def turnDebugMode(cls, on=True):
if on:
cls.DEBUG_MODE = True
else:
cls.DEBUG_MODE = False
XLog.resetLog()
XLog('root')
def _LScoupled_MatrixElement(self):
if not hasattr(self, "_kin_factor"):
## Real constant, but COM taurus multiplies by 2/(A*b^2)
# self._kin_factor = (Constants.HBAR_C**2) / (
# 2 * Constants.M_MEAN
# * (self.PARAMS_SHO[SHO_Parameters.b_length]**2)
# * self.PARAMS_SHO[SHO_Parameters.A_Mass])
self._kin_factor = 0.5 * (Constants.HBAR_C**2) / Constants.M_MEAN #= 20.74
# self._kin_factor = 1
# self._kin_factor = 1 / (self.PARAMS_SHO[SHO_Parameters.A_Mass]
# * (self.PARAMS_SHO[SHO_Parameters.b_length]**2)
# * 2 * Constants.M_MEAN)
fact = safe_wigner_6j(self.bra.l1, self.bra.l2, self.L_bra,
self.ket.l2, self.ket.l1, 1)
fact *= ((-1)**(self.ket.l1 + self.bra.l2 + self.L_bra))
nabla_1 = self._nablaReducedMatrixElement(1)
nabla_2 = self._nablaReducedMatrixElement(2)
if self.DEBUG_MODE:
XLog.write("Lme", nabla1=nabla_1, nabla2=nabla_2, f=fact,
kin_f= self._kin_factor)
return fact * self._kin_factor * nabla_1 * nabla_2
def _getQRadialNumbers(self, exchanged):
""" Auxiliary method to exchange the quantum numbers
returns:
bra_l1, bra_l2, ket_l1, ket_l2, <tuple>(bra1, bra2, ket1, ket2)
"""
if exchanged:
l1, l2 = self.ket.l2, self.ket.l1
l1_q, l2_q = self.bra.l2, self.bra.l1
qn_cc1 = QN_1body_radial(self.bra.n2, self.bra.l2) # conjugated
qn_cc2 = QN_1body_radial(self.bra.n1, self.bra.l1) # conjugated
qn_3 = QN_1body_radial(self.ket.n2, self.ket.l2)
qn_4 = QN_1body_radial(self.ket.n1, self.ket.l1)
if self.DEBUG_MODE:
XLog.write('Ltens', t="EXCH", wf=(qn_cc1, qn_cc2, qn_3, qn_4))
else:
l1, l2 = self.ket.l1, self.ket.l2
l1_q, l2_q = self.bra.l1, self.bra.l2
qn_cc1 = QN_1body_radial(self.bra.n1, self.bra.l1) # conjugated
qn_cc2 = QN_1body_radial(self.bra.n2, self.bra.l2) # conjugated
qn_3 = QN_1body_radial(self.ket.n1, self.ket.l1)
qn_4 = QN_1body_radial(self.ket.n2, self.ket.l2)
if self.DEBUG_MODE:
XLog.write('Ltens', t="DIR", wf=(qn_cc1, qn_cc2, qn_3, qn_4))
return l1_q, l2_q, l1, l2, (qn_cc1, qn_cc2, qn_3, qn_4)
def _LScoupled_MatrixElement(self):
"""
<(n1,l1)(n2,l2) (LS)| V |(n1,l1)'(n2,l2)'(L'S') (T)>
"""
aux_sum = 0.0
# Sum of gaussians and projection operators
for i in range(self.numberGaussians):
self._part = i
# Radial Part for Gaussian Integral
radial_energy = self.centerOfMassMatrixElementEvaluation()
if self.DEBUG_MODE:
XLog.write(
'BB',
mu=self.PARAMS_FORCE[i][CentralMEParameters.mu_length])
prod_part = radial_energy * self.PARAMS_FORCE[i].get(
CentralMEParameters.constant)
aux_sum += prod_part
if self.DEBUG_MODE:
XLog.write('BB', radial=radial_energy, val=prod_part)
return aux_sum
def __init__(self, bra, ket, run_it=True):
self.__checkInputArguments(bra, ket)
self.bra = bra
self.ket = ket
self.J = bra.J
self.T = bra.T
self.exchange_phase = None
self.exch_2bme = None
if (bra.J != ket.J) or (bra.T != ket.T):
print("Bra JT [{}]doesn't match with ket's JT [{}]"
.format(bra.J, bra.T, ket.J, ket.T))
self._value = 0.0
else:
self._nullConditionForSameOrbit()
if not self.isNullMatrixElement and run_it:
# evaluate the normal and antisymmetrized me
if self.DEBUG_MODE:
XLog.write('nas', bra=bra.shellStatesNotation,
ket=ket.shellStatesNotation, J=self.J, T=self.T)
self._run()
def saveXLog(self, title=None):
#raise MatrixElementException("define the string for the log xml file (cannot have ':/\\.' etc)")
if title == None:
title = 'me'
XLog.getLog("{}_({}_{}_{}).xml"
.format(title,
self.bra.shellStatesNotation.replace('/2', '.2'),
self.__class__.__name__,
self.ket.shellStatesNotation.replace('/2', '.2')))
def saveXLog(self, title=None):
if title == None:
title = 'me'
auxT_ = 'T{}'.format(self.T) if hasattr(self, 'T') else ''
XLog.getLog("{}_({}_{}_{})J{}{}.xml"
.format(title,
self.bra.shellStatesNotation.replace('/2', '.2'),
self.__class__.__name__,
self.ket.shellStatesNotation.replace('/2', '.2'),
self.J, auxT_))
def _L_tensor_MatrixElement(self, exchanged=False):
b = self.PARAMS_SHO.get(SHO_Parameters.b_length)
l1_q, l2_q, l1, l2, qqnn = self._getQRadialNumbers(exchanged)
qn_cc1, qn_cc2, qn_3, qn_4 = qqnn
if ((l1 + l2) + (l1_q + l2_q)) % 2 == 1:
return 0
factor = np.sqrt(
(2 * self.L_bra + 1) * (2 * self.L_ket + 1) * (2 * l1 + 1) *
(2 * l2 + 1) * (2 * l1_q + 1) * (2 * l2_q + 1))
factor /= 4 * np.pi * (b**6)
# Factor include the effect of oscillator length b!= 1
aux0 = ((-1)**self.L_ket) * np.sqrt(
2 * l2 *
(l2 + 1)) * (safe_3j_symbols(l1_q, l2_q, self.L_bra, 0, 0, 0) *
safe_3j_symbols(l2, l1, self.L_ket, 1, 0, -1) *
safe_3j_symbols(1, self.L_bra, self.L_ket, 1, 0, -1))
aux1 = ((-1)**self.L_bra) * np.sqrt(2 * l1_q * (l1_q + 1)) * (
safe_3j_symbols(l1_q, l2_q, self.L_bra, 1, 0, -1) *
safe_3j_symbols(l2, l1, self.L_ket, 0, 0, 0) *
safe_3j_symbols(1, self.L_ket, self.L_bra, 1, 0, -1))
aux2 = ((-1)**(self.L_bra + self.L_ket + l1 + l2)) \
* np.sqrt(l1_q*(l1_q + 1) * l2*(l2 + 1)) * (
safe_3j_symbols(l1_q, l2_q, self.L_bra, 1,0,-1)
* safe_3j_symbols(l2, l1, self.L_ket, 1,0,-1)
* safe_3j_symbols(1, self.L_ket, self.L_bra, 0,1,-1))
if self.DEBUG_MODE:
XLog.write('Ltens', fact=factor, aux0=aux0, aux1=aux1, aux2=aux2)
_RadialIntegralsLS.DEBUG_MODE = True
if not self.isNullValue(aux0):
