Fukunaga, Kiyoji

Kakigi, Shigeru

Ohsawa, Takao

Okihana, Akira

Sekioka, Tsuguhisa

Kyoto University Research Information Repository

Title Computation of the Effective Solid Angle for Gas ScatteringExperimentAuthor(s)Sekioka, Tsuguhisa; Fukunaga, Kiyoji; Kakigi, Shigeru;Ohsawa, Takao; Okihana, AkiraCitationBulletin of the Institute for Chemical Research, KyotoUniversity (1988), 66(1): 1-10Issue Date1988-03-29URL http://hdl.handle.net/2433/77218RightType Departmental Bulletin PaperTextversionpublisherKyoto UniversityBull. Inst. Chem. Res., Kyoto Univ., Vol. 66, No. 1, 1988         Computation of the Effective Solid Angle             for Gas Scattering Experiment            Tsuguhisa SEKIOKA,  Kiyoji FUKUNAGA*, Shigeru KAKIGI*,                    Takao OHSAWA* and Akira OKIHANA**                              Received January18,1988    A simple numerical integration method is presented to calculate the effective solid angle for a corre-lation experiment using a gas target. The method is described for the case of a double slit system using a front aperture composed of two parallel edges of infinite height and a rear (detector) rectangular aperture. It is possible to calculate the angular spread for each telescope. The method is applicable even when the beam line does not interesect he center of the rotation of the telescopes. A FORTRAN program is presented in the appendix.      KEY WORDS: Gas target/ Solid angle/ Angular correlation/                          1. INTRODUCTION    In nuclear scattering experiments with gas targets, the target thickness is defined by a pair of collimators in front of each telescope. For each telescope we have a certain section of the target which is "seen" with 100% efficiency (umbra) and an upper and lower penumbra. Since the situation for a correlation experiment using a gas target is very complicated we propose a numerical integration method.    The method described in the following section permits us to calculate the angular spread for each collimator. This is important for the theoretical analysis of the experimental data. Since this method is applicable for the case that the beam line does not intersect the center of the rotation of the telescopes we can examine the influence of the finite size of the beam.                    2. THE METHOD OF CALCULATION    In this section the method of calculation of the effective solid angle is given for the case of a double slit system using a front aperture composed of two parallel edges of infinite height and a rear (detector) rectangular aperture. The top view of the situation is given in fig. 1. The meanings of the symbols are as follows (see fig. 1).    2b1 the width of the first collimator.    2b2 the width of the second collimator.     