High resolution spectrometric measurement of energy and natural line widths of 2p-1s pionic X ray transitions, as well as muonic transition energies in Li, Be, B, and C isotope

Eckhause, M.

Harris, R. J., Jr.

Shuler, W. B.

Siegel, R. T.

Welsh, R. E.

English

NASA Technical Reports Server

WM - 11 
ENERGY AND WIDTH MEASUREMENTS OF LOW-2 
PIONIC X-RAY TRANSITIONS* 
A / S O - S G  7 
R. J .  Harris, Jr.,' W. B. Shuler, M. Eckhause, 
R. T. Siegel, and R. E. Welsh 
College of William and Mary, Williamsburg, Virginia 
line widths of 2p-1s pionic X-ray transitions, as well as muonic transition 
energies, in Li6, Li7, Be9, B I O ,  B l l ,  and C12. 
Ge(Li) spectrometers were used, resulting in a more precise determination 
than previously reported of the transition energies and natural line 
widths. 
transitions has been made with the theory of the Ericsons and good agree- 
ment found. 
High-resolution Si(Li) and 
Comparison of the measured complex energy shifts in the pionic 
Several measurements "*) of the energies and natural line widths of 
pionic 2p-1s X-ray transitions have recently been given in the literature. 
We wish to report new and more precise measurements, in addition to 
theoretical calculations,for pionic transitions in Li6, Li7, Be9, Bl0, B1', 
and C1*. a 
Most of the data was obtained using a 75-MeV negative pion beam ' 
(with approximately 15% muon contamination) at the Carnegie-Mellon synchro- 
cyclotron, a small portion being obtained with a 100 MeV beam at the Space 
https://ntrs.nasa.gov/search.jsp?R=19680007940 2020-03-12T09:12:20+00:00Z
- 2 -  
Radiation Effec ts  Laboratory (SREL). 
i n t o  a s c i n t i l l a t i o n  counter array and standard coincidence techniques 
insured t h a t  t he  1600-channel analyzer used t o  s o r t  and s t o r e  pulses  from 
t h e  Si(Li)  o r  Ge(Li) de tec tor  did so only when a fast timing coincidence 
ex is ted  between the  n-stop s ignal  and the  de t ec to r  s igna l .  
more important experimental considerations were: 
Each o f  these  pion beams was focussed 
Some of  t h e  
(1) t h e  de t ec to r  used with each of  t h e  elements was chosen 
on the  bases of both reso lu t ion  and ef f ic iency  require-  
ments. For the  L i 6 ,  L i 7 ,  and Be9 t a r g e t s ,  t h e  80 nun2 x 
3 mm S i (Li )  de tec tor  was used; f o r  B I O ,  Bll, and C12, 
t he  3.5 cm2 x 5 m?l Ge(Li) de tec tor .  
t h e  de tec tors  were operated out of the  d i r e c t  beam so 
as t o  minimize pulse  pile-up problems. 
c a l i b r a t i o n  runs of  the  de tec t ion  system, using well- 
known l i n e s  of Am241 and Tal6’, were taken before and 
a f t e r  each X-ray run. 
(2) 
(3) 
(4) f o r  runs wi th  the  Ge(Li) spectrometer, which was used 
f o r  t he  energy range of 50-100 keV, gain dr i f ts  were 
minimized by use o f  a d i g i t a l  gain s t a b i l i z e r  whose 
reference peak was the 59.57 keV y-ray l i n e  of  Am241. 
The instrumental  resolut ions of t he  cooled FET Si (Li )  and Ge(Li) 
spectrometers under beam conditions were respec t ive ly  0.62 keV (FWSW) at  
33 keV and 1.1 keV (FWI-M) a t  75 keV, as determined from muonic X-rays. 
These figures represent  less than a 10% degradation i n  r e so lu t ion  as 
b 
4 
- 3 -  
previously determined with radioactive sources under laboratory conditions. 
The operation and characteristics of these spectrometers have been de- 
scribed elsewhere 3 J 4 )  . 
