What is Yukawa potential: Definition and 22 Discussions

In particle, atomic and condensed matter physics, a Yukawa potential (also called a screened Coulomb potential) is a potential of the form










{\displaystyle V_{\text{Yukawa}}(r)=-g^{2}{\frac {e^{-\alpha mr}}{r}},}
where g is a magnitude scaling constant, i.e. is the amplitude of potential, m is the mass of the particle, r is the radial distance to the particle, and α is another scaling constant, so that




{\displaystyle r\approx {\tfrac {1}{\alpha m}}}
is the approximate range. The potential is monotonically increasing in r and it is negative, implying the force is attractive. In the SI system, the unit of the Yukawa potential is (1/meters).
The Coulomb potential of electromagnetism is an example of a Yukawa potential with the



{\displaystyle e^{-\alpha mr}}
factor equal to 1, everywhere. This can be interpreted as saying that the photon mass m is equal to 0.
In interactions between a meson field and a fermion field, the constant g is equal to the gauge coupling constant between those fields. In the case of the nuclear force, the fermions would be a proton and another proton or a neutron.

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  1. Riccardo Marinelli

    A Boundary conditions of eigenfunctions with Yukawa potential

    Hello, I was going to solve numerically the eigenfunctions and eigenvalues problem of the schrödinger equation with Yukawa Potential. I thought that the Boundary condition of the eigenfunctions could be the same as in the case of Coulomb potential. Am I wrong? In that case, do you know some...
  2. Riccardo Marinelli

    Initial condition of Wave functions with Yukawa Potential

    Hello, I was going to solve with a calculator the eigenvalues problem of the Schrödinger equation with Yukawa potential and I was thinking that the boundary conditions on the eigenfunctions could be the same as in the case of Coulomb potential because for r -> 0 the exponential term goes to 1...
  3. M

    Yukawa Potential: Find Value of Parameter 'a

    So this is the problem: My only point of confusion right now is in what the value of a is... I'm having trouble finding it anywhere, and online stuff about the yukawa potential just states that it's a parameter. Thanks for any help! Edit: It might be worth noting that gamma equals kq1q2.
  4. L

    I Estimate of ground state energy for the Yukawa potential

    I’ve seen the uncertainty principle used to calculate the ground state energy for things like hydrogen and the harmonic oscillator, but can this be done for the Yukawa potential where you have an exponential?
  5. Phi6er

    A What is the value of the pion-nucleon coupling constant?

    Links for context: 1. https://en.wikipedia.org/wiki/Yukawa_potential 2. https://en.wikipedia.org/wiki/Yukawa_interaction#Classical_potential I'm working on my BSc right now and I'm solving the energies of 2 nucleon systems (so basically just deuteron) by treating them as non-relativistic two...
  6. Warda Anis

    Perturbation for Yukawa Potential

    Homework Statement The photon is normally assumed to have zero rest mass. If the photon did have a tiny mass, this would alter the potential energy the electron feels in the hydrogen atom (due to the Coulomb interaction with the proton). The potential then becomes yukawa potential...
  7. S

    Yes, your working is correct so far. Keep going with the rest of the problem!

    Homework Statement (a) Calculate the equations of motion for a massive vector ##A_{\mu}## from the Lagrangian ##\mathcal{L}=-\frac{1}{4}F_{\mu\nu}^{2}+\frac{1}{2}m^{2}A_{\mu}^{2}-A_{\mu}J_{\mu},## where ##F_{\mu\nu}=\partial_{\mu}A_{\nu}-\partial_{\nu}A_{\mu}##. Assuming...
  8. P

    Problem with Fourier bessel transform of Yukawa potential

    Hello, I am trying to find Fourier Bessel Transform (i.e. Hankel transform of order zero) for Yukuwa potential of the form f(r) = - e1*e2*exp(-kappa*r)/(r) (e1, e2 and kappa are constants). I am using the discrete sine transform routine from FFTW ( with dst routine). For this potential...
  9. N

    Angular momentum & Energy using Yukawa's potential

    Hello there! I was doing my Gravitation problems and I found this problem that I'm unable to solve. Yukawa's theory for nuclear forces states that the potential energy corresponding to the attraction force produced by a proton and a neutron is: U(r) = \frac{k}{r}e^{-\alpha r},\ k<0,\ \alpha > 0...
  10. U

