- E 12
~10
0 z -
~
8 u w
0::
0::
6 u 0 w
<..9
z 4
<t 0::
o~----~----~----~----~----~
0 50 100 150 200 250
ENERGY (MeV)
The range corrections obtained for 4He, 14N, and 160 are listed in Tables C-2, C-3, and C-4 as a function of energy.
To estimate the uncertainty in the range correction, we must first estimate the uncertainty in the mass response. The mass re-
sponse to 1H, 4He, 14N, and 160 is plotted in Figures C-3, C-4, C-5, and C-7. It is convenient to divide the uncertainties into two categories: those due to electronics (gain and offset shifts and non-linearities) and those due to all other effects. The effects of the electronics have been discussed in Section C-2. To estimate the importance of the second category, two contributions will be con- sidered. Uncertainties in the data points due to statistics result in uncertainties in the mass response curve. In addition there are systematic uncertainties which can be estimated by the deviation of the smoothed mass response curve from the individual data points.
These systematic uncertainties result either from fluctuations of the data points about the response curve or from an imperfect fit of the response curve to the data points.
The rms contributions to the mass uncertainties are estimated in Table C-5. For the flight data, it is necessary to know the nitrogen and oxygen mass response relative to the helium response.
(See Section III-D.) Therefore, the contribution of the uncertainty in the helium response to the uncertainties in the relative nitrogen and oxygen responses is indicated in Table C-5. The total rms mass uncertainty is obtained by combining the individual contributions in quadrature.
TABLE C -2 Range Correction for 4He in Silicon \leV ~m MeV IJffi MeV IJffi MeV pm XeV IJm J • ..; c..u l ( 0.2 -0.051 ( 0.4 -0.09) ( 0.6 -0.141 ( ~.d -i).1tl) 1.0 -U.23l ( 1.2 -0.271 ( 1.4 -0.32) ( l.o -o. 3ol ( l. (j -0.41) Z.J -0.4:, I ( 2.2 -o. 5ul ( 2.4 -0.541 ( 2.6 -0.5'1) ( 2.8 -0.6Jl :LJ -u.6bl 3.2 -0.72 3.4 -0.76 3.1> -o.ao 3.8 -O.tl5 ; • L -O.i2. 3.4 -o.ro 3.6 -o.ao J.d -o.tl:, 4.li -J.tl9
...
::. -c..·, 4 ... 4 -U.'1o 4.o -1.02 4.d -1. J7 S.J -1. ll ;J • L -l. i..) :,...
-l..W 5.6 -1.25 :).8 -l. 29 c..J -! . .)~ ~-2 -1. .>0 6.4 -1.43 6.6 -1.47 o.d -1. :i2 7.J -1.?6 7.2 -1. t; 1 7.4 -1. tl5 7.6 -1.70 7.6 -1.7::> o.O -1.7'1 .::.
.:.. -l.t.."'t 8.4 -1.di 8.6 -1.94 8.8 -1.99 9.u -2. 04"·2
-2.09 9.4 -2..14 9.6 -2.18 9.8 -2.24 10.0 -2.29 i. J -,!.:;;6 12.0 -2.8' 13 .o -3.15 1 ... o -3.47 15.0 -3. 79 ,.u -<t.l3 17.0 -4.4d 13.0 -4.83 19.0 _,.19 LU.O _,_:57 i.J -~.~5 22.0 -o.34 23.0 -6.73 24.J -7.142'.
