Line data Source code
1 : ! ***********************************************************************
2 : !
3 : ! Copyright (C) 2010-2019 The MESA Team
4 : !
5 : ! This program is free software: you can redistribute it and/or modify
6 : ! it under the terms of the GNU Lesser General Public License
7 : ! as published by the Free Software Foundation,
8 : ! either version 3 of the License, or (at your option) any later version.
9 : !
10 : ! This program is distributed in the hope that it will be useful,
11 : ! but WITHOUT ANY WARRANTY; without even the implied warranty of
12 : ! MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.
13 : ! See the GNU Lesser General Public License for more details.
14 : !
15 : ! You should have received a copy of the GNU Lesser General Public License
16 : ! along with this program. If not, see <https://www.gnu.org/licenses/>.
17 : !
18 : ! ***********************************************************************
19 :
20 : module paquette_coeffs
21 :
22 : use const_def, only: dp, qe
23 : use math_lib
24 :
25 : implicit none
26 :
27 : private
28 : public :: paquette_coefficients
29 : public :: initialise_collision_integrals
30 : public :: free_collision_integrals
31 :
32 : logical :: have_initialized = .false.
33 :
34 : real(dp), allocatable, target, dimension(:) :: DC1, DD1, DCAT1, DDAT1
35 :
36 : real(dp), pointer :: DC(:,:,:) => null()
37 : real(dp), pointer :: DD(:,:) => null()
38 : real(dp), pointer :: DCAT(:,:,:) => null()
39 : real(dp), pointer :: DDAT(:,:) => null()
40 :
41 : contains
42 :
43 : ! ********************************************************
44 : ! PAQUETTE_COEFFICIENTS:
45 : ! Compute atomic diffusion coefficients, according to Paquette et al. (1986)
46 : ! The coefficients are derived from a screened resistive/attractive Coulomb potential.
47 : ! The input parameters are
48 : ! rho: density [gcm^-3]
49 : ! T: temperature [K]
50 : ! nn number of elements
51 : ! CAN1: mass [amu], note element NN is electrons
52 : ! KZN1: charge [e]
53 : ! NA1: number density [cm^-3]
54 : ! The output are the resistance coefficients in Burgers equations K_ij, z_ij, z'_ij and z''_ij
55 : ! It is also possible to output diffusion coefficients D_ij and thermal diffusion coefficient
56 : ! A_th used in Cowling&Chapman formalism, note Ath(NN,i) is Ath_ei
57 :
58 0 : subroutine paquette_coefficients(rho, T, NN, CAN1, KZN1, NA1, Ddiff, Kdiff, Zdiff, Zdiff1, Zdiff2, Ath)
59 :
60 : use const_def, only : pi4, boltzm, amu
61 :
62 :
63 : ! Input and output variables
64 : integer :: NN
65 : real(dp), intent(in) :: rho, T, CAN1(NN), KZN1(NN), NA1(NN)
66 : real(dp), intent(out) :: Ddiff(nn, nn), Kdiff(nn, nn), Zdiff(nn, nn), &
67 : Zdiff1(nn, nn), Zdiff2(nn, nn), Ath(nn, nn)
68 : ! Local variables
69 : ! Lengthscales for the plasma
70 0 : real(dp) :: LAMBDA_I2, LAMBDA_D2, LAMBDA2
71 : ! Ion density
72 0 : real(dp) :: NI
73 : ! Convenience, to precalculate as much as possible
74 0 : real(dp) :: KT, GAMMA2
75 : ! Collision integrals Omega (eqn. (18) in Paquette et al)
76 0 : real(dp) :: OMEGA1(3), OMEGA22, OMEGA2(NN)
77 : ! Dimensionless collision integrals (eqn. (65) in Paquette et al)
78 0 : real(dp) :: F1(3), F22
79 : ! Local variables
80 0 : real(dp) :: PSI_ST, EPS_ST, GAMMA_ST2, A, E_PSI_ST
81 0 : real(dp) :: AA, BB, CC, EE, Ps, Pt, Pst, Qs, Qt, Qst, Ss, &
82 0 : St, Ms, Mt, Xs, Xt, DELTA
83 0 : real(dp) :: DPSI_N1, DPSI_N
84 : integer :: i, J, N, K, NREF
85 0 : real(dp) :: NZZ, NE
86 :
87 0 : NE = NA1(NN) ! number density is per cm^3
88 0 : NI = 0.0D0
89 0 : NZZ = 0.0D0
90 0 : do i = 1, NN-1
91 0 : NI = NI + NA1(i)
92 0 : NZZ = NZZ + KZN1(i)*KZN1(i) * NA1(i)
93 : end do
94 :
95 0 : KT = BOLTZM*T
96 : ! Typical distance between ions (squared)
97 0 : LAMBDA_I2 = pow(3.0D0/(pi4*NI),2.0D0/3.0D0)
98 : ! Debye length (squared)
99 0 : LAMBDA_D2 = (KT/(pi4 * qe*qe * (NE + NZZ)))
100 : ! Use max of lambda_i and lambda_d as typical distance
101 0 : LAMBDA2 = MAX(LAMBDA_D2, LAMBDA_I2)
102 :
103 0 : F22 = 1d0
104 : ! First evaluate the collision intergrals OMEGA22_SS, that appear in Ps (eq (9) of Paquette 1986)
105 0 : do I = 1, NN
106 0 : NREF = I
107 0 : GAMMA2 = pow2(4.0D0*KT/(qe*qe*KZN1(NREF)))*LAMBDA2
108 0 : GAMMA_ST2 = GAMMA2/pow2(KZN1(I))
109 : ! Reduced mass of the two particles
110 0 : A = (CAN1(I)*CAN1(NREF)/(CAN1(I)+CAN1(NREF))) ! HH, in units of AMU
111 : ! Units of Omega: length^2 * velocity
112 0 : EPS_ST = pi4*LAMBDA2/GAMMA_ST2 * SQRT(2.0D0*KT/(pi4 * AMU*A))
113 : ! Find interpolation interval for dimensionless collision integral
114 0 : E_PSI_ST = log(1.0D0+GAMMA_ST2)
115 0 : PSI_ST = log(E_PSI_ST)