P l X: Himeji Institute of Technology, Himeji. * rg7K{=, 4$* / , : Facility of Nuclear Science Research, Institute for Chemical   Research, Kyoto University, Kyoto. ** (cP 3Z: Kyoto University of Education, Kyoto. ( 1 )                T. SEKIOKA, K.  FUKUNAGA, S. KAKIGI, T. OHSAWA and A. OKIHANA Y C D ~6~A .>\'g-            0 \Mirm4 j II       Fig. 1. Top view of the telescope for the explanation of the meanings of the symbols.    12 the height of the second collimator. O the center of the rotation of the telescope.    R1 the distance between the first collimator AB and O.    R2 the distance between the second collimator CD and O. Bo the angle between X-axis and the center line of the slit system.    I and III the upper and lower penumbra region. IIthe umbra region. Writing c for cos Go and s for sin Bo, the X and Y co-ordinates of A, B, C, D are given as                   (XA, YA)=(Rlc+bis, Rls—blc), (Xs, Ys) _ (Ric—bis, Ris+bic),                   (Xc, Yc)=(R2c+b2s, R2s—b2c),                   (XD, YD)=(R2c—b2s, R2s+b2c). Let a point P lie on the beam line. We can calculate the solid angle from P as follows. We can get which region (I, II, III) P exists in. If P is in the region I, the solid Y •C                                           v            IQ P~/Ii y x     Fig. 2. Top view of the telescope showing the contribution to the solid angle from a point             P on the X—Y plane. ( 2 )                       Computation of the Effective Solid Angle angle is defined by the two points A and D, if in the region II, by C and D and if in the region III, by B and C. For example let P be in the region III, that is B and C are the two points which define the solid angle, and we define  01 and 02 as (see fig. 2) 01=arctan {(Y—Yc)/(X—Xc)}, 02=arctan { (Y—YB) /(X—XB)}. Then (02—Or) turns to be the angular spread for the point P to see the rear slit in the X—Y plane. Defining r as the distance between P and the intersection of the line through P with an angle of inclination (191+02)/2 which is the mean angle for the point P to see the telescope, and the segment CD, the solid angle from the point P is given as 4.Q= (02-01)12/r.    In the case of an angular correlation measurement we have to get the values 49 for the two detectors and multiply them to have the solid angle 401492.    To calculate the solid angle for one detector or for the coincidence measurement with two detectors, we proceed as follows. We divide the segment of the beam line which is seen simultaneously by the two telescopes into small sections and compute the contribution of each section to the solid angle 49 (for a single measurement) or 4,(214 92 (for a coincidence measurement). By adding the contributions of each section we get the total solid angle multiplied by the length of the target. Since the solid angle from any point can be calculated the method is applicable even when the beam line shifts from the X-axis. In the case that the finite size of the beam cannot be neglected, the solid angle can be calculated by dividing the cross section perpendicular to the beam line into small sections and adding the contributions from each section.    