Muonic X-ray lines were present in the II runs because of the muon 
contamination in the beam and constituted a substantial background because 
of the relatively low yield of pionic 2p-1s transitions. However, in most 
cases, spectrometer resolution permitted unambiguous separation of the 
pionic 2p-1s peaks and the more intense of the contaminating muonic lines. 
Fig. 1 illustrates raw pionic and muonic X-ray data for a l'nlf-beam run in 
Be9 (Si[Li] detector). The v-K background line, lying approximately 3 
keV below the respective primary r-Ka peak, is clearly separated from the 
pion peak. 
appeared directly under the pionic lines, separate v-beam data were 
accumulated, 
intensities of the p-Ka, u-Kg, p-K 
the background subtraction analysis for the pionic X-ray data. 
B 
In order to account properly for those muonic lines which 
This permitted an independent determination of the relative 
and v-K6 lines which were used in 
Y' 
Briefly, the major features of the analysis for the 2p-1s pionic 
peaks were: 
(1) subtraction of the muon contaminating lines under the 
pionic X-ray peaks. 
determination of the center channels of the pionic peaks 
by fitting the contaminant-free pionic data to both 
Gaussian and Lorentzian functions and a linear background 
term. For a given peak, the center channel value obtained 
(2) 
i 
- 4 -  
from each of these two fits was the same within the sta- 
tistical error. 
(3) determination of the natural line widths by using Voigt 
profiles (convolution integrals of a Gaussian and a 
Lorentzian function) t o  fit the pionic data. 
be noted that, in contrast to extracting a center channel 
value, the determination of the natural line width was 
very shape-dependent, as verified by the differences in 
widths obtained from separate Gaussian and Lorentzian 
fits. 
It should 
(4) use of a precision pulser to determine uncertainties 
introduced into the energy measurements as a result of 
system non-linearities. 
The experimental results for the measured transition energies and 
The errors quoted in- natural line widths are given in Tables I and 11. 
clude statistical uncertainties as well as the uncertainties in background 
subtraction and system linearity. The agreement between the corresponding 
measured energies given in Table IA is, in general, quite satisfactory. 
The values of Ecalc quoted for the 2p-1s pionic transition energies were 
obtained by correcting the Klein-Gordon value for (a) vacuum polarization 
effects (including finite size) according to the method of Mickelwait and 
Corben') and (b) Coulomb effects using Pustovalov' s technique6) with 
nuclear radii determined from electron scattering data 8-14). 
ence between Ecalc and E 
The differ- 
constitutes the measured nuclear shift Enuc. 
exP 
I '  
- 5 -  
The theoretical values of Enuc have been obtained from the work of Ericson 
and Eric~on'~'~~). An expression for the complex energy shift is obtained 
by them in expansion form by solving the Schrodinger equation for an 
optical potential with constant parameters representing the pion-nucleus 
interaction. 
potential primarily responsible for the level shifts were obtained from 
The constant parameters which specify the single-nucleon 
n-N scattering data and have been corrected, as outlined by the Ericsons 16) , 
for nuclear binding, Fermi motion, finite nuclear correlation lengths, and 
the shift induced by the real part of the two-nucleon potential. 
estimated error on the theoretical values of E 