116 : ! Evaluate the collision integral
117 0 : if (PSI_ST<=3.0D0) then
118 : ! if PSI_ST falls outside range of Paquette's fit, then just take border value
119 0 : PSI_ST = MAX(-7.D0, PSI_ST)
120 : ! Use spline interpolation to evaluate the collision integrals
121 : ! Determine interval in the table
122 0 : N = 1 + MIN(49, FLOOR((PSI_ST +7.d0)/0.2d0))
123 0 : DPSI_N1 = (-7.2D0 + 0.2D0*(N+1)) - PSI_ST
124 0 : DPSI_N = PSI_ST - (-7.2D0 + 0.2D0*N)
125 : if (NREF==NN .and. NREF/=I .or. I==NN .and. NREF/=I) then
126 : ! attractive potential (electron-ion)
127 : F22 = exp(DDAT(1,N)*DPSI_N1*DPSI_N1*DPSI_N1 + DDAT(2,N)*DPSI_N*DPSI_N*DPSI_N &
128 : + DDAT(3,N)*DPSI_N1 + DDAT(4,N)*DPSI_N)
129 : else
130 : ! repulsive potential (ion-ion or electron-electron)
131 : F22 = exp(DD(1,N)*DPSI_N1*DPSI_N1*DPSI_N1 + DD(2,N)*DPSI_N*DPSI_N*DPSI_N &
132 0 : + DD(3,N)*DPSI_N1 + DD(4,N)*DPSI_N)
133 : end if
134 0 : elseif (PSI_ST > 3.0D0 .and. PSI_ST < 4.0d0) then
135 : ! repulsive potential (ion-ion or electron-electron)
136 : if (NREF==NN .and. NREF/=I .or. I==NN .and. NREF/=I) then
137 : F22 = 2.08699D0*E_PSI_ST - 5.81444D0
138 : else
139 : ! attractive potential (electron-ion)
140 0 : F22 = 1.99016D0*E_PSI_ST - 4.56958D0
141 : end if
142 : elseif (PSI_ST >= 4.0D0) then
143 : ! repulsive and attractive coefficients are the same in this range
144 0 : F22 = 1.99016D0*E_PSI_ST - 4.56958D0
145 : end if
146 0 : OMEGA2(I) = EPS_ST*F22
147 : end do ! I
148 :
149 0 : do K = 1, NN
150 0 : NREF = K
151 0 : GAMMA2 = pow2(4.0D0*KT/(qe*qe*KZN1(NREF))) * LAMBDA2
152 0 : do I = 1, NN
153 0 : GAMMA_ST2 = GAMMA2/pow2(KZN1(I))
154 : ! Reduced mass of the two particles
155 0 : A = (CAN1(I)*CAN1(NREF)/(CAN1(I)+CAN1(NREF))) ! in units of AMU
156 : ! Units of Omega: length^2 * velocity
157 0 : EPS_ST = pi4*LAMBDA2/GAMMA_ST2 * SQRT(2.0D0*KT/(pi4 * AMU*A))
158 : ! Find interpolation interval for dimensionless collision integral
159 0 : E_PSI_ST = log(1.0D0+GAMMA_ST2)
160 0 : PSI_ST = log(E_PSI_ST)
161 : ! Evaluate the collision integral
162 0 : if (PSI_ST <= 3.0D0) then
163 0 : PSI_ST = MAX(-7.D0, PSI_ST)
164 : ! if PSI_ST falls outside range of Paquette fit, then just take border value, will probably never happen
165 : ! Use spline interpolation to evaluate the collision integrals
166 : ! Determine interval in the table
167 0 : N = 1 + MIN(49, FLOOR((PSI_ST +7.d0)/0.2d0))
168 0 : DPSI_N1 = (-7.2D0 + 0.2D0*(N+1)) - PSI_ST
169 0 : DPSI_N = PSI_ST - (-7.2D0 + 0.2D0*N)
170 0 : if (NREF==NN .and. NREF/=I .or. I==NN .and. NREF/=I) then
171 : ! attractive potential (electron-ion)
172 0 : do J=1,3
173 : F1(J) = exp(DCAT(1,N,J)*DPSI_N1*DPSI_N1*DPSI_N1 &
174 : + DCAT(2,N,J)*DPSI_N*DPSI_N*DPSI_N &
175 : + DCAT(3,N,J)*DPSI_N1 &
176 0 : + DCAT(4,N,J)*DPSI_N)
177 : end do
178 : F22 = exp(DDAT(1,N)*DPSI_N1*DPSI_N1*DPSI_N1 &
179 : + DDAT(2,N)*DPSI_N*DPSI_N*DPSI_N &
180 : + DDAT(3,N)*DPSI_N1 &
181 0 : + DDAT(4,N)*DPSI_N)
182 : ! repulsive potential (ion-ion or electron-electron)
183 : else
184 0 : do J=1,3
185 : F1(J) = exp(DC(1,N,J)*DPSI_N1*DPSI_N1*DPSI_N1 &
186 : + DC(2,N,J)*DPSI_N*DPSI_N*DPSI_N &
187 : + DC(3,N,J)*DPSI_N1 &
188 0 : + DC(4,N,J)*DPSI_N)
189 : end do
190 : F22 = exp(DD(1,N)*DPSI_N1*DPSI_N1*DPSI_N1 &
191 : + DD(2,N)*DPSI_N*DPSI_N*DPSI_N &
192 : + DD(3,N)*DPSI_N1 &
193 0 : + DD(4,N)*DPSI_N)
194 : end if
195 0 : elseif (PSI_ST > 3.0D0 .and. PSI_ST < 4.0d0) then
196 0 : if (NREF==NN .and. NREF/=I .or. I==NN .and. NREF/=I) then
197 : ! attractive potential (electron-ion)
198 0 : F1(1) = 1.01101D0*E_PSI_ST - 3.19815D0
199 0 : F1(2) = 1.04230D0*E_PSI_ST - 1.89637D0
200 0 : F1(3) = 2.15672D0*E_PSI_ST - 2.81038D0
201 0 : F22 = 2.08699D0*E_PSI_ST - 5.81444D0
202 : else
203 : ! repulsive potential (ion-ion or electron-electron)
204 0 : F1(1) = 1.00141D0*E_PSI_ST - 3.18209D0
205 0 : F1(2) = 0.99559D0*E_PSI_ST - 1.29553D0
206 0 : F1(3) = 1.99814D0*E_PSI_ST - 0.64413D0
207 0 : F22 = 1.99016D0*E_PSI_ST - 4.56958D0
208 : end if
209 : elseif (PSI_ST>=4.0D0) then
210 : ! repulsive and attractive coefficients are the same in this range
211 0 : F1(1) = 1.00141D0*E_PSI_ST - 3.18209D0
212 0 : F1(2) = 0.99559D0*E_PSI_ST - 1.29553D0
213 0 : F1(3) = 1.99814D0*E_PSI_ST - 0.64413D0
214 0 : F22 = 1.99016D0*E_PSI_ST - 4.56958D0
215 : end if
216 0 : OMEGA1(:) = EPS_ST*F1(:)
217 0 : OMEGA22 = EPS_ST*F22 ! for particle species NREF & K
218 :
219 : ! Binary diffusion coefficient for Chapman and Cowling formalism (first approximation)
220 0 : Ddiff(NREF, I) = 3.0D0*KT/(16.0D0*(NA1(NREF)+NA1(I))*(A*AMU)*OMEGA1(1))
221 :
222 0 : AA = OMEGA22/(5.D0*OMEGA1(1))
223 0 : BB = (5.D0*OMEGA1(2)-OMEGA1(3))/(5.D0*OMEGA1(1))