Fig. 3 shows an illustration of the effect of the shift of the beam line. The first telescope is set at 12.5° with 2b1=3.75 mm, 2b2=2.50 mm, R1=81.1 mm, R2=            9-                  8-                y' 1    7-1; 1•                                            1 6-' 1 5- i 4-i 1 i /A I                3302° ; 30.5° / 30.8°31.6°11 2- _7,____i._L .011_                                   9.6j30.0°130,G 3 .0° 131.6° 11 9.8° 304°1 30.8 31,4 1 III  11.5° 11.75° 12.0° 12.25° 12.5° 12.75°      Fig. 3. Angular spread for a coplanar angular correlation experiment for the cases that            the shift of the beam line is 0 mm (the solid line), 1 mm (the dashed line) and             2 mm (the dotted line). The abscissa represents the weighting factor in arbitrary             units. The ordinate represents the angle of the first telescope. The angle of the             second telescope is given for each spectrum. ( 3 )                T. SEKIOKA, K.  FUKUNAGA, S. KAKIGI, T. OHSAWA and A. OKIHANA 257.5 mm, 12=6.4 mm. The second telescope is set at 30.6° with 2b1=3.23 mm, 2b2=3.50 mm, R1=80.2 mm, R2=258.6 mm, 12=6.5 mm. The solid angles for the cases that the shift of the beam line is 0 mm, 1 mm and 2 mm are 7.56 X 10-7 (sr2•mm), 7.31 X 10-7 (sr2.mm) and 4.02 X 10-7 (sr2•mm) respectively. The solid angle is very much affected when the shift of the beam line amounts to 2 mm for the setting of this illustration.                             3. PROGRAM    In appendix a program written in FORTRAN which calculates the effective solid angle for coplanar correlation experiment using a gas target and the slit system of a front aperture composed of two parallel edges of infinite height with a rear rectangular aperture for each telescope.    The input quantities are the 2b1, 2b2, R1, R2, 12 for each telescope and the pa-rameters A and B for the equation of the beam line                    Y=AX+B and the radius of the beam R, which is 0.0 if the beam can be represented by a straight line, and DX, DR which are the length of the small section along the beam line (DX) and that of perpendicular to the beam axis (DR) and TH(1), TH(2) which are the polar angles of two detectors. The program gets the input parameters from a file whose name is given from the key board.    The program permits us to calculate the influence of the finite size of the beam if we input R and DR. The weighting function is assumed to be SQRT{R2 — (XR) 2} where XR is the distance from the center line of the beam.    