A new method for detecting the positronium minus ion is described, and the possibility of a long positronium mean free path in a solid is discussed

Friedman, P. G.

Mills, A. P., Jr.

Zuckerman, D. M.

English

NASA Technical Reports Server

N90-18987
Decay Rate and Other Properties of the Positronium
Negative Ion
A. P. Mills, Jr., P. G. Friedman, and D. M. Zuckerman
AT&T Bell Laboratories
Murray Hill, New Jersey 07974
ABS TRA CT
A new method for detecting the
positronium minus ion is described, and the
possibility of a long positronium mean free
path in a solid is discussed.
1. INTR OD UCTION
I am going to talk about the decay rate
and other properties of the positronium
minus ion. This is a workshop, so I don't
have to apologize for the fact that you're
catching our experiment in mid air: we don't
have an answer yet, unfortunately, for Y. K.
Ho's table. The reason I put "other
properties" into the title is that in the
process of trying to do the experiment we
found out a little bit more than what we
wanted to know about how positrons and
positronium interact with a foil. I will be
asking my theoretician friends to help out in
figuring what a positronium atom does going
through a foil. How does it break up? By way
of introduction, I'll remind you about John
Wheeler's famous paper, in which he
invented the polyelectron at the same time as
a couple of other people invented
positronium; I'll describe the slow positron
source that is used to do these experiments
with positrons; I'll show you the ancient
method for the production of positronium
minus by beam foil and the old lifetime
measurement; I'll tell you briefly about our
new effort to detect positronium minus by
double charge exchange; Finally I'll be asking
what's wrong. This will be the meat of the
talk where you can help me out. I will show
you our one pitiful lifetime curve which
unfortunately needs to be extrapolated to
infinite energy to get the answer: we're still
working on it. At the end I'll say just a
couple of words about what's next.
o2. POL YELECTR ONS
Lest we forget the inventor of the
polyeIectron, John Wheeler, I will remind you
that his 1946 article asked the question, "Can
you get clusters of various of various sizes of
electrons?"(1) Wheeler predicted that
positronium and the positronium minus ion
would be bound, but he was unable to get
binding for positronium molecules with his
simple wave function. You have heard from
Y. K. Ho that lots of work has been done
since that time. (2) In particular, the lifetime
of Ps- has been calculated and would be
interesting to measure accurately because of
the current interest in the the triplet lifetime
being measured by the Michigan group for
the last 10 or 15 years. (3) There is a
descrepancy, and we do not know whether
the theory is really going to be right. As an
additional test it would be interesting to
measure the singlet lifetime, but its eighth of
a nanosecond lifetime makes it pretty hard to
do. An alternate would be to measure the
lifetime of positronium minus ions which
contains in it a large factor that is due to the
singlet lifetime. We would need to achieve
parts in ten to the three or four accuracy in
order to make a useful contribution towards
the solution of the controversy.
Unfortunately, I can only tell you about why
we haven't gotten that accuracy yet.
3. EXPERIMENT
The whole experiment starts with the
usual slow positron beam, (4) where slow
213
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positrons are made by moderating them in a
layer of some material, either an insulator or
a metal. For this particular experiment we're
using a solid neon moderator. (5) %re obtain a
beam of roughly a quarter of a million
positrons a second using a 5 mCi source of
Na 22. Positronium minus ions can be made
by putting relatively slow positrons through a
thin foil. (6) In the first experiment the ions
were accelerated with a grid into a field free
region where they annihilated, giving Doppler
shifted photons that were counted by a
germanium detector. In the spectrum shown
in Fig 1 we see a line fi'om positrons that
annihilated somewhere in the foil, and a
Doppler shifted line that moves when you
apply more electric field to shift the
positronium minus velocity in the direction of
the detector.
Especially relevant to our problems
today is Fig 2 which shows (large error bars)
the yield of positronium minus as a function
of the energy with which the positrons are
implanted into the foil. The small dots are
the the transmission of the positrons through
the foil as a function of energy. My
interpretation at the time was that you get
the most positronium minus when you have
the greatest density of straggling particles
