1 | double form_volume(double thick_core, |
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2 | double thick_layer, |
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3 | double radius, |
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4 | double n_stacking); |
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5 | |
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6 | double Iq(double q, |
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7 | double thick_core, |
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8 | double thick_layer, |
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9 | double radius, |
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10 | double n_stacking, |
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11 | double sigma_dnn, |
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12 | double core_sld, |
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13 | double layer_sld, |
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14 | double solvent_sld); |
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15 | |
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16 | double Iqxy(double qx, double qy, |
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17 | double thick_core, |
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18 | double thick_layer, |
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19 | double radius, |
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20 | double n_stacking, |
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21 | double sigma_dnn, |
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22 | double core_sld, |
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23 | double layer_sld, |
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24 | double solvent_sld, |
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25 | double theta, |
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26 | double phi); |
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27 | |
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28 | static |
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29 | double _kernel(double q, |
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30 | double radius, |
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31 | double core_sld, |
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32 | double layer_sld, |
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33 | double solvent_sld, |
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34 | double halfheight, |
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35 | double thick_layer, |
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36 | double sin_alpha, |
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37 | double cos_alpha, |
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38 | double sigma_dnn, |
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39 | double d, |
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40 | double n_stacking) |
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41 | |
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42 | { |
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43 | // q is the q-value for the calculation (1/A) |
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44 | // radius is the core radius of the cylinder (A) |
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45 | // *_sld are the respective SLD's |
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46 | // halfheight is the *Half* CORE-LENGTH of the cylinder = L (A) |
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47 | // zi is the dummy variable for the integration (x in Feigin's notation) |
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48 | |
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49 | const double besarg1 = q*radius*sin_alpha; |
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50 | //const double besarg2 = q*radius*sin_alpha; |
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51 | |
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52 | const double sinarg1 = q*halfheight*cos_alpha; |
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53 | const double sinarg2 = q*(halfheight+thick_layer)*cos_alpha; |
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54 | |
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55 | const double be1 = sas_2J1x_x(besarg1); |
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56 | //const double be2 = sas_J1c(besarg2); |
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57 | const double be2 = be1; |
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58 | const double si1 = sas_sinx_x(sinarg1); |
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59 | const double si2 = sas_sinx_x(sinarg2); |
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60 | |
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61 | const double dr1 = core_sld - solvent_sld; |
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62 | const double dr2 = layer_sld - solvent_sld; |
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63 | const double area = M_PI*radius*radius; |
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64 | const double totald = 2.0*(thick_layer + halfheight); |
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65 | |
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66 | const double t1 = area * (2.0*halfheight) * dr1 * si1 * be1; |
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67 | const double t2 = area * dr2 * (totald*si2 - 2.0*halfheight*si1) * be2; |
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68 | |
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69 | double pq = square(t1 + t2); |
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70 | |
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71 | // loop for the structure factor S(q) |
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72 | double qd_cos_alpha = q*d*cos_alpha; |
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73 | //d*cos_alpha is the projection of d onto q (in other words the component |
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74 | //of d that is parallel to q. |
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75 | double debye_arg = -0.5*square(qd_cos_alpha*sigma_dnn); |
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76 | double sq=0.0; |
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77 | for (int kk=1; kk<n_stacking; kk++) { |
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78 | sq += (n_stacking-kk) * cos(qd_cos_alpha*kk) * exp(debye_arg*kk); |
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79 | } |
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80 | // end of loop for S(q) |
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81 | sq = 1.0 + 2.0*sq/n_stacking; |
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82 | |
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83 | return pq * sq * n_stacking; |
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84 | // volume normalization should be per disk not per stack but form_volume |
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85 | // is per stack so correct here for now. Could change form_volume but |
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86 | // if one ever wants to use P*S we need the ER based on the total volume |
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87 | } |
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88 | |
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89 | |
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90 | static |
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91 | double stacked_disks_kernel(double q, |
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92 | double thick_core, |
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93 | double thick_layer, |
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94 | double radius, |
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95 | double n_stacking, |
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96 | double sigma_dnn, |
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97 | double core_sld, |
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98 | double layer_sld, |
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99 | double solvent_sld) |
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100 | { |
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101 | /* StackedDiscsX : calculates the form factor of a stacked "tactoid" of core shell disks |
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102 | like clay platelets that are not exfoliated |
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103 | */ |
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104 | double summ = 0.0; //initialize integral |
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105 | |
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106 | double d = 2.0*thick_layer+thick_core; |
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107 | double halfheight = 0.5*thick_core; |
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108 | |
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109 | for(int i=0; i<N_POINTS_76; i++) { |
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110 | double zi = (Gauss76Z[i] + 1.0)*M_PI_4; |
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111 | double sin_alpha, cos_alpha; // slots to hold sincos function output |
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112 | SINCOS(zi, sin_alpha, cos_alpha); |
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113 | double yyy = _kernel(q, |
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114 | radius, |
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115 | core_sld, |
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116 | layer_sld, |
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117 | solvent_sld, |
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118 | halfheight, |
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119 | thick_layer, |
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120 | sin_alpha, |
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121 | cos_alpha, |
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122 | sigma_dnn, |
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123 | d, |
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124 | n_stacking); |
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125 | summ += Gauss76Wt[i] * yyy * sin_alpha; |
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126 | } |
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127 | |
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128 | double answer = M_PI_4*summ; |
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129 | |
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130 | //Convert to [cm-1] |
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131 | return 1.0e-4*answer; |
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132 | } |
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133 | |
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134 | double form_volume(double thick_core, |
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135 | double thick_layer, |
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136 | double radius, |
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137 | double n_stacking){ |
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138 | double d = 2.0 * thick_layer + thick_core; |
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139 | return M_PI * radius * radius * d * n_stacking; |
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140 | } |
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141 | |
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142 | double Iq(double q, |
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143 | double thick_core, |
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144 | double thick_layer, |
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145 | double radius, |
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146 | double n_stacking, |
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147 | double sigma_dnn, |
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148 | double core_sld, |
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149 | double layer_sld, |
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150 | double solvent_sld) |
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151 | { |
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152 | return stacked_disks_kernel(q, |
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153 | thick_core, |
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154 | thick_layer, |
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155 | radius, |
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156 | n_stacking, |
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157 | sigma_dnn, |
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158 | core_sld, |
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159 | layer_sld, |
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160 | solvent_sld); |
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161 | } |
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162 | |
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163 | |
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164 | double |
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165 | Iqxy(double qx, double qy, |
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166 | double thick_core, |
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167 | double thick_layer, |
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168 | double radius, |
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169 | double n_stacking, |
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170 | double sigma_dnn, |
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171 | double core_sld, |
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172 | double layer_sld, |
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173 | double solvent_sld, |
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174 | double theta, |
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175 | double phi) |
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176 | { |
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177 | double q, sin_alpha, cos_alpha; |
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178 | ORIENT_SYMMETRIC(qx, qy, theta, phi, q, sin_alpha, cos_alpha); |
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179 | |
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180 | double d = 2.0 * thick_layer + thick_core; |
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181 | double halfheight = 0.5*thick_core; |
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182 | double answer = _kernel(q, |
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183 | radius, |
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184 | core_sld, |
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185 | layer_sld, |
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186 | solvent_sld, |
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187 | halfheight, |
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188 | thick_layer, |
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189 | sin_alpha, |
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190 | cos_alpha, |
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191 | sigma_dnn, |
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192 | d, |
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193 | n_stacking); |
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194 | |
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195 | //convert to [cm-1] |
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196 | answer *= 1.0e-4; |
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197 | |
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198 | return answer; |
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199 | } |
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200 | |
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