What is Gamma: Definition and 711 Discussions

Gamma (uppercase Γ, lowercase γ; Greek: γάμμα gámma) is the third letter of the Greek alphabet. In the system of Greek numerals it has a value of 3. In Ancient Greek, the letter gamma represented a voiced velar stop /ɡ/. In Modern Greek, this letter represents either a voiced velar fricative or a voiced palatal fricative.
In the International Phonetic Alphabet and other modern Latin-alphabet based phonetic notations, it represents the voiced velar fricative.

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  1. S

    Likelihood function of the gamma distribution

    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...
  2. B

    Understanding the incomplete gamma function

    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...
  3. L

    Why do gamma rays accompany other kinds of decay?

    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?
  4. G

    What is the highest frequency gamma ray emitted by any nucleus?

    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
  5. SamRoss

    Am I taking crazy pills or is Einstein missing a factor of gamma?

    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...
  6. G

    Velocity addition expressed as gamma

    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...
  7. D

    Absorption of gamma rays experiment (opinions?)

    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...
  8. L

    Proving \{ \gamma^5 , \gamma^\mu \} = 0 to Gamma 5 Matrix Verification

    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...
  9. S

    The Gamma Matrices, Spinors, Anti-Commutation, and all that Jazz

    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...
  10. T

    Gamma radiation sorce sheilding

    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)...
  11. K

    How much Gamma Radiation does Radium produce

    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.
  12. K

    Can Gamma Rays Make Plasma in a Vaccum

    Alright, If you had a vacuum chamber and put in a gamma ray producing material (say Radium) would it produce plasma? I have seen someone do this with microwaves, so why wouldn't it work way gamma? Heres the site that uses microwaves to produce plasma...
  13. D

    Product of three gamma matrices

    I need help proving the identity \gamma^{\mu}\gamma^{\nu}\gamma^{\rho}=\gamma^{\mu}g^{\nu\rho}+\gamma^{\rho}g^{\mu\nu}-\gamma^{\nu}g^{\mu\rho}+i\epsilon^{\sigma\mu\nu\rho}\gamma_{\sigma}\gamma^{5}
  14. R

    Solvent heat up due to gamma ray

    I am planning to use a gamma ray densitometer to measure the local concentration of slurry flow in a pipe loop. Since i am using an organic solvent(flammable) to make the slurry, i am worried that gamma ray passing through it will heat it up significantly and cause hazard. I would like to...
  15. C

    Gamma Spectroscopy: NAI vs Germanium Detector Accuracy

    What is a difference between NAI and Germanium detector in terms of accuracy?
  16. K

    Stopping or absorbing gamma rays

    Here is a question I have for you. Is there a way to stop gamma rays through a dense material that is transparent? If so what is this transparent material? Can someone help?
  17. O

    Gamma matrices out of pauli matrices - symmetry/group theory

    I'm reading an article (http://prb.aps.org/abstract/PRB/v82/i4/e045122) but I have some problems understanding certain definitions. The authors have introduced a basis of certain bands (four) and then continue to give the transformation matrices of the symmetry operators. One (rotation) of them...
  18. M

    Why is the gamma function equal to (n-1) ?

    Homework Statement Why is the equality below true? \Gamma(n) = (n-1)! Where \Gamma(n) = \int^{\infty}_{0} x^{n-1} e^{-x}dxHomework Equations The Attempt at a Solution I've read the article on wikipedia but I cannot understand it. Is there any special properties in calculus that I must know...
  19. K

    What Causes Alpha, Beta, and Gamma Rays?

    What CAUSES alpha, beta and gamma rays?
  20. W

    Deriving taylor series for v/c and gamma

    Homework Statement The velocity of a proton relative to our galaxy is vp/c = 1-(0.5*10^20), i.e. almost one. Such protons are actually observed. When velocity it very nearly one \gamma is very large. 1/\gamma is very small. Use Taylor series to show that for v almost one we have...
  21. Y

    Approximate formulas for integrals of Gamma functions?