224 0 : CC = 2.D0*OMEGA1(2)/(5.D0*OMEGA1(1))-1.D0
225 0 : Xs = NA1(NREF)/(NA1(I)+NA1(NREF)) !number concentration of reference species NREF
226 0 : Xt = NA1(I)/(NA1(I)+NA1(NREF)) !number concentration of species I
227 0 : Ms = CAN1(NREF)/(CAN1(NREF)+CAN1(I))
228 0 : Mt = CAN1(I)/(CAN1(NREF)+CAN1(I))
229 0 : Pst = 3.0D0*(Ms-Mt)*(Ms-Mt) + 4.D0*Ms*Mt*AA
230 0 : EE = KT/(8.D0*Ms*Mt*OMEGA1(1))
231 0 : Ps = 8.D0*Ms*EE*OMEGA2(NREF)/(5.D0*KT)
232 0 : Pt = 8.D0*Mt*EE*OMEGA2(I)/(5.D0*KT)
233 0 : Ss = Ms*Ps-Mt*(3.D0*(Mt-Ms)+4.D0*Ms*AA)
234 0 : St = Mt*Pt-Ms*(3.D0*(Ms-Mt)+4.D0*Mt*AA)
235 0 : Qs = Ps*(6.D0*Mt*Mt + 5.D0*Ms*Ms - 4.D0*Ms*Ms*BB + 8.D0*Ms*Mt*AA)
236 0 : Qt = Pt*(6.D0*Ms*Ms + 5.D0*Mt*Mt - 4.D0*Mt*Mt*BB + 8.D0*Mt*Ms*AA)
237 0 : Qst = 3.D0*(Ms-Mt)*(Ms-Mt)*(5.D0-4.D0*BB) + 4.D0*Ms*Mt*AA*(11.D0-4.D0*BB) + 2.D0*Ps*Pt
238 0 : DELTA = 5.0D0*CC*CC*(Ms*Ms*Ps*Xs*Xs + Mt*Mt*Pt*Xt*Xt + Pst*Xs*Xt)/(Xs*Xs*Qs + Xt*Xt*Qt + Xs*Xt*Qst)
239 :
240 : ! second approximation
241 0 : Ddiff(NREF, I) = Ddiff(NREF, I)/(1.0D0 - DELTA)
242 :
243 : ! thermal coefficients
244 0 : Ath(NREF,I) = 5.D0*CC*(Xs*Ss-Xt*St)/(Xs*Xs*Qs+Xt*Xt*Qt+Xs*Xt*Qst)
245 : ! resistance coefficients for Burgers equations
246 0 : Kdiff(NREF, I) = 16.D0/3.D0*NA1(NREF)*NA1(I)*(A*AMU)*OMEGA1(1)
247 0 : Zdiff(NREF, I) = - CC
248 0 : Zdiff1(NREF, I) = -2.D0*BB+2.5D0
249 0 : Zdiff2(NREF, I) = 5.D0*AA
250 :
251 : end do !I
252 : end do !K
253 0 : return
254 :
255 : end subroutine paquette_coefficients
256 : ! ****************************************************
257 :
258 :
259 : ! Initialise collision integrals for atomic diffusion
260 1 : subroutine initialise_collision_integrals
261 :
262 1 : if (have_initialized) return
263 :
264 1 : !$omp critical (collision_integrals)
265 1 : if (.not. have_initialized) then
266 :
267 1 : allocate(DC1(4*50*3), DD1(4*50), DCAT1(4*50*3), DDAT1(4*50))
268 1 : DC(1:4,1:50,1:3) => DC1(1:4*50*3)
269 1 : DD(1:4,1:50) => DD1(1:4*50)
270 1 : DCAT(1:4,1:50,1:3) => DCAT1(1:4*50*3)
271 1 : DDAT(1:4,1:50) => DDAT1(1:4*50)
272 :
273 : DC1 = [ &
274 : +1.19599D-02,-2.39198D-02,-3.02547D+01,-2.94860D+01, &
275 : -2.39198D-02,-1.48010D-02,-2.94860D+01,-2.87231D+01, &
276 : -1.48010D-02,-1.77390D-02,-2.87231D+01,-2.79637D+01, &
277 : -1.77390D-02,-1.74423D-02,-2.79637D+01,-2.72086D+01, &
278 : -1.74423D-02,-1.80040D-02,-2.72086D+01,-2.64576D+01, &
279 : -1.80040D-02,-1.83218D-02,-2.64576D+01,-2.57110D+01, &
280 : -1.83218D-02,-1.86847D-02,-2.57110D+01,-2.49688D+01, &
281 : -1.86847D-02,-1.90073D-02,-2.49688D+01,-2.42310D+01, &
282 : -1.90073D-02,-1.93026D-02,-2.42310D+01,-2.34978D+01, &
283 : -1.93026D-02,-1.95555D-02,-2.34978D+01,-2.27693D+01, &
284 : -1.95555D-02,-1.97557D-02,-2.27693D+01,-2.20454D+01, &
285 : -1.97557D-02,-1.98886D-02,-2.20454D+01,-2.13263D+01, &
286 : -1.98886D-02,-1.99373D-02,-2.13263D+01,-2.06120D+01, &
287 : -1.99373D-02,-1.98810D-02,-2.06120D+01,-1.99024D+01, &
288 : -1.98810D-02,-1.96948D-02,-1.99024D+01,-1.91976D+01, &
289 : -1.96948D-02,-1.93486D-02,-1.91976D+01,-1.84975D+01, &
290 : -1.93486D-02,-1.88059D-02,-1.84975D+01,-1.78021D+01, &
291 : -1.88059D-02,-1.80227D-02,-1.78021D+01,-1.71112D+01, &
292 : -1.80227D-02,-1.69459D-02,-1.71112D+01,-1.64246D+01, &
293 : -1.69459D-02,-1.55109D-02,-1.64246D+01,-1.57421D+01, &
294 : -1.55109D-02,-1.36394D-02,-1.57421D+01,-1.50633D+01, &
295 : -1.36394D-02,-1.12361D-02,-1.50633D+01,-1.43878D+01, &
296 : -1.12361D-02,-8.18466D-03,-1.43878D+01,-1.37150D+01, &
297 : -8.18466D-03,-4.34258D-03,-1.37150D+01,-1.30441D+01, &
298 : -4.34258D-03,+4.65253D-04,-1.30441D+01,-1.23743D+01, &
299 : +4.65253D-04,+6.45493D-03,-1.23743D+01,-1.17044D+01, &
300 : +6.45493D-03,+1.38941D-02,-1.17044D+01,-1.10329D+01, &
301 : +1.38941D-02,+2.31151D-02,-1.10329D+01,-1.03581D+01, &
302 : +2.31151D-02,+3.45317D-02,-1.03581D+01,-9.67777D+00, &
303 : +3.45317D-02,+4.86585D-02,-9.67777D+00,-8.98913D+00, &
304 : +4.86585D-02,+6.61321D-02,-8.98913D+00,-8.28881D+00, &
305 : +6.61321D-02,+8.77309D-02,-8.28881D+00,-7.57261D+00, &
306 : +8.77309D-02,+1.14383D-01,-7.57261D+00,-6.83537D+00, &
307 : +1.14383D-01,+1.47142D-01,-6.83537D+00,-6.07066D+00, &
308 : +1.47142D-01,+1.87092D-01,-6.07066D+00,-5.27065D+00, &
309 : +1.87092D-01,+2.35096D-01,-5.27065D+00,-4.42573D+00, &
310 : +2.35096D-01,+2.91268D-01,-4.42573D+00,-3.52439D+00, &
311 : +2.91268D-01,+3.53977D-01,-3.52439D+00,-2.55315D+00, &
312 : +3.53977D-01,+4.18217D-01,-2.55315D+00,-1.49695D+00, &
313 : +4.18217D-01,+4.73499D-01,-1.49695D+00,-3.40379D-01, &
314 : +4.73499D-01,+5.02343D-01,-3.40379D-01,+9.29832D-01, &
315 : +5.02343D-01,+4.82140D-01,+9.29832D-01,+2.32060D+00, &
