Add examples

[ohno]

Meng, Wang, Oka (2024) https://doi.org/10.48550/arXiv.2404.01238

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

mass   = [1.836, 1.836]
σσ   = -3
l      = 0
m      = 0
Λ     = 0.8321
λ     = 0.1653
p      = 1
κ     = 0.5069
κκ   = 1.8609
A      = 1.6553
B      = 0.2204
μ     = 1 / (1/mass[1] + 1/mass[2]) # reduction mass
r₀     = A*(2*mass[1]*mass[2]/(mass[1]+mass[2]))^(-B)

H = Hamiltonian(
    RestEnergy(c=1, m=1.836),
    RestEnergy(c=1, m=1.836),
    NonRelativisticKinetic(ℏ=1, m=μ),
    CoulombPotential(-κ),
    LinearPotential(λ),
    ConstantPotential(-Λ),
    GaussianPotential(2*π*κκ/3/mass[1]/mass[2] / ((sqrt(π)*r₀)^3) * σσ, 1/r₀^2),
)

solve(
    H,
    BasisSet(
        SimpleGaussianBasis(13.00773),
        SimpleGaussianBasis(1.962079),
        SimpleGaussianBasis(0.444529),
        SimpleGaussianBasis(0.1219492),
    ),
)

[ohno]

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:

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

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)