & I \\ I & 0\end{bmatrix}=I \otimes...

How many gamma photons are in the galaxy, and what can we know about the distribution? Which kind of process can absorb them?

Homework Statement This is a special relativity question: Two gamma rays of identical energies E collide with an angle \theta between their velocities. Show that positron-electron pair creation is impossible in the limiting case \theta=0. Find the minimum \theta value for p-e creation to...

Hi I've just read the statement that a matrix that commutes with all four gamma matrices / Dirac matrices has to be a multiple of the identity. I don't see that; can anyone tell me why this is true? Thanks in advance

Hi, I need to make a project to demonstrate Gamma rays. I have cesium as a source to use and a geiger counter to detect gamma rays. Ideas are welcome!

Hello Guys, I have some questions relating to Cold Fusion / Low Energy Fusion. It seems Gamma Rays are not present from Cold Fusion experiments and Neutrons cannot be seen released from a sonar luminance reaction within the same nanosecond of time as the Alpha Process Completes...

Typically I understand that projection operators are defined as P_-=\frac{1}{2}(1-\gamma^5) P_+=\frac{1}{2}(1+\gamma^5) where typically also the fifth gamma matrices are defined as \gamma^5=i\gamma^0\gamma^1\gamma^2\gamma^3 and.. as we choose different representations the projection...

Typically I understand that projection operators are defined as P_-=\frac{1}{2}(1-\gamma^5) P_+=\frac{1}{2}(1+\gamma^5) where typically also the fifth gamma matrices are defined as \gamma^5=i\gamma^0\gamma^1\gamma^2\gamma^3 and.. as we choose different representations the projection...

I need to do a presentation to teach the rest of my class about Gamma rays. We need to do some sort of experiment to demonstrate Gamma Rays. Any ideas?

Homework Statement What is the cause for the bump in the lower energies of this spectrum: http://en.wikipedia.org/wiki/File:Gammaspektrum_Uranerz.jpg The Attempt at a Solution Is it just normal Compton? I'm doubting that because that is very asymmetric. I can't find anything in any textbook I...

Hi all, I'm looking at the http://en.wikipedia.org/wiki/Gamma_function#General" for the gamma function, and it lists equations for the gamma function of half-integer orders (i.e. gamma(0.5+n) and gamma(0.5-n)). But, it doesn't list a reference as to where this equation comes from. Does...

Gamma Function on negative Fractions! If we take a look at the Gamma Function and evaluate the integral by parts then we will get infinity in the first step of Integration by Parts eg: Integral e^-1*x^-5/3 Limits being 0 to Infinity as usual! If we try to integrate this we will get...

Homework Statement In attachment The Attempt at a Solution I can't see the link in the steps, a little help pls.

we know that \Gamma (s)= \int_{0}^{\infty}dxe^{-x}x^{s-1} however every factor of the Riemann Zeta can be obtained also from a Mellin transform \int_{0}^{\infty}dxf(x)x^{s-1} =(1-p^{-s})^{-1} where f(x) is the distribution \sum_{n=0}^{\infty}x \delta (x-p^{-n}) is there any...

Can a faraday cage be used to stop the radiation at the Japanese reactor? If not why not? I know the frequencty is high but what if you pulsed DC current at the same frequency would that stop it?

Question about Gamma Radiation. I understand that Gamma Radiation, like X-Rays, are just photons (light particles) at different frequencies. I was reading an article about the Nuclear Plant problems in Japan, and the article stated that photons from Gamma Radiation for the most part pass...

Homework Statement Let X1,...,Xn be independent, identically distributed random variables with exponential distribution of parameter λ. Find the density function of S = X1+...+Xn. (This distribution is called the gamma distribution of parameters n and λ). Hint: Proceed by induction...

It's known that light can have particles characteristic in a particular condition.

Hi All, How can a high energy (above 1 MeV) gamma ray interact with a protium (hydrogen with only a proton in nucleus)? Does it only ionize it? Does it break it up? Does a chain reaction occur where antiparticles are formed and then annihilated, spitting out another gamma ray? I've been...

Dear Physics Forums, I am currently conducting an experiment on gamma ray coincidence from Co-60. Co-60 decays to an excited state, then de-excited by emitting two gamma rays. The aim is to deduce the angular momentum L of the first excited state. Apparently L indicates the type of...

Homework Statement \int xe^{-x^{3}}dx from 0 to infinity Homework Equations \Gamma = \int x^{p-1}e^{-x} from 0 to infinity The Attempt at a Solution my problem is I'm not sure what i am supposed to do with the exponent of 3 on the e, because it seems to affect the answer...

Consider I(c)= \int_0^\infty \frac{x^{1-\epsilon}}{x+c} dx For what values of \epsilon are these integrals convergent? Would it be \epsilon \geq 0? Then I'm asked to use x^{-\lambda} \Gamma(\lambda) = \int_0^\infty d \alpha \alpha^{\lambda-1}e^{-\alpha x} for x>0 and the identity...

i was told that high emergy gamma rays had a finite range in water. how can this be if they are both massless and chargeless. is it because they are absorbed/produce electrons/positrons thanks

hi, am i right in saying that for gamma rays of energies above 10MeV, the main interaction mechanism is pair production? and this is independent on energy? (or is it compton scattering for example?) thanks

***Please skip ahead to post # 6 where I have better formulated my question. Thank you! *** I have an equation AY'' + B\eta^2Y'=0 \qquad(1) where A and B are known constants and Y is a function of η. By using the substitution X = Y' I have reduced the problem to a first order ODE of...

