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Calculations of recoils of elastically scattered 4He projectiles
Thin Solid Films, 19 (1973) 289-290 © Elsevier Sequoia S.A., Lausanne---Printed in Switzerland
CALCULATIONS PROJECTILES*
289
OF RECOILS OF ELASTICALLY
SCATTERED
4He
J. F. ZIEGLER IBM Thomas J. Watson Research Center, Yorktown Heights, N.Y. 10598 (U.S.A.) (Received August 17, 1973)
Nuclear back-scattering is a new tool for analyzing surface structure in solids. One problem it encounters is the presence of contamination. Table I was prepared to facilitate the identification of contamination. It equates the final energy of an elastically scattered ~He projectile to all stable elements. TABLE I
f ,,=,~==
• ,.(~,
,~,..=.=o
,.,=..
H e4 I 0 0 0
,,~,
KEV
C
6
12,01
257.6
260,~
273,8
7g7,8
318,7
851,8
397,9
Ww2.~
o
o
16
367.6
a~%[8
38~.,
&%w[~
,30.8
,,8~5
802,7
6~e.3
633.0
w50.3
~58,~
~72,1
W91.3
516.2
5q6,6
582.6
623,6
669
10
20,19
560,1
VG
12
2q.31
517.1
52~.8
537~7
5S6.8
578
607.1
639.9
676,8
7~7.3
SI
~,
78.09
565.7
673.1
585,2
602,2
623.9
650
600,2
713.9
750.5
S
16
32.06
607.7
81q.5
626
6q1,8
662
666,1
713,9
?W~,8
778
AR
~8
39.95
670.8
677
687°1
701
718.6
739°5
763°~
769.8
8~7.9
CA
20
~O.OB
671.8
677.8
688
702,9
719.~
7W0.3
76".1
790.~
818.~
TT
2~
97.9
717.1
7~2.5
731.5
7W3.9
759.~
777.8
788.6
621.5
8~5,8
CP
2~
52
736.2
7~1°a
7q9.8
762,$
776,1
793. L,
813
83q.w
857
rF NI CU ZM
26 27 28 ~9 30
56,85 58,93 58.71 63.54 65.37
752 763TW 752.8 77,.$ 78W
756.9 ~.I ?67.3 7g~,g 7F8.3
7~W.9 ~$.8 7?5 7~0.2 795.5
776 ~&~ 785,7 ~3~3~ 805.3
769.6 7~9~7 799 aI~B 817.5
806,2 815.~ 813,7 s27.6 632
824.7 • 33.1 ~32.5 8.4.2 P48.3
B.W.g 652~t~ _ @51.9 552.~ ~66
868.2 879.8 877.q 88J.~5~ 88qo8
CF A~ $F ~R M-
32 ~3 3~ 35 3£
7P.Sq 7~.92 78.9~ 7~.91 P3.8
003.2 808.7 617.6 81~,5 827.2
807.2 812.7 821.3 823.3 £38.?
813.8 619.1 827.5 8~g.~ 836.6
62~.9 627,9 835.9 g37.7 8WW.8
83~,1 838.9 846.~ 8~3.1 85W.5
8WT.q 851.8 858.6 860.~ 566,~
862,3 866.3 872.7 879.i 879,6
878.5 882 ~87.7 889 99~.9
895.5 893.5 903.5 80M.6 908.8
SP y ~p N~ "0 9C PU
38 3~ ,10 hl ~2 W3 W~ ~5 ~5
87,6~ 88.91 q~.22 9~.9t 95.9q 9~9 I~1.1 16~.~ I06.~
833 83&.2 8~0.1 6~2.7 887.3 65!.$ fl54.5 85&,9 861°2
8~7.5 8;9.6 8~3.W g~6 850.5 9£'~.9857.5 ~,%9. g 86~.2
893.1 ~;5.3 8W6.9 851.~ 8~5.7 959.9 8~2.5 8~.8 86~
850.9 852.9 855.3 658.8 86~.9 on=o 869.W 871.6 875.5
860.5 862°~ 865*7 867.% 871.8 87~_5 873.9 8S0 863.7
871.6 873.6 876,6 878*7 882.3 8R~ 7 887.9 8~9.6 803.2
889.5 885.1 888.~ 890.7 69~ RqT.1 899.1 SOD~8 903.9
P p.2 899.6 907.~ 903.8 g06.7 ~ 9~1.2 812.7 q15.~
912.6 913.8 9~5.9 917.½ 919.9 q77.~ 925.8 SIS ~i 827.5
CO
Ru
PD
-
C~
~6
Ii~."
