1 | static double |
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2 | shell_volume(double length_a, double b2a_ratio, double c2a_ratio, double thickness) |
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3 | { |
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4 | const double length_b = length_a * b2a_ratio; |
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5 | const double length_c = length_a * c2a_ratio; |
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6 | const double form_volume = length_a * length_b * length_c; |
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7 | const double a_core = length_a - 2.0*thickness; |
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8 | const double b_core = length_b - 2.0*thickness; |
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9 | const double c_core = length_c - 2.0*thickness; |
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10 | const double core_volume = a_core * b_core * c_core; |
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11 | return form_volume - core_volume; |
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12 | } |
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13 | |
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14 | static double |
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15 | form_volume(double length_a, double b2a_ratio, double c2a_ratio, double thickness) |
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16 | { |
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17 | const double length_b = length_a * b2a_ratio; |
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18 | const double length_c = length_a * c2a_ratio; |
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19 | const double form_volume = length_a * length_b * length_c; |
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20 | return form_volume; |
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21 | } |
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22 | |
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23 | static double |
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24 | radius_from_excluded_volume(double length_a, double b2a_ratio, double c2a_ratio) |
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25 | { |
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26 | const double r_equiv = sqrt(length_a*length_a*b2a_ratio/M_PI); |
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27 | const double length_c = length_a*c2a_ratio; |
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28 | return 0.5*cbrt(0.75*r_equiv*(2.0*r_equiv*length_c + (r_equiv + length_c)*(M_PI*r_equiv + length_c))); |
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29 | } |
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30 | |
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31 | static double |
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32 | effective_radius(int mode, double length_a, double b2a_ratio, double c2a_ratio, double thickness) |
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33 | // NOTE length_a is external dimension! |
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34 | { |
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35 | switch (mode) { |
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36 | default: |
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37 | case 1: // equivalent cylinder excluded volume |
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38 | return radius_from_excluded_volume(length_a, b2a_ratio, c2a_ratio); |
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39 | case 2: // equivalent outer volume sphere |
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40 | return cbrt(cube(length_a)*b2a_ratio*c2a_ratio/M_4PI_3); |
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41 | case 3: // half length_a |
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42 | return 0.5 * length_a; |
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43 | case 4: // half length_b |
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44 | return 0.5 * length_a*b2a_ratio; |
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45 | case 5: // half length_c |
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46 | return 0.5 * length_a*c2a_ratio; |
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47 | case 6: // equivalent outer circular cross-section |
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48 | return length_a*sqrt(b2a_ratio/M_PI); |
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49 | case 7: // half ab diagonal |
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50 | return 0.5*sqrt(square(length_a) * (1.0 + square(b2a_ratio))); |
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51 | case 8: // half diagonal |
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52 | return 0.5*sqrt(square(length_a) * (1.0 + square(b2a_ratio) + square(c2a_ratio))); |
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53 | } |
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54 | } |
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55 | |
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56 | static void |
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57 | Fq(double q, |
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58 | double *F1, |
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59 | double *F2, |
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60 | double sld, |
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61 | double solvent_sld, |
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62 | double length_a, |
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63 | double b2a_ratio, |
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64 | double c2a_ratio, |
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65 | double thickness) |
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66 | { |
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67 | const double length_b = length_a * b2a_ratio; |
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68 | const double length_c = length_a * c2a_ratio; |
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69 | const double a_half = 0.5 * length_a; |
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70 | const double b_half = 0.5 * length_b; |
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71 | const double c_half = 0.5 * length_c; |
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72 | const double vol_total = length_a * length_b * length_c; |
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73 | const double vol_core = 8.0 * (a_half-thickness) * (b_half-thickness) * (c_half-thickness); |
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74 | |
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75 | //Integration limits to use in Gaussian quadrature |
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76 | const double v1a = 0.0; |
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77 | const double v1b = M_PI_2; //theta integration limits |
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78 | const double v2a = 0.0; |
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79 | const double v2b = M_PI_2; //phi integration limits |
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80 | |
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81 | double outer_sum_F1 = 0.0; |
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82 | double outer_sum_F2 = 0.0; |
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83 | for(int i=0; i<GAUSS_N; i++) { |
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84 | |
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85 | const double theta = 0.5 * ( GAUSS_Z[i]*(v1b-v1a) + v1a + v1b ); |
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86 | double sin_theta, cos_theta; |
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87 | SINCOS(theta, sin_theta, cos_theta); |
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88 | |