near the surface of the foil. The six or seven
measured data points agree with what you
Would expect: the derivative-of the stopping
curve does have a peak roughly coinciding
with the maximum yield of Ps-. It looks like
the yield has a single broad peak, but more
precise data suggest that things are more
complieated.
The lifetime was measured some years
ago by carefully determining the amplitude of
the Doppler shifted peak again with the
germanium detector (7J As you change the
distance between the formation foil and the
acceleration foil, the proper time that the
positronium minus spends is proportional to
the distance. By plotting amplitude versus
calculated time, you can get the lifetime, as
shown in Fig 3. Unfortunately, the
ORIGINAL PAGE IS
OF POOR QUALITY
Of' '' ' I' '' ' I ' '' 'F2' "' I!'' 'I_.. • .... i,,,,i,,,,i,,,,i,,,, 1
"= . :'.,. '-"
• -. .. ,_
: -.4 ...
g • " ", _ It
O L ° "
• 207B i ",-p._
500 520 540 560 580
PHOTON ENERGY (keV)
Fig, 1 Annihilation q-ray energy spectra
obtained for five different ps-
acceleration voltages W. [From Ref
6]
1.0
1:.08
_0
0.6
i
_ (3.4
4-
o 0.2
0
Fig. 2
t i
i
t°
I L
500
e + ENERGY {eV)
, . 20
15 f
0
1.0 ,..,
_J
laJ
' ' 1000
Positron transmission probability r/
and Ps- formatioin fraction f-
plotted vs positron incident energy
E. To account for grid losses, F-
should be multiplied by 2.0-X).2.
[From Ref 6]
positronium minus is coming out of the foil
with velocities comparable to atomic
velocities, so you have to extrapolate to
infinite acceleration in order to get the right
answer. The extrapolation to infinite energy
is right on top of Y. K. Ho's prediction.(s)
214
To do a better experiment, we would
like to get rid of the germanium detector,
which is inefficient, and we have to go to
higher voltages to reduce the size of the
extrapolation needed. There has to be an
improved way of moving the loll because, in
the previous experiment, the foil was on the
end of a manipulator about one foot away,
and I had to measure the distance with a
traveling microscope. The present attempt
has a much better moving mechanism: three
synchronous linear motion vacuum
feedthroughs define the foil position to 10-2
mm precision.
Our new effort uses a tandem
acceleration method depicted in Fig 4. A
positronium formation foil is bombarded by a
quarter of a million positrons a second. Any
positronium minus formed is accelerated by
what we call "the analysis grid", which has a
potential W across it for measuring the
lifetime. As before, the distance d between
the analysis grid and the formation foil is
variable. By varying d while measuring the
count rate, you determine the lifetime.
Following the analysis grid is another
electrode that accelerates the positronium
minus to some large voltage on the order of
fifty kilovolts. At this point, there is a thick
carbon film that is supposed to strip the
positronium minus and turn it back into two
electrons and a positron. On the other side is
a grounded electrode that repels the
electrons, but accelerates the positrons. The
positrons emerge with four-thirds times the
acceleration potential on the stripping foil,
which would be about 67 kilovolts if the
stripping potential is 50 kV. We thus have a
definite Ps- signature of rather high energy
positrons which cannot be produced any
other way except by having taken a torturous
route of making positronium minus and
getting stripped. About two and a half
meters away, to get rid of gamma rays, we
have a charged particle detector (a silicon
detector) which detects the energy spectrum
of the positrons to distinguish them from any
background that might be there from ions.
4
4
iX
v
•E 3
2
1
0
I I , i T t I I 1 _ I 1 I l 1
f22"e( )2o
a -
=x _16 = *
X 0 0.5 t
1.00 _X_'i , _ , i , I_ _"_
085,' ' ' I
d(mm)
I I I t ] L=_J,_ _L__ . I I I i 1
0.5 t.0 t.5
t/(1- T'_-W)(nsee)
Fig. 3 Log of the relative amount of Ps-
surviving for a time t corrected for
the initial Ps- kinetic energy 7'.
The inset shows the extrapolation of
the decay rate to infinite
acceleration potential W. [From Ref
71
An ion shield, one tenth mil of mylar, covers
the detector. Unfortunately, there were so
many ions that we had to use a plastic
scimill_tor in coincidence to cut the
background rate.
Fig 5 shows spectra taken with the
silicon detector at three different acceleration
voltages. The potential applied to the
stripping foil is 20, 34, or 45 kilovolts. The
peak due to the positrons that make it
through the whole apparatus is evident, and
215
there is a sloping background due to ions (o<d<Scm)-__ _ //which looks like it's not important, at least at
MOVABLE _
the higheracce]erationpetentials. Thereis a ,_ . _ _ __, ,_ I I // _plateau below the peak, and I don't know msc
