- Email: [email protected]
Study of nuclear magnetic transitions by inelastic electron scattering
1.E.4: I
2.L
[
Nuclear Physics 41 (1963) 461---481; (~) North-Holland -Publishing Co., Amsterdam Not to be reproduced by photoprint or microfilm without written permission from the publisher
STUDY OF NUCLEAR MAGNETIC TRANSITIONS BY I N E L A S T I C E L E C T R O N S C A T T E R I N G W. C. BARBER, J. GOLDEMBERG t, G. A. PETERSON tt and Y. T O R I Z U K A ttt
High-Energy Physics Laboratory, Stanford University, Stanford, California Received 22 October
1962
Abstract: The energy spectrum ofinelastically scattered electrons at 180° was measured for 41.5 MeV electrons from the Stanford Mark II Linear Accelerator for the following elements: ~Dz, 8Lie, 3Li7, 7Nx', sO xe, 9Fx', x0Ne*°, n N a m, 1,Mg, isAlsv, xsPsl , lsSn2, leAr*°, agK3', 20Ca'° and 8sBi*°9. Some of the elements investigated show clear evidence of excitation of nuclear levels. It is shown that these excitations are most likely due to magnetic dipole transitions. The experiment was performed under conditions in which the "long wave approximation" is approximately valid, so radiation widths were derived for the excited states. A comparison is made with the single particle model predictions. A systematic behaviour of some M1 transitions in light nuclei suggested recently by Kurath is supported by the data. The radiation tail was investigated in some detail and the large-angle bremsstrahlung formula of McCormick, Keiffer and Parzen was found to agree with the data for gas targets.
1. Introduction In this paper we report measurements of the spectrum of inelastically scattered electrons at 180 ° where magnetic transitions are most clearly seen. Measurements were made in 1D 2, zLi 7, 7N 14, 8016, 9F19, lone 2°, 11Na 23, 12Mg, 13A127, 15P31, 16832, 1BAr4°, 19K39, 29C.a40 and 83Bi 2°9. Combined with the previous measurements reported in refs. 1, 2), this experiment represents an exploratory investigation of most light nuclei as far as magnetic inelastic scattering is concerned. In sect. 2 we describe briefly the experimental method and apparatus; in sect. 3 we present the data; in sect. 4we discuss the radiation tail at 180°; in sect. 5 the method of analysis and the information obtained on levels of the elements listed above,are presented; finally, in sect. 6 some conclusions are listed. 2. Experimental Method The experimental arrangement for 180 ° scattering measurements in use at the Mark I I Stanford Lineac was described before 2-4). The 41.5 MeV electrons from the accelerator are deflected approximately 10 ° by an auxiliary magnet before striking t On leave from University ofS. Paulo, S. Paulo, Brazil. tt Now at Yale University, New Haven, Connecticut. tt* On leave from Tohoku University, Sendal, Japan. This work was supported in part by the joint programm of the Office o f Naval Research, the U.S. Atomic Energy Commission and Air Force Office of Scientific Research. 461
462
w . c . BARBERet aL
the target, a n d the ones that u n d e r g o 180 ° scattering are deflected again in the same m a g n e t before entering a magnetic spectrometer located at 160 ° with respect to the incident b e a m (fig. 1). The energy spread o f the incident b e a m was 1.5 %. The m e a s u r e m e n t s were made with the centrally scattered electrons at exactly 180°; this was d o n e b y adjusting the c u r r e n t in the auxiliary m a g n e t until the c o u n t i n g rate in the elastic peak for charge scattering in a c a r b o n target was a m i n i m u m ; MAGNETIC METER
SCATTERED ELECTRON BEAM
D INCIDENT
E'ECTRON
DE,.
•
I
~ ....
;
•
"~
/
\T, RGET
L AUXILIARY DEFLECTING MAGNET
Fig. 1. Sketch of the experimental arrangement. This drawLog is not to scale.
since 6C12 has a zero spin, n o magnetic elastic scattering is expected, a n d the c o u n t i n g rate should be zero at 180°; two effects are present which m a k e it appreciable; in the first place the entrance angle o f the spectrometer is finite a n d i n the second place multiple scattering o f the electrons in the target increases the angle o f acceptance o f TABLE 1
Properties of targets Element lH 1 ID2 aLP aLi7 eN14 80 I~ 9F1' xoNe2° axNass I=Mg a~Al~ asP3~ 1~S~2 19K39 . A r ~° =oCa~° asBi2°°
Target CH2 H gas D gas metal metal Melamine (NrCsHr) N gas O gas Teflon (CF2) Ne gas metal metal metal red phosphorus powder metal Ar gas metal metal
Thickness (mg/cm~)
Thickness in radiation lengths
233 33.5 28.8 149 170 180 200 228 150 143 150 174 150 241 192 135 205 98 156
0.0052 0.00058 0.00050 0.0028 0.0028 0.0046 0.0050 0.0065 0.0061 0.0050 0.0054 0.0068 0.0061 0.01 i 0.0091 0.0074 0.014 0.0054 0.024
463
NUCLEAR MAGNETIC TRANSITIONS
the spectrometer. F o r most of the solid targets the multiple scattering was such that the effective angle of the spectrometer was g 177.4 °. Solid and gas targets were used in the experiment. The solid targets were in the form of disks 3.8 cm in diameter and about 0.16 cm thick. The gas target was a cylinder 7.5 cm in diameter and 30 cm long with 0.0125 cm Dural windows. A gas pressure o f 5.7 atm was used. The effective thickness of the gas target was determined by comparing its counting rate with a solid target of known thickness containing the same element. This was done for a C H z solid target and hydrogen gas. Table 1 fists all targets used with relevant information. The procedure for data taking was to measure the number of electrons per unit monitor reading at different currents in the spectrometer. The spectrometer current was changed by small steps each corresponding to an energy change of approximately 150 keV. Three independent counters detected the electrons; in some eases the data of the three counters were combined; in others the data from only one of them were used. Absolute values were determined by comparison with the proton elastic scattering cross section from I H ~. This cross section is well-known from the work of Bumiller
et al. s). 3. Data Figs. 2 to 19 show the spectra of electrons scattered at 180 ° for all the elements investigated including I H 1. The solid lines were drawn as smooth curves to fit the data. In some cases such as aLi 6 or 12Mg very outstanding peaks are present which indicate clearly scattering by levels.
(CH2 - C) 1 -31
0 . 5 -xlO
H2
0.4
";
0.3,
IE
0.1
0.0 28
30
32
34 MeV
36
38
40
Fig. 2. S p e c t r u m o f 41.5 MoV electrons scattered at 180 ° from two targets c o n t a i n i n g hydrogen.
464
W.
C. BARBER et
aL
TABLE 2
Spin and parity
Isotope
sLi e
Energy o f level Ground (MeV) state
3.56
1+
5.7
14.0
15.8
3LF
9.6
80xs 9F t~ x0Ne~° uNa ~
19.0 7.7 ~ 9 13 3.0
0+ ½+ 0+ ½-
4.6 6.1 8.0 lzMg z4
11.0 14
0+
a3A127
4.8
~}+
8.0
4.7 { 0.9 0.3 0.16
Weisskopf
0.42
O. 15
50
0.03
1+ 2+
0.6
30
0.20
1~ + 2+ 0 1+ 2+
0.25
50
0.14
0.25
50
0.17
[37.5 {12.5 I 7.5
80
0.18
50
0.06
I'4 1.7
18
1.1 [19.2 /9:6
23
I
0.82 3.6
16
t 3 58
0.78
30
0.30
_-
0.48
40
0.27
{15.6 (10.4
58
1+ 2+
0.92
30
0.30
7.8 4.6
17
1+ 2+ 1+ ~-+ 1+ 1+ /~ + / ~+ i+ ½+ I].+ I ~+ 1+ 1÷
0.65
30
0.25
25
0.45 2.0 3.0 2.0 0.2
40 25 20 20 50
0.41 0.54 0.9 1.0 0.02
0.5 1.0 2.5
40 40 30
0.07 0.20 0.68
4.4 1.5
20 30
1.76 0.83
8.2 4.9 14.1 4.7 7.1 16.6 •0.05 10.035 0.43 4.4 t12.8 [ 8.6 21.0 15.8
0.7
30
0.10
1.9
30
0.50
l°
10.6
This experiment 4)
20
{i I+
Estimated error (%) M e V ' m b
Radiation width to ground state (eV)
4.0
{_-
14.0
9.3
0+ 0+ I[ I+ 2+
~-
10.5
7N 14
Excited state
(
9.3
Inelastic electron scattering cross section (cm~/sr) X 10 -as
l"
t÷ ~+ ~+ ~+
{
/46
{ "°
0.67 0.50 (14.0
145 9.0 14.5 48 0.45 1.8 4.6 10.8 29 58 2.1
465
NUCLEAR MAGNETIC TRANSITIONS TABLE 2 ( C o n t i n u e d ) .1.+ 10.6
½+
5.6 8.9 5.7 8.5 11.4
16S 32
40
0.23
t÷
1.4
30
0.65
t+
0.9
30
0.1
~-+
0.7
30
0.12
~+ 0.7 1÷ 1.3 1+ 1.7 1+ 2.6 no resonances 110 resonances no resonances no resonances
30 30 30 30
0.22 0.24 0.51 1.11
½+
3.6
15P31
0.6
~+
12.8
0+
zsAr4°
0+
,gK s9
-,~-+
2oCa ~°
0+
S3Bi2O9
~-
11.5
2.+
25 46.5 31.2 23.5 0.29 1.1 0.81 0.55 4.0 0.76 3.5 14.2
45 0.82 3.6 14.5 3.6 12.5 32
a) T h e results in this c o l u m n were derived in the " l o n g w a ve a p p r o x i m a t i o n " . 3 DZ (GAS)
26
28
30
32
34
• 36
38
40
MeV Fig. 3. Spectrum o f 41.5 M e V electrons inelasticaily scattered f r o m deuterium gas at 180 °.
It is realized immediately by inspection of the curves that large radiation tails are present. This point is discussed in more detail in sect. 4. The integrated inelastic scattering cross section Ii, = S (da(O)/dfI)de for each level was defined as the area above a smooth line drawn through the points in the adjacent regions of the electron spectrum. For the levels which are not outstanding, this procedure permits only a rough estimate of the cross sections. The position of the levels found in this work and estimates of/in are listed in table 2. The estimated error is stated in each case.