u -7.:>'t :-;. j -7.9o 2.7 .J -8.3o 28.0 -8.79 29.0 -'1.22 3J.u -l,. 6't .>1.0 -lJ.07 32.0 -li.l. 51 33.0 -10.94 34.0 -11.39 35.0 -ll.b4 Values in parentheses are based on linear extrapolation from higher energies.MeV J • .J 1.0 Z.J j. J ~. 0 5.u >.J 7.J ~. ,j ( -l.) ! I J. J ( lJ. J (7,). J U>.J IJLJ 3 J. J .::J.O 4J.v 4:i.u ~j.J ~ j. j 0.;. v ~~.v 7.J.u 7J.u d3.J bo.U 93.J 9~.0 10).1) I<J;.J I I J. u 1 i ~. J l.!J.V 1/.d.J IJJ.J 133.0 14 j. 0 l4L:> 153.u l5d. J lcd.O lb1oU I 7 J. u I lb.O li J. 0 loci .0 HJ.O 1 ~ ~. J lJJ.J LJ l • v Zl J.J l!J. J 22 J.O zz~.J lJJ.J 2B.v ,m 0.0 I .J.Odl u. I 7 I v • .25J 0. 33 I "· 421 J.~J) ~.~nl u. b 71 J.7'.;) v. oJ I I.<> I 1. "" j l.IJ,I
2., ·"
1..7; J.OJ 3.25 3. 3 J J.4; 3.4> J.4l J.J4 >.2J J. lu 2.~. I.. 17 l.57 I..J; .;.)~ l.o7 I. <>I l.~.J 1.05 u.7'> 0,44 0.11. -o.,v -1).5, -v.'IO -l.io -I.' j -I.. Ul -L.4J -z.~u -J. i I -J.bJ -~. oo -4.50 -4.'to -~. 41 -5.e~ -o. Jo ·b.&S -7.3 ~ -7.85 ·d.H MeV O.l 1.2 2.1. J.2 4.1. '>.2 ;.z 7. 2 o.l ( .; • 2 ( 11. \) ! I o • J (,\.) L:o.J (J I. J J4.J H.J 44.0 49.1) 54.1) ,~.J 04.0 ~ -1. J 14.\) n. u :l4 .v a~.v •4.0 99.0 tv •• o lJ-l.O 114 .o ll~.J 124.0 lU.u 134.0 lH.O H4.U t.~.u 15 •• 0 159.0 lo4.0 loq.v )/ •• 0 17'1 • .) 1l4. u ld9.0 1'~~.o 1'19.U 2v4.u 2u'I.U l14.0 ll-l.o <.:4.0 229.0 lJ4.1) lJ9.J Values in parentheses are TABU C -3 RJnge Correction for 1'N in Silicon ,m u. O.ll O.IJI 0.1~1 U.L71 O.J5J v. 4 )J J. '>2) v.oJ) u. be I o. 77) 0.9<'1 1. J 3 I 1.1,) <• lo) 2. 5o I 2.7~ J.~7 3 ••• J.4u J.45 )..
., J.4J j • .)" ;.n J.J7 2.-;1 I. • I J .<.SJ 2.31 .<.u7 1. o2 1.5> •• 1.1 J.-i'1 u.o9 v.3b u.uo -0.1.7 -J.ol -u.97 -l.3J -I. 71) -L.uo -L ... d -l.oo • Jo 2'1 -J.72 --.1~ -4.59 ·).05 -5.~1 -5.9~ -o ... o -o.~~ -7 ... 5 -1. "'~ ·o.'o7MeV v.4 1.4
'··
J ... 4 .• s.• o., 7.4 ~.4 I '1.4 112.0 I I 7. v I /.2 • v Ill. J 1 JL.o JS.J 40.0 ~5.0 SJ.O 55.0 oJ.iJ t>S.O 7u.v 7S.J t-.0.U s;.J ~J.O '15. 0 100.0 IUS. 0 11o.v 115.0 l<u.J 125.0 13-.I.J 135. \) 140.0 14S.il 15.).1) ts;.o loJ.oJ los.J 17u.o 1 7).0 loo.v 1as.v 19v.o 195.0 20J.J 205.<.1 Llv.O 215.0 22v.o n~.ll 230.0 2 35 .v £40.0,m v.OJ> C.I2J <J.LI)) 0.1.~1 C. HI o. •>I u.SJ) G. ~Jt. J c. 7 \)' 0. 7 d I t. Ovl 1.411 1. d j l <::.251 2.o>l i.do 3. 12 3.32 3.42 J.•s 3.4 ... J. 39 3.3u J.h 3.J~ 2.37 2.&9 2.~& 2.2b z.oz I. 76 1.50 1.22 0.9J
o.oz o.