Readers, Hi, I'm new here, and have a question that has piqued my interest, and have not found a solution elsewhere. My question is as such: is there an equation to determine the energy or frequency of the gamma ray emitted as a byproduct of radioactive decay for a given isotope...

Homework Statement The problem is listed as follows: Show that conservation of energy and momentum require at least two gamma rays to e emitted in the annihilation of an electron by a positron. Homework Equations p(initial) = p(final) E(initial) = E(final) Total rest mass = 1.0218...

Homework Statement Homework Equations γ = Cp/Cv ε = W/Qh PiVi^γ = PfVf^γ The Attempt at a Solution I know I have to find the gamma firstly in order to determine what type of gas is present here. And to do that I have to pick one of the adiabatic processes. I chose to do AD. But I am...

Hello, I need help proving this: http://mathworld.wolfram.com/images/equations/GammaFunction/Inline177.gif = http://mathworld.wolfram.com/images/equations/GammaFunction/Inline179.gif

What would be the best protection from these two at the same time? Lead alone or a mixture of something like lead and Plexiglas?

Hey guys, I just had a conceptual question as to the meaning of gamma in thermodynamics. I mean, I know that gamma = cp/cv, where cp = at constant pressure the amount of heat to raise one kg of substance 1 degree, and cv = amount of heat to raise one kg of substance 1 degree at constant volume...

I was just curious as to how I can show the following properties of the Gamma Function, they came up in some lecture notes but were just stated? Notation: G(z) = Gamma function 2^(z) = 2 to the power of z I = Integral from 0 to infinity (1) G(z)*G(1-z) =...

Hi, I am interested in performing the following integration: \int _{-\infty }^{\infty }\Gamma\left[k,\frac{x+u}{v}\right]e^{-\frac{(x-m)^2}{2\sigma ^2}}dx . I would appreciate anyone's help. I have been trying to do it in Mathematica but it runs out of time returning the same integral...

Hello. When one is converting between coordinate systems, the Jacobian arises as a necessary consequence of the conversion. Does this occur with transformations between relativistic systems, and, if so, is this manifested through the prevalence of gamma in the transforms? Any guidance would...

Homework Statement

Why in gamma ray emission there is no change in A or Z ? We know that in Alpha decay 2 protons and 2 neutrons are subtracted from the element. and in Beta decay there is change in atomic number by + or - 1. but why there is no any change in Gamma Decay in mass number A or atomic number. i...

In most of the physics textbooks I read they only give one or two representations of gamma matrices, but none gives a proof, so how can I prove it from the Clifford algebra?

There is a random sample of size n from a gamma distribution, with known r. Please help me formulate the likelihood function of the gamma distribution. I understand that the density function is the following: f\left(y;r,\lambda\right)=\frac{\lambda}{\Gamma\left(r\right)}\left(\lambda...

I know that the gamma function (from 0 to infinity): \int e-t tx-1 dt = \Gamma(x) and that the relation exists... \int e-ut tx-1 dt = 1/ux \Gamma(x) Now for the lower bound incomplete gamma function... I see that from http://people.math.sfu.ca/~cbm/aands/page_260.htm (equation...

I read that gamma rays are usually emitted by the nucleus of an atom after it emits an alpha particle, but have been wondering: If the alpha particle being emitted was meant to stabilize the atom, and should have, why does the nucleus need to emit such high energy waves?

whats the highest frequency gamma ray normally emitted by any nucleus something that I read said that gamma rays were normally less than 10 Mev

This has been bothering me for a while. In Einstein's original derivation of the Lorentz transformations, he finds... \epsilon=\frac{c^2}{c^2-v^2}x' Here, \epsilon is what we would normally call x', and x'=x-vt (sorry if that's a bit confusing). He then says, "Substituting for x' its...

if object A is moving with gamma=x in one direction and object B is moving with gamma=y in the opposite direction then what is the gamma factor for object A as it would be calculated by object B? I know the velocity addition rule for relativity but I can't find anything on the net about...

Hey I recently did an experiment on the absorption of gamma rays I calculated the thickness and the no. of counts, got a nice exponential curve. So, I used lead as the absorbent or shielding material for gamma... Any suggestions what else I can use for gamma? I thought about sausages or...

How do I verify \{ \gamma^5 , \gamma^\mu \} = 0 I have \{ \gamma^5 , \gamma^\mu \} = \gamma^5 \gamma^\mu + \gamma^\mu \gamma^5 = -i ( \gamma^0 \gamma^1 \gamma^2 \gamma^3 \gamma^5 + \gamma^5 \gamma^0 \gamma^1 \gamma^2 \gamma^3 ) = -i ( \gamma^0 \gamma^1 \gamma^2 \gamma^3 \gamma^5 - \gamma^0...

So since I learning QFT a while ago, I've always struggled to understand fermions. I can do computations, but I feel at some level, something fundamental is missing in my understanding. The spinors encountered in QFT develop a lot from "objects that transform under the fundamental representation...

Homework Statement a gamma raidiation source (226Ra) is used in hospital laboratory. if shielding is considered as a means of control how many centimeters are needed to reduce the radiation to 1% of what a worker would be exposed to without shielding? assume the shield material is a)...

Alright, I've confirmed that Radium produces Gamma rays. But how much does it put off? Is it a really high level or a tolerable level that can be stopped.