466
w . C . BARBERe t al.
0.5'
'_9.~...... ; Li i_8,_3~
-31 -xlO
6
~55_ ~4 ~ _1+~
0.4
3.56 MeV
3Li s (4L5 MeV)
;3.5.60+ I :2J84 3~J
>o.3
t
~E /..._.~ i. L 0 I'+ ~'.~. 0 . 2 I 15"8/MeV14.0MeV 9.3 MeV
5.7 MeV
.kJ
0.1
24
26
28
30
32
34
36
38
40
42
MeV
Fig. 4. Spectrum of 41.5 MoV electrons scattered from LP at 180 °. 17.5 16.2
L i7
k4
.
Li?(NATURAL LITHIUM)
J
i
lO.8 9.6
0.4 xlO31
7.475~
O. 3
6.S4 ,4,63
14MeV
24
ZI6
0
28
30
X~ l
3/2-
FROMLi 6
32
34 36 38 40 42 MeV F i g . 5. S p e c t r u m o f 41.5 M e V electrons scattered f r o m L i 7 a t 180 °.
7
0.6
NI 4
xlO31 2.31 0~-,I
0.4 ~>
~o.2
1
L___
~t r P'~
10.6 MeV 0 I+ 1 9.3MeV
' '"/.~, ~r~'~.~.
24
26
28
'
30
~(~,s
N6C3H6
32
34
36
38
40
4 :)
MeV
Fig. 6. Spectrum of 41.5 MoV electrons scattered from two nitrogen targets at 180°.
467
NUCLEAR MAGNETIC TRANSITIONS
In some of the figures we show the position and spin of well-known levels taken from Ajzenberg and Lauritsen et al. 6) and from Endt and Van der Leun v).
-31 0.6 - x l O
0.5
0 (H20)
T>¢ 0.4
0.3 ej~. 0.2 ~.
•
j,
,
0.1 0.0
20
22
a,
2;
a8
io
~2
i,
MeV
3~
3~
,o
,2
Fig. 7. Spectrum of 41.5 MeV electrons scattered from an H=O target at 180 °.
r .
-3l 0.75 i xlO
sO16(GAS)
: o,o I ~o.ool{
Jl
~
26
28
30
{,
f ~
32
~
54
~ 4 36
:
38
40
42
MeV
Fig. 8. Spectrum of 41.5 MeV electrons scattered from an oxygen gas target at 180 °.
riO3' ~
sFI9
1.00 0.75
0
1/2~7.7 MeV
~. 0.50 ~E 0.25 u
0.00
26
I
I
I
l
I
r
I
28
30
32
34 MeV
56
58
40
42
Fig. 9. Spectrum of 41.5 MeV electrons scattered from CF, at {80 °.
468
w.c.
BARBER et aL
~zz iz31 loNe
'7
i
-31 KIO
I .00
14-
20
0.75 13 Mev
o,5o
8 Mev
i
I
1
"E 0.25 0.00 28
26
50
32
34 MeV
36
38
40
42
Fig. 10. Spectrum o f 41.5 M e V electrons scattered f r o m a n e o n gas target at 180 °.
-31
[rzC u3~2÷~,z"
1.75 - x I0
162.7. . . . ,,2 •
t.50
~47_8.___ i t / z * 3/2 * '3.85
b/z • ~z?*
2.64
. i z z , 5Fz *
x
II
$
--11 ......
t.25 ir 5M~V
I.O0 ,
g 0.75
i N023
,
:
~
~--~;;.
'
{
8o.ev ! ~"~'eX.~%Mo v
;
~ .
~ 0.50 0.25 0.00' _ . _ _
22
2',
26
z~
3'o
32
3,~
3'6
~8
,;o
4=
MeV
Fig. 11. Spectrum of41.5 M e V electrons scattered f r o m N a ~ at 180 °.
1,501
....
I -~i 1.25 xlO
•;
1.00"
14MeV
~: 0.75
Mg 12
I x~
ii }
IIMeV
+
~E O.5t3 0.25
;~ ~ ; ~ . ~ {
o.oo L
26
28
30
3t2
34
36
3r8
~
410
f 42
MeV
Fig. 12. Spectrum o f 41.5 M e V electrons scattered f r o m a m a g n e s i u m target at 180 °.
NUCLEAR MAONETIC TRANSITIONS
'I
r"
I ~ ,
";
469
I
I I-
~-tt~
"°r °"
o
"
4.s~v
' ~
,
,..
1
O/ 24
'
[
i
I
I
1
~
~
I
t
26
28
30
32
34
36
38
40
42
MeV
Fig. 13. Spectrum o f 41.5 M e V electrons scattered f r o m an A [ =7 target at ]80 °.
~3/2
r
,o~ ~'
, ' t'kt,
/
"~= o 8 ~ "
'~
"~
,sp 3'
o
S.gMeV
* I
37~-
t,
~
"h-L
÷
0.6 P
~s..v ......
~r,~
/
,,..v I
t
#,
~,
' ÷ ~ . = ~
~ t
"~'
0.4"
0.0.
~
i
50
,
3'4 5]8 3]8 4'0 42 MeV Fig. 14. Spectrum o f 41.5 MeV electrons scattered from a ps~ target at 180 °. 26
2]8
52
3Z S 16 /
z.O
17.co
\F
1.5
I±1
'~
~,,~s ,~!
x\lO
X
\ \
~
.
11.4MRV i ,
~E ~0.5
,
t
8.5 MeV
÷
0.0
:
16
18
I .......
20
~
22
:
I
24
26
J
._.
28
i
i
30
32
.....
"
34
....
l
56
38
40
42
MeV
Fig. 15. Spectrum o f 41.5 M e V electrons scattered f r o m a s u l p h u r target at 180 °.
470
w.c.
BARBER et aL
3 40 18A r -31 xlO
2
{{{{{ ~ -
BREMSSTRAHLUNG
~t
{ ¢ 0
I
16
I
I
20
I
1
I
24
I
I
;>8 32 MeV
I
I
36
i
{ r {
410 44
Fig. 16. Spectrum o f 41.5 MeV electrons scattered from a n A r 40 gas t a r g e t a t 180 ° X I/2
-31 4 -xlO 19 K
t
3
o
26
28
30
32
34 3,6 38 40 42 MeV Fig. 17. Spectrum o f 41.5 M e V electrons scattered f r o m a potassium target at 180 °. I.OF t-
40
o.81-,,1~3'
,oCO
0.6 Iz. 0.4 ~
~
; 18
20
22
24
26
28
30 32 :34 36 38 410 42 MeV Fig, 18, Spectrum o f 41.5 M e V electrons scattered from a calcium target at 180 °, 8
i6 o ¢n z w4 o > _ uP
S3 Ri2°9 ..¢=
GIANT RESONANCE REGION , 0,
1 ELASTIC PEAK
<,z
MeV Fig. 19. Spectrum o f 41.5 M e V ine|asticaHy scatterec[ electrons f r o m a Bi m target.
471
NUCLEAR MAG.NETIC TRANSITIONS
4. Radiation Tail Since an elastic peak is present in the curves, one expects a radiation tail. The effects responsible for that have been discussed by Barber et aL 1) and Friedman a); they are: a) radiation during scattering, b) radiation before or after scattering, c) electron-electron scattering before or after elastic scattering and d) energy loss by ionization, the most important effects being a) and b). It turns out 1) that for the usual angles used in electron scattering and for targets of approximately 0.01 radiation length, the radiation tail amounts to approximately 1 or 2 % of the elastic peak height in a region of a few MeV below the elastic peak. It is quite clear from figs. 2 to 19 that in some of our measurements (at ~ 180°) the radiation tail amounts to ~ 10% of the elastic peak in that energy region. The main reason for this is large-angle bremsstrahlung. The Bethe-Heitler formula for the case in which the electron goes in a specified direction regardless of the direction of the emitted photon has been integrated by McCormick, Keiffer and Parzen 9). The cross section for such a process when the electron scatters in a backward direction is
d (E, 0) dO
-
z2 1
i (e2 \rnc2!
R',
/m c 2\2 t 2E ° R' : [ ~ ) ,~A(~'0)In - + B(7 , 0).j mo c2
(1)
(2)
Here E o and E are the energy of incident and outgoing electron, k = E o - E , V = E/Eo, A(y, 0) = 5 (1 +72) 2 cos 2 50 73 sin" ½0' B(V, 0) = 5 1 +~2 /cos2 50 In 7 + ~ -V sin" ½0 2 sin 4 ½0 +
(3)
In (sin 2 ½0) (1--7+~ 2)
2~2 - In (sin 2 50) • (4) 1 + ~2 sin 2 t0
The contribution of these two terms to the total bremsstrahlung cross section is plotted in fig. 20. It is seen that the A term for a given 7 has the same behaviour of the Mott cross section and goes to zero at 180°; at other angles it is the dominant term. The B term is fairly constant around 180°, for a given 7. The ratio of the bremsstrahlung cross section to the Mott cross section increases as 0 ~ 180 ° (fig. 21). For the conditions of our experiments it amounted to ~ 5%, for ~ ~ 0 . 5 . We found that for gas targets the McCormick, Keiffer and Parzen formula represents the radiation tail quite accurately, at least for the light elements. Fig. 16 shows our results for the case of xsAr 4°.
472
w.c.
BARBER et al.
For the solid targets there are other effects that complicate matters considerably; although the thickness of the targets was quite small, it introduced effects due to multiple scattering. I f the tail is measured as a function of thickness, one finds deviations from linearity; these deviations are larger as the final energy of the electron becomes smaller. This is seen in fig. 22.
