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Mass defects of the lightest nucleons
Physica XV, no 3--4
Me* 1949
MASS DEFECTS OF THE LIGHTEST NUCLEONS b y A. H. W A P S T R A Instituut voor Kernphysisch Onderzoek, Amsterdam, Nederland
Summary L e a s t s q u a r e s m e t h o d s a r e u s e d t o o b t a i n t h e m a s s d e f e c t s of s o m e l i g h t isotopes, combining data from the mass spectrograph and from nuclear reactions.
I. Introduction. Until recently for the mass defect of He 4 a value obtained from mass spectrographical data was exlusively used: He 4 = 28,20 4- 0,03 MeV
(1)
It is also possible to determine exact values of the mass defect by combining data from nuclear reactions and mass-spectrographical data, given in the following tables. TABLE M No.
Doublet
1
He**--O **++ D2 - - H e ( Li ~ - - N 1.++ B1°H--B *l
2 3
Value (10 -4 M.U.) 77,2 4255,8 4144,34116,0 4-
1,2 0,4 1 1,0
No.
Doublet
4 5 6
B n H - - C *8 B t° --Be*H C 1 a H - - C 1~
Value (10 .4 M.U.) 171,4 4- 1,0 70,2 4- 1,5 44,10 4- 0,08
These values have been taken from Mattauch and Fluegge *) ; only 6 has been taken from H. Ewald, Z. Naturf. l, 131. 1946. TABLE R No.
5 6 7 8 9 10 II 12 13 14 15
Reaction D (y, n) H D (d, p) H* D (d, n) He* He' (n, p.) H' H* (/~-) He' Li" (n, a) H' Li* (p,a) He 8 LP (d, a) He 4 Li v (p, a) He' Li 7 (p, n) Be v Li v (d, p) Li s Be 8--> 2a Be ° (p, a) LP Be 9 (d, a) Li v Be' (7, n) Be* Be* (p, d) Be* Be' (p, n) B'
Q --2,186 3,98 3,23 0,736 0,011 4,67 3,94 22,20 17,28 --1,62 --0,20 0,110 2,115 7.093 --1,629 0,547 --1,83
4q444444444444444-
I No. 0,004 0,02 0,02 0,025 0,002 0,05 0,05 0,04 0,03 0,02 0,03 0,010 0,04 0,022 0,006 0,006 0,01
- -
Reaction Be* (d, p.) B *° (n, a) B** (d, a) C '° (fl+) Be *o (fl-) B'* (d, p.) B** (p, a) Bl! (d, a) B n (p, n) Ctt (3 + )
Cta CSa Cta NlS N*4 B P-
3 8 0
- -
(d, p) (d, n)
"(d, a) (p, n)
(3+ )
(n, a)
¢,8-)
Be '° Li T Be* B *° B to Bn BeS Be' C** B I* C" N *s Bn N l' C Is B .I C 12
Q 4,52 4- 0,03 2,75 4- 0,08 17,76 + 0 , O8 3,36 • 4- 0, I0 0,560 4- 0,010 9,14 4- 0,06 8,60 4- 0,II 8,13 -{- 0,12 2,72 4- 0,01 0,981 + 0,005 2,71 4- 0,05 --0,26 -4- 0,02 5,24 q- 0,II --2,79 4- 0,03 1,21 4- 0,005 ---0,24 4- 0,08 14,43 4- 0,06
MASS D E F E C T S OF T H E L I G H T E S T NUCLEONS
38.l
Literature/or table R Where no literature has been quoted, the value of the reaction energy has been taken from M a t t a u c h and F l u e g g e l ) ; in some cases an average value is given. 1), 14} F. E. M i j e r s and L. C. v. A t t a , Phys. Rev. 61, 19, 1942; M. L. W i e denbeck and C. J. M a r h o e f e r , Phys. Rev. 67, 54, 1945. 3) L i v e s e y and W i l k i n s o n , mentioned in K. W. A l l e n ; W. E. B u r cham and D. H. W i l k i n s o n , Proc. Roy. Soc. 192, 121, 1948. 4) D . J . H u g h e s a n d C . E g g l e r , Phys. Rev. 73,809, 1948. R . J . W a t t s and D. W i 11 i a m s, Phys. Rev. 70, 640, 1947. 9) According to R. S h e r r , H. R. M u e t h e r and M. G. W h i t e , Phys. Rev. 74, 1239. 1948 the fl+ energy of C ~Q is about 2MeV. 11) A. H e m m e n d i n g e r , Phys. Rev, 73,806, 1938 (corrected with our value for RI4). 12), 14) S. K. A l l i s o n , L. S. S k a g g s and N. M. S m i t h , Phys. Rev. 57,550, 1940. 30) W . F . H o r n y a k , C . B . Dougherty andT. La urits e n, Phys. Rev. 74, 1727, 1948.