316 : +4.82140D-01,+3.92303D-01,+2.32060D+00,+3.82709D+00, &
317 : +3.92303D-01,+2.20401D-01,+3.82709D+00,+5.42773D+00, &
318 : +2.20401D-01,-5.31156D-02,+5.42773D+00,+7.08127D+00, &
319 : -5.31156D-02,-3.94063D-01,+7.08127D+00,+8.72205D+00, &
320 : -3.94063D-01,-5.99574D-01,+8.72205D+00,+1.02683D+01, &
321 : -5.99574D-01,-4.71033D-01,+1.02683D+01,+1.16706D+01, &
322 : -4.71033D-01,-4.68969D-01,+1.16706D+01,+1.29598D+01, &
323 : -4.68969D-01,+2.34484D-01,+1.29598D+01,+1.41366D+01, &
324 :
325 : +1.34102D-02,-2.68205D-02,-2.55941D+01,-2.48408D+01, &
326 : -2.68205D-02,-1.66309D-02,-2.48408D+01,-2.40939D+01, &
327 : -1.66309D-02,-1.99547D-02,-2.40939D+01,-2.33511D+01, &
328 : -1.99547D-02,-1.96575D-02,-2.33511D+01,-2.26130D+01, &
329 : -1.96575D-02,-2.03264D-02,-2.26130D+01,-2.18796D+01, &
330 : -2.03264D-02,-2.07272D-02,-2.18796D+01,-2.11511D+01, &
331 : -2.07272D-02,-2.11843D-02,-2.11511D+01,-2.04276D+01, &
332 : -2.11843D-02,-2.16034D-02,-2.04276D+01,-1.97091D+01, &
333 : -2.16034D-02,-2.20005D-02,-1.97091D+01,-1.89959D+01, &
334 : -2.20005D-02,-2.23602D-02,-1.89959D+01,-1.82879D+01, &
335 : -2.23602D-02,-2.26732D-02,-1.82879D+01,-1.75853D+01, &
336 : -2.26732D-02,-2.29256D-02,-1.75853D+01,-1.68881D+01, &
337 : -2.29256D-02,-2.31017D-02,-1.68881D+01,-1.61965D+01, &
338 : -2.31017D-02,-2.31822D-02,-1.61965D+01,-1.55103D+01, &
339 : -2.31822D-02,-2.31439D-02,-1.55103D+01,-1.48298D+01, &
340 : -2.31439D-02,-2.29591D-02,-1.48298D+01,-1.41548D+01, &
341 : -2.29591D-02,-2.25945D-02,-1.41548D+01,-1.34853D+01, &
342 : -2.25945D-02,-2.20100D-02,-1.34853D+01,-1.28212D+01, &
343 : -2.20100D-02,-2.11574D-02,-1.28212D+01,-1.21624D+01, &
344 : -2.11574D-02,-1.99787D-02,-1.21624D+01,-1.15087D+01, &
345 : -1.99787D-02,-1.84040D-02,-1.15087D+01,-1.08598D+01, &
346 : -1.84040D-02,-1.63488D-02,-1.08598D+01,-1.02153D+01, &
347 : -1.63488D-02,-1.37108D-02,-1.02153D+01,-9.57474D+00, &
348 : -1.37108D-02,-1.03658D-02,-9.57474D+00,-8.93745D+00, &
349 : -1.03658D-02,-6.16232D-03,-8.93745D+00,-8.30266D+00, &
350 : -6.16232D-03,-9.15489D-04,-8.30266D+00,-7.66934D+00, &
351 : -9.15489D-04,+5.60137D-03,-7.66934D+00,-7.03625D+00, &
352 : +5.60137D-03,+1.36664D-02,-7.03625D+00,-6.40181D+00, &
353 : +1.36664D-02,+2.36209D-02,-6.40181D+00,-5.76409D+00, &
354 : +2.36209D-02,+3.58820D-02,-5.76409D+00,-5.12070D+00, &
355 : +3.58820D-02,+5.09546D-02,-5.12070D+00,-4.46870D+00, &
356 : +5.09546D-02,+6.94376D-02,-4.46870D+00,-3.80447D+00, &
357 : +6.94376D-02,+9.20141D-02,-3.80447D+00,-3.12357D+00, &
358 : +9.20141D-02,+1.19403D-01,-3.12357D+00,-2.42059D+00, &
359 : +1.19403D-01,+1.52233D-01,-2.42059D+00,-1.68896D+00, &
360 : +1.52233D-01,+1.90763D-01,-1.68896D+00,-9.20788D-01, &
361 : +1.90763D-01,+2.34333D-01,-9.20788D-01,-1.06834D-01, &
362 : +2.34333D-01,+2.80392D-01,-1.06834D-01,+7.63360D-01, &
363 : +2.80392D-01,+3.23003D-01,+7.63360D-01,+1.70085D+00, &
364 : +3.23003D-01,+3.51091D-01,+1.70085D+00,+2.71586D+00, &
365 : +3.51091D-01,+3.47669D-01,+2.71586D+00,+3.81513D+00, &
366 : +3.47669D-01,+2.93155D-01,+3.81513D+00,+4.99784D+00, &
367 : +2.93155D-01,+1.77064D-01,+4.99784D+00,+6.25091D+00, &
368 : +1.77064D-01,+1.68817D-02,+6.25091D+00,+7.54647D+00, &
369 : +1.68817D-02,-1.37836D-01,+7.54647D+00,+8.84609D+00, &
370 : -1.37836D-01,-2.36519D-01,+8.84609D+00,+1.01126D+01, &
371 : -2.36519D-01,-2.49035D-01,+1.01126D+01,+1.13224D+01, &
372 : -2.49035D-01,-1.95933D-01,+1.13224D+01,+1.24724D+01, &
373 : -1.95933D-01,-1.60453D-01,+1.24724D+01,+1.35754D+01, &
374 : -1.60453D-01,+8.02267D-02,+1.35754D+01,+1.46398D+01, &
375 :
376 : +1.46130D-02,-2.92259D-02,-1.93212D+01,-1.85804D+01, &
377 : -2.92259D-02,-1.81472D-02,-1.85804D+01,-1.78467D+01, &
378 : -1.81472D-02,-2.17897D-02,-1.78467D+01,-1.71173D+01, &
379 : -2.17897D-02,-2.14905D-02,-1.71173D+01,-1.63931D+01, &
380 : -2.14905D-02,-2.22463D-02,-1.63931D+01,-1.56741D+01, &
381 : -2.22463D-02,-2.27134D-02,-1.56741D+01,-1.49604D+01, &
382 : -2.27134D-02,-2.32457D-02,-1.49604D+01,-1.42522D+01, &
383 : -2.32457D-02,-2.37412D-02,-1.42522D+01,-1.35496D+01, &
384 : -2.37412D-02,-2.42183D-02,-1.35496D+01,-1.28526D+01, &
385 : -2.42183D-02,-2.46613D-02,-1.28526D+01,-1.21615D+01, &
386 : -2.46613D-02,-2.50615D-02,-1.21615D+01,-1.14763D+01, &
387 : -2.50615D-02,-2.54057D-02,-1.14763D+01,-1.07971D+01, &
388 : -2.54057D-02,-2.56787D-02,-1.07971D+01,-1.01240D+01, &
389 : -2.56787D-02,-2.58623D-02,-1.01240D+01,-9.45709D+00, &
390 : -2.58623D-02,-2.59347D-02,-9.45709D+00,-8.79637D+00, &
391 : -2.59347D-02,-2.58697D-02,-8.79637D+00,-8.14187D+00, &
392 : -2.58697D-02,-2.56362D-02,-8.14187D+00,-7.49358D+00, &