~~
RAHLUNG=A+B
2.0
1.5 "7 IE ..~ 1.0
~
% X
\\~A
0.5
% % % %%
0.0
I
160
170 DEGREES
180
Fig. 20. T h e large angle brernsstraklung cross section near 180 ° f o r Z = 1 and an incident electr energy o f 41.5 M e V (), = (K]E,) = 0 . 6 ) . 20%
I I I I I I I
I0% I _
I
jl S¢
-
160 F i g . 21. R a t i o
I
of the large-angle bremsstrahhmg
I 170 DEGREES
I
t
180
t o t h e M o t t cross
section
near
180 ° ( y = 0 . 6 )
The amount of target material in the direction perpendicular to the incident beam is also important. This is evidenced in fig. 6 which shows measurements for a solid target containing nitrogen (N6C3Hs-melamine) and for a nitrogen gas target of about the same total mass per unit area in the beam direction, but much less at 90°; the levels at 9.4 and 10.7 MeV stand up above the tail in the solid target, but are more
NUCLEAR
MAGNETIC
TRANSITIONS
473
prominent in the N gas measurements where the tail is much reduced. The same behaviour is apparent for H (fig. 2); a tail is present when one uses a CH 2 target and subtracts the C contribution obtained from a graphite target with the same number of carbon atoms. The curve obtained for H gas does not show any measurable tail. The probable explanation of these facts is that if a 90 ° scattering event occurs in a solid target, there is a large amount of material viewed by the spectrometer that can contribute to the tail by bremsstrahlung radiation at large angles. With gas targets this is no longer the case. 400
300
?_. z 200
I00
0 0
,'o
2'o
~o
io
50
go
~o
THICKNESS MILS
600
400 o o
200
o
,o
~o
3'0
'.ICKNESS M,,S
Fig. 22. The tail as a function of target thickness in aluminium for an incident energy of 41.5 MeV and final energies of 25 and 16.7 MeV. (1 mil = 25.4/,m.) Unfortunately, the electron intensity available did not permit the use of extremely thin targets, and the use of targets with very small transverse dimensions would have introduced monitoring problems. Since the radiation tail for solid targets would require a considerable amount of calculations which could not be done very reliably, we adopted the procedure outlined in sect. 3 to obtain the inelastic cross section integrated over the levels.
5. Analysis of the Data and Discussion of the Results The Hamiltonian for the interaction between the electrons and nucleus can be split into two parts, the electrostatic (Coulomb) and the magnetic interaction 1o). The Coulomb interaction is Vc=e2~
1 y c -- r k
,
(5)
474
BARBER et al.
w.C.
where rc is the coordinate of the electron and the sum extends over the positions of the protons k. The Coulomb interaction Vc can be expanded as a series of multipoles 1 r~ Y~.(0., q~.)Yl*(0k, ~Ok), Vc = 4xe 2 k,l,m 2 l + 1 r ~ + l
r k < r.,
(6)
r~ > ,o.
(7)
!
1 ro Yl.,(O~, ~o)Y,.(0~, * ~), ~,t.,, 2 l + 1 r ~ + l
Vc = 4he z ~,
A term of order l leads to the excitation of an electric transition EL i.e., a change of the angular momentum of the nucleus of l units and a change of parity ( - 1)~; I runs from 0 to oo which means that monopole transitions can also be excited by Vo In other words the electrostatic interaction can be represented by the absorption of photons of angular momentum l and parity ( - 1 ) t (longitudinal photons). Explicit formulas for the cross section of the transitions induced by Vc have been calculated by Schiff 11) in Born approximations for the extreme relativistic case, i.e., neglect of the electron rest mass and nuclear excitation energy docl(0) _ (Ze~) ~ cos ~ ½0 ie~(z~--, If, q)l 2,
dO
\2Eo/
sin 4
½0
q -- p o - p ,
(8)
where Po and Eo are the initial momentum and energy of the electron, and E and p are the final momentum and energy of the electron. The factor Fcz(li ~ If, q) can be considered a form factor for inelastic transitions;
q)[2
JF~li --, It,
B(CI, q) --
4nq2' B(CI, _- z2[( 2 / + 1)! l] 2
q),
[(2/+ 1)l l] 2
q2'(2Ii+1) m,,EM,.=[(If mr Ek [j,(qr~)Ylm(Ok, ~,~)[zimi>l ~.
(9)
(10)
Here B(C/, q) is a reduced matrix transition probability. It is seen (eq. (8)) that this cross section goes to zero for 0 ~ 180 ° just as the Mott cross section, and is, therefore, absent if the inelastically scattered electrons are observed at that angle. The magnetic interaction is e
VA=
-
-C ,,.-A(,o),
(11)
where v, is the velocity of the electrons and A(rc) is the vector potential. The vector potential can be expanded in multipoles which have electric and, magnetic field components. The expressions for the cross sections due to these multipoles are dO'El(0) (Ze2) 2 ½(1 +sin 2 ½0)[FEI(/i --~ If, q)[2, dQ = \ ~ o / sin 4 ½0
(12)
NUCLEAR MAGNETIC TRANSITIONS
475
daMl(O) -- /7~2\/L~© / 2 ½(1 +sin 2 ½0)IFMI(Ii ~ If, q)l 2. dO \2Eo/ sin4 ½0
(13)
Expressions for FEI and Ful similar to (5) in terms of the reduced matrix transition probabilities with the appropriate operators can be found in ref. 1o). One can say that these cross sections correspond to the absorption of (transverse) photons of angular momentum l and parity ( - 1)l and ( - 1)t÷l for electric and magnetic transitions, respectively. It is seen (eqs. (12)and (13))that the angular factor cos2½0in the electrostatic case becomes ½(l+sin2~tr0) for the magnetic interaction which means that the vector potential interaction cross sections do not vanish at 180°. This is then an optimum angle at which experiments should be performed in order to investigate this type of process. The expressions above are appropriate for scattering at high energies (> 200 MeV) and have been used extensively in the literature. Alder et aL 12)worked out expressions similar to the ones of Schiffbut more adequate for our energies ( ~ 50 MeV); this calculation is also made in Born approximation but does not make the assumption, which Schiff did, of having the excitation energy negligible compared to the incident energy. The expressions of Alder et al. are repeated here for completeness
dacI(O)_(e2~ 2 4n(l+l) q2____llB(CI, q)VL(O), d-~ \hc/ /[(21+1)![] 2 p2 /+1 daFa(O)_ (e2'~2 4n(I+I)
dr2
q2, B(EI, q)VT(O), I[(21+I)!!'] 2 pg
\hc/
d~o(O)
_
(e2~ 2
q2!
4n(l+l)
B(MI, q)VT(O),
\he/ t[(21+l)!!y 1,o2 Po + P -
VL(O)=
e2
-
p
Po
PPo
(14)
(15) (16)
+ 2 cos 0
(17)
Po+ P_2cos0 Po
,o+, v (o) =
\Po/
PPo
(-
P
eP-~o)cos 0 + 2 cos20 Po
(PP+ P--Po--2c°sO) IP:+ PPo Ppoe2 2cos01 2
(18)
The transition probabilities B(C/, q), B(FI, q) and B(M/, q) are similar to those found in photon emission or absorption processes; in the case when the nuclear radius r is very small compared with 1/q (qr << 1) these quantities are identical in electron scattering and photon absorption.
w.c. BARBERet aL
476
This equivalence has given rise to the "virtual photon" method of analysis of inelastic electron scattering x, la, 14). In this method one says that the incident electrons create a field in space (virtual photon field) and that these photons induce transitions in the bombarded nucleus. The cross section for inelastic scattering is written as dtr(O) _ n(l, e, Eo, O)a,(e, l) = 1 dN(l, e, Eo, O) a~,(e, l),
dr2
~
(19)
dO
= E o-E,
where try(e, l) is the absorption cross section for real photons of energy e and multipolarity l; H(l, e, Eo, 0) is the virtual photon spectrum. Using the Moiler potentials, H(l, e, E o, 0) has been calculated for different multipoles la). The cross section a~(e,/) in the expression above contains reduced matrix transition probabilities which are similar to the ones involved in expressions (14), (15) and 0 6 ) with the difference that in the absorption of photons q --* 0. It can be shown easily that
dNc(l, e, Eo, O) _ ct p 2 ( l + c o s 0 ) 2 1 [q_~2t-2 B(Cl, q) dr2 rt2 q2 I + 1 k e] B(CI, e) dNE(l, e, Eo, O) _ dr2
dNr~(l, z, Eo, O) _ dr2
for longitudinal photons,
(2O)
et [p2 + p2 + ppo(l_cos O)] [q_~ 21-2 B(El, q) for electric trans(21) 4~z2 p ~ ( 1 - c o s O) ke] B(EI, e) verse photons, ct [p2o+p2 + ppo(1--cos O)] [q_]2'-2 B(Ml, q) formagnetictrans(22) p 2 ( 1 - c o s O) ~e] B(MI, e) verse photons.
4n 2
In the "long wave approximation", i.e., in the case qr << 1, B(CI, q)/B(El, e) ~ 1, B(EI, q)/B(El, e) .~. (e2/q) and B(MI, q)/B(MI, e) ~ 1. This approximation is made in general in calculations of radiation widths in electromagnetic transitions and means that only the lowest possible multipole order contributes; the reason is that in the reduced matrix elements there appears a Bessel function jl(qr); since jl(qr) ~ (qr)l/ (2l+ 1)I! for qr small, it is clear that for qr << 1 only the first term will contribute. The virtual photon spectrum, which has the peculiarity of involving the matrix elements of the nucleus in which it induces transitions, becomes more significant in this case since it involves only kinematic factors. It is quite clear from formulas (20), (21) and (22) that in the case of 180 ° scattering, the longitudinal spectrum is zero, and out of the transverse spectrum a Ml transition is dominant by the factor (q2//~) over an El; although the absorption cross sections of real photons for El transitions is usually about 10 times larger than those for a MI absorption ts); this is not enough in general to upset the dominant Ml character of 180 ° scattering. This feature has been confirmed in cases where levels of known spins and parities have been excited by inelastic scattering at 180°. In table 2 are listed the integrated inelastic scattering cross sections for the levels seen in our measurements.
NUCLEAR MAGNETICTRANSITIONS
477
Since we are assigning an MI character to the transitions seen at 180 °, one can use eq. (19) and obtain f o'),(g)dg m_
/in
(23)
1 ~ (Po+p)2' e 47rz
2poz
where lin is the integral defind in sect. 3. On the other hand, the Breit-Wigner formula for one isolated resonance of width F~ gives
fa.~(e)de
7r2 (2I~+ 1) (2Ii + 1) r , .
