def Hfs(L,S,I):
"""Provides the L dot S matrix (fine structure)"""
gS=int(2*S+1) #number of mS values
Sx=jx(S)
Sy=jy(S)
Sz=jz(S)
Si=identity(gS)
gL=int(2*L+1)
Lx=jx(L)
Ly=jy(L)
Lz=jz(L)
Li=identity(gL)
gJ=gL*gS
Jx=kron(Lx,Si)+kron(Li,Sx)
Jy=kron(Ly,Si)+kron(Li,Sy)
Jz=kron(Lz,Si)+kron(Li,Sz)
J2=dot(Jx,Jx)+dot(Jy,Jy)+dot(Jz,Jz)
gI=int(2*I+1)
Ii=identity(gI)
gF=gJ*gI
Fi=identity(gF)
Hfs=0.5*(kron(J2,Ii)-L*(L+1)*Fi-S*(S+1)*Fi) # fine structure in m_L,m_S,m_I basis
return Hfs
def Hhfs(L,S,I):
"""Provides the I dot J matrix (magnetic dipole interaction)"""
gS=int(2*S+1)
Sx=jx(S)
Sy=jy(S)
Sz=jz(S)
Si=identity(gS)
gL=int(2*L+1)
Lx=jx(L)
Ly=jy(L)
Lz=jz(L)
Li=identity(gL)
gJ=gL*gS
Jx=kron(Lx,Si)+kron(Li,Sx)
Jy=kron(Ly,Si)+kron(Li,Sy)
Jz=kron(Lz,Si)+kron(Li,Sz)
Ji=identity(gJ)
J2=dot(Jx,Jx)+dot(Jy,Jy)+dot(Jz,Jz)
gI=int(2*I+1)
gF=gJ*gI
Ix=jx(I)
Iy=jy(I)
Iz=jz(I)
Ii=identity(gI)
Fx=kron(Jx,Ii)+kron(Ji,Ix)
Fy=kron(Jy,Ii)+kron(Ji,Iy)
Fz=kron(Jz,Ii)+kron(Ji,Iz)
Fi=identity(gF)
F2=dot(Fx,Fx)+dot(Fy,Fy)+dot(Fz,Fz)
Hhfs=0.5*(F2-I*(I+1)*Fi-kron(J2,Ii))
return Hhfs
def Hhfs(L, S, I):
"""Provides the I dot J matrix (magnetic dipole interaction)"""
gS = int(2 * S + 1)
Sx = jx(S)
Sy = jy(S)
Sz = jz(S)
Si = identity(gS)
gL = int(2 * L + 1)
Lx = jx(L)
Ly = jy(L)
Lz = jz(L)
Li = identity(gL)
gJ = gL * gS
Jx = kron(Lx, Si) + kron(Li, Sx)
Jy = kron(Ly, Si) + kron(Li, Sy)
Jz = kron(Lz, Si) + kron(Li, Sz)
Ji = identity(gJ)
J2 = dot(Jx, Jx) + dot(Jy, Jy) + dot(Jz, Jz)
gI = int(2 * I + 1)
gF = gJ * gI
Ix = jx(I)
Iy = jy(I)
Iz = jz(I)
Ii = identity(gI)
Fx = kron(Jx, Ii) + kron(Ji, Ix)
Fy = kron(Jy, Ii) + kron(Ji, Iy)
Fz = kron(Jz, Ii) + kron(Ji, Iz)
Fi = identity(gF)
F2 = dot(Fx, Fx) + dot(Fy, Fy) + dot(Fz, Fz)
Hhfs = 0.5 * (F2 - I * (I + 1) * Fi - kron(J2, Ii))
return Hhfs
def Hfs(L, S, I):
"""Provides the L dot S matrix (fine structure)"""
gS = int(2 * S + 1) #number of mS values
Sx = jx(S)
Sy = jy(S)
Sz = jz(S)
Si = identity(gS)
gL = int(2 * L + 1)
Lx = jx(L)
Ly = jy(L)
Lz = jz(L)
Li = identity(gL)
gJ = gL * gS
Jx = kron(Lx, Si) + kron(Li, Sx)
Jy = kron(Ly, Si) + kron(Li, Sy)
Jz = kron(Lz, Si) + kron(Li, Sz)
J2 = dot(Jx, Jx) + dot(Jy, Jy) + dot(Jz, Jz)
gI = int(2 * I + 1)
Ii = identity(gI)
gF = gJ * gI
Fi = identity(gF)
Hfs = 0.5 * (kron(J2, Ii) - L * (L + 1) * Fi - S *
(S + 1) * Fi) # fine structure in m_L,m_S,m_I basis
return Hfs
def fz(L, S, I):
gS = int(2 * S + 1)
Sz = jz(S)
Si = identity(gS)
gL = int(2 * L + 1)
Lz = jz(L)