    Suppose f(n,p)=integral(n!/(x! (n - x)!dx, for x from -1/2 to p) where n>1, p<n+1/2 Are approximate formulas known for this kind of integral? Empirically, f(n,n+1/2) seems to be close to 2^n More generally, I'm looking for approximate formulas for integrals of n!/(x1!x2!...xn!) over nice...
  22. I

    Hermitianity of gamma matrices

    Dear guys, I know that gamma matrices have some relations, like \gamma^0{\gamma^\mu}^\dagger\gamma^0 = \gamma^\mu \quad---(*) And I am wondering if this is representation independent? Consider, S\gamma^0S^{-1}S{\gamma^\mu}^\dagger S^{-1}S\gamma^0 S^{-1} = S\gamma^\mu S^{-1}...
  23. P

    Fermi Gamma Ray Telescope: Ruling Out Lorentz-Violating Theories

    The almost simultaneous detection of low energy and high energy photons puts tight constraints on models predicting linear dependence of c on E. But it's very far from ruling out quadratic dependence. My question is, why do Lorentz-violating theories commonly predict linear rather than quadratic...
  24. J

    Proof that gamma matrices form a complete basis

    Hi all, I'm interested in proving/demonstrating/understanding why the Dirac gamma matrices, plus the associated tensor and identity, form a complete basis for 4\times4 matrices. In my basic QFT course, the Dirac matrices were introduced via the Dirac equation, and we proved various...
  25. S

    What is incomplete gamma function? How are they evaluated

    What is incomplete gamma function? How are they evaluated? thks for any ans.
  26. Saladsamurai

    Incomplete Gamma Function Notation

    I am using a particular form of the incomplete gamma function (which I have never seen before) in my probability course. It is denoted: F(x;\alpha) = \int_0^x \frac{y^{\alpha - 1}e^{-y}}{\Gamma(\alpha)}\,dy\qquad(1)Question 1 Why the bounds in terms of 'x' ? I am just a little confused by...
  27. Saladsamurai

    Probability Poisson Process and Gamma Distribution

    Homework Statement The Attempt at a Solution Part (a) is no problem, it is simply P(X>10) = 1 - P(X<=10) which requires the use of tabulated cumulative poisson values. Part (b) is throwing for a loop. I know that I need to invoke the Gamma distribution since that is what the...
  28. V

    Understanding Gamma Ray Bursts: Can We Predict & Model?

    I've been reading up on Gamma-Ray bursts, and one thing which has struck me is that, when described through light curves, no burst appears to be the same. Given the phenomenon seem to be based on standard principles, that doesn't make sense to me - behavior cannot be random. Is there any way to...
  29. I

    Gamma 5 Dirac Matrice: Understanding Pseudo-Scalar

    Hi, i wonder somethin' when I see that definition of the matrice: \gamma^5=\gamma^0\gamma^1\gamma^2\gamma^3 I don't see why it is a pseudo-scalar.
  30. C

    Exploring Gamma Function: Practical Uses and Applications

    What are practical applications of the gamma function?
  31. L

    Unbiased Estimator for Gamma Distribution Parameter

    Homework Statement I need to show that c / (sample mean X) is unbiased for b, for some c. Where {X} are iid Gamma (a,b). Homework Equations N.A. The Attempt at a Solution I know how to show that (sample mean X) / a is unbiased for 1/b : 1) E(sample mean X / a) =...
  32. C

    Detection of Gamma Rays | Atomic Nucleus Decay

    Hi I'm studying decay of atomic nucleus. Alpha and beta rays are essentially particles and their path are easily traced. But high frequency gamma rays easily penetrate metal foils, and I wonder that how gamma rays are practically detected and measured in lab experiments? Is photo-electric...
  33. N

    Collapsed hypergiant forms a gamma ray pulsating black hole

    I am having a hard time understanding the theory that a collapsed hypergiant forms a gamma ray pulsating black hole. Can someone explain how the em radiation can travel so fast with such energy as to not only escape the event horizon but also do so with such intensity?
  34. Jonnyb42

    Potential for Gamma Ray Bursts to Pose a Threat to Earth?

    Are there any known celestial bodies that at any time could collapse and produce a GRB directed towards earth? I know WR 104 used to be one, but they discovered it to be off at an angle.
  35. M

    Are gamma rays produced in fusion reactions?

    Lots of articles and papers I read talk about the gamma rays produced during fusion reactions. And yet, when I look at equations for fuel cycles, the sum of the energies of the fusion products equals the total energy liberated. Since this implies that all of the energy released in the fusion...
  36. K

    How to read a Gamma Ray Spectrum

    For some of my work, I am investigating methods of scanning for nuclear material. As part of my study, I have run across Gamma Ray Spectroscopy: http://en.wikipedia.org/wiki/Gamma_spectroscopy" What I am having trouble with is reading a gamma ray spectrum (I am a software engineer with a...
  37. R

    Need help solving an equation involving the Gamma function.