393 : -2.56362D-02,-2.51970D-02,-7.49358D+00,-6.85144D+00, &
394 : -2.51970D-02,-2.45075D-02,-6.85144D+00,-6.21534D+00, &
395 : -2.45075D-02,-2.35146D-02,-6.21534D+00,-5.58513D+00, &
396 : -2.35146D-02,-2.21544D-02,-5.58513D+00,-4.96057D+00, &
397 : -2.21544D-02,-2.03503D-02,-4.96057D+00,-4.34132D+00, &
398 : -2.03503D-02,-1.80104D-02,-4.34132D+00,-3.72695D+00, &
399 : -1.80104D-02,-1.50236D-02,-3.72695D+00,-3.11691D+00, &
400 : -1.50236D-02,-1.12556D-02,-3.11691D+00,-2.51047D+00, &
401 : -1.12556D-02,-6.54378D-03,-2.51047D+00,-1.90674D+00, &
402 : -6.54378D-03,-6.90518D-04,-1.90674D+00,-1.30457D+00, &
403 : -6.90518D-04,+6.54438D-03,-1.30457D+00,-7.02574D-01, &
404 : +6.54438D-03,+1.54523D-02,-7.02574D-01,-9.90038D-02, &
405 : +1.54523D-02,+2.63848D-02,-9.90038D-02,+5.08275D-01, &
406 : +2.63848D-02,+3.97599D-02,+5.08275D-01,+1.12189D+00, &
407 : +3.97599D-02,+5.60625D-02,+1.12189D+00,+1.74504D+00, &
408 : +5.60625D-02,+7.58259D-02,+1.74504D+00,+2.38165D+00, &
409 : +7.58259D-02,+9.95773D-02,+2.38165D+00,+3.03645D+00, &
410 : +9.95773D-02,+1.27708D-01,+3.03645D+00,+3.71516D+00, &
411 : +1.27708D-01,+1.60207D-01,+3.71516D+00,+4.42451D+00, &
412 : +1.60207D-01,+1.96165D-01,+4.42451D+00,+5.17232D+00, &
413 : +1.96165D-01,+2.32939D-01,+5.17232D+00,+5.96720D+00, &
414 : +2.32939D-01,+2.64985D-01,+5.96720D+00,+6.81799D+00, &
415 : +2.64985D-01,+2.82691D-01,+6.81799D+00,+7.73238D+00, &
416 : +2.82691D-01,+2.72481D-01,+7.73238D+00,+8.71461D+00, &
417 : +2.72481D-01,+2.20588D-01,+8.71461D+00,+9.76224D+00, &
418 : +2.20588D-01,+1.23271D-01,+9.76224D+00,+1.08628D+01, &
419 : +1.23271D-01,+5.64105D-05,+1.08628D+01,+1.19930D+01, &
420 : +5.64105D-05,-1.01669D-01,+1.19930D+01,+1.31231D+01, &
421 : -1.01669D-01,-1.45351D-01,+1.31231D+01,+1.42289D+01, &
422 : -1.45351D-01,-1.12670D-01,+1.42289D+01,+1.52998D+01, &
423 : -1.12670D-01,-1.25510D-01,+1.52998D+01,+1.63436D+01, &
424 : -1.25510D-01,+4.14471D-02,+1.63436D+01,+1.73573D+01, &
425 : +4.14471D-02,-2.07236D-02,+1.73573D+01,+1.83810D+01 &
426 602 : ]
427 :
428 : DD1 = [ &
429 : +1.18229D-02,-2.36458D-02,-2.55112D+01,-2.47319D+01, &
430 : -2.36458D-02,-1.46794D-02,-2.47319D+01,-2.39583D+01, &
431 : -1.46794D-02,-1.76226D-02,-2.39583D+01,-2.31882D+01, &
432 : -1.76226D-02,-1.73748D-02,-2.31882D+01,-2.24223D+01, &
433 : -1.73748D-02,-1.79780D-02,-2.24223D+01,-2.16606D+01, &
434 : -1.79780D-02,-1.83439D-02,-2.16606D+01,-2.09032D+01, &
435 : -1.83439D-02,-1.87580D-02,-2.09032D+01,-2.01502D+01, &
436 : -1.87580D-02,-1.91359D-02,-2.01502D+01,-1.94017D+01, &
437 : -1.91359D-02,-1.94907D-02,-1.94017D+01,-1.86579D+01, &
438 : -1.94907D-02,-1.98074D-02,-1.86579D+01,-1.79186D+01, &
439 : -1.98074D-02,-2.00758D-02,-1.79186D+01,-1.71842D+01, &
440 : -2.00758D-02,-2.02817D-02,-1.71842D+01,-1.64545D+01, &
441 : -2.02817D-02,-2.04080D-02,-1.64545D+01,-1.57298D+01, &
442 : -2.04080D-02,-2.04344D-02,-1.57298D+01,-1.50099D+01, &
443 : -2.04344D-02,-2.03360D-02,-1.50099D+01,-1.42949D+01, &
444 : -2.03360D-02,-2.00828D-02,-1.42949D+01,-1.35848D+01, &
445 : -2.00828D-02,-1.96388D-02,-1.35848D+01,-1.28796D+01, &
446 : -1.96388D-02,-1.89603D-02,-1.28796D+01,-1.21790D+01, &
447 : -1.89603D-02,-1.79946D-02,-1.21790D+01,-1.14830D+01, &
448 : -1.79946D-02,-1.66781D-02,-1.14830D+01,-1.07913D+01, &
449 : -1.66781D-02,-1.49334D-02,-1.07913D+01,-1.01036D+01, &
450 : -1.49334D-02,-1.26670D-02,-1.01036D+01,-9.41952D+00, &
451 : -1.26670D-02,-9.76488D-03,-9.41952D+00,-8.73845D+00, &
452 : -9.76488D-03,-6.08817D-03,-8.73845D+00,-8.05974D+00, &
453 : -6.08817D-03,-1.46688D-03,-8.05974D+00,-7.38248D+00, &
454 : -1.46688D-03,+4.30758D-03,-7.38248D+00,-6.70557D+00, &
455 : +4.30758D-03,+1.14919D-02,-6.70557D+00,-6.02763D+00, &
456 : +1.14919D-02,+2.04026D-02,-6.02763D+00,-5.34694D+00, &
457 : +2.04026D-02,+3.14302D-02,-5.34694D+00,-4.66134D+00, &
458 : +3.14302D-02,+4.50547D-02,-4.66134D+00,-3.96821D+00, &
459 : +4.50547D-02,+6.18616D-02,-3.96821D+00,-3.26426D+00, &
460 : +6.18616D-02,+8.25526D-02,-3.26426D+00,-2.54546D+00, &
461 : +8.25526D-02,+1.07939D-01,-2.54546D+00,-1.80685D+00, &
462 : +1.07939D-01,+1.38897D-01,-1.80685D+00,-1.04234D+00, &
463 : +1.38897D-01,+1.76234D-01,-1.04234D+00,-2.44487D-01, &
464 : +1.76234D-01,+2.20387D-01,-2.44487D-01,+5.95659D-01, &
465 : +2.20387D-01,+2.70814D-01,+5.95659D-01,+1.48870D+00, &
466 : +2.70814D-01,+3.24880D-01,+1.48870D+00,+2.44673D+00, &
467 : +3.24880D-01,+3.76096D-01,+2.44673D+00,+3.48274D+00, &
468 : +3.76096D-01,+4.11895D-01,+3.48274D+00,+4.60901D+00, &
469 : +4.11895D-01,+4.12194D-01,+4.60901D+00,+5.83413D+00, &
470 : +4.12194D-01,+3.52176D-01,+5.83413D+00,+7.15818D+00, &
