| 1 | double form_volume(double length_a, double b2a_ratio, double c2a_ratio); |
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| 2 | double Iq(double q, double sld, double solvent_sld, double length_a, |
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| 3 | double b2a_ratio, double c2a_ratio); |
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| 4 | |
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| 5 | double form_volume(double length_a, double b2a_ratio, double c2a_ratio) |
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| 6 | { |
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| 7 | double b_side = length_a * b2a_ratio; |
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| 8 | double c_side = length_a * c2a_ratio; |
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| 9 | double vol_shell = 2.0 * (length_a*b_side + length_a*c_side + b_side*c_side); |
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| 10 | return vol_shell; |
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| 11 | } |
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| 12 | |
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| 13 | double Iq(double q, |
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| 14 | double sld, |
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| 15 | double solvent_sld, |
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| 16 | double length_a, |
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| 17 | double b2a_ratio, |
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| 18 | double c2a_ratio) |
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| 19 | { |
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| 20 | double b_side = length_a * b2a_ratio; |
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| 21 | double c_side = length_a * c2a_ratio; |
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| 22 | double a_half = 0.5 * length_a; |
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| 23 | double b_half = 0.5 * b_side; |
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| 24 | double c_half = 0.5 * c_side; |
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| 25 | |
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| 26 | //Integration limits to use in Gaussian quadrature |
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| 27 | double v1a = 0.0; |
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| 28 | double v1b = M_PI_2; //theta integration limits |
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| 29 | double v2a = 0.0; |
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| 30 | double v2b = M_PI_2; //phi integration limits |
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| 31 | |
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| 32 | //Order of integration |
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| 33 | int nordi=76; |
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| 34 | int nordj=76; |
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| 35 | |
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| 36 | double sumi = 0.0; |
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| 37 | |
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| 38 | for(int i=0; i<nordi; i++) { |
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| 39 | |
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| 40 | double theta = 0.5 * ( Gauss76Z[i]*(v1b-v1a) + v1a + v1b ); |
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| 41 | |
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| 42 | // To check potential problems if denominator goes to zero here !!! |
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| 43 | double termAL_theta = 8.0*cos(q*c_half*cos(theta)) / (q*q*sin(theta)*sin(theta)); |
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| 44 | double termAT_theta = 8.0*sin(q*c_half*cos(theta)) / (q*q*sin(theta)*cos(theta)); |
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| 45 | |
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| 46 | double sumj = 0.0; |
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| 47 | |
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| 48 | for(int j=0; j<nordj; j++) { |
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| 49 | |
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| 50 | double phi = 0.5 * ( Gauss76Z[j]*(v2b-v2a) + v2a + v2b ); |
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| 51 | |
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| 52 | // Amplitude AL from eqn. (7c) |
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| 53 | double AL = termAL_theta * sin(q*a_half*sin(theta)*sin(phi)) * |
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| 54 | sin(q*b_half*sin(theta)*cos(phi)) / (sin(phi)*cos(phi)); |
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| 55 | |
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| 56 | // Amplitude AT from eqn. (9) |
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| 57 | double AT = termAT_theta * ( (cos(q*a_half*sin(theta)*sin(phi))*sin(q*b_half*sin(theta)*cos(phi))/cos(phi)) |
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| 58 | + (cos(q*b_half*sin(theta)*cos(phi))*sin(q*a_half*sin(theta)*sin(phi))/sin(phi)) ); |
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| 59 | |
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| 60 | sumj += Gauss76Wt[j] * (AL+AT)*(AL+AT); |
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| 61 | |
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| 62 | } |
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| 63 | |
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| 64 | sumj = 0.5 * (v2b-v2a) * sumj; |
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| 65 | sumi += Gauss76Wt[i] * sumj * sin(theta); |
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| 66 | |
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| 67 | } |
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| 68 | |
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| 69 | double answer = 0.5*(v1b-v1a)*sumi; |
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| 70 | |
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| 71 | // Normalize as in Eqn. (15) without the volume factor (as cancels with (V*DelRho)^2 normalization) |
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| 72 | // The factor 2 is due to the different theta integration limit (pi/2 instead of pi) |
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| 73 | answer /= M_PI_2; |
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| 74 | |
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| 75 | // Multiply by contrast^2. Factor corresponding to volume^2 cancels with previous normalization. |
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| 76 | answer *= (sld-solvent_sld)*(sld-solvent_sld); |
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| 77 | |
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| 78 | // Convert from [1e-12 A-1] to [cm-1] |
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| 79 | answer *= 1.0e-4; |
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| 80 | |
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| 81 | return answer; |
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| 82 | |
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| 83 | } |
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