(24)
Table 2 includes values of S a~(e)d~ and F~ for each of the levels measured. We assumed always the ratio of the matrix elements present in the virtual photon spectrum to be given by the long wave approximation, although this is not a good approximation in some of the levels. A first order correction to this assumption is given by Barber et al. x) and may amount to ~ 30% for light elements and low excitation energies. Better corrections would require the explicit calculation of the matrix elements in some assumed model. We now discuss in detail some of the levels investigated. Unless otherwise noted, previous information about the levels was taken from refs. 6, v). 5.1. THE ID s NUCLEUS
This element has been the object of a recent extensive investigation in this laboratory by Peterson and Barber 4). The only difference between this measurement and the ones reported there is the use of a gas target instead of a CD2 solid target. The use of a solid target introduces the necessity of subtracting the carbon background so the problem of the radiation tail becomes quite involved. Fig. 2 for hydrogen indicates that this problem should be much simpler using gas targets. Our results are shown in fig. 3 which includes the Jankus theoretical cross section t6) for magnetic scattering at 180 °. The Jankus theoretical cross section was folded by the resolution function of the experimental arrangement and a radiation correction applied as in ref. 4). It is seen that good agreement is obtained between experiment and the Jankus cross section; this indicates that the interaction assumed by Jankus is sufficient to account for the experimental measurements at 41.5 MeV. 5.2. THE 8Lie and aLi* NUCLEI
The Li 6 nucleus presents an outstanding level at 3.56 MeV which was studied previously by electron scattering 2). Our results agree reasonably well with the values reported there. Other structures seen in this nucleus are at 5.7 and 14.0 MeV; there exists a known level at 5.35 MeV (1 +) which could be the one seen in this experiment (figs. 4 and 5).
478
w.C.
BARBER et aL
In Li 7 no outstanding structure is seen, but small peaks at 7.5, 12.5 and 14.0 MeV are present. The 7.5 MeV transition is known to have an MI character. Using a bremsstrahlung spectrum Goldemberg and Katz 17) observed breaks in the (V, n) activation curve at positions indicating levels at 12.5 and 14 MeV. It is worthwhile to mention that Li 6 also shows a level at 14.0 MeV. Since Li 6 and Li 7 have the same "core" this may be indicative of some sort of "core excitation" of magnetic character. A careful search was made for the 0.478 MeV level in Li 7, but no evidence was found for it. This is in agreement with calculations made by R. Willey is) for the magnetic dipole excitation of that level. 5.3. THE 7N14 NUCLEUS Levels are found at 9.3 and 10.6 MeV; the closest known levels are located at 9.18 and 10.43 MeV (fig. 6). Assignments for these levels have been discussed by Warburton ~9) and are compatible with 1 ÷, 2 ÷ or 2 - . Polarization measurements seem to indicate they have even parity 6); if these are the levels seen by us our measurements confirm this assignment. Another interesting feature of N 14 is the broad region at ,,~ 14 MeV which indicates a group of unresolved levels; this energy corresponds to the "shoulder" found in some 0', n) reactions and have been interpreted as due to M1 or E2 absorption 20). 5.4. THE 8016 NUCLEUS The only level seen in this case is one at 19.0 MeV which seems to be the same one reported by Bishop and Isabelle 2t), as an E2 level with some mixture of M 1 (figs. 7 and 8). A measurement was made with an oxygen gas target of approximately the same number of atoms as the water target to confirm the behaviour of the radiation tail in gases. 5.5. THE ,F 1~ NUCLEUS This nucleus shows only one level at 7.4 MeV which was known, although no spin assignment had been made (fig. 9). 5.6. THE loNe2° NUCLEUS A whole group of levels at ~ 13 MeV is known and some indication of these is seen in the data (fig. 10). A level at an energy of 9 MeV is also seen. 5.7. THE ltNa 23 NUCLEUS Four low energy levels show up quite clearly in this case (fig. 11). Within an accuracy of 200 keV all these levels can be correlated to known levels. A known level missing is the first excited state in Na 23 at 0.439 MeV and spin i +; since it is near the elastic peak it could have escaped detection. At an energy of 15 MeV, a broad peak is seen which could be due to excitation of the giant resonance by transverse electric photons. See discussion on lsAr 4°, below.
NUCLEAR MAGNETIC TRANSITIONS
,479
5.8. THE l~Mg NUCLEUS Magnesium has 3 isotopes the most abundant of which is 12Mg24(78.8%); we attribute the observed structure to this isotope. We found an outstanding level at 11.1 MeV and a broad structure which corresponds to a group of levels at 14 MeV (fig. 12). The 1 I. 1 MeV is known from elastic scattering ofT-rays 22) and our measurement establishes the M 1 character of the transition between it and the ground state. 5.9. THE 1sAW NUCLEUS Although several M1 transitions can be expected in aluminium below an energy of 4 MeV, no clear structure is seen there. Levels are seen, however, at 4.8, 10.6 and 12.8 MeV. The first and third of these can be associated with known levels of AI. Since aluminium is in general used as window or support in scattering experiments, the presence of this structure can be quite bothersome at times. 5.10. THE t6Psl NUCLEUS Many M1 transitions are possible in this case, but we see only three at 3.6, 5.6 and 9.0 MeV (fig. 14). The 3.6 MeV level is known, but the others are not found in the literature. 5.11. THE leS3~ NUCLEUS Although sulphur has two other isotopes, S 32 is the most abundant (94 %), transitions are seen at 8.4 and 11.4 MeV (fig. 15). The closest levels known in S 32 are 8.5 and 11.88 neither of which have spin assignments. 5.12. THE 1sAt4°,
19K a9
AND
soCa40
NUCLEI
No levels were found in these elements nor was scattering with excitation of the giant resonance observed (figs. 16-18). Fairly thin targets were used in these experiments so the statistical accuracy was not very good; it is conceivable that the giant resonance was not big enough in our experimental conditions to stand significantly above the radiation tail at 180 ° . The giant resonance in some elements was measured at a scattering angle of 160 ° in an experiment in which fairly thick targets were used 1). This point will be the object of further investigation. 5.13. THE 8aBi2°9 NUCLEUS Our interest in investigating such a heavy nucleus was to find out what fraction of the giant resonance is the result of magnetic dipole transitions. There is convincing evidence for the dominant El character of the giant resonance, but it comes somewhat indirectly. In the first place, there is the electric dipole sum which seems to account satisfactorily for the total photon absorption cross scction 23). In the second place, the angular dependence of elastically scattered photons supports this assignment 2z" 24). The angular distribution of fa,t photo-protons or photo-neutrons does not distin-
480
w.c.
BARBER
et aL
guish between E1 or M l transitions; this ambiguity can be solved by using a linearly polarized beam of y-rays 2~, 26); this has been used in a few cases of isolated levels 27). An experiment of this kind was done on the fast photoneutrons of bismuth 28) and indicated the presence of Ml transitions in the giant resonance of Bi 2°9. Our results indicate that no important contribution of M1 transitions is present in this element. One can estimate from the results in fig. 19 and formula (23) that the integrated cross section for M 1 transitions in bismuth is smaller than 10 MeV. mb; the integrated absorption cross section for photons in this element is 23) 4100 M e V . mb; it is clear, however, that the long wave approximation is not good in bismuth and the matrix elements neglected could decrease by a factor of ~ 10 the virtual photon intensity; our upper limit for M1 transitions in bismuth would then be ,~ 100 MeV • mb or g 3 ~o of the total absorption cross-section.
6. Conclusions The main general conclusions one can derive from the measurements reported in this paper are the following: i) The radiation widths listed in table 2 are within an order of magnitude in agreement with the single particle predictions of Weisskopf 29). ii) The outstanding transitions found in previous work 1'2) for C 12 and Si 2s seem to be related to the ones found here for Ne 2°, Mg 24 and S 32. A suggestion has been made recently by Kurath 3o) along these lines. He argues that the well-known C 12 15.1 MeV M1 transition is caused by the action of an operator 1~II10 ~ / ~~ stk)r Z ~k) Z, k
which flips both the spin and isobaric spin. He calculates then the integrated cross section of the transitions induced by this operator and finds that it should be a maximum when the J = l+½ shell is full and the J = l - ½ shell is still empty. The transition strength is expected to be concentrated in one or a few levels. Kurath suggests that in the 2s-ld region, there are several nuclei in which to expect such an M1 transition, such as Ne 2°, Mg 24, Si 28, S 32 and Ar 4°. Our data show that such is indeed the case for Ne 2°, Mg 24 and $32; Si 28 was investigated before2). The Ar 4° nucleus does not show any structure as might be expected, since the d~ shell begins to be filled, and the mechanism suggested by Kurath is weak in this case. iii) It is worth remarking that a number of M I transitions expected from previous level assignments are not seen in our measurements. This indicates that they have very small radiation widths upon which limits can be placed using eq. (24). Reasons for that might be found in calculations using specific models such as the ones made in Li 7 for higher m o m e n t u m transfers 18). These calculations would allow also a more significant analysis of the data that will not have to rely on the long wave approximation.