The contribution for the effective solid angle together with the angle and the angular spread for each small section to see each telescope are represented in a matrix form. They are useful for theoretical calculation taking account of the experimental angular setting. (4 )                       Computation  of  the Effective Solid Angle APPENDIX SOURCE.FOR C COMPUTATION OF SOLID ANGLE FOR GAS TARGET SCATTERING EXPERIMENT C CODED BY T. SEKIOKA AT HIMEJI INSTITUTE OF TECHNOLOGY JAN.88      COMMON B1(2), B2(2), R1(2), R2(2), FL2(2), FNAME, FONAME       DIMENSION D0MEGA(500), ANG(2,500), SMEGA(500,2), ARNG(2,2) X,AANG(2),BB1(2), BB2(2),TH(2),SAG(2),AANGR(2),DANG(2,500)       CHARACTER*64 FNAME, FONAME C WEIT IS A RADIAL FUNCTION OF BEAM INTENSITY DISTRIBUTION. WEIT(R,XR)=SQRT(R*R-XR*XR) PAI=3.141593 RTI=PAI/180.0       WRITE(*,950)   950 FORMAT(' ENTER INPUT FILE NAME (OR SPACE) - ' Xin) READ (*t, 910) FNAME   910 FORMAT(A) WRITE(*,940)   940 FORMAT(' ENTER OUTPUT FILE NAME - ' Xlfn)      READ(*,910) FONAME OPEN(4,FILE=FONAME,STATUS='NEW')       IF(FNAME .EQ. ' ') GO TO 200 0PEN(3,FILE=FNAME)   210 READ(3,*,END=900) BB1(1),BB2(1),R1(1),R2(1),FL2(1) WRITE(*,6999) BB1(1),BB2(1),R1(1),R2(1),FL2(1)       WRITE(4,6999) BB1(1),BB2(1),R1(1),R2(1),FL2(1)  6999 FORMAT(1H ,'2B1,2B2,R1,R2,FL2 FOR LEFT ',6F7.2)       IF (BB1(1) .EQ. 0.0) GO TO 900 READ(3,*,END=900) BB1(2),BB2(2),R1(2),R2(2),FL2(2)      WRITE(*,6996) BB1(2),BB2(2),R1(2),R2(2),FL2(2)      WRITE(4,6996) BB1(2),BB2(2),R1(2),R2(2),FL2(2)  6996 FORMAT(1H ,'2B1,2B2,R1,R2,FL2 FOR RIGHT ',6F7.2)   310 READ(3,*,END=900) ARCT, B, R, DX, DR       WRITE(*,6998) ARCT, B, R, DX, DR      WRITE(4,6998) ARCT, B, R, DX, DR       IF (DX .EQ. 0.0) GO TO 210   410 READ(3,*,END=900) TH(1), TH(2) WRITE(*,6997) TH(1),TH(2)      WRITE(4,6997) TH(1),TH(2)       IF (TH(1) .EQ. 0.0) GO TO 310       IF (TH(2) .EQ. 0.0) GO TO 310  6998 FORMAT(1H ,'ARCT, B, R, DX, DR ',5F7.3)  6997 FORMAT(1H ,'THETA(1)=',F8.3,' THETA(2)=',F8.3)      GOTO 750   200 WRITE(*,6001)      READ(*,*) BB1(1),BB2(1),R1(1),R2(1),FL2(1)      WRITE(*,6999) BB1(1),BB2(1),R1(1),R2(1),FL2(1)      WRITE(4,6999) BB1(1),BB2(1),R1(1),R2(1),FL2(1)       IF (BB1(1) .EQ. 0.0) GO TO 900 WRITE(*,6002)      READ(*,*) BB1(2),BB2(2),R1(2),R2(2),FL2(2)  6001 FORMAT(1H ,' 2B1 2B2 R1 R2 L2 FOR LEFT COUNTER') 60Q2 FORMAT(1H ,' 2B1 2B2 R1 R2 L2 FOR RIGHT COUNTER') WRITE(*,6996). BB1(2),BB2(2),R1(2),R2(2),FL2(2)      WRITE(4,6996) BB1(2),BB2(2),R1(2),R2(2),FL2(2)   300 WRITE(*,6003)       READ(*,*) ARCT, B, R, DX, DR  6003 FORMAT(1H ,'(EQ. OF BEAM LINE Y=TAN(ARCT)*X+B, R=RADIUS, IF=0 LINE)'.     X,' DX OR DR =LENGTH OF SEGMENT'/    X,' ARCT B R DX DR')       WRITE(*,6998) ARCT, B, R, DX, DR ( 5 )         T.  