471 : +3.52176D-01,+2.14860D-01,+7.15818D+00,+8.56675D+00, &
472 : +2.14860D-01,+1.56932D-02,+8.56675D+00,+1.00269D+01, &
473 : +1.56932D-02,-1.84529D-01,+1.00269D+01,+1.14908D+01, &
474 : -1.84529D-01,-3.17740D-01,+1.14908D+01,+1.29104D+01, &
475 : -3.17740D-01,-3.51796D-01,+1.29104D+01,+1.42538D+01, &
476 : -3.51796D-01,-2.86379D-01,+1.42538D+01,+1.55127D+01, &
477 : -2.86379D-01,-2.68214D-01,+1.55127D+01,+1.67029D+01, &
478 : -2.68214D-01,+1.34107D-01,+1.67029D+01,+1.78287D+01 &
479 202 : ]
480 :
481 : DCAT1 = [ &
482 : -4.85605D+00,+9.71211D+00,-2.44778D+01,-2.50688D+01, &
483 : +9.71211D+00,-9.31384D+00,-2.50688D+01,-2.33288D+01, &
484 : -9.31384D+00,+9.24600D+00,-2.33288D+01,-2.38242D+01, &
485 : +9.24600D+00,-5.09678D+00,-2.38242D+01,-2.21005D+01, &
486 : -5.09678D+00,-3.51130D-01,-2.21005D+01,-2.16001D+01, &
487 : -3.51130D-01,-5.73409D-01,-2.16001D+01,-2.11839D+01, &
488 : -5.73409D-01,+1.83302D+00,-2.11839D+01,-2.09054D+01, &
489 : +1.83302D+00,-7.68878D-01,-2.09054D+01,-2.01869D+01, &
490 : -7.68878D-01,+9.36371D-01,-2.01869D+01,-1.96529D+01, &
491 : +9.36371D-01,-8.65172D-01,-1.96529D+01,-1.88943D+01, &
492 : -8.65172D-01,-1.42540D+00,-1.88943D+01,-1.83432D+01, &
493 : -1.42540D+00,+4.34705D+00,-1.83432D+01,-1.81343D+01, &
494 : +4.34705D+00,+3.61550D-01,-1.81343D+01,-1.68820D+01, &
495 : +3.61550D-01,-3.50574D+00,-1.68820D+01,-1.55430D+01, &
496 : -3.50574D+00,+2.59550D+00,-1.55430D+01,-1.50454D+01, &
497 : +2.59550D+00,-1.44563D+00,-1.50454D+01,-1.39249D+01, &
498 : -1.44563D+00,-8.64470D-01,-1.39249D+01,-1.31513D+01, &
499 : -8.64470D-01,+8.82476D-01,-1.31513D+01,-1.25851D+01, &
500 : +8.82476D-01,+1.35231D-01,-1.25851D+01,-1.18072D+01, &
501 : +1.35231D-01,+8.48986D-02,-1.18072D+01,-1.09968D+01, &
502 : +8.48986D-02,-5.89033D-02,-1.09968D+01,-1.01661D+01, &
503 : -5.89033D-02,-1.07275D-01,-1.01661D+01,-9.34947D+00, &
504 : -1.07275D-01,-1.53774D-01,-9.34947D+00,-8.55860D+00, &
505 : -1.53774D-01,-6.39482D-02,-8.55860D+00,-7.80464D+00, &
506 : -6.39482D-02,-1.27604D-01,-7.80464D+00,-7.06602D+00, &
507 : -1.27604D-01,-3.16007D-01,-7.06602D+00,-6.35803D+00, &
508 : -3.16007D-01,-7.55843D-02,-6.35803D+00,-5.72588D+00, &
509 : -7.55843D-02,+6.48945D-02,-5.72588D+00,-5.11188D+00, &
510 : +6.48945D-02,+5.15827D-02,-5.11188D+00,-4.48229D+00, &
511 : +5.15827D-02,-4.79565D-01,-4.48229D+00,-3.84033D+00, &
512 : -4.79565D-01,+3.59783D-01,-3.84033D+00,-3.31347D+00, &
513 : +3.59783D-01,-3.04381D-01,-3.31347D+00,-2.70025D+00, &
514 : -3.04381D-01,+1.12514D-01,-2.70025D+00,-2.16009D+00, &
515 : +1.12514D-01,+1.90268D-01,-2.16009D+00,-1.59292D+00, &
516 : +1.90268D-01,+1.96365D-01,-1.59292D+00,-9.80089D-01, &
517 : +1.96365D-01,+1.78507D-01,-9.80089D-01,-3.20131D-01, &
518 : +1.78507D-01,+1.77190D-01,-3.20131D-01,+3.82669D-01, &
519 : +1.77190D-01,+1.92652D-01,+3.82669D-01,+1.12800D+00, &
520 : +1.92652D-01,+2.20472D-01,+1.12800D+00,+1.91956D+00, &
521 : +2.20472D-01,+2.52940D-01,+1.91956D+00,+2.76403D+00, &
522 : +2.52940D-01,+2.82221D-01,+2.76403D+00,+3.66921D+00, &
523 : +2.82221D-01,+3.00417D-01,+3.66921D+00,+4.64213D+00, &
524 : +3.00417D-01,+2.99089D-01,+4.64213D+00,+5.68714D+00, &
525 : +2.99089D-01,+2.69658D-01,+5.68714D+00,+6.80394D+00, &
526 : +2.69658D-01,+2.08129D-01,+6.80394D+00,+7.98545D+00, &
527 : +2.08129D-01,+1.12949D-01,+7.98545D+00,+9.21692D+00, &
528 : +1.12949D-01,+9.86067D-03,+9.21692D+00,+1.04755D+01, &
529 : +9.86067D-03,-1.12290D-01,+1.04755D+01,+1.17364D+01, &
530 : -1.12290D-01,-2.95924D-02,+1.17364D+01,+1.29704D+01, &
531 : -2.95924D-02,+1.47962D-02,+1.29704D+01,+1.41973D+01, &
532 :
533 : -3.80453D+00,+7.60906D+00,-2.08526D+01,-2.11137D+01, &
534 : +7.60906D+00,-1.00677D+01,-2.11137D+01,-1.95486D+01, &
535 : -1.00677D+01,+1.09298D+01,-1.95486D+01,-2.03997D+01, &
536 : +1.09298D+01,-3.76938D+00,-2.03997D+01,-1.86277D+01, &
537 : -3.76938D+00,-2.50868D+00,-1.86277D+01,-1.77604D+01, &
538 : -2.50868D+00,+2.83415D+00,-1.77604D+01,-1.74951D+01, &
539 : +2.83415D+00,-1.06745D+00,-1.74951D+01,-1.65496D+01, &
540 : -1.06745D+00,-2.73597D-01,-1.65496D+01,-1.58604D+01, &
541 : -2.73597D-01,+5.70462D-01,-1.58604D+01,-1.52368D+01, &
542 : +5.70462D-01,+1.17072D-01,-1.52368D+01,-1.44762D+01, &
543 : +1.17072D-01,-4.26755D-01,-1.44762D+01,-1.36876D+01, &
544 : -4.26755D-01,+1.84166D+00,-1.36876D+01,-1.30014D+01, &
545 : +1.84166D+00,-4.51420D-02,-1.30014D+01,-1.18732D+01, &
546 : -4.51420D-02,-1.68106D+00,-1.18732D+01,-1.07559D+01, &
547 : -1.68106D+00,+7.40637D-01,-1.07559D+01,-1.00419D+01, &
548 : +7.40637D-01,-4.15277D-01,-1.00419D+01,-9.15028D+00, &
549 : -4.15277D-01,-5.31841D-01,-9.15028D+00,-8.35829D+00, &
