Beta Definition and 403 Threads

Assume that players A and B play a match where the probability that A will win each point is p, for B its 1-p and a player wins when he reach 11 points by a margin of >= 2The outcome of the match is specified by $$P(y|p, A_{wins})$$ If we know that A wins, his score is specified by B's score; he...

Specifically, this would be beta plus decay and not electron capture, and assumes an electrically neutral radionuclide. Since beta plus decay is the emission of a positron from the nucleus as a proton transmutes into a neutron, the resulting atom now has 1 less elementary charge than before, but...

I'm reviewing history of subatomic physics. By 1931AD the nuclear physics community had decided to propose the neutrino because they couldn't explain beta decay without it. Alpha and Gamma decays were more confined wrt the energy they would extract from the nucleus i.e. they had energy bands. By...

I 've been trying find ##\beta## as a function of ##\theta## for this linkage. It's quite the trigonometric mess. Start with the Law of Sines: $$ \frac{\sin \beta}{x} = \frac{\sin \varphi}{R} \implies \boxed{ x = R \frac{\sin \beta}{\sin \varphi} \tag{1} }$$ Relating angles: $$ \theta +...

An example of physical applications for the gamma (or beta) function(s) is http://sces.phys.utk.edu/~moreo/mm08/Riddi.pdf (I refer to the beta function related to the gamma function, not the other functions with this name) The applications in Wikipedia...

So, I've recently played around a little with the Gamma Function and eventually managed to find an expression for the Beta Function I have not yet seen. So I'm asking you guys, if you've ever seen this expression somewhere or if this is a new thing. Would be cool if it was, so here's the...

Hello all. I'm an undergraduate student looking to conduct an experiment with an isotope that undergoes beta decay. I am curious as to the degree to which the isotope geometry will reduce the energy of/deflect beta particles emitted from the isotope. By geometry, I mean the "shape" of the...

Hello! Can someone point me towards a derivation (whether with Fermi Golden rule, or full QFT calculations) of the decay rate for the neutrinoless double beta decay: $$\Gamma_{\beta\beta}^{0\nu} = G^{0\nu}|M^{0\nu}|^2<m_{\beta\beta}>^2$$ Thank you!

During beta decay an electron and neutrino are emitted at very high speeds. I thought that the electron and neutrino were the product of w boson decay but I recently learned w bosons are over 80 GeV worth of energy. My question is, where does this mass come from? I know that atoms get enough...

On Wikipedia one can read in the article Beta-binomial distribution: > It also approximates the binomial distribution arbitrarily well for > large ##\alpha## and ##\beta##. where 'It' refers to the beta-binomial distribution. What does 'arbitrarily well' mean here?

Hi all, I am currently studying renormalization group and beta functions. Since I'm not in school there is no one to fix my mis-understandings if any, so I'd really appreciate some feedback. PART I: I wrote this short summary of what I understand of the beta function: Is this reasoning...

Hi, Please note that I'm trying to understand it at very basic level. I'd really appreciate if you could help me with the queries below. I was reading this article, https://www.space.com/four-fundamental-forces.html, on the four fundamental forces of nature. Under the section The weak force...

I have calculated $Z$s as $$ \begin{aligned} Z_1 & = 1 + \frac{3g^2}{16\pi^2} \left[ 2 C(R) - \frac12 T(A) \right] \frac1{\epsilon} + \cdots, \\ Z_2 &= 1 + \frac{3g^2}{8\pi^2} C(R) \frac1{\epsilon} + \cdots, \\ Z_3 &= 1 + \frac{g^2}{24\pi^2} \left[ 5 T(A) - T(R) \right] \frac1{\epsilon} +...

Hello, When you have a beta decay you get the typical continuos spectrum representing counts against the kinetic energy of the electron. But what's the shape and how I get the spectrum of the kinetic energy of the neutrinos? Thanks

In the 4-dimensional representation of ##\beta##, ## \beta=\begin{pmatrix}\mathbf I & \mathbf 0 \\ \mathbf0 & -\mathbf I\end{pmatrix} ,## and we can suppose ## \alpha_i=\begin{pmatrix}\mathbf A_i & \mathbf B_i \\ \mathbf C_i & \mathbf D_i\end{pmatrix} ##. From the anti-commutation relation...