NUCLEAR MAGNETICTRANSITIONS
481
We acknowledge Mr. J. Carson, Mr. E. Wright and E. Pathway for technical help given to us during the experiment. One of us (Y.T.) wishes to acknowledge the Ministry of Education of Japan which made possible his stay at Stanford. J. G. acknowledges partial support from the Pan American Union. References 1) 2) 3) 4) 5) 6) 7) 8) 9) 10) 11) 12) 13) 14) 15) 16) 17) 18) 19) 20) 21) 22) 23) 24) 25) 26) 27) 28) 29) 30)
W. C. Barber, F. Berthold, G. Fricke and F. F. Gudden, Phys. Rev. 120 (1960) 2081 R. Edge and G. A. Peterson, Phys. Roy., submitted for publication G. A. Peterson, Phys. Lett. 2 (1962) 162 G. A. Peterson and W. C. Barber, Phys. Rev. 128 (1962) 812; in Prec. Rutherford Jubilee Int. Conf. Manchester, 1961 p. 831 (Heyward, London, 1961) F. Bumiller, M. Croissiaux, E. Dally and R. Hofstadter, Phys. Roy. 124 (1961) 1623 F. Ajzenberg-Selove and T. Lauritsen, Nuclear Physics 11 (1959) 1 P. M. Endt and C. van der Leun, Nuclear Physics 34 (1962) 1 J. I. Friedman, Phys. Rev. 116 (1959) 1257 P. T. McCormick, D. G. Keiffer and G. Parzen, Phys. Rev. 103 (1956) 29 R. Huby, Report on Progress in Physics, 21 (1958) 59 L. I. Schiff, Phys. Rev. 96 (1954) 765 K. Alder, A. Bohr, T. Huus, B. Mottelson and A. Winther, Revs. Mod. Phys. 28 (1956) 432 R. H. Dalitz and D. R. Yennie, Phys. Rev. 105 (1957) 1598 W. C. Barber, Ann. Rev. Nucl. Sci. (1962) J. M. Blatt and V. F. Weisskopf, Theoretical nuclear physics, (Wiley, New York, 1952) V. Z. Jankus, Phys. Rev. 102 (1956) 1586 J. Goldemberg and L. Katz, Phys. Rev. 95 (1954) 471 R. Willey, Nuclear Physics 40 (1963) 529 F. K. Warburton, Phys. Roy. 113 (1959) 595 H. E. Johns, R. J. Horsley, R. N. H. Haslam and A. Quinton, Phys. Roy. 84 (1951) 856 D. B. Isabelle and G. R. Bishop, private communication A. Brussiere de Nerey, Ann. de Phys. 6 (1961) 89 R. Montalbetti, L. Katz and J. Goldemberg, Phys. Rev. 91 (1953) 659 E. G. Fuller and E. Hayward, Phys. Rev. 101 (1956) 692 A. Agodi, Nuovo Cim. 5 (1957) 21 A. G. Pinho Filho, Nuclear Physics 18 (1960) 271 K. Shoda, J. Phys. See. Japan 16 (1961) 1841 P. Dyal, J. O'Connell and J. Goldemberg, unpublished D. H. Wilkinson, Phil. Mag. 44 (1953) 450,1 (1956) 127, in Prec. Rehovoth Conf. Nucl. Structure (North-Holland Publ. Co., Amsterdam, 1957) D. T. Kurath, private communication
2.L
[
Nuclear Physics 41 (1963) 461---481; (~) North-Holland -Publishing Co., Amsterdam Not to be reproduced by photoprint or microfilm without written permission from the publisher
STUDY OF NUCLEAR MAGNETIC TRANSITIONS BY I N E L A S T I C E L E C T R O N S C A T T E R I N G W. C. BARBER, J. GOLDEMBERG t, G. A. PETERSON tt and Y. T O R I Z U K A ttt
High-Energy Physics Laboratory, Stanford University, Stanford, California Received 22 October
1962
Abstract: The energy spectrum ofinelastically scattered electrons at 180° was measured for 41.5 MeV electrons from the Stanford Mark II Linear Accelerator for the following elements: ~Dz, 8Lie, 3Li7, 7Nx', sO xe, 9Fx', x0Ne*°, n N a m, 1,Mg, isAlsv, xsPsl , lsSn2, leAr*°, agK3', 20Ca'° and 8sBi*°9. Some of the elements investigated show clear evidence of excitation of nuclear levels. It is shown that these excitations are most likely due to magnetic dipole transitions. The experiment was performed under conditions in which the "long wave approximation" is approximately valid, so radiation widths were derived for the excited states. A comparison is made with the single particle model predictions. A systematic behaviour of some M1 transitions in light nuclei suggested recently by Kurath is supported by the data. The radiation tail was investigated in some detail and the large-angle bremsstrahlung formula of McCormick, Keiffer and Parzen was found to agree with the data for gas targets.
1. Introduction In this paper we report measurements of the spectrum of inelastically scattered electrons at 180 ° where magnetic transitions are most clearly seen. Measurements were made in 1D 2, zLi 7, 7N 14, 8016, 9F19, lone 2°, 11Na 23, 12Mg, 13A127, 15P31, 16832, 1BAr4°, 19K39, 29C.a40 and 83Bi 2°9. Combined with the previous measurements reported in refs. 1, 2), this experiment represents an exploratory investigation of most light nuclei as far as magnetic inelastic scattering is concerned. In sect. 2 we describe briefly the experimental method and apparatus; in sect. 3 we present the data; in sect. 4we discuss the radiation tail at 180°; in sect. 5 the method of analysis and the information obtained on levels of the elements listed above,are presented; finally, in sect. 6 some conclusions are listed. 2. Experimental Method The experimental arrangement for 180 ° scattering measurements in use at the Mark I I Stanford Lineac was described before 2-4). The 41.5 MeV electrons from the accelerator are deflected approximately 10 ° by an auxiliary magnet before striking t On leave from University ofS. Paulo, S. Paulo, Brazil. tt Now at Yale University, New Haven, Connecticut. tt* On leave from Tohoku University, Sendal, Japan. This work was supported in part by the joint programm of the Office o f Naval Research, the U.S. Atomic Energy Commission and Air Force Office of Scientific Research. 461
462
w . c . BARBERet aL
the target, a n d the ones that u n d e r g o 180 ° scattering are deflected again in the same m a g n e t before entering a magnetic spectrometer located at 160 ° with respect to the incident b e a m (fig. 1). The energy spread o f the incident b e a m was 1.5 %. The m e a s u r e m e n t s were made with the centrally scattered electrons at exactly 180°; this was d o n e b y adjusting the c u r r e n t in the auxiliary m a g n e t until the c o u n t i n g rate in the elastic peak for charge scattering in a c a r b o n target was a m i n i m u m ; MAGNETIC METER
SCATTERED ELECTRON BEAM
D INCIDENT
E'ECTRON
DE,.
•
I
~ ....
;
•
"~
/
\T, RGET
L AUXILIARY DEFLECTING MAGNET
Fig. 1. Sketch of the experimental arrangement. This drawLog is not to scale.
since 6C12 has a zero spin, n o magnetic elastic scattering is expected, a n d the c o u n t i n g rate should be zero at 180°; two effects are present which m a k e it appreciable; in the first place the entrance angle o f the spectrometer is finite a n d i n the second place multiple scattering o f the electrons in the target increases the angle o f acceptance o f TABLE 1
Properties of targets Element lH 1 ID2 aLP aLi7 eN14 80 I~ 9F1' xoNe2° axNass I=Mg a~Al~ asP3~ 1~S~2 19K39 . A r ~° =oCa~° asBi2°°
Target CH2 H gas D gas metal metal Melamine (NrCsHr) N gas O gas Teflon (CF2) Ne gas metal metal metal red phosphorus powder metal Ar gas metal metal
Thickness (mg/cm~)
Thickness in radiation lengths
233 33.5 28.8 149 170 180 200 228 150 143 150 174 150 241 192 135 205 98 156
0.0052 0.00058 0.00050 0.0028 0.0028 0.0046 0.0050 0.0065 0.0061 0.0050 0.0054 0.0068 0.0061 0.01 i 0.0091 0.0074 0.014 0.0054 0.024
463
NUCLEAR MAGNETIC TRANSITIONS
the spectrometer. F o r most of the solid targets the multiple scattering was such that the effective angle of the spectrometer was g 177.4 °. Solid and gas targets were used in the experiment. The solid targets were in the form of disks 3.8 cm in diameter and about 0.16 cm thick. The gas target was a cylinder 7.5 cm in diameter and 30 cm long with 0.0125 cm Dural windows. A gas pressure o f 5.7 atm was used. The effective thickness of the gas target was determined by comparing its counting rate with a solid target of known thickness containing the same element. This was done for a C H z solid target and hydrogen gas. Table 1 fists all targets used with relevant information. The procedure for data taking was to measure the number of electrons per unit monitor reading at different currents in the spectrometer. The spectrometer current was changed by small steps each corresponding to an energy change of approximately 150 keV. Three independent counters detected the electrons; in some eases the data of the three counters were combined; in others the data from only one of them were used. Absolute values were determined by comparison with the proton elastic scattering cross section from I H ~. This cross section is well-known from the work of Bumiller
et al. s). 3. Data Figs. 2 to 19 show the spectra of electrons scattered at 180 ° for all the elements investigated including I H 1. The solid lines were drawn as smooth curves to fit the data. In some cases such as aLi 6 or 12Mg very outstanding peaks are present which indicate clearly scattering by levels.
(CH2 - C) 1 -31
0 . 5 -xlO
H2
0.4
";
0.3,
IE
0.1
0.0 28
30
32
34 MeV
36
38
40
Fig. 2. S p e c t r u m o f 41.5 MoV electrons scattered at 180 ° from two targets c o n t a i n i n g hydrogen.
464
W.
C. BARBER et
aL
TABLE 2
Spin and parity
Isotope
sLi e
Energy o f level Ground (MeV) state
3.56
1+
5.7
14.0
15.8
3LF
9.6
80xs 9F t~ x0Ne~° uNa ~
19.0 7.7 ~ 9 13 3.0
0+ ½+ 0+ ½-
4.6 6.1 8.0 lzMg z4
11.0 14
0+
a3A127
4.8
~}+
8.0
4.7 { 0.9 0.3 0.16
Weisskopf
0.42
O. 15
50
0.03
1+ 2+
0.6
30
0.20
1~ + 2+ 0 1+ 2+
0.25
50
0.14
0.25
50
0.17
[37.5 {12.5 I 7.5
80
0.18
50
0.06
I'4 1.7
18
1.1 [19.2 /9:6
23
I
0.82 3.6
16
t 3 58
0.78
30
0.30
_-
0.48
40
0.27
{15.6 (10.4
58
1+ 2+
0.92
30
0.30
7.8 4.6
17
1+ 2+ 1+ ~-+ 1+ 1+ /~ + / ~+ i+ ½+ I].+ I ~+ 1+ 1÷
0.65
30
0.25
25
0.45 2.0 3.0 2.0 0.2
40 25 20 20 50
0.41 0.54 0.9 1.0 0.02
0.5 1.0 2.5
40 40 30
0.07 0.20 0.68
4.4 1.5
20 30
1.76 0.83
8.2 4.9 14.1 4.7 7.1 16.6 •0.05 10.035 0.43 4.4 t12.8 [ 8.6 21.0 15.8
0.7
30
0.10
1.9
30
0.50
l°
10.6
This experiment 4)
20
{i I+
Estimated error (%) M e V ' m b
Radiation width to ground state (eV)
4.0
{_-
14.0
9.3
0+ 0+ I[ I+ 2+
~-
10.5
7N 14
Excited state
(
9.3
Inelastic electron scattering cross section (cm~/sr) X 10 -as
l"
t÷ ~+ ~+ ~+
{
/46
{ "°
0.67 0.50 (14.0
145 9.0 14.5 48 0.45 1.8 4.6 10.8 29 58 2.1
465
NUCLEAR MAGNETIC TRANSITIONS TABLE 2 ( C o n t i n u e d ) .1.+ 10.6
½+
5.6 8.9 5.7 8.5 11.4
16S 32
40
0.23
t÷
1.4
30
0.65
t+
0.9
30
0.1
~-+
0.7
30
0.12
~+ 0.7 1÷ 1.3 1+ 1.7 1+ 2.6 no resonances 110 resonances no resonances no resonances
30 30 30 30
0.22 0.24 0.51 1.11
½+
3.6
15P31
0.6
~+
12.8
0+
zsAr4°
0+
,gK s9
-,~-+
2oCa ~°
0+
S3Bi2O9
~-
11.5
2.+
25 46.5 31.2 23.5 0.29 1.1 0.81 0.55 4.0 0.76 3.5 14.2
45 0.82 3.6 14.5 3.6 12.5 32
a) T h e results in this c o l u m n were derived in the " l o n g w a ve a p p r o x i m a t i o n " . 3 DZ (GAS)
26
28
30
32
34
• 36
38
40
MeV Fig. 3. Spectrum o f 41.5 M e V electrons inelasticaily scattered f r o m deuterium gas at 180 °.
