def price_element_real(self,nu,tau,q_value):
p1 = m.exp(-(nu**2-q_value**2)*tau/2)
p2 = (q_value*m.gamma((nu+q_value)/2))/(4*self.eta_q(nu=nu,eigenval=q_value,b=self.b)*m.gamma(1+q_value))
const = (2*self.k)**((nu+3)/2)*m.exp(-1/(4*self.k))
w1 = m.whitw(-(nu+3)/2,q_value/2,1/(2*self.k))
m1 = m.whitm((1-nu)/2,q_value/2,1/(2*self.b))
return p1 * p2 * const * w1 * m1
def price_element_imag(self,nu,tau,p_value):
p1 = m.exp(-(nu**2+p_value**2)*tau/2)
p2 = (p_value*m.gamma(complex(nu/2,p_value/2)))/(4*self.xi_p(nu=nu,eigenval=p_value,b=self.b)*m.gamma(complex(1,p_value)))
const = (2*self.k)**((nu+3)/2)*m.exp(-1/(4*self.k))
w1 = m.whitw(-(nu+3)/2,complex(0,p_value/2),1/(2*self.k))
m1 = m.whitm((1-nu)/2,complex(0,p_value/2),1/(2*self.b))
return p1 * p2 * const * w1 * m1
def __init__(self, system_params, wf_params, potential_params, r):
system = NuclearSystem(wf_params, system_params, potential_params)
system.calculate_energy()
self.bound_energy = system.energies[0]
wf = WaveFunction(wf_params)
radial_wavefunctions = r * np.matmul(system.C.transpose(), wf.phi(r))
self.bound_wavefunction = np.abs(radial_wavefunctions[0, :])
k = np.sqrt(-2 * self.bound_energy * system.mass / system.const1)
eta = system.mass * system.z1 * system.z2 * system.const2 / k / system.const1
self.whitw_ = np.array(
[whitw(-eta, wf.l + 0.5, 2 * k * r_i) for r_i in r], dtype=float)
def psi(index, variable, b, a, beta):
if b == 0:
if beta < 0:
return math.pow(variable, 0.5) * besseli(
v(beta), sqrt(2 * index * q(a, beta, variable)))
else:
return math.pow(variable, 0.5) * besselk(
v(beta), sqrt(2 * index * q(a, beta, variable)))
else:
if beta < 0:
return math.pow(variable, beta + 0.5) * math.exp(
0.5 * eps(b, beta) * h(b, a, beta, variable)) * whitm(
k(b, beta, index), m(beta), h(b, a, beta, variable))
else:
return math.pow(variable, beta + 0.5) * math.exp(
0.5 * eps(b, beta) * h(b, a, beta, variable)) * whitw(
k(b, beta, index), m(beta), h(b, a, beta, variable))
def xi_p(self, eigenval):
nu = self.nu()
func = lambda x: m.whitw((1 - nu) / 2, complex(0, x / 2), 1 / (2 * self.b))
return complex(derivative(func, eigenval, dx=1e-12))
def eta_q(self, eigenval):
nu = self.nu()
f = lambda x: m.whitw((1 - nu) / 2, x / 2, 1 / (2 * self.b))
return complex(-derivative(f, eigenval, dx=1e-12))
def xi_p(self,nu,eigenval,b):
f = lambda x: m.whitw((1-nu)/2,complex(0,x/2),1/(2*b))
return complex(derivative(f,eigenval,dx=1e-12))
def eta_q(self,nu,eigenval,b):
f = lambda x: m.whitw((1-nu)/2,x/2,1/(2*b))
return complex(-derivative(f,eigenval,dx=1e-12))