As an example we compute the mass defect of He 4 from the following combinations: R7, R12, R14 and R l l R8, R13, R14 and R1 l R23, R14, R11 and M4 R27, R29 and M4 R11, R22 and M4 R11, R22 and R27
28,03 28,08 28,20 28,20
4- 0,06 -t-- 0,04 ::::E0,05 -4- O, 11
28,17 + 0,05 28,19 4- 0,04
It is possible to contrive more combinations. These however are not mutually independent. Thus in order to determine a best value we are obliged to apply least squares methods to the results of reactions between definite sets of isotopes. In doing so we shall also have the opportunity to discuss the discrepancy between the first two values of the mass defect of He 4 and the other ones. II. Preparatory calculations. For the conversion of mass units into energy units, we start from the obvious formula
1 M . U . = 10-7 c" eV F (c = velocity of light in cm/sec; F----- Faraday's constant in Coulomb). Substituting the values c = 2,99776 ~- 0,00004.101° cm/sec. 3) F = 96522 4- 7 Coulomb 3)
382
A . H . WAPSTRA
we o b t a i n :
1 M.U.
= 931,04 4- 0,07 s MeV.
T h e m a s s of the electron, n e c e s s a r y for the calculation of e n e r g y differences in fl-transitions, is: mo = 0,51079 4- 0,00006 MeV = 5,4862 4- 0,0007.10 - 4 M . U. 3) F o r the masses of t h e isotopes H ~, D 2, C 12 a n d N t4 (electrons included), we use the values of C o h e n a n d H o r n 3; a k 4). H I ----- 1,0081284 D2= 2,014718 C 12 ----- 12,003847 N 14 -~ 14,007539
4- 0,0000027 -4-0,000005 4- 0,000016 -4- 0,000015
I n order to calculate m a s s defects we n e e d t h e m a s s of the n e u t r o n . G e n e r a l l y we calculate this f r o m R 1 ; this yields D-
n-
H = 2 , 1 8 6 3 4- 0,0042 MeV = 23,48 4- 0 , 0 4 . 1 0 - 4 M.U.
W i t h Cohen a n d H o r n y a k ' s best v a l u e for the H2-D d o u b l e t we find for the m a s s difference of t h e H - a t o m a n d the n e u t r o n , which we need in order to calculate e n e r g y differences in fl-transitions : n - - H = 0,753 4- 0,005 MeV = 8,09.10 - 4 M . U . F r o m this it follows n = 1,008937 4- 0,000005 M.U. Using this value the m a s s defects of t h e q u o t e d nuclei b e c o m e : D 2 ----- 2,186 4- 0,004 MeV C 12 = 91,747 4- 0,035 MeV N 14 = 104,198 4- 0,040 MeV 016 = 127,106 4- 0,040 MeV T h e n the m a s s defects of H 3 a n d H e 3 follow f r o m R2, R3, R 4: H 3 ---- 8,348 4- 0,015 MeV H e 3 = 7,606 4- 0,015 MeV F o r C 13 a n d N 13 we find following m a s s differences: M 6 C 13 - - C 12 = 37,18 q- 0,09.10 - 4 M.U.