It is realized immediately by inspection of the curves that large radiation tails are present. This point is discussed in more detail in sect. 4. The integrated inelastic scattering cross section Ii, = S (da(O)/dfI)de for each level was defined as the area above a smooth line drawn through the points in the adjacent regions of the electron spectrum. For the levels which are not outstanding, this procedure permits only a rough estimate of the cross sections. The position of the levels found in this work and estimates of/in are listed in table 2. The estimated error is stated in each case.
466
w . C . BARBERe t al.
0.5'
'_9.~...... ; Li i_8,_3~
-31 -xlO
6
~55_ ~4 ~ _1+~
0.4
3.56 MeV
3Li s (4L5 MeV)
;3.5.60+ I :2J84 3~J
>o.3
t
~E /..._.~ i. L 0 I'+ ~'.~. 0 . 2 I 15"8/MeV14.0MeV 9.3 MeV
5.7 MeV
.kJ
0.1
24
26
28
30
32
34
36
38
40
42
MeV
Fig. 4. Spectrum of 41.5 MoV electrons scattered from LP at 180 °. 17.5 16.2
L i7
k4
.
Li?(NATURAL LITHIUM)
J
i
lO.8 9.6
0.4 xlO31
7.475~
O. 3
6.S4 ,4,63
14MeV
24
ZI6
0
28
30
X~ l
3/2-
FROMLi 6
32
34 36 38 40 42 MeV F i g . 5. S p e c t r u m o f 41.5 M e V electrons scattered f r o m L i 7 a t 180 °.
7
0.6
NI 4
xlO31 2.31 0~-,I
0.4 ~>
~o.2
1
L___
~t r P'~
10.6 MeV 0 I+ 1 9.3MeV
' '"/.~, ~r~'~.~.
24
26
28
'
30
~(~,s
N6C3H6
32
34
36
38
40
4 :)
MeV
Fig. 6. Spectrum of 41.5 MoV electrons scattered from two nitrogen targets at 180°.
467
NUCLEAR MAGNETIC TRANSITIONS
In some of the figures we show the position and spin of well-known levels taken from Ajzenberg and Lauritsen et al. 6) and from Endt and Van der Leun v).
-31 0.6 - x l O
0.5
0 (H20)
T>¢ 0.4
0.3 ej~. 0.2 ~.
•
j,
,
0.1 0.0
20
22
a,
2;
a8
io
~2
i,
MeV
3~
3~
,o
,2
Fig. 7. Spectrum of 41.5 MeV electrons scattered from an H=O target at 180 °.
r .
-3l 0.75 i xlO
sO16(GAS)
: o,o I ~o.ool{
Jl
~
26
28
30
{,
f ~
32
~
54
~ 4 36
:
38
40
42
MeV
Fig. 8. Spectrum of 41.5 MeV electrons scattered from an oxygen gas target at 180 °.
riO3' ~
sFI9
1.00 0.75
0
1/2~7.7 MeV
~. 0.50 ~E 0.25 u
0.00
26
I
I
I
l
I
r
I
28
30
32
34 MeV
56
58
40
42
Fig. 9. Spectrum of 41.5 MeV electrons scattered from CF, at {80 °.
468
w.c.
BARBER et aL
~zz iz31 loNe
'7
i
-31 KIO
I .00
14-
20
0.75 13 Mev
o,5o
8 Mev
i
I
1
"E 0.25 0.00 28
26
50
32
34 MeV
36
38
40
42
Fig. 10. Spectrum o f 41.5 M e V electrons scattered f r o m a n e o n gas target at 180 °.
-31
[rzC u3~2÷~,z"
1.75 - x I0
162.7. . . . ,,2 •
t.50
~47_8.___ i t / z * 3/2 * '3.85
b/z • ~z?*
2.64
. i z z , 5Fz *
x
II
$
--11 ......
t.25 ir 5M~V
I.O0 ,
g 0.75
i N023
,
:
~
~--~;;.
'
{
8o.ev ! ~"~'eX.~%Mo v
;
~ .
~ 0.50 0.25 0.00' _ . _ _
22
2',
26
z~
3'o
32
3,~
3'6
~8
,;o
4=
MeV
Fig. 11. Spectrum of41.5 M e V electrons scattered f r o m N a ~ at 180 °.
1,501
....
I -~i 1.25 xlO
•;
1.00"
14MeV
~: 0.75
Mg 12
I x~
ii }
IIMeV
+
~E O.5t3 0.25
;~ ~ ; ~ . ~ {
o.oo L
26
28
30
3t2
34
36
3r8
~
410
f 42
MeV
Fig. 12. Spectrum o f 41.5 M e V electrons scattered f r o m a m a g n e s i u m target at 180 °.
NUCLEAR MAONETIC TRANSITIONS
'I
r"
I ~ ,
";
469
I
I I-
~-tt~
"°r °"
o
"
4.s~v
' ~
,
,..
1
O/ 24
'
[
i
I
I
1
~
~
I
t
26
28
30
32
34
36
38
40
42
MeV
Fig. 13. Spectrum o f 41.5 M e V electrons scattered f r o m an A [ =7 target at ]80 °.
~3/2
r
,o~ ~'
, ' t'kt,
/
"~= o 8 ~ "
'~
"~
,sp 3'
o
S.gMeV
* I
37~-
t,
~
"h-L
÷
0.6 P
~s..v ......
~r,~
/
,,..v I
t
#,
~,
' ÷ ~ . = ~
~ t
"~'
0.4"
0.0.
~
i
50
,
3'4 5]8 3]8 4'0 42 MeV Fig. 14. Spectrum o f 41.5 MeV electrons scattered from a ps~ target at 180 °. 26
2]8
52
3Z S 16 /
z.O
17.co
\F
1.5
I±1
'~
~,,~s ,~!
x\lO
X
\ \
~
.
11.4MRV i ,
~E ~0.5
,
t
8.5 MeV
÷
0.0
:
16
18
I .......
20
~
22
:
I
24
26
J
._.
28
i
i
30
32
.....
"
34
....
l
56
38
40
42
MeV
Fig. 15. Spectrum o f 41.5 M e V electrons scattered f r o m a s u l p h u r target at 180 °.
470
w.c.
BARBER et aL
3 40 18A r -31 xlO
2
{{{{{ ~ -
BREMSSTRAHLUNG
~t
{ ¢ 0
I
16
I
I
20
I
1
I
24
I
I
;>8 32 MeV
I
I
36
i
{ r {
410 44
Fig. 16. Spectrum o f 41.5 MeV electrons scattered from a n A r 40 gas t a r g e t a t 180 ° X I/2
-31 4 -xlO 19 K
t
3
o
26
28
30
32
34 3,6 38 40 42 MeV Fig. 17. Spectrum o f 41.5 M e V electrons scattered f r o m a potassium target at 180 °. I.OF t-
40
o.81-,,1~3'
,oCO
0.6 Iz. 0.4 ~
~
; 18
20
22
24
26
28
30 32 :34 36 38 410 42 MeV Fig, 18, Spectrum o f 41.5 M e V electrons scattered from a calcium target at 180 °, 8
i6 o ¢n z w4 o > _ uP
S3 Ri2°9 ..¢=
GIANT RESONANCE REGION , 0,
1 ELASTIC PEAK
<,z
MeV Fig. 19. Spectrum o f 41.5 M e V ine|asticaHy scatterec[ electrons f r o m a Bi m target.
471
NUCLEAR MAG.NETIC TRANSITIONS
4. Radiation Tail Since an elastic peak is present in the curves, one expects a radiation tail. The effects responsible for that have been discussed by Barber et aL 1) and Friedman a); they are: a) radiation during scattering, b) radiation before or after scattering, c) electron-electron scattering before or after elastic scattering and d) energy loss by ionization, the most important effects being a) and b). It turns out 1) that for the usual angles used in electron scattering and for targets of approximately 0.01 radiation length, the radiation tail amounts to approximately 1 or 2 % of the elastic peak height in a region of a few MeV below the elastic peak. It is quite clear from figs. 2 to 19 that in some of our measurements (at ~ 180°) the radiation tail amounts to ~ 10% of the elastic peak in that energy region. The main reason for this is large-angle bremsstrahlung. The Bethe-Heitler formula for the case in which the electron goes in a specified direction regardless of the direction of the emitted photon has been integrated by McCormick, Keiffer and Parzen 9). The cross section for such a process when the electron scatters in a backward direction is
d (E, 0) dO
-
z2 1
i (e2 \rnc2!
R',
/m c 2\2 t 2E ° R' : [ ~ ) ,~A(~'0)In - + B(7 , 0).j mo c2
(1)
(2)
Here E o and E are the energy of incident and outgoing electron, k = E o - E , V = E/Eo, A(y, 0) = 5 (1 +72) 2 cos 2 50 73 sin" ½0' B(V, 0) = 5 1 +~2 /cos2 50 In 7 + ~ -V sin" ½0 2 sin 4 ½0 +
(3)
In (sin 2 ½0) (1--7+~ 2)
2~2 - In (sin 2 50) • (4) 1 + ~2 sin 2 t0
The contribution of these two terms to the total bremsstrahlung cross section is plotted in fig. 20. It is seen that the A term for a given 7 has the same behaviour of the Mott cross section and goes to zero at 180°; at other angles it is the dominant term. The B term is fairly constant around 180°, for a given 7. The ratio of the bremsstrahlung cross section to the Mott cross section increases as 0 ~ 180 ° (fig. 21). For the conditions of our experiments it amounted to ~ 5%, for ~ ~ 0 . 5 . We found that for gas targets the McCormick, Keiffer and Parzen formula represents the radiation tail quite accurately, at least for the light elements. Fig. 16 shows our results for the case of xsAr 4°.