868.1
870.9
875.5
881.8
88~.5
898.6
908.8
919°8
931.2
D ~' S~
50 51
118.7 ~21.8
67~.7 877.6
877.3 380.~
881.7 88~.5
887.7 S~D.3
695,1 8~7°6
q03.7 ~o~
913.~ 915.5
923.9 925.7
93~,8 336.5
* Paper presented at the International Conference on Ion Beam Surface Layer Analysis, Yorktown
Heights, New York, U.S.A., June 18-20, 1973.
290 Tr r
J.F. 52 53 54
127.6 126,9 131.3
882.9 8B2.8 885
R~S.~ ~84.8 888.q
889.5 a89,8 892.~
~95.1 Bg&.$
X£
P/ #A C" P~ tin
56 57 59 59 60
137.3
890.7 891.9 E9#.e aQ3.3 ~95,7
993.1 ~o~,2
896.9 898 898.9 a~fi.~ 901,6
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897.9
902
ZIEGLER
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152 157.3 158.9 162.5
q00.7 903,9 90~.8 906.8
907,8 8Of g06,9 908.0
906,~ 909.~ 910.3 912.2
~11,1 91~ 914.9 916.7
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63 6~ 65 66
92~.£
931.7 9~3.n 93~1.£ 936
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167,3 169,~
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924.4 925.1
930.7 931.4
937.~ 938.q
9~5.~ 9~5.9
953.3 95~.7
~B
70
173
912.3
q1~*2
917.3
921.5
926,8
932,q
939,E
9~7.1
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175 178.5 ~} 183.9 186.2 lqO.2
913.2 91W.8 9{~;9 917,# %18.2 919.8
91B.I 916.7 9!7.9 91q 920 9~I.6
918.2 9~9.7 920.7 922 ~'~,9 92~.5
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927.6 q29 92%.9
933.7
OS
71 72 -79 7~ 75 76
03~.8 933.2
9qO.~ 947.7 955.3 941.6 £hS.7 956.1 995. ~ - - ~ - - q W ~ . W ~__956-7-936.8 9~3.2 950.2 957.4 g37.5 ~3.9 9~D.8 957.9 938.8 9~5.I 951.8 958.8
PT
78
195.1
921.8
923°5
926.3
930.]
93h.8
9~0. 3
9~6. h
953
~C
80
200.6
923,8
925.5
928.2
931.9
936.5
941.9
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960.9
PP
82 83
207.2
926.2 926,0
927.8 9~8.~
930.4
93U 9~'~.E
938.5
943.7 ga~.2
949.S g~. ~
955.7 956
962.1
rU CO TP
R~
BI
209
--
~t
-
931
839
927.2
q3a.~
959.8
~fi~=.~
This enables any contamination to be identified if it lies on the target surface. The table is for an incident energy of 1000 keV and laboratory scattering angles of 9ff-170". The equation of recoil is
{m, cos O-F(m2--m2 sin2 0)t/2 }2 Ef = Eo m ~+ m2 where E0 is the initial energy, E r the final energy, m 1 the projectile mass, m 2 the target mass and 0 the laboratory angle of scatter. It should be re-stated that this identification of contaminants assumes that the contaminant atoms lie on the target surface. This can be ascertained in a second run by tilting the target to the beam, or rotating the detector to a different angle. In either case, if the contaminant is below the surface its peak will shift anomalously in energy. N o t e that the mass of each element is its atomic weight, and individual isotopes of the same element are not considered separately. However, since the recoil energy of the 4He ion is independent of Z, the table may be interpolated to find the recoil energy from any specific isotope.
CALCULATIONS PROJECTILES*
289
OF RECOILS OF ELASTICALLY
SCATTERED
4He
J. F. ZIEGLER IBM Thomas J. Watson Research Center, Yorktown Heights, N.Y. 10598 (U.S.A.) (Received August 17, 1973)
Nuclear back-scattering is a new tool for analyzing surface structure in solids. One problem it encounters is the presence of contamination. Table I was prepared to facilitate the identification of contamination. It equates the final energy of an elastically scattered ~He projectile to all stable elements. TABLE I
f ,,=,~==
• ,.(~,
,~,..=.=o
,.,=..