    Yukawa potential and the Klein Gordon

    Homework Statement a)Show that the yukawa potential is a valid static-field euation b)Show this solution also works Homework EquationsThe Attempt at a Solution Part (a) Using the relation given, I got LHS = \frac{e^{-\mu r}}{r} \left[ (m^2 - \mu^2) - \frac{2\mu}{r} - \frac{2}{r^2}...
  11. Breo

    Yukawa Potential derivation

    Please, can anyone explain me the steps made in the resolution of this integral? http://en.wikipedia.org/wiki/Common_integrals_in_quantum_field_theory#Yukawa_Potential:_The_Coulomb_potential_with_mass
  12. C

    Why does the integral of the Yukawa potential converge for q/alpha >= 1?

    While preparing for an exam I came across an integral of the form \int_0^\infty dx\;e^{-\alpha x}\sin{q x} with q,\alpha>0. My question will be regarding my solution to the integral which I present as follows: I expand the sine function as a Taylor series and differentiate with respect to...
  13. C

    Two Questions: Yukawa Potential and Weak Force

    1. Yukawa Potential So reading about the yukawa potential I notice that the constant k is related to the inverse of the effective distance of the force from what I've been reading. Thing is everything I read about the strong force states it has infinite range but simply has a maximum potential...
  14. A

    Yukawa potential energy function

    Homework Statement This is not yet an attempt at solving a problem. I just need confirmation on that I'm on the right track. So, I am supposed to derive an expression for the radial force function from the given Yukawa-function. Homework Equations U(r) = -(r/r0)U0 exp-(-r/r0) The...
  15. H

    Yukawa Potential Homework: Sketch, Schrodinger Eq & Perturbation Theory

    Homework Statement The Yukawa potential is given by: V_{\gamma}(r) = -\frac{q^{2}}{4\pi \epsilon_{0}r}e^{-\gamma r} Where \gamma is a constant. This describes a screened Coulomb potential. I. Sketch the radial dependence of this potential. II. State the radial Schodinger...
  16. D

    Bound states of Yukawa potential

    Say you have a Yukawa potential (a.k.a. screened coulomb potential) V(r) = -\frac{e^2}{r}e^{-rq} where q is the inverse screening length, how would you find the critical q for having bound states? I'm working on reproducing N.F. Mott's argument about the critical spacing of a lattice of...
  17. W

    Explanation of Yukawa potential

    I would appreciate an explanation of Yukawa potential
  18. R

    Yukawa Potential Homework: Calculating Meson Energy Levels

    Homework Statement I have been given the following assignment: "The meson moves within the nucleus under the influence of a screened Coulomb potential known as the Yukawa potential. Given that the mass of a meson is about 270 times the mass ot the electron and that the effective extent of...
  19. K

    Exploring Yukawa Potential with Coupling Constant 0.3

    If I had was given a yukawa potential of the form: \text{YL}[\text{r$\_$}]=\left(\left.g_L{}^{\wedge}2\right/r\right) \text{Exp}\left[-\mu _Lr (c/\hbar )\right] I put the c/h in the exponent to make it unitless, but what do I do about the outside? i'm given the coupling constant is 0.3. Just...
  20. A

    Derivation of Yukawa potential: quandry

    Can someone provide some help with a derivation in Peskin and Schroeder (equation 4.126, p.122): V(\bold{x}) = \int \frac{d^3q}{(2\pi)^3} \frac{-g^2}{|\bold{q}|^2+m^2}e^{i\bold{q}\cdot\bold{r}} = \frac{-g^2}{4\pi^2}\int_0^\infty dq\; q^2\; \frac{e^{iqr}-e^{-iqr}}{iqr}}...
  21. T

    Yukawa Potential: Analyzing Shapes & Angular Momentum

    Homework Statement A particle moves under the Yukawa Potential of (-alpha)*exp(-kr)/r where k is real. Discuss all possible shapes of the effective potential. At what values of angular momentum L can the particle move in the potential with finite/bounded motion The Attempt at a Solution The...
  22. F

    Yukawa potential ,confused

    could anyone help me also with this question as i am very confused,i have read my notes but i really have a problem with this stuff making anysense, any help would be appreciated thanks:redface: question 6)) The Yukawa potential is given by V°(gamma)(r) = (q)^2/{ 4(pi)(eo)0r...