Jl -0.01 -0.34 -O.o9 -1.04 -1.40 -1. 7d -~.16 -.:.so -2.9b -3. 3d ·3. dO -4.24 -4.69 -s. 14 ·'>.oO -o.Od -o.)S -7. 0) -7.55 -s.oo -b. 57 MeV v.o l.o L.o J.o :J.!> o.o 7.o d.~ '-l.o ll>.v II o. J ( 2J.J (io.J 3J.J jO,J .. l.J <oo.J Sl.<.l 5o.u ol.J oo.J 71.1) 7;,.() "l.J oo.O ~ 1.J '1b.J IJ l.u lJo.J 111. J llb.J II. 1. J l<o.u IJ 1. J t;o.J 1-o I • .J l .. b.J 1)) • .) 15o.v ltd.J 1<><>.J 1 7 I. J 17o.J I o I. J loo.u I 9 I. v hb.-.1 lJI.J lJo.<.l dl.J ll o.O Ul. J Uo.J 2Jl.J 2Jo.v l4l.J
'"" v.JSJ 0.131 o.L~, 0. J _I) u. J ·•,) U.-17) u., ., l v.oJI v ./1) 0.ou) l . .):;J l . ,..; ' I.' l j £.J.)) 2.1J ~-~· , .1 7 3.J4 ;,.4j J.•'> J.~J .J ... H$ 3.~d J.lo :; .Jl 2.:l4 2.6> ~.44t 2.21. 1.97 I. 71 1 ... l.lo O.o7 u.Sv u.~, -<J.-J7 -0·""' -o.1; -1.11 -l.·d -I. d> -.... .:4 -~ • tl.) -J.J) -J. 4o -J.J'I -... J) -... 7e -S.lJ -5.7.1 -o.l7 -o.o'> -7.1) -7.o5 -d.lb -B.bo based on linear extrlpolation from hi9her energies MeV o.o 1. e I.. d J,d 4. ~ '>. 0 o.M 7. 8 o.o ~.d ( 1'·· u ( 1 ~.<I ( '-.... J 'a..'-1. u J4.i.) 3/. v 4/.oU <o7.0 52.v 57.0 ol.O b/.(J 7L.U 77. u cL.U t7.0 "it.. v '11.1) IUl.u IU7.0 l!l.J 117.~ l£L.v ILl .u L:J.!..O tJ7.u hl.O 1•7.u 152.0 157.0 l~t.O 1<>7 • .1 "7 2. J I 77. u lui..J I o 7 .v IGl.O I~ I.(; lul.J lv7 .u ~lt..U 1.17.0 li..L.u a1.o 232.0 2J 7 .u
•m o. 07) o. l 0) o. ;,,) ~. j l} v.~vJ j. J. ;J J., c j o.~~J 0. 73) :J.ol) 1. l c l l .. ·") L ..... Ji 4. 41 J L. 7., '·'" J. il 3.J7 J.44 3.45 ; .4, ,.]~ 3.lo J.IJ L.':io L.C~ .:.ol 2.'tU l. I 7 1.42 1.ob 1., .. I. 1U u.bl .;.'>u o. 1 a -u.l4 ... 0.4tl -J.~3 -1. 19 -1. s; -I. '3 -~..J~ -~. 7 2- -J. 1 j
.,.,,
-3.98 -4.42 -4. ~7 -;.Jz -s. N -o .n -o.75 -7.l5 -7.75 -b.loTABLE C · 4 Range Correction for 16Q in Silicon Me-V ~m MeV ~m MeV ~m MeY ~m MeV ~m O.J 0.0 I ( 0.2 0.121 ( 0.4 0.24) ( 0.6 0.37) ( o.8 o. 49) l.J 0.61) ( 1.2 o. 731 ( ~.
