Add examples #39

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1. ohno commented on Aug 19, 2026

   

   ohno

   on Aug 19, 2026

   Last edited by ohno

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   Discard the above code. Please add the following three examples to the section of GEM.

   Kim, Hiyama, Oka, Suzuki (2020)

   • URL: https://doi.org/10.48550/arXiv.2003.03525
   • System: $\Lambda_c (1 / 2^{+})$
   • Mass: 2286
   • Hamiltonian:

   $$\hat{H} = \frac{\pmb{p}^2}{2 \mu} + M_Q + M_d - \frac{\alpha}{r} + \lambda r + C$$

   Mqq = 0.725
   Mc = 1.750
   μ = 1 / (1/Mqq + 1/Mc)
   α = 0.06 / μ
   λ = 0.165
   C = -0.83116597
   
   H = Hamiltonian(
       RestEnergy(c=1, m=Mqq),
       RestEnergy(c=1, m=Mc),
       Kinetic(hbar=1, m=μ),
       Coulomb(-α),
       Linear(λ),
       Constant(C),
   )
   
   BS = GeometricBasisSet(GaussianBasis, 0.01, 9.0, 40)
   
   solve(H, BS)
   

   Meng, Wang, Oka (2024)

   • URL: https://doi.org/10.48550/arXiv.2404.01238
   • System: $\eta_c(1S)$
   • Mass: 3005 MeV
   • Hamiltonian:

   $$\hat{H} = \frac{\pmb{p}^2}{2\mu} + m_1 + m_2 - \frac{\kappa}{r} + \lambda r - \Lambda+\frac{2 \pi \kappa^{\prime}}{3 m_1 m_2} \frac{\exp(-r^2 / r_0^2)}{\pi^{3 / 2} {r_0}^3} \boldsymbol{\sigma}_1 \cdot \boldsymbol{\sigma}_2$$

   m₁     = 1.836
   m₂     = 1.836
   σσ   = -3
   l      = 0
   m      = 0
   Λ     = 0.8321
   λ     = 0.1653
   p      = 1
   κ     = 0.5069
   κ_    = 1.8609
   A      = 1.6553
   B      = 0.2204
   μ     = 1 / (1/m₁ + 1/m₂) # reduction mass
   r₀     = A*(2*m₁*m₂/(m₁+m₂))^(-B)
   
   H = Hamiltonian(
       RestEnergy(c=1, m=m₁),
       RestEnergy(c=1, m=m₂),
       Kinetic(hbar=1, m=μ),
       Coulomb(-κ),
       Linear(λ),
       Constant(-Λ),
       Gaussian(2*π*κκ/3/m₁/m₂ / ((sqrt(π)*r₀)^3) * σσ, 1/r₀^2),
   )
   
   BS = GeometricBasisSet(GaussianBasis, 0.1, 80.0, 20)
   
   solve(H, BS)
   

   Arifi, Happ, Ohno, Oka (2024)

   • URL: https://doi.org/10.48550/arXiv.2401.07933
   • System: $\eta_c(1S)$
   • Mass: 3019
   • Hamiltonian:

   $$\hat{H} = \sqrt{m_q^2+\pmb{k}^2} + \sqrt{m_{\bar{q}}^2 + \pmb{k}^2} + a + b r - \frac{4 \alpha_s}{3 r} + \frac{32 \alpha_s \tilde{\delta}^3(r)}{9 m_q m_{\bar{q}}}\left(\pmb{S}_q \cdot \pmb{S}_{\bar{q}}\right)$$

   m₁  = 1.515
   m₂  = 1.515
   αₛ  = 0.285
   Λ  = 1.437
   a   = -0.189
   b   = 0.092
   μ  = 1/(1/m₁ + 1/m₂)
   λ = Λ * sqrt(μ)
   SS  = -3/4
   
   H = Hamiltonian(
     RestEnergy(m = m₁),
     RestEnergy(m = m₂),
     RelativisticKinetic(m = m₁),
     RelativisticKinetic(m = m₂),
     Constant(constant = a),
     Linear(coefficient = b),
     Coulomb(coefficient = -4αₛ/3),
     Gaussian(coefficient = 32π * αₛ * (λ / sqrt(π))^3 / (9 * m₁ * m₂) * SS, exponent=λ^2),
   )
   
   BS = GeometricBasisSet(GaussianBasis, 0.358, 2.720, 10)
   
   solve(H, BS)
   
2. ohno

   changed the title [-]Add charmonium example[/-] [+]Add examples[/+] on Aug 20, 2026
3. ohno

   added a commit that references this issue on Sep 16, 2026

   Document issue #39 hadron spectroscopy examples in GEM

   c2df553
4. ohno

   closed this as completedin #56on Sep 16, 2026
5. ohno commented on Sep 16, 2026

   

   ohno

   on Sep 16, 2026

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   Remove AI slop
6. ohno

   reopened this on Sep 16, 2026