[a807206] | 1 | double form_volume(double thick_core, |
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| 2 | double thick_layer, |
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[66d119f] | 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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[a807206] | 7 | double thick_core, |
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| 8 | double thick_layer, |
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[66d119f] | 9 | double radius, |
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| 10 | double n_stacking, |
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[a807206] | 11 | double sigma_dnn, |
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[66d119f] | 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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[6831fa0] | 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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[66d119f] | 28 | static |
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[3ac4e1b] | 29 | double _kernel(double q, |
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[66d119f] | 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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[a807206] | 35 | double thick_layer, |
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[6831fa0] | 36 | double sin_alpha, |
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| 37 | double cos_alpha, |
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[a807206] | 38 | double sigma_dnn, |
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[66d119f] | 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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[3ac4e1b] | 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_J1c(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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[1e7b0db0] | 58 | const double si1 = sas_sinx_x(sinarg1); |
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| 59 | const double si2 = sas_sinx_x(sinarg2); |
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[3ac4e1b] | 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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[98ce141] | 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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[3ac4e1b] | 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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[98ce141] | 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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[66d119f] | 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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[a807206] | 92 | double thick_core, |
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| 93 | double thick_layer, |
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[66d119f] | 94 | double radius, |
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| 95 | double n_stacking, |
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[a807206] | 96 | double sigma_dnn, |
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[66d119f] | 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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[3ac4e1b] | 101 | /* StackedDiscsX : calculates the form factor of a stacked "tactoid" of core shell disks |
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[66d119f] | 102 | like clay platelets that are not exfoliated |
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| 103 | */ |
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[3ac4e1b] | 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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[66d119f] | 132 | } |
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| 133 | |
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[a807206] | 134 | double form_volume(double thick_core, |
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| 135 | double thick_layer, |
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[66d119f] | 136 | double radius, |
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| 137 | double n_stacking){ |
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[6831fa0] | 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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[66d119f] | 140 | } |
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| 141 | |
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| 142 | double Iq(double q, |
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[a807206] | 143 | double thick_core, |
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| 144 | double thick_layer, |
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[66d119f] | 145 | double radius, |
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| 146 | double n_stacking, |
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[a807206] | 147 | double sigma_dnn, |
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[66d119f] | 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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[a807206] | 153 | thick_core, |
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| 154 | thick_layer, |
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[66d119f] | 155 | radius, |
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| 156 | n_stacking, |
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[a807206] | 157 | sigma_dnn, |
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[66d119f] | 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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[6831fa0] | 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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