I was wondering if the resulting daughter element is ionized after the parent undergoes beta(or any other kind) of radioactive decay,

We have a question about highly energized beta particles (6 to 22 MeV). Is it possible fore this radiation to affect the nucleus of an isotope and not just ionize it? In our case a copper-65 and copper- 63 isotope become their unstable neighbors Cu-64 and Cu-62 due to the high beta radiation...

Recently, I received an email from my university notifying me that I have been selected to be a Phi Beta Kappa member. The email, to say the least, had a way to shower an excessive amount of praise and make a lot of promises related to how PBK (Phi Beta Kappa) can propel my chances of success in...

Well, gamma photons are pure energy, so surely a gamma photon would have the most energy since gamma-ray photons generally have energies greater than 100 keV. An alpha particle has the highest ionising power of the three on account of its mass, it roughly has a kinetic energy of 5 MeV, whereas...

Integral \int^{\pi}_0\sin^3xdx=\int^{\pi}_0\sin x \sin^2xdx=\int^{\pi}_0\sin x (1-\cos^2 x)dx=\frac{4 \pi}{3} Is it possible to write integral ##\int^{\pi}_0\sin^3xdx## in form of Beta function, or even Bessel function?

My idea was to consider first the structure of the matrix element and to see if there are any possible constraints that we could use for parametrization. If I am not mistaken, we are dealing with the hadronic decay governed by QCD which conserves parity. Since we have a derivative operator...

I am confused about the disintegration energies of beta minus and beta plus decay. Regarding beta minus decay, the textbook says that "the number of electron masses has been accounted for in Equation (12.38)." What does that mean? Usually the disintegration energy is simply the mass of the...

So far it seems to be limited to very few participants. It is SAE level 2 ("hands off"): The car drives itself but a human needs to watch it and needs to be able to take over at any time. Normally the phrase "self-driving" is only used for SAE levels 4 and 5 (you can sleep in the car, or you...

This problem really confused me, since I can't get the link between particles emitted(alpha and beta, but which are the differences between those?) and changes in mass and atomic number of the isotope. For this one, I can't really show you my attempt since there ain't one...

I was looking at the decay scheme (https://www-nds.iaea.org/relnsd/vcharthtml/VChartHTML.html) of ##^{112}Ag## which ##\beta##-decays to ##^{112}Cd##. ##Cd## is most likely left in an excited states, so it decays to its ground state by ##\gamma##-emission. As you can see there are tons of...

Hi! This is a very very noob question, but I am starting to get into particle physics and I don't understand the application of crossing symmetry in the inverse beta decay. Crossing symmetry says (from Griffiths) that, in a reaction "any of these particles can be 'crossed' over to the other...

Hi: Source: https://en.wikipedia.org/wiki/Radium Question 1: I think that the first statement suggests that it's the emission of alpha particles, beta particles and gamma rays which raises the temperature of radium sample; possibly on their way out from the sample, those particles and gamma...

I have the following integral (in Maple notation): Int(exp(c[0]*ln(y)/a[0]+c[1]*M*ln(M-y)/a[1]), y = 0 .. M); with (in Maple notation): 0<a[0], 0<a[1], 0<c[0], 0<c[1], 0<y, y<M, 0<M. What is the solution of this integral? I suspect that the solution has something to do with a beta distribution.

Suppose you are analyzing this image. The question to answer is: Explain why the alpha particle's path has a larger radius than either of the beta particle paths. Justify your answer using either momentum or charge-to-mass ratio. When you are answering this, suppose you know that , in...

Hello all, I've got a question on nuclear decay "reversal" in beta emitters. I've been researching the Cowan-Reines experiment, which used neutrinos to convert protons into neutrons. Recently, I found out that the particle which hits the proton need not necessarily be a neutrino in order to...

Alpha particle has two protons and neutrons so mass = 4. 4x = 238 -206. x = 1/4(238-206) = 8 Alpha decays. How would I determine the number of Beta decays? Since the mass doesn't change here.

I know you can use Moseley's law to calculate K Alpha X-ray energy. Can this law be used to calculate the K Beta energy? $$ \Delta E = (-13.6eV)(Z-1)^2\left(\frac{1}{n_{1}^2}-\frac{1}{n_{2}^2}\right) $$ I saw on http://minerva.union.edu/labrakes/PIXE_Physics100_Lecture3_F14.pdf that they use...