aux0 *= _RadialIntegralsLS.integral(1, qn_cc1, qn_cc2, qn_3, qn_4,
b)
if not self.isNullValue(aux1):
aux1 *= _RadialIntegralsLS.integral(1, qn_4, qn_3, qn_cc2, qn_cc1,
b)
if not self.isNullValue(aux2):
aux2 *= _RadialIntegralsLS.integral(2, qn_cc1, qn_cc2, qn_3, qn_4,
b)
if self.DEBUG_MODE:
XLog.write('Ltens', value=factor * (aux0 + aux1 + aux2))
return factor * (aux0 + aux1 + aux2)
def _r_dependentIntegral(self, No2, A, Z, alpha):
""" Radial integral for (factors omitted)
exp(-(alpha + 2)r**2) * r^2*No2 * fermi_density
:No2 stands for N over 2, being N = 2*(p+p') + sum{l} + 2
"""
if self._DENSITY_APROX:
cte = 2**(No2 + 1.5)
else:
## TODO (MOVED): pon la constante del llenado aqui tras la prueba
pass
cte = 2 * ((alpha + 2)**(No2 + 0.5))
aux = GaussianQuadrature.laguerre(self._auxFunction_static,
(100, 0.5), No2, A, Z, alpha)
if self.DEBUG_MODE: XLog.write("Ip_q", Lag_int=aux)
return aux / cte
def _angularRecouplingCoefficiens(self):
"""
:L for the Bra <int>
:S for the Bra <int>
:L for the Ket <int>
:S for the Ket <int>
Return
:null_values <bool> To skip Moshinky transformation
:recoupling_coeff <float>
"""
# j attribute is defined as 2*j
w9j_bra = safe_wigner_9j(
*self.bra.getAngularSPQuantumNumbers(1, j_over2=True),
*self.bra.getAngularSPQuantumNumbers(2, j_over2=True),
self.L_bra, self.S_bra, self.bra.J)
if not self.isNullValue(w9j_bra):
recoupling = np.sqrt((self.bra.j1 + 1)*(self.bra.j2 + 1)) * w9j_bra
if self.DEBUG_MODE:
re1 = ((self.bra.j1 + 1)*(self.bra.j2 + 1)*(2*self.S_bra + 1)
*(2*self.L_bra + 1))**.5 * w9j_bra
XLog.write('recoup', Lb=self.L_bra, Sb=self.S_bra, re_b=re1)
w9j_ket = safe_wigner_9j(
*self.ket.getAngularSPQuantumNumbers(1, j_over2=True),
*self.ket.getAngularSPQuantumNumbers(2, j_over2=True),
self.L_ket, self.S_ket, self.ket.J)
if not self.isNullValue(w9j_ket):
recoupling *= w9j_ket
recoupling *= np.sqrt((self.ket.j1 + 1)*(self.ket.j2 + 1))
recoupling *= np.sqrt((2*self.S_bra + 1)*(2*self.L_bra + 1)
*(2*self.S_ket + 1)*(2*self.L_ket + 1))
if self.DEBUG_MODE:
re2 = ((self.ket.j1 + 1)*(self.ket.j2 + 1)*(2*self.S_ket + 1)
*(2*self.L_ket + 1))**.5 * w9j_ket
XLog.write('recoup', Lk=self.L_ket, Sk=self.S_ket, cts=re1*re2)
return (False, recoupling)
return (True, 0.0)
def _integral(self, wf1_bra, wf2_bra, wf1_ket, wf2_ket, b_length, A, Z, alpha):
n1_q, l1_q = wf1_bra.n, wf1_bra.l
n2_q, l2_q = wf2_bra.n, wf2_bra.l
n1, l1 = wf1_ket.n, wf1_ket.l
n2, l2 = wf2_ket.n, wf2_ket.l
self.b_length = b_length ## keep for _DensityProfile
if (l1 + l2 + l1_q + l2_q) % 2 == 1:
raise IntegralException("(l1 + l2 + l1_q + l2_q) not even")
sum_ = 0
if self.DEBUG_MODE:
XLog.write("R_int", a=wf1_bra, b=wf2_bra, c=wf1_ket, d=wf2_ket)
# for p1 in range(n1_q+n2_q +1):
for p1 in range(n1_q+n1 +1):
ket_coeff = self._B_coeff(n1_q, l1_q, n1, l1, p1)
# ket_coeff = self._B_coeff(n1_q, l1_q, n2_q, l2_q, p1)
if self.DEBUG_MODE: XLog.write("Ip", p1=p1, ket_C=ket_coeff)
for p2 in range(n2_q+n2 +1):
bra_coeff = self._B_coeff(n2_q, l2_q, n2, l2, p2)
# for p2 in range(n1+n2 +1):
# bra_coeff = self._B_coeff(n1, l1, n2, l2, p2)
# l1 + l2 + l1_q + l2_q is even
No2 = (p1 + p2) + ((l1 + l2 + l1_q + l2_q)//2) + 1
I_dd = self._r_dependentIntegral(No2, A, Z, alpha)
if self.DEBUG_MODE:
XLog.write("Ip_q", p2=p2, bra_C=bra_coeff, N=No2, Idd=I_dd)
aux = ket_coeff * bra_coeff * I_dd
sum_ += aux
if self.DEBUG_MODE: XLog.write("Ip_q", val= aux)
norm_fact = 1 / ((4*np.pi)**alpha * b_length**(3)) # b_length**(3*(1 - 2))
if not self._DENSITY_APROX:
norm_fact /= b_length**(3*alpha)
if self.DEBUG_MODE:
XLog.write("R_int", sum=sum_, norm=norm_fact, value=norm_fact*sum_)
return norm_fact * sum_
def _LScoupled_MatrixElement(self):
"""
<(n1,l1)(n2,l2) (LS)| V |(n1,l1)'(n2,l2)'(L'S') (T)>
"""
aux_sum = 0.0
# Sum of gaussians and projection operators
for i in range(2):
self._part = i
# Radial Part for Gaussian Integral
radial_energy = self.centerOfMassMatrixElementEvaluation()
if self.DEBUG_MODE:
XLog.write(
'BB',
mu=self.PARAMS_FORCE[i][CentralMEParameters.mu_length])
# Exchange Part
# W + P(S)* B - P(T)* H - P(T)*P(S)* M
_S_aux = (-1)**(self.S_bra + 1)
_T_aux = (-1)**(self.T)
_L_aux = (-1)**(self.T + self.S_bra + 1)
exchange_energy = (self.PARAMS_FORCE[i].get(
bb_p.Wigner), self.PARAMS_FORCE[i].get(bb_p.Bartlett) * _S_aux,
self.PARAMS_FORCE[i].get(bb_p.Heisenberg) *
_T_aux,
self.PARAMS_FORCE[i].get(bb_p.Majorana) *
_L_aux)
# Add up
prod_part = radial_energy * sum(exchange_energy)
aux_sum += prod_part
if self.DEBUG_MODE:
XLog.write('BB',
radial=radial_energy,
exch=exchange_energy,
exch_sum=sum(exchange_energy),
val=prod_part)
return aux_sum
def _run(self):
"""
Calculates the NON antisymmetrized_ matrix element value.
This overwriting allow to implement the antysimmetrization in the inner
process to avoid the explicit calculation of the whole m.e.
"""
if self.isNullMatrixElement:
return
if self.DEBUG_MODE:
XLog.write('nas_me', ket=self.ket.shellStatesNotation)
# antisymmetrization_ taken in the inner evaluation
self._value = self._LS_recoupling_ME()
if self.DEBUG_MODE:
XLog.write('nas_me', value=self._value, norms=self.bra.norm()*self.ket.norm())
# value is always M=0, M_T=0
self._value *= self.bra.norm() * self.ket.norm()
def _BrodyMoshinskyTransformation(self):
"""
