我试图绘制相对于光子能量 的横截面，但对于在同一轴上$h\nu$$\gamma = 1.0, 1.2, 2.0$

$\sigma = \left[\left(\frac{\xi_{eff}}{\xi_{0}}\right)^2 \frac{n_r}{\varepsilon}\right]\frac{4\pi}{3}\alpha_{fs}h\nu|\frac{1}{2}\frac{R}{2^\beta \Gamma(\beta + 1)}\int_{0}^\infty \left(\gamma\rho\right)^{2\beta}e^{-\frac{1}{2}\gamma^2\rho^2}\gamma^2\rho^2d\rho|^{2} \frac{\hbar\Gamma_f}{\left(\lambda_{01} - \lambda_{00} - h\nu\right)^2 + \left(\hbar\Gamma_f\right)^2}$

在哪里

$\lambda_{00} = 2\gamma^2\left(\beta + 1\right) - \frac{\gamma^4}{4}$

e $\lambda_{01} = 2\gamma^2\left(\beta + 3\right) - \frac{\gamma^4}{4}$

是最终态和基态的能量，并且 $\beta =\sqrt{ \left(m - \Phi\right)^2) - \frac{\gamma^4}{4} }$

这是我在 Python 中解决这个问题的尝试：

from scipy.integrate import quad
import numpy as np
from scipy.special import gamma
from scipy.constants import  pi, alpha
import matplotlib.pyplot as plt

#Constants
epsilon = 13.1 #dielectric constant of the material
gamma_C = 0.5 # donor impurity linewidth 
nr = 3.2 #refractive index of semiconductor
m = 0 # magnetic number
flux = 0  # Phi in eqn 8 magnetic flux
R = 5  #radius of the qunatum ring in nm
r = np.linspace(0, 6 * R)
rho = r / R
m_0 = 0.0067*0.511 # electron effective mass
h = 4.13e-15 # Planck constant in eV
hbar =  6.58e-16 # reduced Planck constant in eV
#Photon energy
h_ni = np.linspace(0, 100/h) #in eV


#Function that calculates the integrand
def func(rho, gama):
    beta = np.sqrt((m - flux)**2 + gama**4/4)
    return ((gama * rho)**2*beta * np.exp(-1/2*(gama * rho)**2) 
         * (gama * rho)**2/2   ) 

def cross_section(h_ni, gama):
    #function that calculates the photoionisation cross sectio
    beta = np.sqrt((m - flux)**2 + gama**4/4)
    Ei = gama**2*(1+beta)-gama**4/2
    Ef = gama**2*(3+beta)-gama**4/2

    return ((nr/epsilon) * 4*pi/3 * alpha * h_ni * 
          R ** 2 / (2**beta * gamma(beta + 1)) * 
          abs(quad(func, 0, np.infty))**2  *
            hbar*gamma_C/(((Ef-Ei-h_ni))**2 + ( hbar*gamma_C)**2))

#Plot

plt.figure();plt.clf()

for gama in [1.0, 1.5, 2.0]:
    plt.plot(h_ni, cross_section(h_ni, gama))

但我收到以下错误

   TypeError: func() missing 1 required positional argument: 'gama'

我该如何解决这个问题？欢迎任何帮助。