SEKIOKA, K. FUKUNAGA, S. KAKIGI, T. OHSAWA and A. OKIHANA     WRITE(4,6998) ARCT, B, R, DX, DR      IF (DX .EQ. 0.0) GO TO 200 400 WRITE(*,6004) 6004 FORMAT(1H ,'TH1 TH2 IF INPUT=0 GO TO SET OF BEAM LINE')     READ(*,*) TH(1), TH(2)     WRITE(*,6997) TH(1),TH(2)     WRITE(4,6997) TH(1),TH(2)      IF (TH(1) .EQ. 0.0) GO TO 300      IF (TH(2) .EQ. 0.0) GO TO 300 750 CONTINUE      A=TAN(ARCT*RTI) B1(1)=0.5*BB1(1) B1(2)=0.5*BB1(2) B2(1)=0.5*BB2(1) B2(2)=0.5*BB2(2)      IF (R .EQ. 0.0) GO TO 500      IF (DR.EQ. 0.0) GO TO 500 FR=R/DR NR=FR      IF(NR .GT. 500) NR=500 FNR=NR DDR=R/FNR SRWEIT=0 SMG=0.0 SAG(1)=0.0 SAG(2)=0.0 WRITE(*,6110) R,DDR      WRITE(4,6110) R,DDR 6110 FORMAT(1H ,'CALCULATION OF FINITE SIZE OF BEAM. R=',F6.3     X,' DDR=',F5.3)      DO 1000 KR=1, NR FKR=KR XR=(FKR-0.5)*DDR RWEIT=WEIT(R,XR) SRWEIT=SRWEIT+RWEIT BR=B+XR*SQRT(1+A*A)      CALL SLDANG(A,BR,DX,DDDX,TH,ANG,DANG,     X DOMEGA,AANG,SMEGA(KR,1),KMAX,ILL) ARNG(1,1)=AANG(1) ARNG(1,2)=AANG(2)      IF(ILL .EQ. 0) GO TO 610      WRITE(*,6901) ILL  610 CONTINUE      WRITE(*,6100) XR,KR,SMEGA(KR,1), AANG(1), AANG(2)     WRITE(4,6100) XR,KR,SMEGA(KR,1), AANG(1), AANG(2) BR=B-XR*SQRT(1+A*A)      CALL SLDANG(A,BR,DX,DDDX,TH,ANG,DANG,     X DOMEGA,AANG,SMEGA(KR,2),KMAX,ILL) ARNG(2,1)=AANG(1) ARNG(2,2)=AANG(2)      IF(ILL .EQ. 0) GO TO 620     WRITE(*,6901) ILL  620 CONTINUE WRITE(*,6100) -XR,KR,SMEGA(KR,2), AANG(1), AANG(2)      WRITE(4,6100) -XR,KR,SMEGA(KR,2), AANG(1), AANG(2) 6100 FORMAT(1H ,'XR=',F8.4,' SMEGA(',I3,')=',E13.6 X,' AANG1=',F10.5,' AANG2=',F10.5) SMG=SMG + RWEIT*(SMEGA(KR,1)+SMEGA(KR,2))*0.5 SAG(1)=SAG(1) + RWEIT*(ARNG(1,1)+ARNG(2,1))*0.5 SAG(2)=SAG(2) + RWEIT*(ARNG(1,2)+ARNG(2,2))*0.5 ( 6 )                            Computation of the Effective Solid Angle           1000 CONTINUE  TOMEGA=SMG/SRWEIT AANGR(1)=SAG(1)/SRWEIT AANGR(2)=SAG(2)/SRWEIT                 WRITE(*,6200) TOMEGA, AANGR(1),AANGR(2)                 WRITE(4,6200) TOMEGA, AANGR(1),AANGR(2)             6200 FORMAT(' TOMEGA=',E13.6, ' ATH1=',F10.5,' ATH2=',F10.5)                  IF (FNAME .EQ. ' ') GO TO 400                GO TO 410            500 CONTINUE                 CALL SLD NG(A,B,DX,DDDX,TH,ANG,DANG,                 X DOMEGA,AANG,SOMEGA,KMAX,ILL)                 WRITE(*,6120) KMAX,DDDX                 WRITE(4,6120) KMAX,DDDX             6120 FORMAT(1H ,'KMAX=',I3,' LENGTH OF SEGMENT=',F7.5)                 IF(ILL .EQ. 0) GO TO 600 WRITE(*,6901) ILL                GO TO 900             600 CONTINUENKMAX=KMAX/5                  DO 550 NK=1, NKMAX NK5=(NK-1)*5 WRITE(*,6310) NK5,(DOMEGA(J),J=(NK-1)*5+1,NK*5)                  WRITE(*,6320) (ANG(1,J),DANG(1,J),J=(NK-1)*5+1,NK*5)                 WRITE(*,6320) (ANG(2,J),DANG(2,J),J=(NK-1)*5+1,NK*5)                 WRITE(4,6310) NK5,(DOMEGA(J),J=(NK-1)*5+1,NK*5)                 WRITE(4,6320) (ANG(1,J),DANG(1,J),J=(NK-1)*5+1,NK*5) WRITE(4,6320) (ANG(2,J),DANG(2,J),J=(NK-1)*5+1,NK*5)             550 CONTINUE NK5=NKMAX*5                 IF(NK5 .GE. KMAX) GO TO 