R25C 1 3 - C 12=36,9 q-0,5 R26 a n d R28 C .3 - - C 12 = 36,63 4- 0,3 T h e first v a l u e disagrees w i t h t h e o t h e r ones. N o w E w a 1 d 5) d e m o n s t r a t e d t h a t the m a s s s p e c t o g r a p h in its p r e s e n t f o r m h a s sources of errors, w h i c h m a k e the m e a n error m u c h larger t h a n t h e i n d i c a t e d values. T h e r e f o r e we e s t i m a t e t h e m e a n error to be a b o u t
MASS
DEFECTS
OF
THE
LIGHTEST
NUCLEONS
383
0,2; we find an average value: C la - - C 12 = 37,02 4- 0,17 M . U . F r o m this follows: C 13 = 13,007549 + 0,000022 N 13 = 13,009946 4- 0,000023 Thus the mass defects are C la = 96,621 + 0,045 MeV N 13 = 93,636 4- 0,045 MeV III. A p p l i c a t i o n o~ least squares methods. We discussed the mentioned mass defects separately because their precision is m u c h greater t h a n t h a t of the following. Considering the other items from the tables, we see t h a t the nuclef Be 7, B 9, Li 8, C I° and C n only occur in one reaction. Therefore we omit t h e m from our calculation scheme. Moreover the d a t a from R11 and R I4 are m u c h more exact and more reliable t h a n t h e ' o t h e r ones. So we consider t h e m exact and eliminate Be 8 a n d Be 9. In this w a y we obtain the following equations: a)
MI
b) M 2 c) R S ; R 6 ; R I 2 , d)
RI4and
RII
R7
e) R I 3 , R l 4 a n d 1) R 8 g) R I 7
RII
h) i)
Rl8andRll Rl6, R20, Rl4and
k) l)
M4 R21
m)
1%27; R 2 9
n)
R22andRll;R23,
Rll
R14andRll
He 4
=
28,19
= =
39,04 ± 0,10 3 , 6 5 6 4- 0 , 0 2 7
4- 0 , 0 3 M e V
Li s
--
Li T He 4
2He*
--
Li 6
=
24,39
4- 0 , 0 4
Li ~ -- He ( 2 H e 4 -- Li ~ Li 7 + H e ~ -- B '°
= = =
10,80 17,28 2,75
-4- 0 , 0 2 3 4. 0,03 4. 0,08
3He' B t°
---
B *° = 2He 4 =
20,06 8,04
+0,08 4. 0 , 0 3
Bn
--
Bn B to
= =
75,79 11,33
4. 0 , 0 9 4. 0 , 0 6
Bn
+
He 4 =
103,99
4. 0 , 0 6
8,75
4- 0 , 0 8
3He 4 --
Bn
=
The equations d) + c) and e) + ]) are responsible for the discrep a n c y between the values of the mass defect of He 4 in the introduction. Because equation c) has been derived with good agreement in three independent ways, we m a y suppose t h a t in the first combination equation d) does not fit: the energy of the 2a-particles of the reaction Li 6 (d, a). He* m u s t surpass 22.20 MeV. This is m a d e still more reasonable as the same seems to be true for equation ]), which has been investigated b y the same a u t h o r e). Assuming equation e) to be true the discrepancy is about the same in both cases.