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89 | const double termC1 = sas_sinx_x(q * c_half * cos(theta)); |
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90 | const double termC2 = sas_sinx_x(q * (c_half-thickness)*cos(theta)); |
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91 | |
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92 | double inner_sum_F1 = 0.0; |
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93 | double inner_sum_F2 = 0.0; |
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94 | for(int j=0; j<GAUSS_N; j++) { |
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95 | |
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96 | const double phi = 0.5 * ( GAUSS_Z[j]*(v2b-v2a) + v2a + v2b ); |
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97 | double sin_phi, cos_phi; |
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98 | SINCOS(phi, sin_phi, cos_phi); |
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99 | |
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100 | // Amplitude AP from eqn. (13), rewritten to avoid round-off effects when arg=0 |
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101 | |
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102 | const double termA1 = sas_sinx_x(q * a_half * sin_theta * sin_phi); |
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103 | const double termA2 = sas_sinx_x(q * (a_half-thickness) * sin_theta * sin_phi); |
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104 | |
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105 | const double termB1 = sas_sinx_x(q * b_half * sin_theta * cos_phi); |
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106 | const double termB2 = sas_sinx_x(q * (b_half-thickness) * sin_theta * cos_phi); |
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107 | |
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108 | const double AP1 = vol_total * termA1 * termB1 * termC1; |
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109 | const double AP2 = vol_core * termA2 * termB2 * termC2; |
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110 | |
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111 | inner_sum_F1 += GAUSS_W[j] * (AP1-AP2); |
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112 | inner_sum_F2 += GAUSS_W[j] * square(AP1-AP2); |
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113 | } |
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114 | inner_sum_F1 *= 0.5 * (v2b-v2a); |
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115 | inner_sum_F2 *= 0.5 * (v2b-v2a); |
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116 | |
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117 | outer_sum_F1 += GAUSS_W[i] * inner_sum_F1 * sin(theta); |
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118 | outer_sum_F2 += GAUSS_W[i] * inner_sum_F2 * sin(theta); |
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119 | } |
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120 | outer_sum_F1 *= 0.5*(v1b-v1a); |
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121 | outer_sum_F2 *= 0.5*(v1b-v1a); |
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122 | |
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123 | // Normalize as in Eqn. (15) without the volume factor (as cancels with (V*DelRho)^2 normalization) |
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124 | // The factor 2 is due to the different theta integration limit (pi/2 instead of pi) |
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125 | const double form_avg = outer_sum_F1/M_PI_2; |
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126 | const double form_squared_avg = outer_sum_F2/M_PI_2; |
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127 | |
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128 | // Multiply by contrast^2. Factor corresponding to volume^2 cancels with previous normalization. |
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129 | const double contrast = sld - solvent_sld; |
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130 | |
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131 | // Convert from [1e-12 A-1] to [cm-1] |
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132 | *F1 = 1.0e-2 * contrast * form_avg; |
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133 | *F2 = 1.0e-4 * contrast * contrast * form_squared_avg; |
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134 | } |
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135 | |
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136 | static double |
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137 | Iqabc(double qa, double qb, double qc, |
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138 | double sld, |
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139 | double solvent_sld, |
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140 | double length_a, |
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141 | double b2a_ratio, |
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142 | double c2a_ratio, |
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143 | double thickness) |
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144 | { |
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145 | const double length_b = length_a * b2a_ratio; |
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146 | const double length_c = length_a * c2a_ratio; |
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147 | const double a_half = 0.5 * length_a; |
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148 | const double b_half = 0.5 * length_b; |
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149 | const double c_half = 0.5 * length_c; |
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150 | const double vol_total = length_a * length_b * length_c; |
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151 | const double vol_core = 8.0 * (a_half-thickness) * (b_half-thickness) * (c_half-thickness); |
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152 | |
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153 | // Amplitude AP from eqn. (13) |
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154 | |
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155 | const double termA1 = sas_sinx_x(qa * a_half); |
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156 | const double termA2 = sas_sinx_x(qa * (a_half-thickness)); |
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157 | |
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158 | const double termB1 = sas_sinx_x(qb * b_half); |
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159 | const double termB2 = sas_sinx_x(qb * (b_half-thickness)); |
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160 | |
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161 | const double termC1 = sas_sinx_x(qc * c_half); |
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162 | const double termC2 = sas_sinx_x(qc * (c_half-thickness)); |
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163 | |
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164 | const double AP1 = vol_total * termA1 * termB1 * termC1; |
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165 | const double AP2 = vol_core * termA2 * termB2 * termC2; |
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166 | |
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167 | // Multiply by contrast^2. Factor corresponding to volume^2 cancels with previous normalization. |
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168 | const double delrho = sld - solvent_sld; |
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169 | |
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170 | // Convert from [1e-12 A-1] to [cm-1] |
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171 | return 1.0e-4 * square(delrho * (AP1-AP2)); |
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172 | } |
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