Li = identity(gL)
gJ = gL * gS
Jz = kron(Lz, Si) + kron(Li, Sz)
Ji = identity(gJ)
gI = int(2 * I + 1)
Iz = jz(I)
Ii = identity(gI)
Fz = kron(Jz, Ii) + kron(Ji, Iz)
return Fz
def fz(L,S,I):
gS=int(2*S+1)
Sz=jz(S)
Si=identity(gS)
gL=int(2*L+1)
Lz=jz(L)
Li=identity(gL)
gJ=gL*gS
Jz=kron(Lz,Si)+kron(Li,Sz)
Ji=identity(gJ)
gI=int(2*I+1)
Iz=jz(I)
Ii=identity(gI)
Fz=kron(Jz,Ii)+kron(Ji,Iz)
return Fz
def Iz(L, S, I):
gS = int(2 * S + 1)
gL = int(2 * L + 1)
Si = identity(gS)
Li = identity(gL)
Iz_num = jz(I)
Iz = kron(kron(Li, Si), Iz_num)
return Iz
def lz(L, S, I):
gS = int(2 * S + 1)
Si = identity(gS)
Lz = jz(L)
gI = int(2 * I + 1)
Ii = identity(gI)
lz = kron(kron(Lz, Si), Ii)
return lz
def sz(L, S, I):
Sz = jz(S)
gL = int(2 * L + 1)
Li = identity(gL)
gI = int(2 * I + 1)
Ii = identity(gI)
sz = kron(kron(Li, Sz), Ii)
return sz
def Iz(L,S,I):
gS=int(2*S+1)
gL=int(2*L+1)
Si=identity(gS)
Li=identity(gL)
Iz_num=jz(I)
Iz=kron(kron(Li,Si),Iz_num)
return Iz
def lz(L,S,I):
gS=int(2*S+1)
Si=identity(gS)
Lz=jz(L)
gI=int(2*I+1)
Ii=identity(gI)
lz=kron(kron(Lz,Si),Ii)
return lz
def sz(L,S,I):
Sz=jz(S)
gL=int(2*L+1)
Li=identity(gL)
gI=int(2*I+1)
Ii=identity(gI)
sz=kron(kron(Li,Sz),Ii)
return sz
def Bbhfs(L, S, I):
"""Calculates electric quadrupole matrix.
Calculates the part in square brakets from
equation (8) in manual
"""
gS = int(2 * S + 1)
Sx = jx(S)
Sy = jy(S)
Sz = jz(S)
Si = identity(gS)
gL = int(2 * L + 1)
Lx = jx(L)
Ly = jy(L)
Lz = jz(L)
Li = identity(gL)
gJ = gL * gS
Jx = kron(Lx, Si) + kron(Li, Sx)
Jy = kron(Ly, Si) + kron(Li, Sy)
Jz = kron(Lz, Si) + kron(Li, Sz)
gI = int(2 * I + 1)
gF = gJ * gI
Ix = jx(I)
Iy = jy(I)
Iz = jz(I)
Fi = identity(gF)
IdotJ = kron(Jx, Ix) + kron(Jy, Iy) + kron(Jz, Iz)
IdotJ2 = dot(IdotJ, IdotJ)
if I != 0:
Bbhfs = 1. / (6 * I * (2 * I - 1)) * (3 * IdotJ2 + 3. / 2 * IdotJ - I *
(I + 1) * 15. / 4 * Fi)
else:
Bbhfs = 0
return Bbhfs
def Bbhfs(L,S,I):
"""Calculates electric quadrupole matrix.
Calculates the part in square brakets from
equation (8) in manual
"""
gS=int(2*S+1)
Sx=jx(S)
Sy=jy(S)
Sz=jz(S)
Si=identity(gS)
gL=int(2*L+1)
Lx=jx(L)
Ly=jy(L)
Lz=jz(L)
Li=identity(gL)
gJ=gL*gS
Jx=kron(Lx,Si)+kron(Li,Sx)
Jy=kron(Ly,Si)+kron(Li,Sy)
Jz=kron(Lz,Si)+kron(Li,Sz)
gI=int(2*I+1)
gF=gJ*gI
Ix=jx(I)
Iy=jy(I)
Iz=jz(I)
Fi=identity(gF)
IdotJ=kron(Jx,Ix)+kron(Jy,Iy)+kron(Jz,Iz)
IdotJ2=dot(IdotJ,IdotJ)
if I != 0:
Bbhfs=1./(6*I*(2*I-1))*(3*IdotJ2+3./2*IdotJ-I*(I+1)*15./4*Fi)
else:
Bbhfs = 0
return Bbhfs