384
A. H. WAPSTRA
It would be i m p o r t a n t to examine these reactions again, also because these reactions are used for the d e t e r m i n a t i o n of the range e n e r g y relation in photographical emulsions 7). F o r the reasons m e n t i o n e d we drop R7 and R8 in our c o m p u t a t i o n . T h e n we m a y omit Li 6 too; which means we drop e q u a t i o n s c), d) a n d / ) . The least squares best fit for the mass defects from the remaining e q u a t i o n s becomes H e 4 = 28,188 -4- 0 , 0 1 7 MeV Li 7 = 38,991 + 0,030 B I° ---- 64,432 + 0,047 B 11 ---- 75,790 4- 0,045 a n d t h e b e s t fit for t h e u s e d e q u a t i o n s e) g)
Li 7 -- He 4 He 4 +Li 7
h) 3 H e 4 +
B 1°
i)
B t°
-- 2He 4
l)
B 11
-- B m
m)
B 11
+He
4
n) 3 H e 4 - - B 11
is
10,803 2,747 = 20,132 = 8,056 = 11,358 = 103,978 = 8,774 =
__BtO=
+ 0,022 MeV + 0,032 q- 0,032 ~ 0,026 -1- 0,045 4- 0,038 -q- 0,052
The c o m p a r i s o n o f e x t e r n a l to internal consistency following B i r g e lo) and using his n o t a t i o n gives : Re/R i = 0,40 This m a y indicate t h a t the precision of the e n e r g y values is b e t t e r t h a n assumed b y the authors. In the following table we give a review of the results, t o g e t h e r with some o t h e r mass defects c o m p u t e d with the aid of the reactions indicated. Nucleon D2 H S He s He 4
Li u LU Be T Be 8 Li . Be 9 B*
Mass-defect 2,186 8,348 7,606 28,188 31,844 38,991 37,37 56,266 40,98 57,900 56,07
4- 0,004 MeV 4- 0,015 4- 0.015 4- 0,017 4- 0,032 (eq. c) + 0.030 i 0,04 (R9) + 0,04 ( R I I ) -- 0,04 (RI0) 4- 0,04) (RI4 4- 0,05 (Ri5)
*) See our remark in table R.
Nucleon Bt0
BetO CtO BIl Ctl Btz CI2 NI3 Nl4 Ot6
lVlass-defect '64,432 64,625 59,28 75,790 73,034 78,07 91,747 96,621 93,636 104,198 127,106
4- 0,047 4- 0,05 4- 0,11 4- 0,045 4- 0,05 4- 0,07 4- 0,035 q- 0,045 4- 0,045 4- 0,040 4- 0,040
MeV (R20) (RI9*) (R24) (R30)
MASS D E F E C T S OF THE L I G H T E S T NUCLEONS
385
Addendum : After our calculations were c o m p l e t e d a new value 8) has been published for R3: D+d-+He
3+n+3,30i0,01MeV.
W i t h this we calculate the mass defect H e a = 7,672 + 0,015 MeV. This value is in disagreement with the results of R2 and R4, even with the new value for R2 9): H3(fl -) H e 3, fl-- 0,0169 :k 0,0003 MeV. It also slightly disagrees with values of o t h e r reactions: we deduce with the new value R5 L P - - a = 3,73 4- 0,05 MeV. (old value 3,67 -t- 0,05), b u t R4 L P a = 3,68 + 0,05 R l l , R 1 2 a n d R 1 4 L i 6 - a -----3,634 + 0,04. -
-
Therefore we prefer the old value. Accepting the new value would not alter our calculation, because we have o m i t t e d Li 6 from our calculation scheme; b u t it alters only the mass defects of H a, He a and Li 6. My t h a n k s are due to Prof. Dr. C. J. B a k k e r for reading the manuscript. Received J a n u a r y 24th, 1949.
REFERENCES 1) 2) 3) 4) 5) 6) 7) 8) 9) 10)
J. M a t t a u c h and S. F l u e g g e , Nuclear Physics Tables 1942. R . T . B i r g e , Rev. Mod. Phys. 1:~,233, 1941. J. VV.M. D u m o n d a n d E . R. C o h e n , Rex,.Mod. Phys. 20, 82, 1948. E. R. C o h e n and W. F. H o r n y a k , Phys. Rev. 7 ° , 1127, 1947. H. E w a l d , Z. Naturforsch. °A, 384, 1947. N. M. S m i t h, Phys .Rev. 56, 548, 1939. C.M.G. L a t t e s , P.H. Fowler a n d P . C u e r , Proc. Phys. Soc. 5~,883, 1947. H . V . A r g o , Phys. Rev. 74, 1293, 1948. S.C. C u r r a n , J. A n g u s a n d A . L. C o c k r o f t , Nature 162,302~ 1948. R.T. Birge, Phys. Rev. 40, 207, 1932.