550 : -5.31841D-01,+7.54067D-02,-8.35829D+00,-7.69393D+00, &
551 : +7.54067D-02,+3.64437D-02,-7.69393D+00,-7.01148D+00, &
552 : +3.64437D-02,+8.52374D-03,-7.01148D+00,-6.32029D+00, &
553 : +8.52374D-03,-5.24956D-02,-6.32029D+00,-5.62704D+00, &
554 : -5.24956D-02,-8.76527D-02,-5.62704D+00,-4.94640D+00, &
555 : -8.76527D-02,-1.07693D-01,-4.94640D+00,-4.28679D+00, &
556 : -1.07693D-01,-1.02441D-01,-4.28679D+00,-3.65303D+00, &
557 : -1.02441D-01,-1.04497D-01,-3.65303D+00,-3.04386D+00, &
558 : -1.04497D-01,-1.16430D-01,-3.04386D+00,-2.45976D+00, &
559 : -1.16430D-01,-8.20446D-02,-2.45976D+00,-1.90361D+00, &
560 : -8.20446D-02,-5.53768D-02,-1.90361D+00,-1.36715D+00, &
561 : -5.53768D-02,-4.31036D-02,-1.36715D+00,-8.43977D-01, &
562 : -4.31036D-02,-8.94580D-02,-8.43977D-01,-3.31151D-01, &
563 : -8.94580D-02,+1.74820D-02,-3.31151D-01,+1.60205D-01, &
564 : +1.74820D-02,-4.17248D-02,+1.60205D-01,+6.55758D-01, &
565 : -4.17248D-02,+2.16009D-02,+6.55758D-01,+1.14130D+00, &
566 : +2.16009D-02,+5.02965D-02,+1.14130D+00,+1.63202D+00, &
567 : +5.02965D-02,+7.34150D-02,+1.63202D+00,+2.13481D+00, &
568 : +7.34150D-02,+9.68269D-02,+2.13481D+00,+2.65522D+00, &
569 : +9.68269D-02,+1.25372D-01,+2.65522D+00,+3.19888D+00, &
570 : +1.25372D-01,+1.59190D-01,+3.19888D+00,+3.77262D+00, &
571 : +1.59190D-01,+1.96991D-01,+3.77262D+00,+4.38456D+00, &
572 : +1.96991D-01,+2.35595D-01,+4.38456D+00,+5.04379D+00, &
573 : +2.35595D-01,+2.69792D-01,+5.04379D+00,+5.75956D+00, &
574 : +2.69792D-01,+2.92272D-01,+5.75956D+00,+6.54007D+00, &
575 : +2.92272D-01,+2.95067D-01,+6.54007D+00,+7.39073D+00, &
576 : +2.95067D-01,+2.70564D-01,+7.39073D+00,+8.31221D+00, &
577 : +2.70564D-01,+2.20440D-01,+8.31221D+00,+9.29863D+00, &
578 : +2.20440D-01,+1.38511D-01,+9.29863D+00,+1.03379D+01, &
579 : +1.38511D-01,+8.80848D-02,+1.03379D+01,+1.14105D+01, &
580 : +8.80848D-02,-7.78941D-02,+1.14105D+01,+1.25042D+01, &
581 : -7.78941D-02,+3.60071D-01,+1.25042D+01,+1.35792D+01, &
582 : +3.60071D-01,-1.80035D-01,+1.35792D+01,+1.47406D+01, &
583 :
584 : -2.06818D+00,+4.13636D+00,-1.54059D+01,-1.51150D+01, &
585 : +4.13636D+00,-8.93460D+00,-1.51150D+01,-1.38314D+01, &
586 : -8.93460D+00,+1.08282D+01,-1.38314D+01,-1.46921D+01, &
587 : +1.08282D+01,-2.97377D+00,-1.46921D+01,-1.29540D+01, &
588 : -2.97377D+00,-2.25377D+00,-1.29540D+01,-1.19296D+01, &
589 : -2.25377D+00,+2.79041D+00,-1.19296D+01,-1.14462D+01, &
590 : +2.79041D+00,-1.37253D+00,-1.14462D+01,-1.02930D+01, &
591 : -1.37253D+00,-3.87183D-01,-1.02930D+01,-9.46928D+00, &
592 : -3.87183D-01,+3.36588D-01,-9.46928D+00,-8.73845D+00, &
593 : +3.36588D-01,+2.05509D-01,-8.73845D+00,-7.92684D+00, &
594 : +2.05509D-01,-9.13383D-02,-7.92684D+00,-7.06591D+00, &
595 : -9.13383D-02,+5.02385D-01,-7.06591D+00,-6.22691D+00, &
596 : +5.02385D-01,-1.25938D-01,-6.22691D+00,-5.26733D+00, &
597 : -1.25938D-01,-6.87925D-01,-5.26733D+00,-4.33797D+00, &
598 : -6.87925D-01,+8.12958D-02,-4.33797D+00,-3.57372D+00, &
599 : +8.12958D-02,-2.46616D-01,-3.57372D+00,-2.78995D+00, &
600 : -2.46616D-01,-3.03295D-01,-2.78995D+00,-2.06538D+00, &
601 : -3.03295D-01,-9.83392D-02,-2.06538D+00,-1.41359D+00, &
602 : -9.83392D-02,-7.94911D-02,-1.41359D+00,-7.85408D-01, &
603 : -7.94911D-02,-7.66879D-02,-7.85408D-01,-1.76302D-01, &
604 : -7.66879D-02,-8.63431D-02,-1.76302D-01,+4.14399D-01, &
605 : -8.63431D-02,-9.05049D-02,+4.14399D-01,+9.84378D-01, &
606 : -9.05049D-02,-9.00801D-02,+9.84378D-01,+1.53264D+00, &
607 : -9.00801D-02,-8.47287D-02,+1.53264D+00,+2.05927D+00, &
608 : -8.47287D-02,-7.78775D-02,+2.05927D+00,+2.56558D+00, &
609 : -7.78775D-02,-7.05918D-02,+2.56558D+00,+3.05319D+00, &
610 : -7.05918D-02,-5.90727D-02,+3.05319D+00,+3.52386D+00, &
611 : -5.90727D-02,-4.74236D-02,+3.52386D+00,+3.98035D+00, &
612 : -4.74236D-02,-3.62205D-02,+3.98035D+00,+4.42546D+00, &
613 : -3.62205D-02,-2.90446D-02,+4.42546D+00,+4.86188D+00, &
614 : -2.90446D-02,-8.69943D-03,+4.86188D+00,+5.29133D+00, &
615 : -8.69943D-03,-2.75832D-04,+5.29133D+00,+5.71869D+00, &
616 : -2.75832D-04,+1.96726D-02,+5.71869D+00,+6.14599D+00, &
617 : +1.96726D-02,+3.91533D-02,+6.14599D+00,+6.57800D+00, &
618 : +3.91533D-02,+6.09268D-02,+6.57800D+00,+7.01941D+00, &
619 : +6.09268D-02,+8.60213D-02,+7.01941D+00,+7.47545D+00, &
620 : +8.60213D-02,+1.15234D-01,+7.47545D+00,+7.95213D+00, &
621 : +1.15234D-01,+1.48588D-01,+7.95213D+00,+8.45646D+00, &
622 : +1.48588D-01,+1.85161D-01,+8.45646D+00,+8.99646D+00, &
623 : +1.85161D-01,+2.22451D-01,+8.99646D+00,+9.58090D+00, &
624 : +2.22451D-01,+2.55866D-01,+9.58090D+00,+1.02187D+01, &
625 : +2.55866D-01,+2.78501D-01,+1.02187D+01,+1.09180D+01, &