marily due to the uncertainty in the two-nucleon correction. Within 
this uncertainty, agreement between the experimental and theoretical 
values of Enuc is quite good. 
The 
is 20-30% and is pri- nuc 
The nuclear radii listed in Table IB were obtained following the 
method of Jenkins et. al.'), in which the measured muonic transition 
energies are compared with the corresponding Dirac values after correction 
for vacuum polarization. 
are compared in Table I B  with the values obtained from electron scattering 
data, the latter being more precise for these light nuclei. 
The radii computed from our muonic X-ray data 
Table I1 consists of experimental results of the natural line widths 
rn obtained by us and other workers, in addition to theoretical values for 
l' . n 
the experimental results is satisfactory, this work being more precise. 
The theoretical values of rn have also been calculated from the complex 
With the exception of the Be9 and BIO widths, the agreement between 
- 6 -  
energy s h i f t  given by t h e  Ericsons 15’ 16). The parameters specifying the  
two-nucleon po ten t i a l  were obtained from 2N pion production da ta  and have 
been corrected f o r  binding, Fermi motion, and 1 / A  spin- isospin r f f ec t s .  
I t  should be noted t h a t  t he  pion s-wave in t e rac t ion  amplitude 611 des- 
c r ib ing  absorption onto two nucleons i n  a r e l a t i v e  
ent  i n  value from t h a t  given by the Ericsons. The 
Ericsons was obtained from an ear ly  measurement 17) 
+ f o r  t he  react ion p + p -+ n + d i n  an energy range 
t r i p l e t  s t a t e  i s  d i f f e r -  
value used by the  
of  the  cross  sec t ion  
where the  p-wave 
in t e rac t ion  dominates. 
presumzbly more r e l i a b l e  s ince it was taken from t h e  more recent  measure- 
ment18) of  t he  IT+ + d -+ p + p cross sec t ion  a t  low energies where the  
s-wave in te rac t ion  dominates. 
i n  calculated widths which a re  approximately 35% lower than those shown 
i n  Table 11. 
t r u e  f o r  t he  l eve l  s h i f t s ,  there  is good agreement between the  experimental 
and theo re t i ca l  r e s u l t s .  
The value of 611 used i n  our ca lcu la t ion  i s  
Use of  the  o lde r  value of 611 would r e s u l t  
We estimate a 15% er ror  i n  t h e  calculated widths and, as is 
Final ly ,  it should be noted t h a t  f i r s t - o r d e r  per turbat ion theory with 
hydrogen-like wave functions closely approximates t h e  theo re t i ca l  values f o r  
both t h e  energy s h i f t s  and widths l i s t e d  i n  Tables I and 11, respect ively,  
Per turbat ion theory resul ts  i n  s h i f t s  and widths which are respect ively 15% 
and 4% l a rger  than t h e  l i s t e d  theore t ica l  values.  These r e s u l t s  contradict  
t h e  conclusion of Seki and Cromer”) based on e a r l i e r  width measurements 
t h a t  f i r s t -o rde r  per turbat ion theory is  inva l id  f o r  ana lys i s  of low-Z pionic 
atoms. 
- 7 -  
We are indebted t o  Messrs. G .  H. Miller, W. W. Sapp, D.  G .  Eisenhut, 
and W. H. Hunt f o r  a i d  rendered during t h e  experimental runs and with the  
da t a  ana lys i s .  We would a l so  l i ke  t o  thank Mr. S .  Hummel and t h e  W i l l i a m  
and Mary machine shop f o r  constructing much of t he  cryogenic equipment. 
Lastly,  we express our g ra t i t ude  to  Prof. R .  B. Sutton and the  Carnegie- 