Physica XV
25
Me* 1949
MASS DEFECTS OF THE LIGHTEST NUCLEONS b y A. H. W A P S T R A Instituut voor Kernphysisch Onderzoek, Amsterdam, Nederland
Summary L e a s t s q u a r e s m e t h o d s a r e u s e d t o o b t a i n t h e m a s s d e f e c t s of s o m e l i g h t isotopes, combining data from the mass spectrograph and from nuclear reactions.
I. Introduction. Until recently for the mass defect of He 4 a value obtained from mass spectrographical data was exlusively used: He 4 = 28,20 4- 0,03 MeV
(1)
It is also possible to determine exact values of the mass defect by combining data from nuclear reactions and mass-spectrographical data, given in the following tables. TABLE M No.
Doublet
1
He**--O **++ D2 - - H e ( Li ~ - - N 1.++ B1°H--B *l
2 3
Value (10 -4 M.U.) 77,2 4255,8 4144,34116,0 4-
1,2 0,4 1 1,0
No.
Doublet
4 5 6
B n H - - C *8 B t° --Be*H C 1 a H - - C 1~
Value (10 .4 M.U.) 171,4 4- 1,0 70,2 4- 1,5 44,10 4- 0,08
These values have been taken from Mattauch and Fluegge *) ; only 6 has been taken from H. Ewald, Z. Naturf. l, 131. 1946. TABLE R No.
5 6 7 8 9 10 II 12 13 14 15
Reaction D (y, n) H D (d, p) H* D (d, n) He* He' (n, p.) H' H* (/~-) He' Li" (n, a) H' Li* (p,a) He 8 LP (d, a) He 4 Li v (p, a) He' Li 7 (p, n) Be v Li v (d, p) Li s Be 8--> 2a Be ° (p, a) LP Be 9 (d, a) Li v Be' (7, n) Be* Be* (p, d) Be* Be' (p, n) B'
Q --2,186 3,98 3,23 0,736 0,011 4,67 3,94 22,20 17,28 --1,62 --0,20 0,110 2,115 7.093 --1,629 0,547 --1,83
4q444444444444444-
I No. 0,004 0,02 0,02 0,025 0,002 0,05 0,05 0,04 0,03 0,02 0,03 0,010 0,04 0,022 0,006 0,006 0,01
- -
Reaction Be* (d, p.) B *° (n, a) B** (d, a) C '° (fl+) Be *o (fl-) B'* (d, p.) B** (p, a) Bl! (d, a) B n (p, n) Ctt (3 + )
Cta CSa Cta NlS N*4 B P-
3 8 0
- -
(d, p) (d, n)
"(d, a) (p, n)
(3+ )
(n, a)
¢,8-)
Be '° Li T Be* B *° B to Bn BeS Be' C** B I* C" N *s Bn N l' C Is B .I C 12
Q 4,52 4- 0,03 2,75 4- 0,08 17,76 + 0 , O8 3,36 • 4- 0, I0 0,560 4- 0,010 9,14 4- 0,06 8,60 4- 0,II 8,13 -{- 0,12 2,72 4- 0,01 0,981 + 0,005 2,71 4- 0,05 --0,26 -4- 0,02 5,24 q- 0,II --2,79 4- 0,03 1,21 4- 0,005 ---0,24 4- 0,08 14,43 4- 0,06
MASS D E F E C T S OF T H E L I G H T E S T NUCLEONS
38.l
Literature/or table R Where no literature has been quoted, the value of the reaction energy has been taken from M a t t a u c h and F l u e g g e l ) ; in some cases an average value is given. 1), 14} F. E. M i j e r s and L. C. v. A t t a , Phys. Rev. 61, 19, 1942; M. L. W i e denbeck and C. J. M a r h o e f e r , Phys. Rev. 67, 54, 1945. 3) L i v e s e y and W i l k i n s o n , mentioned in K. W. A l l e n ; W. E. B u r cham and D. H. W i l k i n s o n , Proc. Roy. Soc. 192, 121, 1948. 4) D . J . H u g h e s a n d C . E g g l e r , Phys. Rev. 73,809, 1948. R . J . W a t t s and D. W i 11 i a m s, Phys. Rev. 70, 640, 1947. 9) According to R. S h e r r , H. R. M u e t h e r and M. G. W h i t e , Phys. Rev. 74, 1239. 1948 the fl+ energy of C ~Q is about 2MeV. 11) A. H e m m e n d i n g e r , Phys. Rev, 73,806, 1938 (corrected with our value for RI4). 12), 14) S. K. A l l i s o n , L. S. S k a g g s and N. M. S m i t h , Phys. Rev. 57,550, 1940. 30) W . F . H o r n y a k , C . B . Dougherty andT. La urits e n, Phys. Rev. 74, 1727, 1948.