560                 WRITE(*,6310) NK5,(DOMEGA(J),J=NK5+1,KMAX)                 WRITE(*,6320) (ANG(1,J),DANG(1,J),J=NK5+1,KMAX)                 WRITE(*,6320) (ANG(2,J),DANG(2,J),J=NK5+1,KMAX)                 WRITE(4,6310) NK5,(DOMEGA(J),J=NK5+1,KMAX)                 WRITE(4,6320) (ANG(1,J),DANG(1,J),J=NK5+1,KMAX)                 WRITE(4,6320) (ANG(2,J),DANG(2,J),J=NK5+1,KMAX)            6310 FORMAT(1H ,I3,5E15.6)             6320 FORMAT(1H ,3X,5(F8.3,'(',F5.3,')'))            560 CONTINUE                WRITE(*,6250) SOMEGA, AANG(1), AANG(2)                WRITE(4,6250) SOMEGA, AANG(1), AANG(2)             6250 FORMAT(' SOMEGA=',E13.6,' AANG1=',F8.3,' AANG2=',F8.3)            6901 FORMAT(' ERROR ILL=',I2)                  IF (FNAME .EQ. ' ') GO TO 400                 GO TO 410 CLOSE(3,STATUS='KEEP') CLOSE(4,STATUS='KEEP')            900 CONTINUE                STOP                END                 SUBROUTINE SLDANG(A,B,DX,DDX,TH,ANG,DANG,                X DOMEGA,AANG,SOMEGA,KMAX,ILL)                COMMON B1(2), B2(2), R1(2), R2(2), FL2(2)                DIMENSION DOMEGA(500), ANG(2,500), AANG(2),TH(2) 1,XA(2),YA(2),XB(2),YB(2),XC(2),YC(2),XD(2),YD(2) 2,NCH(2),AL(2),BL(2),CL(2,4),DL(2,4),NREG(2)               3,DMG(2),SANG(2),XISC(2,4),THR(2),ANGCA(2),DANG(2,500)                  DO 10 J=1,500 ( 7 )                T.  SEKIOKA, K. FUKUNAGA, S. KAKIGI,T. OHSAWA and A. OKIHANA DOMEGA(J)=0.0 ANG(1,J)=0.0 ANG(2,J)=0.0 DANG(1,J)=0.0 DANG(2,J)=0.0          10 CONTINUE PAI=3..141593 RTI=PAI/180.0 THR(1)=TH(1)*RTI THR(2)=TH(2)*RTI             ILL=0             DO 100 I=1,2 C=COS(THR(I)) S=SIN(THR(I)) XA(I)=R1(I)*C + B1(I)*S YA(I)=R1(I)*S - B1(I)*C XB(I)=R1(I)*C - B1(I)*S YB(I)=R1(I)*S + B1(I)*C XC(I)=R2(I)*C + B2(I)*S YC(I)=R2(I)*S - B2(I)*C XD(I)=R2(I)*C - B2(I)*S YD(I)=R2(I)*S + B2(I)*C AL(I)=(YD(I)-YC(I))/(XD(I)-XC(I)) BL(I)=(YC(I)*XD(I)-XC(I)*YD(I))/(XD(I)-XC(I)) CL(I,1)=(XD(I)-XA(I))/(YD(I)-YA(I)) DL(I,1)=(YD(I)*XA(I)-XD(I)*YA(I))/(YD(I)-YA(I)) CL(I,2)=(XC(I)-XA(I))/(YC(I)-YA(I)) DL(I,2)=(YC(I)*XA(I)-XC(I)*YA(I))/(YC(I)-YA(I)) CL(I,3)=(XD(I)-XB(I))/(YD(I)-YB(I)) DL(I,3)=(YD(I)*XB(I)-XD(I)*YB(I))/(YD(I)-YB(I)) CL(I,4)=(XC(I)-XB(I))/(YC(I)-YB(I)) DL(I,4)=(YC(I)*XB(I)-XC(I)*YB(I))/(YC(I)-YB(I))             DO 200 J=1,4             IF(I.EQ.1) XISC(I,J)=(B*CL(I,J) + DL(I,J))/(1-A*CL(I,J))             IF(I.EQ.2) XISC(I,J)=(-B*CL(I,J) + DL(I,J))/(1+A*CL(I,J))        200 CONTINUE NCH(I)=1             IF (XISC(I,2) .LT. XISC(I,3)) NCH(I)=2            IF (NCH(I) .EQ. 1) GO TO 100XISC(1,3)=BBB XISC(I,3)=XISC(I,2) XISC(I,2)=BBB        100 CONTINUE             DO 119 I=1,2 C WRITE(*,6997) I,(XISC(I,J),J=1,4)        6997 FORMAT(1H ,'XISC I='I2,2X,4F10.5) C WRITE(*,6995) I,(CL(I,J),J=1,4)        6995 FORMAT(1H ,'CL I='I2,2X,4F•10.5) C WRITE(*,6994) I,(DL(I,J),J=1,4)        6994 FORMAT(1H ,'DL I='I2,2X,4F10.5) C