H e4 I 0 0 0
,,~,
KEV
C
6
12,01
257.6
260,~
273,8
7g7,8
318,7
851,8
397,9
Ww2.~
o
o
16
367.6
a~%[8
38~.,
&%w[~
,30.8
,,8~5
802,7
6~e.3
633.0
w50.3
~58,~
~72,1
W91.3
516.2
5q6,6
582.6
623,6
669
10
20,19
560,1
VG
12
2q.31
517.1
52~.8
537~7
5S6.8
578
607.1
639.9
676,8
7~7.3
SI
~,
78.09
565.7
673.1
585,2
602,2
623.9
650
600,2
713.9
750.5
S
16
32.06
607.7
81q.5
626
6q1,8
662
666,1
713,9
?W~,8
778
AR
~8
39.95
670.8
677
687°1
701
718.6
739°5
763°~
769.8
8~7.9
CA
20
~O.OB
671.8
677.8
688
702,9
719.~
7W0.3
76".1
790.~
818.~
TT
2~
97.9
717.1
7~2.5
731.5
7W3.9
759.~
777.8
788.6
621.5
8~5,8
CP
2~
52
736.2
7~1°a
7q9.8
762,$
776,1
793. L,
813
83q.w
857
rF NI CU ZM
26 27 28 ~9 30
56,85 58,93 58.71 63.54 65.37
752 763TW 752.8 77,.$ 78W
756.9 ~.I ?67.3 7g~,g 7F8.3
7~W.9 ~$.8 7?5 7~0.2 795.5
776 ~&~ 785,7 ~3~3~ 805.3
769.6 7~9~7 799 aI~B 817.5
806,2 815.~ 813,7 s27.6 632
824.7 • 33.1 ~32.5 8.4.2 P48.3
B.W.g 652~t~ _ @51.9 552.~ ~66
868.2 879.8 877.q 88J.~5~ 88qo8
CF A~ $F ~R M-
32 ~3 3~ 35 3£
7P.Sq 7~.92 78.9~ 7~.91 P3.8
003.2 808.7 617.6 81~,5 827.2
807.2 812.7 821.3 823.3 £38.?
813.8 619.1 827.5 8~g.~ 836.6
62~.9 627,9 835.9 g37.7 8WW.8
83~,1 838.9 846.~ 8~3.1 85W.5
8WT.q 851.8 858.6 860.~ 566,~
862,3 866.3 872.7 879.i 879,6
878.5 882 ~87.7 889 99~.9
895.5 893.5 903.5 80M.6 908.8
SP y ~p N~ "0 9C PU
38 3~ ,10 hl ~2 W3 W~ ~5 ~5
87,6~ 88.91 q~.22 9~.9t 95.9q 9~9 I~1.1 16~.~ I06.~
833 83&.2 8~0.1 6~2.7 887.3 65!.$ fl54.5 85&,9 861°2
8~7.5 8;9.6 8~3.W g~6 850.5 9£'~.9857.5 ~,%9. g 86~.2
893.1 ~;5.3 8W6.9 851.~ 8~5.7 959.9 8~2.5 8~.8 86~
850.9 852.9 855.3 658.8 86~.9 on=o 869.W 871.6 875.5
860.5 862°~ 865*7 867.% 871.8 87~_5 873.9 8S0 863.7
871.6 873.6 876,6 878*7 882.3 8R~ 7 887.9 8~9.6 803.2
889.5 885.1 888.~ 890.7 69~ RqT.1 899.1 SOD~8 903.9
P p.2 899.6 907.~ 903.8 g06.7 ~ 9~1.2 812.7 q15.~
912.6 913.8 9~5.9 917.½ 919.9 q77.~ 925.8 SIS ~i 827.5
CO
Ru
PD
-
C~
~6
Ii~."
868.1
870.9
875.5
881.8
88~.5
898.6
908.8
919°8
931.2
D ~' S~
50 51
118.7 ~21.8
67~.7 877.6
877.3 380.~
881.7 88~.5
887.7 S~D.3
695,1 8~7°6
q03.7 ~o~
913.~ 915.5
923.9 925.7
93~,8 336.5
* Paper presented at the International Conference on Ion Beam Surface Layer Analysis, Yorktown
Heights, New York, U.S.A., June 18-20, 1973.