472
w.c.
BARBER et al.
For the solid targets there are other effects that complicate matters considerably; although the thickness of the targets was quite small, it introduced effects due to multiple scattering. I f the tail is measured as a function of thickness, one finds deviations from linearity; these deviations are larger as the final energy of the electron becomes smaller. This is seen in fig. 22.
~~
RAHLUNG=A+B
2.0
1.5 "7 IE ..~ 1.0
~
% X
\\~A
0.5
% % % %%
0.0
I
160
170 DEGREES
180
Fig. 20. T h e large angle brernsstraklung cross section near 180 ° f o r Z = 1 and an incident electr energy o f 41.5 M e V (), = (K]E,) = 0 . 6 ) . 20%
I I I I I I I
I0% I _
I
jl S¢
-
160 F i g . 21. R a t i o
I
of the large-angle bremsstrahhmg
I 170 DEGREES
I
t
180
t o t h e M o t t cross
section
near
180 ° ( y = 0 . 6 )
The amount of target material in the direction perpendicular to the incident beam is also important. This is evidenced in fig. 6 which shows measurements for a solid target containing nitrogen (N6C3Hs-melamine) and for a nitrogen gas target of about the same total mass per unit area in the beam direction, but much less at 90°; the levels at 9.4 and 10.7 MeV stand up above the tail in the solid target, but are more
NUCLEAR
MAGNETIC
TRANSITIONS
473
prominent in the N gas measurements where the tail is much reduced. The same behaviour is apparent for H (fig. 2); a tail is present when one uses a CH 2 target and subtracts the C contribution obtained from a graphite target with the same number of carbon atoms. The curve obtained for H gas does not show any measurable tail. The probable explanation of these facts is that if a 90 ° scattering event occurs in a solid target, there is a large amount of material viewed by the spectrometer that can contribute to the tail by bremsstrahlung radiation at large angles. With gas targets this is no longer the case. 400
300
?_. z 200
I00
0 0
,'o
2'o
~o
io
50
go
~o
THICKNESS MILS
600
400 o o
200
o
,o
~o
3'0
'.ICKNESS M,,S
Fig. 22. The tail as a function of target thickness in aluminium for an incident energy of 41.5 MeV and final energies of 25 and 16.7 MeV. (1 mil = 25.4/,m.) Unfortunately, the electron intensity available did not permit the use of extremely thin targets, and the use of targets with very small transverse dimensions would have introduced monitoring problems. Since the radiation tail for solid targets would require a considerable amount of calculations which could not be done very reliably, we adopted the procedure outlined in sect. 3 to obtain the inelastic cross section integrated over the levels.
5. Analysis of the Data and Discussion of the Results The Hamiltonian for the interaction between the electrons and nucleus can be split into two parts, the electrostatic (Coulomb) and the magnetic interaction 1o). The Coulomb interaction is Vc=e2~
1 y c -- r k
,
(5)
474
BARBER et al.
w.C.
where rc is the coordinate of the electron and the sum extends over the positions of the protons k. The Coulomb interaction Vc can be expanded as a series of multipoles 1 r~ Y~.(0., q~.)Yl*(0k, ~Ok), Vc = 4xe 2 k,l,m 2 l + 1 r ~ + l
r k < r.,
(6)
r~ > ,o.
(7)
!
1 ro Yl.,(O~, ~o)Y,.(0~, * ~), ~,t.,, 2 l + 1 r ~ + l
Vc = 4he z ~,
A term of order l leads to the excitation of an electric transition EL i.e., a change of the angular momentum of the nucleus of l units and a change of parity ( - 1)~; I runs from 0 to oo which means that monopole transitions can also be excited by Vo In other words the electrostatic interaction can be represented by the absorption of photons of angular momentum l and parity ( - 1 ) t (longitudinal photons). Explicit formulas for the cross section of the transitions induced by Vc have been calculated by Schiff 11) in Born approximations for the extreme relativistic case, i.e., neglect of the electron rest mass and nuclear excitation energy docl(0) _ (Ze~) ~ cos ~ ½0 ie~(z~--, If, q)l 2,
dO
\2Eo/
sin 4
½0
q -- p o - p ,
(8)
where Po and Eo are the initial momentum and energy of the electron, and E and p are the final momentum and energy of the electron. The factor Fcz(li ~ If, q) can be considered a form factor for inelastic transitions;
q)[2
JF~li --, It,
B(CI, q) --
4nq2' B(CI, _- z2[( 2 / + 1)! l] 2
q),
[(2/+ 1)l l] 2
q2'(2Ii+1) m,,EM,.=[(If mr Ek [j,(qr~)Ylm(Ok, ~,~)[zimi>l ~.
(9)
(10)
Here B(C/, q) is a reduced matrix transition probability. It is seen (eq. (8)) that this cross section goes to zero for 0 ~ 180 ° just as the Mott cross section, and is, therefore, absent if the inelastically scattered electrons are observed at that angle. The magnetic interaction is e
VA=
-
-C ,,.-A(,o),
(11)
where v, is the velocity of the electrons and A(rc) is the vector potential. The vector potential can be expanded in multipoles which have electric and, magnetic field components. The expressions for the cross sections due to these multipoles are dO'El(0) (Ze2) 2 ½(1 +sin 2 ½0)[FEI(/i --~ If, q)[2, dQ = \ ~ o / sin 4 ½0
(12)
NUCLEAR MAGNETIC TRANSITIONS
475
daMl(O) -- /7~2\/L~© / 2 ½(1 +sin 2 ½0)IFMI(Ii ~ If, q)l 2. dO \2Eo/ sin4 ½0
(13)
Expressions for FEI and Ful similar to (5) in terms of the reduced matrix transition probabilities with the appropriate operators can be found in ref. 1o). One can say that these cross sections correspond to the absorption of (transverse) photons of angular momentum l and parity ( - 1)l and ( - 1)t÷l for electric and magnetic transitions, respectively. It is seen (eqs. (12)and (13))that the angular factor cos2½0in the electrostatic case becomes ½(l+sin2~tr0) for the magnetic interaction which means that the vector potential interaction cross sections do not vanish at 180°. This is then an optimum angle at which experiments should be performed in order to investigate this type of process. The expressions above are appropriate for scattering at high energies (> 200 MeV) and have been used extensively in the literature. Alder et aL 12)worked out expressions similar to the ones of Schiffbut more adequate for our energies ( ~ 50 MeV); this calculation is also made in Born approximation but does not make the assumption, which Schiff did, of having the excitation energy negligible compared to the incident energy. The expressions of Alder et al. are repeated here for completeness
dacI(O)_(e2~ 2 4n(l+l) q2____llB(CI, q)VL(O), d-~ \hc/ /[(21+1)![] 2 p2 /+1 daFa(O)_ (e2'~2 4n(I+I)
dr2
q2, B(EI, q)VT(O), I[(21+I)!!'] 2 pg
\hc/
d~o(O)
_
(e2~ 2
q2!
4n(l+l)
B(MI, q)VT(O),
\he/ t[(21+l)!!y 1,o2 Po + P -
VL(O)=
e2
-
p
Po
PPo
(14)
(15) (16)
+ 2 cos 0
(17)
Po+ P_2cos0 Po
,o+, v (o) =
\Po/
PPo
(-
P
eP-~o)cos 0 + 2 cos20 Po
(PP+ P--Po--2c°sO) IP:+ PPo Ppoe2 2cos01 2
(18)
The transition probabilities B(C/, q), B(FI, q) and B(M/, q) are similar to those found in photon emission or absorption processes; in the case when the nuclear radius r is very small compared with 1/q (qr << 1) these quantities are identical in electron scattering and photon absorption.
w.c. BARBERet aL
476
This equivalence has given rise to the "virtual photon" method of analysis of inelastic electron scattering x, la, 14). In this method one says that the incident electrons create a field in space (virtual photon field) and that these photons induce transitions in the bombarded nucleus. The cross section for inelastic scattering is written as dtr(O) _ n(l, e, Eo, O)a,(e, l) = 1 dN(l, e, Eo, O) a~,(e, l),
dr2
~
(19)
dO
= E o-E,
where try(e, l) is the absorption cross section for real photons of energy e and multipolarity l; H(l, e, Eo, 0) is the virtual photon spectrum. Using the Moiler potentials, H(l, e, E o, 0) has been calculated for different multipoles la). The cross section a~(e,/) in the expression above contains reduced matrix transition probabilities which are similar to the ones involved in expressions (14), (15) and 0 6 ) with the difference that in the absorption of photons q --* 0. It can be shown easily that
dNc(l, e, Eo, O) _ ct p 2 ( l + c o s 0 ) 2 1 [q_~2t-2 B(Cl, q) dr2 rt2 q2 I + 1 k e] B(CI, e) dNE(l, e, Eo, O) _ dr2
dNr~(l, z, Eo, O) _ dr2
for longitudinal photons,
(2O)
et [p2 + p2 + ppo(l_cos O)] [q_~ 21-2 B(El, q) for electric trans(21) 4~z2 p ~ ( 1 - c o s O) ke] B(EI, e) verse photons, ct [p2o+p2 + ppo(1--cos O)] [q_]2'-2 B(Ml, q) formagnetictrans(22) p 2 ( 1 - c o s O) ~e] B(MI, e) verse photons.
4n 2
In the "long wave approximation", i.e., in the case qr << 1, B(CI, q)/B(El, e) ~ 1, B(EI, q)/B(El, e) .~. (e2/q) and B(MI, q)/B(MI, e) ~ 1. This approximation is made in general in calculations of radiation widths in electromagnetic transitions and means that only the lowest possible multipole order contributes; the reason is that in the reduced matrix elements there appears a Bessel function jl(qr); since jl(qr) ~ (qr)l/ (2l+ 1)I! for qr small, it is clear that for qr << 1 only the first term will contribute. The virtual photon spectrum, which has the peculiarity of involving the matrix elements of the nucleus in which it induces transitions, becomes more significant in this case since it involves only kinematic factors. It is quite clear from formulas (20), (21) and (22) that in the case of 180 ° scattering, the longitudinal spectrum is zero, and out of the transverse spectrum a Ml transition is dominant by the factor (q2//~) over an El; although the absorption cross sections of real photons for El transitions is usually about 10 times larger than those for a MI absorption ts); this is not enough in general to upset the dominant Ml character of 180 ° scattering. This feature has been confirmed in cases where levels of known spins and parities have been excited by inelastic scattering at 180°. In table 2 are listed the integrated inelastic scattering cross sections for the levels seen in our measurements.