WRITE(*,6993) A, B        6993 FORMAT(1H ,'A=',F10.5,' B=',F10.5)         119 CONTINUE XBIGIN=XISC(1,4)             IF (XISC(1,4) .LT. XISC(2,4)) XBIGIN=XISC(2,4) XEND=XISC(1,1)             IF (XISC(2,1) .LT. XISC(1,1)) XEND=XISC(2,1) XREG=XEND-XBIGIN C WRITE(*,6996) XBIGIN,XEND        6996 FORMAT(1H ,'XBIGN=',F10.5,' XEND=',F10.5) ( 8 )                   Computation of the Effective Solid Angle               IF(XREG .GT. 0.0) GO TO 300  WRITE  (  *  ,  6901  )         6901 FORMAT(' XREG<0.0. ERROR') ILL=1              RETURN          300 CONTINUE FX=XREG/DX NX=FX+1 IF(NX .GT. 500) NX=500 FNX=NX DDX=XREG/FNX NREG(1)=3 NREG(2)=3               DO 400 I=1,2 IF(XBIGIN .GT. XISC(I,3)) NREG(I)=2 IF(XBIGIN .GT. XISC(I,2)) NREG(I)=1 400 CONTINUE SANG(1)=0.0 SANG(2)=0.0 SS=0.0 SSA=0.0               DO 1000 KX=1, NX                FKX=KX X=XBIGIN+(FKX-0.5)*DDX Y=A*X + B ANGCA(1)= ATAN(A)/RTI ANGCA( 2 ) =-ATAN( A) /RTI               DO 2000 I=1,2                IF (I .EQ. 2) Y=-Y               IF (X .GE. XISC(I,NREG(I))) NREG(I)=NREG(I)-1              GOTO (2100,2200,2300) NREG(I)         2100 CONTINUE TH1=ATAN((YA(I)-Y)/(XA(I)-X)) TH2=ATAN((YD(I)-Y)/(XD(I)-X))              GOTO 2500         2200 CONTINUE              GOTO (2210,2220) NCH(I)         2210 TH1=ATAN( (YC(I)-Y)/(XC(I)-X) ) TH2=ATAN((YD(I)-Y)/(XD(I)-X))              GOTO 2500         2220 TH1=ATAN((YA(I)-Y)/(XA(I)-X)) TH2=ATAN((YB(I.)-Y)/(XB(I)-X))              GOTO 2500         2300 CONTINUE TH1=ATAN((YC(I)-Y)/(XC(I)-X)) TH2=ATAN((YB(I)-Y)/(X)3(I)-X))              GOTO 2500         2500 CONTINUE THE=0.5*(TH1+TH2) DTHE=0.5*(TH2-TH1) CTAN=COS( THE) /SIN(THE) YIS=( AL( I)*X+BL(I) -AL (I)*CTAN*Y)/(1-CTAN*AL(I)) R=ABS ( (YIS-Y) /SIN( THE) ) DMG(I)=FL2(I)*(TH2-TH1)/R ANG(I,KX)=THE/RTI - ANGCA(I) DANG(I,KX)=DTHE/RTI C WRITE(*,6998) I,DMG(I),TH2/RTI,TH1/RTI,NREG(I)           6998 FORMAT(1H ,'I=',I2,'. DMG=',E13.6,' TH2=',F10.5                X,' TH1=',F10.5,' NREG=',I2)          2000 CONTINUE 9 )                             T. SEKIOKA, K.  FUKUNAGA, S. KAKIGI, T. OHSAWA and A. OKIHANA DOMEGA(KX)=DMG(1)*DMG(2) SANG(1)=SANG(1) + ANG(1,KX)*DOMEGA(KX)                              SANG(2)=SANG(2) + ANG(2,KX)*DOMEGA(KX) SS=SS + DOMEGA(KX)*DDX*SQRT(1.0+A*A) SSA=SSA + DOMEGA(KX) C WRITE(*,6999) KX, DOMEGA(KX)                            6999 FORMAT(' DOMEGA(',I3,')=',E13.6)                        1000 CONTINUE                              AANG(1)=SANG(1)/SSA AANG(2)=SANG(2)/SSA SOMEGA=SS                                 KMAX=NX DDDX=DDX*SQRT(1.0+A*A)                              RETURN END' ( 10 )

Computation of the Effective Solid Angle for Gas Scattering Experiment

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Computation of the Effective Solid Angle for Gas Scattering Experiment

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