As an example we compute the mass defect of He 4 from the following combinations: R7, R12, R14 and R l l R8, R13, R14 and R1 l R23, R14, R11 and M4 R27, R29 and M4 R11, R22 and M4 R11, R22 and R27
28,03 28,08 28,20 28,20
4- 0,06 -t-- 0,04 ::::E0,05 -4- O, 11
28,17 + 0,05 28,19 4- 0,04
It is possible to contrive more combinations. These however are not mutually independent. Thus in order to determine a best value we are obliged to apply least squares methods to the results of reactions between definite sets of isotopes. In doing so we shall also have the opportunity to discuss the discrepancy between the first two values of the mass defect of He 4 and the other ones. II. Preparatory calculations. For the conversion of mass units into energy units, we start from the obvious formula
1 M . U . = 10-7 c" eV F (c = velocity of light in cm/sec; F----- Faraday's constant in Coulomb). Substituting the values c = 2,99776 ~- 0,00004.101° cm/sec. 3) F = 96522 4- 7 Coulomb 3)
382
A . H . WAPSTRA
we o b t a i n :
1 M.U.
= 931,04 4- 0,07 s MeV.
T h e m a s s of the electron, n e c e s s a r y for the calculation of e n e r g y differences in fl-transitions, is: mo = 0,51079 4- 0,00006 MeV = 5,4862 4- 0,0007.10 - 4 M . U. 3) F o r the masses of t h e isotopes H ~, D 2, C 12 a n d N t4 (electrons included), we use the values of C o h e n a n d H o r n 3; a k 4). H I ----- 1,0081284 D2= 2,014718 C 12 ----- 12,003847 N 14 -~ 14,007539
4- 0,0000027 -4-0,000005 4- 0,000016 -4- 0,000015
I n order to calculate m a s s defects we n e e d t h e m a s s of the n e u t r o n . G e n e r a l l y we calculate this f r o m R 1 ; this yields D-
n-
H = 2 , 1 8 6 3 4- 0,0042 MeV = 23,48 4- 0 , 0 4 . 1 0 - 4 M.U.
W i t h Cohen a n d H o r n y a k ' s best v a l u e for the H2-D d o u b l e t we find for the m a s s difference of t h e H - a t o m a n d the n e u t r o n , which we need in order to calculate e n e r g y differences in fl-transitions : n - - H = 0,753 4- 0,005 MeV = 8,09.10 - 4 M . U . F r o m this it follows n = 1,008937 4- 0,000005 M.U. Using this value the m a s s defects of t h e q u o t e d nuclei b e c o m e : D 2 ----- 2,186 4- 0,004 MeV C 12 = 91,747 4- 0,035 MeV N 14 = 104,198 4- 0,040 MeV 016 = 127,106 4- 0,040 MeV T h e n the m a s s defects of H 3 a n d H e 3 follow f r o m R2, R3, R 4: H 3 ---- 8,348 4- 0,015 MeV H e 3 = 7,606 4- 0,015 MeV F o r C 13 a n d N 13 we find following m a s s differences: M 6 C 13 - - C 12 = 37,18 q- 0,09.10 - 4 M.U.