..
o. !!6) ( l.t. 0.98) ( l.d 1.10) Z.J 1.23) ( 2.2 1.3:)) ( 2.4 l. 4 7) ( 2.6 1.59) ( 2.8 1. 72) 3.J l.d4) ( 3.2 1. '16) ( 3.4 2.08) 3.6 .2.21 3.8 2.33 J.b 2.21 3.8 .!..Jj 4.0 2.4~ 4.2 2.57 4.4 2.70 ... b 2.b2 4.9 2.t!'i 5.0 2.97 5 • .2 3.0 .. 5.4 3. 11 5.& 3.17 S.ti J.n 6.0 3.28 6.2 3.H 6.4 3.39 6.& 3.4) 6.8 3.51 7.0 3.56 7.2 3.6.!. 7.4 ).b8 7.6 3. 73 7.8 3.7d 8.J 3.83 8.2 J.t>8 !l.4 3.93 o.o .>.4d 8.b 4.02 9.0 4.07 9.2. 4.12 9.4 4.17 9.o 4.£.!. 9.8 ... 27 10.0 4.31 11.0 4.54 12.0 4. 76 lJ. J s.oo l4.0 5. 22 15.0 5.42 lb.() 5.61 17. () 5.79 l:J.J 5.S7 1'1.0 6. l.l 20.0 6.30 Zl.J b.4) U.0 o.61 23.0 6.7o 24.0 6.90 25.0 7. 01+ lb.O 7.17 27.0 7. 31 Zo • .:> 7.4J 29.0 7.55 30.0 7.66 31.0 7.<!0 32..0 7. 93 33.0 o.04 34 .o d. l't 35.0 8.23 3b.O !!.3.!. 37.0 8.41 3o.J &.su 39.J d.59 40.0 b.67 4l.ll &.7b 42.0 d.83 4 ). 0 8.9J 44.0 <!.97 45.0 9.03 4&.0 9.09 47.1) 'i. 15 4~.0 9.20 49.0 9.2) :>0.0 9.31 51.0 9.36 52.0 9.40 53.0 9.4) 54.0 9.50 55.0 9.54 56.J 9.5a 57.0 9.62 53.0 9.b6 59.0 9.b9 60.0 ... 73 61.0 9.7b oZ.() }.79 eJ.o 9.82 b4.0 9.~5 65.0 '1.81 b&.O 9.b9 o7.0 'i. 91 6~.1) S.9J 6<,.0 9.95 70.0 9.97 71.0 9.99 72.0 10.0u 73.0 10.02. 74.0 10.04 75.0 10.05 76.0 10.06 77.0 10.07 7o.J 1u.vo 7'1.0 10.()9 80.0 10.10 81.0 10. 11 bl.O 1U. ll 83.0 lO.U d4.0 10.1£ ss.o 10.13 db.0 10.13 o7.0 1ll.l3 i>:l. 0 l 0 .1.3 d9.0 10.13 90.0 10.13 9l.U 10.12 9.2.0 10.12 93.0 l u. 11 94.1,) 10.10 95.0 10.10 96.0 lU .09 97.0 1U.Od 9b.J 1 CI.07 99.0 10.06 100.0 10.05 lJl. 0 10.04 102.0 10.02 103.0 10.01 104.0 9.99 105.0 <;.97 1llb.O 9.96 1U7.0 9.94 10d.O 9.92 109.0 '1.90 110.0 9.88 111.0 9.tl6 112.0 9.d4 ll.l. () 'i.81 11 ... 0 9.79 115.0 9.77 116. () 9.74 117.0 9.72 11a.0 S.c~ 11 '1. L) 9.&6 120.0 9. 64 lll.O 9.&1 1.:.2. 0 9.58 1LJ.O 9.,5 12.4.0 '1.)3 125.0 9.50 ll6.J 9.<t7 1<!7.0 9.43 123.0 9.40 129.0 '1.31 130.0 9.34 131.0 9. 31 132.0 '1.27 l3J. 0 9.£4 134.0 Y.ll 135.0 9.17 136.0 9.14 1.;7. 0 '1.10 l 3ij. 0 s.u7 139.0 '1.03 140.0 8.99 141.0 8.95 14.2.0 ~.92 l•d.O ~.dt! 144.0 d.&) 145.0 8.81 146.0 b. 71 1't 7. 0 d. 73 l4d.J a.69 14'1.U d-65 150.0 6.61 b1.0 o.57 1,.2.0 d. 53 153. •) 6.'-o 154.0 8.44 155.0 6.4() 15o.O &.3b 157.0 8.31 l,6.J o • .n 1~9.0 tl • .Z..I 1&0.0 6.19 lo 1.0 8.14 162..0 8.09 163. J b.\)4 b:..o a.0a 1&,.0 7.95 lob.O 7.90 1o7.0 7.<b l~d.J 7. t! 1 16'1.0 7. 76 l70.J 7. 71 171.0 7.66 172.1) 7. 61 l7.l.J 7. 5~ 174.J 7. 51 1.,5.0 7.45 176.0 7.40 177.0 7. 35 l7:l.() 7. 