## WARNING: This method is final. Do not overwrite!!
Sum over valid p-Talmi integrals range (Energy + Ang. momentum + parity
conservation laws). Call implemented Talmi Coefficients for
Brody-Moshinsky transformation
"""
sum_ = 0.0
if self.DEBUG_MODE:
XLog.write('talmi')
for p in range(max(self.rho_bra, self.rho_ket) + 1):
if self.DEBUG_MODE:
XLog.write('talmi', p=p)
self._p = p
# 2* from the antisymmetrization_ (_deltaConditionsForCOM_Iteration)
series = 2 * self._interactionSeries()
Ip = self.talmiIntegral()
product = series * Ip
sum_ += product
# sum_ += self._interactionSeries() * self.talmiIntegral()
if self.DEBUG_MODE:
XLog.write('talmi', series=series, Ip=Ip, val=product)
return self._globalInteractionCoefficient() * sum_
def _run(self):
if self.isNullMatrixElement:
return
if self.DEBUG_MODE:
XLog.write('nas_me', ket=self.ket.shellStatesNotation)
# antisymmetrization_ taken in the inner evaluation
self._value = self._RadialCoeff()
self._value *= self._AngularCoeff()
if self.DEBUG_MODE:
XLog.write('nas_me', value=self._value, norms=self.bra.norm()*self.ket.norm())
self._value *= self.bra.norm() * self.ket.norm()
if self._evaluateMSDI:
## V_MSDI = V_SDI + B * <tau(1) ยท tau(2)> + C (only off-diagonal)
if self.T == 0:
self._value += self._msdi_T0
elif self.T == 1:
self._value += self._msdi_T1
def _LScoupled_MatrixElement(self):
"""
<(n1,l1)(n2,l2) (LS)| V |(n1,l1)'(n2,l2)'(L'S') (JT)>
This matrix element don't call directly to centerOfMassMatrixElementEvaluation
since this name is reserved for the center of mass transformation.
Extracted from Dr. Tomas Gonzalez Llarena (1999)
"""
skip, spin_me = self._totalSpinTensorMatrixElement()
if skip or self.T == 0:
return 0
# factor = safe_racah(self.L_bra, self.L_ket, self.S_bra, self.S_ket, 1, self.J)
factor = safe_wigner_6j(self.L_bra, 1, self.L_ket, self.S_bra, self.J,
self.S_ket)
factor *= (-1)**(self.L_ket + self.J) * spin_me
if (self.isNullValue(factor) or not self.deltaConditionsForGlobalQN()):
# same delta conditions act here, since tensor is rank 1
return 0
if self.DEBUG_MODE: XLog.write("LSme")
dir_ = self._L_tensor_MatrixElement()
exch = self._L_tensor_MatrixElement(exchanged=True)
# Notice that the matrix element is not antisymmetrized_ (exchanged is
# just a name), tbme_ are permutable, then the factor *2 to antisymmetr_
factor *= self.PARAMS_FORCE.get(CentralMEParameters.constant)
aux = 2 * factor * (dir_ + ((-1)**(self.L_bra + self.L_ket)) * exch)
# ^-- factor 2 for the antisymmetrization_
if self.DEBUG_MODE:
XLog.write("LSme", factor=factor, dir=dir_, exch=exch, value=aux)
return aux
def _interactionSeries(self):
sum_ = 0.0
if self.DEBUG_MODE:
XLog.write('intSer')
for qqnn_bra in self._validCOM_Bra_qqnn():
self._n, self._l, self._N, self._L = qqnn_bra
bmb_bra = BM_Bracket(self._n, self._l, self._N, self._L,
self.bra.n1, self.bra.l1, self.bra.n2,
self.bra.l2, self.L_bra)
if self.isNullValue(bmb_bra):
continue
for l_q in self._validKet_relativeAngularMomentums():
self._l_q = l_q
self._n_q = self._n
self._n_q += (self.rho_ket - self.rho_bra + self._l -
self._l_q) // 2
if self._n_q < 0 or not self._deltaConditionsForCOM_Iteration(
):
continue