R25C 1 3 - C 12=36,9 q-0,5 R26 a n d R28 C .3 - - C 12 = 36,63 4- 0,3 T h e first v a l u e disagrees w i t h t h e o t h e r ones. N o w E w a 1 d 5) d e m o n s t r a t e d t h a t the m a s s s p e c t o g r a p h in its p r e s e n t f o r m h a s sources of errors, w h i c h m a k e the m e a n error m u c h larger t h a n t h e i n d i c a t e d values. T h e r e f o r e we e s t i m a t e t h e m e a n error to be a b o u t
MASS
DEFECTS
OF
THE
LIGHTEST
NUCLEONS
383
0,2; we find an average value: C la - - C 12 = 37,02 4- 0,17 M . U . F r o m this follows: C 13 = 13,007549 + 0,000022 N 13 = 13,009946 4- 0,000023 Thus the mass defects are C la = 96,621 + 0,045 MeV N 13 = 93,636 4- 0,045 MeV III. A p p l i c a t i o n o~ least squares methods. We discussed the mentioned mass defects separately because their precision is m u c h greater t h a n t h a t of the following. Considering the other items from the tables, we see t h a t the nuclef Be 7, B 9, Li 8, C I° and C n only occur in one reaction. Therefore we omit t h e m from our calculation scheme. Moreover the d a t a from R11 and R I4 are m u c h more exact and more reliable t h a n t h e ' o t h e r ones. So we consider t h e m exact and eliminate Be 8 a n d Be 9. In this w a y we obtain the following equations: a)
MI
b) M 2 c) R S ; R 6 ; R I 2 , d)
RI4and
RII
R7
e) R I 3 , R l 4 a n d 1) R 8 g) R I 7
RII
h) i)
Rl8andRll Rl6, R20, Rl4and
k) l)
M4 R21
m)
1%27; R 2 9
n)
R22andRll;R23,
Rll
R14andRll
He 4
=
28,19
= =
39,04 ± 0,10 3 , 6 5 6 4- 0 , 0 2 7
4- 0 , 0 3 M e V
Li s
--
Li T He 4
2He*
--
Li 6
=
24,39
4- 0 , 0 4
Li ~ -- He ( 2 H e 4 -- Li ~ Li 7 + H e ~ -- B '°
= = =
10,80 17,28 2,75
-4- 0 , 0 2 3 4. 0,03 4. 0,08
3He' B t°
---
B *° = 2He 4 =
20,06 8,04
+0,08 4. 0 , 0 3
Bn
--
Bn B to
= =
75,79 11,33
4. 0 , 0 9 4. 0 , 0 6
Bn
+
He 4 =
103,99
4. 0 , 0 6
8,75
4- 0 , 0 8
3He 4 --
Bn
=
The equations d) + c) and e) + ]) are responsible for the discrep a n c y between the values of the mass defect of He 4 in the introduction. Because equation c) has been derived with good agreement in three independent ways, we m a y suppose t h a t in the first combination equation d) does not fit: the energy of the 2a-particles of the reaction Li 6 (d, a). He* m u s t surpass 22.20 MeV. This is m a d e still more reasonable as the same seems to be true for equation ]), which has been investigated b y the same a u t h o r e). Assuming equation e) to be true the discrepancy is about the same in both cases.