    Homework Statement I am to solve the below stated equations for the variables \beta_{1}, \beta_{2}, and \eta, the rest are known given a positive noninteger value. But the problem is that I don't know how to deal with the gamma function as can be seen in my attempt. Should I use some...
  38. R

    What Would Happen if a Gamma Ray Burst Hit Our Sun?

    I enjoy asking myself random questions and then finding the answers online i.e. forums however, I could not find the answer to this one. What would happen if a gamma ray burst hit a star or specifically our sun?
  39. J

    Gamma Distribution Confidence Interval

    How would you go about finding the confidence interval for the parameters of the gamma distribution? I have had a look online and haven't found anything with the answer... Thanks
  40. L

    Does it take a long time or a short time for gamma rays to reach the photosphere

    What happens to gamma rays as they travel outward from the core of the sun through the sun? -also, does it take a long time or short time for neutrinos to reach the photosphere of the sun from the core of the sun? Why? The main question has nothing to do with the earth, it is more...
  41. D

    Calculating Gamma Ray Emission Recoil Speed

    Homework Statement A 67-Zn nucleus is at rest and in its first excited state, 93.3 keV above the ground state. The nucleus then decays to the ground state with the emission of a gamma ray. (One atomic mass unit is 931.5 MeV/c2.) What is the recoil speed of the nucleus? (You can assume...
  42. R

    Gamma matrices and lorentz algebra

    I'm trying to show that the generators of the spinor representation: M^{\mu \nu}=\frac{1}{2}\sigma^{\mu \nu}=\frac{i}{4}[\gamma^\mu,\gamma^\nu] obey the Lorentz algebra: [M^{\mu \nu},M^{\rho \sigma}]=i(\delta^{\mu \rho}M^{\nu \sigma}-\delta^{\nu \rho}M^{\mu \sigma}+\delta^{\nu \sigma}M^{\mu...
  43. Y

    Verify Gamma function, not a homework problem

    I want to verify the procedure of finding .\Gamma(n+p+1). with p =-ve. This is usually found in Bessel's equation. It is well talked about if p=+ve. But books I have don't even talking about in general how to find the series representation when p=-ve. I worked this out and I want to verify with...
  44. B

    Express the following integral in terms of the gamma function

    Homework Statement This is actually part of a probability problem I'm thinking about. I'm trying to find the nth moment of a certain random variable in terms of the gamma function, which is basically equivalent to solving the following integral or expressing it in terms of the gamma function...
  45. E

    How to Integrate the Complementary Error Function with an Exponential Decay?

    Hello, How to integrate the following integral (or what to use in the table of integrals): \int_0^{\infty}\underbrace{\mbox{erfc}\left(\sqrt{\gamma}\right)}_{Complementary Error Function}\,\mbox{e}^{-\gamma}\,d\gamma? Thanks in advance
  46. K

    How Do You Calculate Probabilities in a Standard Gamma Distribution?

    Homework Statement This is an example in my book with omitted steps. Suppose the reaction time X of a randomnly selected individual to a certain stimulus has a standard gamma distribution with alpha=2. When X is continuous P(2<=X<=5) = F(5;2)-F(3;2) = .960-.801 = .159 Homework...
  47. F

    Energy of resulting Gamma Rays after particle annihilation

    Homework Statement An electron and a positron are moving side by side in the +x direction at 0.50c when they annihilate each other creating two gamma rays. What is the energy of each photon? Homework Equations (mc2 + K+) + (mc2 + K-) = E1 + E2 The Attempt at a Solution I solved...
  48. S

    Calculating Distance for Equivalence of Gamma Ray and Solar Radiation Power

    Given the energy if sun were to instantly vaporize (using E = mc^2) = 2.7 x 10^47 J ( E = (mass of sun) * c^2) how far would one have to be from a gamma ray burst is order for the average power from it to be equivalent to the average power from the sun's radiation at the Earth (solar...
  49. S

    Distance from gamma ray?

    Given the energy if sun were to instantly vaporize (using E = mc^2) = 2.7 x 10^47 J ( E = (mass of sun) * c^2) how far would one have to be from a gamma ray burst in order for the average power from it to be equivalent to the average power from the sun's radiation at the Earth (solar...
  50. P

    How could you test that gamma rays spread out in different directions?

    ^ thanks
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