626 : +2.78501D-01,+2.83080D-01,+1.09180D+01,+1.16840D+01, &
627 : +2.83080D-01,+2.62093D-01,+1.16840D+01,+1.25180D+01, &
628 : +2.62093D-01,+2.21026D-01,+1.25180D+01,+1.34149D+01, &
629 : +2.21026D-01,+1.44689D-01,+1.34149D+01,+1.43649D+01, &
630 : +1.44689D-01,+1.33750D-01,+1.43649D+01,+1.53496D+01, &
631 : +1.33750D-01,-1.00279D-01,+1.53496D+01,+1.63664D+01, &
632 : -1.00279D-01,+7.07988D-01,+1.63664D+01,+1.73591D+01, &
633 : +7.07988D-01,-3.53994D-01,+1.73591D+01,+1.85217D+01 &
634 602 : ]
635 :
636 : DDAT1 = [ &
637 : -1.70341D+00,+3.40681D+00,-2.30677D+01,-2.36179D+01, &
638 : +3.40681D+00,-1.49538D-01,-2.36179D+01,-2.33505D+01, &
639 : -1.49538D-01,+5.36125D+00,-2.33505D+01,-2.31190D+01, &
640 : +5.36125D+00,-6.27728D+00,-2.31190D+01,-2.16008D+01, &
641 : -6.27728D+00,+7.81096D+00,-2.16008D+01,-2.15892D+01, &
642 : +7.81096D+00,-6.95942D-01,-2.15892D+01,-1.97029D+01, &
643 : -6.95942D-01,-4.07855D+00,-1.97029D+01,-1.79836D+01, &
644 : -4.07855D+00,-2.58381D+00,-1.79836D+01,-1.72432D+01, &
645 : -2.58381D+00,-9.97977D-01,-1.72432D+01,-1.71229D+01, &
646 : -9.97977D-01,+5.38341D+00,-1.71229D+01,-1.72422D+01, &
647 : +5.38341D+00,-2.04809D+00,-1.72422D+01,-1.60694D+01, &
648 : -2.04809D+00,+3.50576D+00,-1.60694D+01,-1.53881D+01, &
649 : +3.50576D+00,-4.79859D+00,-1.53881D+01,-1.38655D+01, &
650 : -4.79859D+00,+1.16840D+00,-1.38655D+01,-1.34945D+01, &
651 : +1.16840D+00,+8.19462D-01,-1.34945D+01,-1.28431D+01, &
652 : +8.19462D-01,-1.82778D+00,-1.28431D+01,-1.19950D+01, &
653 : -1.82778D+00,-1.65089D-02,-1.19950D+01,-1.15856D+01, &
654 : -1.65089D-02,-4.16448D-01,-1.15856D+01,-1.11802D+01, &
655 : -4.16448D-01,+1.88821D+00,-1.11802D+01,-1.08747D+01, &
656 : +1.88821D+00,+8.26616D-01,-1.08747D+01,-1.01161D+01, &
657 : +8.26616D-01,-2.03576D-01,-1.01161D+01,-9.15902D+00, &
658 : -2.03576D-01,-4.49988D-01,-9.15902D+00,-8.25083D+00, &
659 : -4.49988D-01,-3.23824D-01,-8.25083D+00,-7.45064D+00, &
660 : -3.23824D-01,-1.52158D-01,-7.45064D+00,-6.72817D+00, &
661 : -1.52158D-01,-3.19250D-02,-6.72817D+00,-6.04221D+00, &
662 : -3.19250D-02,+7.02209D-02,-6.04221D+00,-5.36392D+00, &
663 : +7.02209D-02,+4.52255D-02,-5.36392D+00,-4.66877D+00, &
664 : +4.52255D-02,+1.46629D-01,-4.66877D+00,-3.96278D+00, &
665 : +1.46629D-01,+9.38012D-03,-3.96278D+00,-3.22158D+00, &
666 : +9.38012D-03,+1.43265D-01,-3.22158D+00,-2.47814D+00, &
667 : +1.43265D-01,+7.07177D-02,-2.47814D+00,-1.70032D+00, &
668 : +7.07177D-02,+4.40308D-02,-1.70032D+00,-9.05521D-01, &
669 : +4.40308D-02,+4.86217D-02,-9.05521D-01,-1.00156D-01, &
670 : +4.86217D-02,+1.51036D-01,-1.00156D-01,+7.16878D-01, &
671 : +1.51036D-01,+7.56348D-02,+7.16878D-01,+1.57016D+00, &
672 : +7.56348D-02,+6.35608D-02,+1.57016D+00,+2.44160D+00, &
673 : +6.35608D-02,+1.03660D-01,+2.44160D+00,+3.32829D+00, &
674 : +1.03660D-01,+1.48495D-01,+3.32829D+00,+4.23985D+00, &
675 : +1.48495D-01,+1.87179D-01,+4.23985D+00,+5.18706D+00, &
676 : +1.87179D-01,+2.19549D-01,+5.18706D+00,+6.17919D+00, &
677 : +2.19549D-01,+2.34271D-01,+6.17919D+00,+7.22401D+00, &
678 : +2.34271D-01,+2.18239D-01,+7.22401D+00,+8.32506D+00, &
679 : +2.18239D-01,+1.72842D-01,+8.32506D+00,+9.47848D+00, &
680 : +1.72842D-01,+1.06073D-01,+9.47848D+00,+1.06734D+01, &
681 : +1.06073D-01,+3.51672D-02,+1.06734D+01,+1.18938D+01, &
682 : +3.51672D-02,-3.76546D-02,+1.18938D+01,+1.31226D+01, &
683 : -3.76546D-02,-5.81893D-02,+1.31226D+01,+1.43423D+01, &
684 : -5.81893D-02,-1.82463D-01,+1.43423D+01,+1.55481D+01, &
685 : -1.82463D-01,+2.72096D-01,+1.55481D+01,+1.67101D+01, &
686 : +2.72096D-01,-1.36048D-01,+1.67101D+01,+1.79374D+01 &
687 202 : ]
688 :
689 1 : have_initialized = .true.
690 :
691 : end if
692 : !$omp end critical (collision_integrals)
693 : end subroutine initialise_collision_integrals
694 :
695 :
696 1 : subroutine free_collision_integrals
697 :
698 2 : !$omp critical (collision_integrals_shutdown)
699 1 : if (have_initialized) then
700 1 : if (associated(DC) .and. allocated(DC1)) then
701 1 : deallocate(DC1)
702 1 : nullify(DC)
703 : end if
704 1 : if (associated(DD) .and. allocated(DD1)) then
705 1 : deallocate(DD1)
706 1 : nullify(DD)
707 : end if
708 1 : if (associated(DCAT) .and. allocated(DCAT1)) then
709 1 : deallocate(DCAT1)
710 1 : nullify(DCAT)
711 : end if
712 1 : if (associated(DDAT) .and. allocated(DDAT1)) then
713 1 : deallocate(DDAT1)
714 1 : nullify(DDAT)
715 : end if
716 1 : have_initialized = .FALSE.
717 : end if
718 : !$omp end critical (collision_integrals_shutdown)
719 1 : end subroutine free_collision_integrals
720 :
721 : end module paquette_coeffs
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