Hello everyone, We conducted an experiment with a strontium-90 source and some different thicknesses of lead. With 2.1mm of lead the count rate (corrected for the background) was 0.69 counts per second, 3.0mm 19.7cps 6.8mm 15.4cps 13.8mm 10.0 cps This would...

Hi, I'm reading some introductory notes about SR and I'm completely stuck at this problem. I imagine I should consider a transformation ##L## such that $$ \hat \epsilon^{\mu \nu \alpha \beta} = L^{\mu}_{\delta}L^{\nu}_{\gamma}L^{\alpha}_{\theta}L^{\beta}_{\psi} \hat \epsilon^{\delta \gamma...

I try solving it but the answer didn’t match

Hi All We know that beta decay is and ejection of an electron from nucleus, making a proton turn into a neutron (and a neutrino). Is it correct to say that is the weak force responsible for the increasing in the distance between electron and proton during this process (since the feel atracked...

I was learning about beta decay, and how a down quark decays into an up quark by emitting a W- boson which then becomes an electron and an electron antineutrino. I have two main questions - Firstly, how can the down quark be considered a fundamental particle, when it can break down to produce...

I have plastic which contains large amounts of Co-60 and Cs-137. I have already calculated the integrated (50k years) deposited dose from the gamma radiation using Monte-Carlo methods (SCALE). I am now interested in the contribution to deposited dose from the Beta emissions. -I am assuming that...

Hello, The relationship between entropy ##S##, the total number of particles ##N##, the total energy ##U(β)##, the partition function ##Z(β## and a yet to be defined constant ##β## is: $$S(\beta)=k_BN \cdot \ln(Z(\beta)) - \beta k_B \cdot U(\beta)$$ Which leads to: $$\frac{dS}{d\beta} =...

One of the main issues to send orbiters to (light years) faraway locations is the propulsion problem. Conventional chemical fuels cannot provide enough energy by weight to produce that much thrust. Nuclear fission provides a lot of energy by weight, but usually radiation energy doe not produce...

Problem Statement: In beta-decay, a gamma ray that is a fast moving electron is emitted due to the conversion of a neutron to a proton and an electron to increase the stability. As a result, the atomic number increases while the mass number remains the same. But when the atomic no. increases as...

How ,exactly, are gamma and beta radiations produced in electron accelerators? Is the process for gamma almost the same as X-ray in linear accelerators? What about beta?

Hi, I want to develop a Monte Carlo simulation to determine the temperature of a beta radioisotope (Sr-90) of a given mass for my master thesis in Computational Physics. I am rookie to simulations. How much time will take to develop such a code. Thnaks a lot

In Beta+ decay, a W+ boson is created and it decays into positron and electron neutrino. Mass of W+ boson is ~ 80 GeV/c^2, however, the total mass of positron and electron neutrino is very small compared to it. So, what happens to the rest of the mass? Is it converted into kinetic energy of...

Homework Statement Q- a positron emerges normally from a 4-mm thick slab of plastic (density= 1.14g/cm^3) with an energy of 1.62 MeV. What is the energy of the particle when it entered the slab? Homework Equations Range when 0< T <= 2.5 MeV: R= .412+T^[1.27-.0954*ln(T)] where T is kinetic...

This may be a pretty basic question ,but i'll through it out any way. As a project i built a muon detector from 2 matched PMTs and 2 4x6x1 plastic PVT scintillators. And pulse processing NIM modules. I was getting pretty good coincidence reading,some what less than predicted.ie ( 1...

I recently read about a beta decay isotope (Rhenium-187),whose half life was changed from 42 X 109 years to 33 years, just by stripping the nucleus of all it's electrons. Why does this allow for a faster decay, and does this apply to all beta decay nuclei, or just Rhenium 187?

I recently started learning about quarks and leptons and was wondering what happens to the fermions (specifically the quarks and leptons) during a beta decay. How is the electron/positron created and what causes the up quarks and down quarks to change flavours? If this is a bad question please...

Hey everyone, I've learned about double beta decay and neutrinoless double beta decay recently. So we have two "conditions" for decay, 2v decay and 0v decay. Now, to the question I have: There have been a lot of experiments measuring 2v decay rates, and there have been many experiments...