Mellon Nuclear Research Center and t o  t he  staff of SREL f o r  t h e i r  hos- 
p i t a l i t y  and support. 
c 
* * '  . 
E 1 em en t 
Li6 
Li 
Be9 
B' 0 
Bl 1 
C12 
TABLE I 
A. 2p-1s pionic X-ray energies (in keV). 
a 
nuc E nuc E E a exP Ecalc 
(measured) (theoretical) This Work 
24.18*0.06 23.9 '0.2 b 
24.06f0.06 23.8 f0.2 b 
*Ear 1 iei.. Work 
24.53 0.35f0.06 0.47 
24.63 0.57*0.06 0.79 
42.32*0.05 42.38*O.2Oc 43.95*0.06 1.63*0.08 2.12 
65.79f0.11 65.94*0.18' 68.75*0.04 2.96'0.12 3.29 
65.00f0.11 64.98*0.18' 68.85f0.04 3.85f0.12 4.56 
93.19*0.12 92.94f0.15c 99.15f0.03 5.96*0.12 6.50 
Lib 
Li 
Be9 
Bl 0 
Bll 
B. 2p-1s muonic X-ray energies (in keV) and nuclear radii. 
E I Radius (fm) - Equivalent Uniform Charge I FXP 
This Work *Earlier Work This Work Electron Scattering 
18.64*0.07 18.1 f0.4 4.96*6.0 3.28*0.06e 
18.69*0.06 18.1 f0.4 b 4.94f 5 . 0  3.09*0.04e 
3.38*1.16 3.25*0. 70f 33.39*0.05 33.0 '0.2 b 
3.56*0.88 3.16*0. lSg 52.18f0.10 52.23*0. lSd 
52.23*0.09 52.31*0. lSd 3.56f0.78 3.12*0. lSg 
b 
, cI2 I 75.23*0.08 I 75.25f0.1Sd I 3.36f0.34 
See Ref. 8) 
fSee Ref. 9-11) 
gSee Ref. 12) 
hSee Ref. 13) and 14) 
a See text. e 
bSee Ref. 1) 
See Ref. 2) 
dSee Ref. 7) 
C 
3. ll*O.OSh 
*Only the most recent measurement of each X-ray is listed. 
. 
This Nork 
TABLE I1 
2p-1s pionic natural line widths r (in keV). n 
Earlier Wcrk * 
Element 
1.72'0.15 
~i 7 
1.87'0.25' 
Be9 
C1* 
rn (experimental) 
I 
0.15'0.05 b 0.39'0.36 
0.19'0.05 0.59'0.30 
0.58'0.05 I 1.07*0.30C 
1.68'0.12 1.27*O.2Sc 
3.25'0.15 2.96*0,25' 
a 
rn 
(theoretical) 
0.11 
0.18 
0.56 
1.48 
1.75 
3.41 
a See text. 
bSee Ref. 1. 
See Ref. 2. C 
*Only the most recent measurement of each X-ray is listed. 
REFERENCES 
*Work supported in part by the National Aeronautics and Space Administration. 
tNational Aeronautics and Space Administration Pre-Doctoral Trainee, 1966-68. 
D. A. Jenkins, R. Kunselman, M. K. Simmons, and T. Yamazaki, Phys. Rev. 
Letters 17, 1 (1966); D. A .  Jenkins and R. Kunselman, Phys. Rev. Letters 
- 17, 114871966). 
G. Backenstoss, et. al., Physics Letters 25B, 365 (1967). 
R. J. Harris, Jr., and W. B. Shuler, Nucl. Inst. and Meth. 51, 341 (1967). 
R. J. Harris, Jr., William and Mary Report - 8, unpublished (1967). 
-
-
A. B. Mickelwait and H. C. Corben, Phys. Rev. 96, 1145 (1954). 
G. E. Pustovalov, Sov. Phys. JETP 9, 1288 (1959). 
G. Backenstoss, et. al., Physics Letters 25B, 547 (1967). 
L. R. Suelze, M. R. Yearian, and Hall Crannell, Phys. Rev. 162 
-
- 
-
-’ 2 
R. Hofstadter, Rev. Modern Phys. 28, 214 (1956); private communication 
from 3 .  F. Streib. 
-
R. Hofstader, Ann. Rev. Nucl. Sci. -’ 7 231 (1957). 
U .  Meyer-Berkhout, K. W. Ford, and A.E.S. Green, Ann. Phys. E, 119 (1959). 
T. Stovall, J. Goldemberg, and D. B, Isabelle, Nucl. Phys. 86 225 (1966). -’ 
H. Crannell, Phys. Rev. - 148, 1107 (1966). 
R. Engfer and D. Turck, 2.  Physik 205, 60 (1967). -
M. Ericson, Compt. rend. - 257, 3831 (1963). 
M. Ericson and T. E. 0. Ericson, Ann. Phys. -’ 36 323 (1966). 
Frank S .  Crawford, Jr., and M. Lynn Stevenson, Phys. Rev. 97, 1305 (1955). 
Carl M. Rose, Jr., Phys. Rev. 154 1305 (1967). We wish to thank Dr. D. K. 
Anderson for calling our attention to this new measurement. 
-9 
Ryoichi Seki and Alan H. Cromer, Phys. Rev. 156, 93 (1967). -
. . ,  . ~ .... . . ,. . . - - . . , 
' J  
, I' 
c .- 
I 
E= 
-- . 
a 
0 0 
0 0 


Energy and width measurements of low-Z pionic X-ray transitions

Abstract

Similar works

Full text

Available Versions

NASA Technical Reports Server