384
A. H. WAPSTRA
It would be i m p o r t a n t to examine these reactions again, also because these reactions are used for the d e t e r m i n a t i o n of the range e n e r g y relation in photographical emulsions 7). F o r the reasons m e n t i o n e d we drop R7 and R8 in our c o m p u t a t i o n . T h e n we m a y omit Li 6 too; which means we drop e q u a t i o n s c), d) a n d / ) . The least squares best fit for the mass defects from the remaining e q u a t i o n s becomes H e 4 = 28,188 -4- 0 , 0 1 7 MeV Li 7 = 38,991 + 0,030 B I° ---- 64,432 + 0,047 B 11 ---- 75,790 4- 0,045 a n d t h e b e s t fit for t h e u s e d e q u a t i o n s e) g)
Li 7 -- He 4 He 4 +Li 7
h) 3 H e 4 +
B 1°
i)
B t°
-- 2He 4
l)
B 11
-- B m
m)
B 11
+He
4
n) 3 H e 4 - - B 11
is
10,803 2,747 = 20,132 = 8,056 = 11,358 = 103,978 = 8,774 =
__BtO=
+ 0,022 MeV + 0,032 q- 0,032 ~ 0,026 -1- 0,045 4- 0,038 -q- 0,052
The c o m p a r i s o n o f e x t e r n a l to internal consistency following B i r g e lo) and using his n o t a t i o n gives : Re/R i = 0,40 This m a y indicate t h a t the precision of the e n e r g y values is b e t t e r t h a n assumed b y the authors. In the following table we give a review of the results, t o g e t h e r with some o t h e r mass defects c o m p u t e d with the aid of the reactions indicated. Nucleon D2 H S He s He 4
Li u LU Be T Be 8 Li . Be 9 B*
Mass-defect 2,186 8,348 7,606 28,188 31,844 38,991 37,37 56,266 40,98 57,900 56,07
4- 0,004 MeV 4- 0,015 4- 0.015 4- 0,017 4- 0,032 (eq. c) + 0.030 i 0,04 (R9) + 0,04 ( R I I ) -- 0,04 (RI0) 4- 0,04) (RI4 4- 0,05 (Ri5)
*) See our remark in table R.
Nucleon Bt0
BetO CtO BIl Ctl Btz CI2 NI3 Nl4 Ot6
lVlass-defect '64,432 64,625 59,28 75,790 73,034 78,07 91,747 96,621 93,636 104,198 127,106
4- 0,047 4- 0,05 4- 0,11 4- 0,045 4- 0,05 4- 0,07 4- 0,035 q- 0,045 4- 0,045 4- 0,040 4- 0,040
MeV (R20) (RI9*) (R24) (R30)
MASS D E F E C T S OF THE L I G H T E S T NUCLEONS
385
Addendum : After our calculations were c o m p l e t e d a new value 8) has been published for R3: D+d-+He
3+n+3,30i0,01MeV.
W i t h this we calculate the mass defect H e a = 7,672 + 0,015 MeV. This value is in disagreement with the results of R2 and R4, even with the new value for R2 9): H3(fl -) H e 3, fl-- 0,0169 :k 0,0003 MeV. It also slightly disagrees with values of o t h e r reactions: we deduce with the new value R5 L P - - a = 3,73 4- 0,05 MeV. (old value 3,67 -t- 0,05), b u t R4 L P a = 3,68 + 0,05 R l l , R 1 2 a n d R 1 4 L i 6 - a -----3,634 + 0,04. -
-
Therefore we prefer the old value. Accepting the new value would not alter our calculation, because we have o m i t t e d Li 6 from our calculation scheme; b u t it alters only the mass defects of H a, He a and Li 6. My t h a n k s are due to Prof. Dr. C. J. B a k k e r for reading the manuscript. Received J a n u a r y 24th, 1949.
REFERENCES 1) 2) 3) 4) 5) 6) 7) 8) 9) 10)
J. M a t t a u c h and S. F l u e g g e , Nuclear Physics Tables 1942. R . T . B i r g e , Rev. Mod. Phys. 1:~,233, 1941. J. VV.M. D u m o n d a n d E . R. C o h e n , Rex,.Mod. Phys. 20, 82, 1948. E. R. C o h e n and W. F. H o r n y a k , Phys. Rev. 7 ° , 1127, 1947. H. E w a l d , Z. Naturforsch. °A, 384, 1947. N. M. S m i t h, Phys .Rev. 56, 548, 1939. C.M.G. L a t t e s , P.H. Fowler a n d P . C u e r , Proc. Phys. Soc. 5~,883, 1947. H . V . A r g o , Phys. Rev. 74, 1293, 1948. S.C. C u r r a n , J. A n g u s a n d A . L. C o c k r o f t , Nature 162,302~ 1948. R.T. Birge, Phys. Rev. 40, 207, 1932.
Physica XV
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