NUCLEAR MAGNETICTRANSITIONS
477
Since we are assigning an MI character to the transitions seen at 180 °, one can use eq. (19) and obtain f o'),(g)dg m_
/in
(23)
1 ~ (Po+p)2' e 47rz
2poz
where lin is the integral defind in sect. 3. On the other hand, the Breit-Wigner formula for one isolated resonance of width F~ gives
fa.~(e)de
7r2 (2I~+ 1) (2Ii + 1) r , .
(24)
Table 2 includes values of S a~(e)d~ and F~ for each of the levels measured. We assumed always the ratio of the matrix elements present in the virtual photon spectrum to be given by the long wave approximation, although this is not a good approximation in some of the levels. A first order correction to this assumption is given by Barber et al. x) and may amount to ~ 30% for light elements and low excitation energies. Better corrections would require the explicit calculation of the matrix elements in some assumed model. We now discuss in detail some of the levels investigated. Unless otherwise noted, previous information about the levels was taken from refs. 6, v). 5.1. THE ID s NUCLEUS
This element has been the object of a recent extensive investigation in this laboratory by Peterson and Barber 4). The only difference between this measurement and the ones reported there is the use of a gas target instead of a CD2 solid target. The use of a solid target introduces the necessity of subtracting the carbon background so the problem of the radiation tail becomes quite involved. Fig. 2 for hydrogen indicates that this problem should be much simpler using gas targets. Our results are shown in fig. 3 which includes the Jankus theoretical cross section t6) for magnetic scattering at 180 °. The Jankus theoretical cross section was folded by the resolution function of the experimental arrangement and a radiation correction applied as in ref. 4). It is seen that good agreement is obtained between experiment and the Jankus cross section; this indicates that the interaction assumed by Jankus is sufficient to account for the experimental measurements at 41.5 MeV. 5.2. THE 8Lie and aLi* NUCLEI
The Li 6 nucleus presents an outstanding level at 3.56 MeV which was studied previously by electron scattering 2). Our results agree reasonably well with the values reported there. Other structures seen in this nucleus are at 5.7 and 14.0 MeV; there exists a known level at 5.35 MeV (1 +) which could be the one seen in this experiment (figs. 4 and 5).
478
w.C.
BARBER et aL
In Li 7 no outstanding structure is seen, but small peaks at 7.5, 12.5 and 14.0 MeV are present. The 7.5 MeV transition is known to have an MI character. Using a bremsstrahlung spectrum Goldemberg and Katz 17) observed breaks in the (V, n) activation curve at positions indicating levels at 12.5 and 14 MeV. It is worthwhile to mention that Li 6 also shows a level at 14.0 MeV. Since Li 6 and Li 7 have the same "core" this may be indicative of some sort of "core excitation" of magnetic character. A careful search was made for the 0.478 MeV level in Li 7, but no evidence was found for it. This is in agreement with calculations made by R. Willey is) for the magnetic dipole excitation of that level. 5.3. THE 7N14 NUCLEUS Levels are found at 9.3 and 10.6 MeV; the closest known levels are located at 9.18 and 10.43 MeV (fig. 6). Assignments for these levels have been discussed by Warburton ~9) and are compatible with 1 ÷, 2 ÷ or 2 - . Polarization measurements seem to indicate they have even parity 6); if these are the levels seen by us our measurements confirm this assignment. Another interesting feature of N 14 is the broad region at ,,~ 14 MeV which indicates a group of unresolved levels; this energy corresponds to the "shoulder" found in some 0', n) reactions and have been interpreted as due to M1 or E2 absorption 20). 5.4. THE 8016 NUCLEUS The only level seen in this case is one at 19.0 MeV which seems to be the same one reported by Bishop and Isabelle 2t), as an E2 level with some mixture of M 1 (figs. 7 and 8). A measurement was made with an oxygen gas target of approximately the same number of atoms as the water target to confirm the behaviour of the radiation tail in gases. 5.5. THE ,F 1~ NUCLEUS This nucleus shows only one level at 7.4 MeV which was known, although no spin assignment had been made (fig. 9). 5.6. THE loNe2° NUCLEUS A whole group of levels at ~ 13 MeV is known and some indication of these is seen in the data (fig. 10). A level at an energy of 9 MeV is also seen. 5.7. THE ltNa 23 NUCLEUS Four low energy levels show up quite clearly in this case (fig. 11). Within an accuracy of 200 keV all these levels can be correlated to known levels. A known level missing is the first excited state in Na 23 at 0.439 MeV and spin i +; since it is near the elastic peak it could have escaped detection. At an energy of 15 MeV, a broad peak is seen which could be due to excitation of the giant resonance by transverse electric photons. See discussion on lsAr 4°, below.
NUCLEAR MAGNETIC TRANSITIONS
,479
5.8. THE l~Mg NUCLEUS Magnesium has 3 isotopes the most abundant of which is 12Mg24(78.8%); we attribute the observed structure to this isotope. We found an outstanding level at 11.1 MeV and a broad structure which corresponds to a group of levels at 14 MeV (fig. 12). The 1 I. 1 MeV is known from elastic scattering ofT-rays 22) and our measurement establishes the M 1 character of the transition between it and the ground state. 5.9. THE 1sAW NUCLEUS Although several M1 transitions can be expected in aluminium below an energy of 4 MeV, no clear structure is seen there. Levels are seen, however, at 4.8, 10.6 and 12.8 MeV. The first and third of these can be associated with known levels of AI. Since aluminium is in general used as window or support in scattering experiments, the presence of this structure can be quite bothersome at times. 5.10. THE t6Psl NUCLEUS Many M1 transitions are possible in this case, but we see only three at 3.6, 5.6 and 9.0 MeV (fig. 14). The 3.6 MeV level is known, but the others are not found in the literature. 5.11. THE leS3~ NUCLEUS Although sulphur has two other isotopes, S 32 is the most abundant (94 %), transitions are seen at 8.4 and 11.4 MeV (fig. 15). The closest levels known in S 32 are 8.5 and 11.88 neither of which have spin assignments. 5.12. THE 1sAt4°,
19K a9
AND
soCa40
NUCLEI
No levels were found in these elements nor was scattering with excitation of the giant resonance observed (figs. 16-18). Fairly thin targets were used in these experiments so the statistical accuracy was not very good; it is conceivable that the giant resonance was not big enough in our experimental conditions to stand significantly above the radiation tail at 180 ° . The giant resonance in some elements was measured at a scattering angle of 160 ° in an experiment in which fairly thick targets were used 1). This point will be the object of further investigation. 5.13. THE 8aBi2°9 NUCLEUS Our interest in investigating such a heavy nucleus was to find out what fraction of the giant resonance is the result of magnetic dipole transitions. There is convincing evidence for the dominant El character of the giant resonance, but it comes somewhat indirectly. In the first place, there is the electric dipole sum which seems to account satisfactorily for the total photon absorption cross scction 23). In the second place, the angular dependence of elastically scattered photons supports this assignment 2z" 24). The angular distribution of fa,t photo-protons or photo-neutrons does not distin-
480
w.c.
BARBER
et aL
guish between E1 or M l transitions; this ambiguity can be solved by using a linearly polarized beam of y-rays 2~, 26); this has been used in a few cases of isolated levels 27). An experiment of this kind was done on the fast photoneutrons of bismuth 28) and indicated the presence of Ml transitions in the giant resonance of Bi 2°9. Our results indicate that no important contribution of M1 transitions is present in this element. One can estimate from the results in fig. 19 and formula (23) that the integrated cross section for M 1 transitions in bismuth is smaller than 10 MeV. mb; the integrated absorption cross section for photons in this element is 23) 4100 M e V . mb; it is clear, however, that the long wave approximation is not good in bismuth and the matrix elements neglected could decrease by a factor of ~ 10 the virtual photon intensity; our upper limit for M1 transitions in bismuth would then be ,~ 100 MeV • mb or g 3 ~o of the total absorption cross-section.
6. Conclusions The main general conclusions one can derive from the measurements reported in this paper are the following: i) The radiation widths listed in table 2 are within an order of magnitude in agreement with the single particle predictions of Weisskopf 29). ii) The outstanding transitions found in previous work 1'2) for C 12 and Si 2s seem to be related to the ones found here for Ne 2°, Mg 24 and S 32. A suggestion has been made recently by Kurath 3o) along these lines. He argues that the well-known C 12 15.1 MeV M1 transition is caused by the action of an operator 1~II10 ~ / ~~ stk)r Z ~k) Z, k
which flips both the spin and isobaric spin. He calculates then the integrated cross section of the transitions induced by this operator and finds that it should be a maximum when the J = l+½ shell is full and the J = l - ½ shell is still empty. The transition strength is expected to be concentrated in one or a few levels. Kurath suggests that in the 2s-ld region, there are several nuclei in which to expect such an M1 transition, such as Ne 2°, Mg 24, Si 28, S 32 and Ar 4°. Our data show that such is indeed the case for Ne 2°, Mg 24 and $32; Si 28 was investigated before2). The Ar 4° nucleus does not show any structure as might be expected, since the d~ shell begins to be filled, and the mechanism suggested by Kurath is weak in this case. iii) It is worth remarking that a number of M I transitions expected from previous level assignments are not seen in our measurements. This indicates that they have very small radiation widths upon which limits can be placed using eq. (24). Reasons for that might be found in calculations using specific models such as the ones made in Li 7 for higher m o m e n t u m transfers 18). These calculations would allow also a more significant analysis of the data that will not have to rely on the long wave approximation.
NUCLEAR MAGNETICTRANSITIONS
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We acknowledge Mr. J. Carson, Mr. E. Wright and E. Pathway for technical help given to us during the experiment. One of us (Y.T.) wishes to acknowledge the Ministry of Education of Japan which made possible his stay at Stanford. J. G. acknowledges partial support from the Pan American Union. References 1) 2) 3) 4) 5) 6) 7) 8) 9) 10) 11) 12) 13) 14) 15) 16) 17) 18) 19) 20) 21) 22) 23) 24) 25) 26) 27) 28) 29) 30)
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