bmb_ket = BM_Bracket(self._n_q, self._l_q, self._N, self._L,
self.ket.n1, self.ket.l1, self.ket.n2,
self.ket.l2, self.L_ket)
if self.isNullValue(bmb_ket):
continue
_b_coeff = self._B_coefficient(
self.PARAMS_SHO.get(SHO_Parameters.b_length))
_com_coeff = self._interactionConstantsForCOM_Iteration()
aux = _com_coeff * bmb_bra * bmb_ket * _b_coeff
sum_ += aux
# TODO: comment when not debugging
if self.DEBUG_MODE:
XLog.write('intSer',
bmbs=bmb_bra * bmb_ket,
B=_b_coeff,
comCoeff=_com_coeff,
aux=aux)
# self._debbugingTable(bmb_bra, bmb_ket, _com_coeff, _b_coeff)
if self.DEBUG_MODE:
XLog.write('intSer', value=sum_)
return sum_
def _run(self):
""" Calculate the explicit antisymmetric matrix element value. """
if self.isNullMatrixElement:
return
# construct the exchange ket
phase, exchanged_ket = self.ket.exchange()
self.exchange_phase = phase
self.exch_2bme = self.__class__(self.bra, exchanged_ket, run_it=False)
if self.DEBUG_MODE:
XLog.write('na_me', p='DIRECT', ket=self.ket.shellStatesNotation)
# value is always M=0, M_T=0
self._value = self._LS_recoupling_ME()
self._value *= self.bra.norm() * self.ket.norm()
if self.DEBUG_MODE:
XLog.write('na_me', phs=phase)
XLog.write('nas', norms=self.bra.norm()*self.ket.norm(), value=self._value)
def _run(self):
""" Calculate the antisymmetric matrix element value. """
if self.isNullMatrixElement:
return
if self.T != 1:
# Spin-orbit approximation antisymmetrization_ condition 1 - PxPsPt =
# 1 + delta(tau1, tau2) => T=0 is null (factor 2 in the m.e. below)
self._value = 0.0
self._isNullMatrixElement = True
return
if self.DEBUG_MODE:
XLog.write('nas', ket=self.ket.shellStatesNotation)
self._value = self._LS_recoupling_ME()
self._value *= self.bra.norm() * self.ket.norm()
if self.DEBUG_MODE:
XLog.write('nas', value=self._value)
XLog.write('nas', norms=self.bra.norm() * self.ket.norm())
def _integral(self, type_integral, wf1_bra, wf2_bra, wf1_ket, wf2_ket, b_length):
assert type_integral in (1, 2), "type_integral can only be 1 or 2"
n1_q, l1_q = wf1_bra.n, wf1_bra.l
n2_q, l2_q = wf2_bra.n, wf2_bra.l
n1, l1 = wf1_ket.n, wf1_ket.l
n2, l2 = wf2_ket.n, wf2_ket.l
sum_ = 0
if self.DEBUG_MODE:
XLog.write("R_int", type=type_integral, wf1=wf1_bra, wf2=wf2_bra, wf3=wf1_ket, wf4=wf2_ket)
for p in range(n1+n2 +1):
ket_coeff = self._B_coeff(n1, l1, n2, l2, p)
if self.DEBUG_MODE: XLog.write("Ip", p=p, ket_C=ket_coeff)
for p_q in range(n1_q+n2_q +1):
bra_b = self._B_coeff(n1_q, l1_q, n2_q, l2_q, p_q)
No2 = (p + p_q) + ((l1 + l2 + l1_q + l2_q)//2)
I_1 = self._r_dependentIntegral(No2)
if self.DEBUG_MODE:
XLog.write("Ip_q", pq=p_q, bra_B=bra_b, N=No2, I_1=I_1)
if type_integral == 1:
bra_d = self._D_coeff(n1_q, l1_q, n2_q, l2_q, p_q)
I_2 = self._r_dependentIntegral(No2 + 1)
aux = ket_coeff * ((bra_d*I_1) - (bra_b*I_2))
sum_ += aux
if self.DEBUG_MODE:
XLog.write("Ip_q", I_2=I_2, bra_D=bra_d, val= aux)
else:
aux = ket_coeff * bra_b * I_1
sum_ += aux
if self.DEBUG_MODE: XLog.write("Ip_q", val= aux)
# norm_fact = np.prod([self._norm_coeff(wf) for wf in
# (wf1_bra, wf2_bra, wf1_ket, wf2_ket)])
norm_fact = b_length
if self.DEBUG_MODE:
XLog.write("R_int", sum=sum_, norm=norm_fact, value=norm_fact*sum_)
return norm_fact * sum_