290 Tr r
J.F. 52 53 54
127.6 126,9 131.3
882.9 8B2.8 885
R~S.~ ~84.8 888.q
889.5 a89,8 892.~
~95.1 Bg&.$
X£
P/ #A C" P~ tin
56 57 59 59 60
137.3
890.7 891.9 E9#.e aQ3.3 ~95,7
993.1 ~o~,2
896.9 898 898.9 a~fi.~ 901,6
902,2 @~3,2 9oh 90~.5 906.6
t39.9
140.I l&O.g l~u,?
P95,1 895.5 997.9
897.9
902
ZIEGLER
q10.2 009.7 912.6
n19,? 918.C 921,~
929 92B.6 930.9
939.2 938.8 9~0.8
910.~ 910.9 ~12.R
016.3 917.2 917.b 91~.3 ~?O,J
92a,7 925.£ 929.? 926,¢ 9?8,?
~33.9 939.5 935.1 93&.5 q3fn
943.~ 9qq 9a~,5 q~a.£ 9U6
901.5 90#.7
90B,7 gOg,5
62
150.4
R99.7
901.0
905.~
910.2
~lr.2
92?,7
~1
e3q.~
9liP.1
152 157.3 158.9 162.5
q00.7 903,9 90~.8 906.8
907,8 8Of g06,9 908.0
906,~ 909.~ 910.3 912.2
~11,1 91~ 914.9 916.7
917,1 91~.0 920.6 9~2.~
92~ 92r.5
,oY
63 6~ 65 66
92~.£
931.7 9~3.n 93~1.£ 936
990 9~2 942.5 9~3.8
9~B.7 q50,W 950.9 951.9
E,' T~
68 69
167,3 169,~
909.U 910,2
911.~ 8t2.2
91~,5 915.a
918.9 919.~
924.4 925.1
930.7 931.4
937.~ 938.q
9~5.~ 9~5.9
953.3 95~.7
~B
70
173
912.3
q1~*2
917.3
921.5
926,8
932,q
939,E
9~7.1
95q,8
Ll! ,F ~5~
175 178.5 ~} 183.9 186.2 lqO.2
913.2 91W.8 9{~;9 917,# %18.2 919.8
91B.I 916.7 9!7.9 91q 920 9~I.6
918.2 9~9.7 920.7 922 ~'~,9 92~.5
g22.~ ~#3.8 92U.~ 9~6 926.9 928.4
927.6 q29 92%.9
933.7
OS
71 72 -79 7~ 75 76
03~.8 933.2
9qO.~ 947.7 955.3 941.6 £hS.7 956.1 995. ~ - - ~ - - q W ~ . W ~__956-7-936.8 9~3.2 950.2 957.4 g37.5 ~3.9 9~D.8 957.9 938.8 9~5.I 951.8 958.8
PT
78
195.1
921.8
923°5
926.3
930.]
93h.8
9~0. 3
9~6. h
953
~C
80
200.6
923,8
925.5
928.2
931.9
936.5
941.9
9~7.8
95~,2
960.9
PP
82 83
207.2
926.2 926,0
927.8 9~8.~
930.4
93U 9~'~.E
938.5
943.7 ga~.2
949.S g~. ~
955.7 956
962.1
rU CO TP
R~
BI
209
--
~t
-
931
839
927.2
q3a.~
959.8
~fi~=.~
This enables any contamination to be identified if it lies on the target surface. The table is for an incident energy of 1000 keV and laboratory scattering angles of 9ff-170". The equation of recoil is
{m, cos O-F(m2--m2 sin2 0)t/2 }2 Ef = Eo m ~+ m2 where E0 is the initial energy, E r the final energy, m 1 the projectile mass, m 2 the target mass and 0 the laboratory angle of scatter. It should be re-stated that this identification of contaminants assumes that the contaminant atoms lie on the target surface. This can be ascertained in a second run by tilting the target to the beam, or rotating the detector to a different angle. In either case, if the contaminant is below the surface its peak will shift anomalously in energy. N o t e that the mass of each element is its atomic weight, and individual isotopes of the same element are not considered separately. However, since the recoil energy of the 4He ion is independent of Z, the table may be interpolated to find the recoil energy from any specific isotope.