3J 179.0 7 • .25 1&0.0 7.19 1& 1.0 7.14 1 o2 .0 7.0& 1dJ.O 7.03 1d4.0 6.97 185.0 1>.92 1o6.0 6.66 1ti7.0 6.110 1a~.o o.75 lti-}.U 6.b9 1'10.0 6.63 l '11.0 o.57 H2.0 b.51 193.0 1>.45 194.0 b.39 195.0 6.34 196.\) &.n 197.\) 6.21 1-lo.O b. 15 199.0 o.v~ 200.0 6.0..1 ~Jl.J 5.96 l..U2.0 5.90 .2J3.J 5.dJ 2()4.0 5. 71 205.0 5.70 206.0 5.64 .Zu7.o 5.57 zoa.o 5.50 Values 1n parentheses are based on 11near extrapolation from higher energies.Electronics
Uncertainties in Data Points
Systematic Errors
Sub Tota 1
Error Relative to Helium
TOTAL
TABLE C - 5
Rms Uncertainties in Mass
4He (amu) 0.007
0.008
0.004
0. 011
14N
(amu) 0.011
0.030
0.028
0.042
0.038
0.06
160 (amu) 0. 010
0. 011
0.023
0.027
0.044
0.05
For the mass uncertainties listed in Table C-5, the typical accuracy for the difference between the range corrections for any 50 ~m range interval is - 0.1 ~m. The absolute magnitude of the
range correction is more uncertain. To determine the absolute magnitude a linear extrapolation of the range correction to zero
d2
energy was performed although the true second derivative ~ (6R) probably is not zero. However, as noted previously, a shift in the absolute magnitude of the range does not affect the mass response of the instrument.
When the range corrections of Tables C-2, C-3, and C-4 are sub- stituted into equation C-4, one should obtain the correct mass for 4He, 14N, and 160 since the range corrections were actually obtained from these isotopes. According to our assumptions, we should also be able to calculate the proper masses for all other isotopes of helium, nitrogen, and oxygen. Using the new range corrections along with Janni•s proton range- energy table, mass histograms were
obtained for a portion of the hydrogen, helium, nitrogen, and oxygen calibration data. The results are shown in Figure C-12. The iso- topes have the proper masses within the predicted accuracy, thus supporting the validity of the new range corrections.
FIGURE C - 12
Mass histograms for hydrogen, helium, nitrogen, and oxygen calibration data using range corrections in Tables C-2, C-3, and C-4. The hydrogen, nitrogen, and oxygen isotopes resulted from inelastic scattering of an 160 beam. The data from a 14N and an 160 beam were combined to obtain the mass histogram for helium.
300 HYDROGEN 60 HELIUM 600
200 40 400
X5
100 20 .... 200
z
(]) 0 0 0
'-..,..
2 3 4 5 2 3 4 5 6 7
(f)
z
I-w
>
NITROGEN OXYGENw 300 300
200 200
100
0 1----... -
12 13 14 15 16 17 14 15 16 17 18 MASS (amu)
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