what that could possibly be, since the
particles that scatter (g) is _IP-_s-!Ps_re+'Psr_l ] e+ _,nmq_,Fn 4... ,,,_lL_Iy_./_i tfraction of
supposed to be only about 15%. If you z5,1os-_" -- - ; -''/ | iN [ I I45kev/_\
+ -' I | I__ ° [] ] I s] DETECTOR (PIPS)
spread that fraction over a large energy e sec __ i IOOAC_ }125_+3:kV
range, it should not give a 10% amplitude.
That is problem number one; but at least we PLASTICsi:_
are producing t ndem generated positro s. "]_'LL TOR÷w
Using our double charge exchange Ps- Ocm _
signal, we have remeasured the yield of
positrons as a function of energy in Fig 6. As
in Fig 2, we get a blob us a function of
energy, peaking at slightly higher energy Fig. 4
because the film is a little thicker. The film is
nominally 15 angstroms thick, a cloudy
carbon film on top of a glass sI[de that is slid
off onto water, to be picked up with a grid.
The thicknesses are nominal, since there are
obviously layers of grease and water. Notice
in the new data at the low energies, there
seems to be a plateau and a real threshold at
a ridiculously low energy of 25 volts. I have 103
..J
no idea what this structure means. If the uJ
z 100
film is really only 15 angstroms thick, I z
suppose that is an average thickness, and <
-r 10
once in a while there could be a flake that's o
only one crystal layer thick that might be 5 w
w t
angstroms. However, I would think that a.
there would be a series of plateaus for co
different thicknesses and that they shouldn't _z 104
occur down at 50 volts. If anybody has a _ 103
suggestion, I would be happy to hear it. It o
will go right into the book if you have
anything to say. 100
Another mystery is why is the yield so
10
small, about five times smaller than we saw
in 1981 and 1983. We have mapped out the
count rate as the detector is moved around. 1
As far as I can tell, all the fast positrons seem
to be hitting the detector. The grids that the
foil is on and the acceleration grids have 90%
transmission. Putting in all the grid
correction factors does not account for the Fig. 5
apparent losses. The grid corrections are just
about the same as they were in 1981.
0 10 cm
SCALE
Tandem acceleration method of
deiecting Ps _ . :--_:,
100_ '" I ' I t
I'
I l I -i .... ] "" 7
"'1a) 22.5 kV
'[.... i .... i'"
i_ t i 1 i I
b) 34 kV
%
"-L .: ............. ' - ." .......
i I
FWHM =8keV
- _
°o,
..':'..._._--- •:.- ;:.-. .... :.:.
I t I t I _ I I I
0 30 60 90 i20
I t I i I
C) 45 kV
E+ (keV)
Energy spectra Of the fast positrons
detected by the surface barrier
detector.
216
0.4 I I i I i I I ITable I shows the yield of positronium
minus measured at 20, 34, and 45 kilovolts.
The coincidence rate is corrected for decay
loss in various places where the positronium
minus is being accelerated. There's a
negligible loss in the mylar foil. (I°) The
positron beam rate is what you divide by in
order to get the total fractional yield of
positronium minus. There's a constant grid
transmission coincidence efficiency, and a
little bit of back-scatter loss. The net result
is a positronium minus yield of about 7X 10-5
independent of the energy. That is a surprise
to me because the only way that I can think
of to make the yield smaller than the
2--3X10 -4 found previously is to have the
stripping foil be less efficient.
_. DISCUSSION
Now we come to the central point of
the talk where I ask you what happens to
posltronium and posltronium minus when it
gets stripped. There are several convenient
theories. The simplest theory, which turns
out to be the same as Surko's Theory that he
told me about at breakfast, is that you
simply use multiple scattering calculations
and an independent particle approximation.
Let's just talk about positronium going
through the foil. In the time scale over which
the particles are in the solid the positron and
an electron don't orbit at all. They just go
straight through the solid without moving
relative to each other. In this approximation,
you would say each particle gets an
independent kick from scattering off the
potential which, in this case, would be a
frozen potential of the solid because the
electrons don't have time to move either. It's
very easy to calculate the perpendicular kick
that each particle gets: it will be the
perpendicular electric field integrated times
dr. The amplitude for making a transition
turns out to be the perpendicular momentum
kick times the dipole matrix element.
Summing all the dipole moments that lead to
the continuum gives a transition probability
that is perpendicular kick squared over 2m
7
QJ
0.5
tO
,,' 0.2-
rY
o.
0.1
I
5o/
J
0 ?!14
O-
Fig. 6
18
17/
5.1
J
 L;fi /
t _ I I I i I
200 400 600 800
E+CV)
Yield of Ps- versus positron energy
uncorrected for transverse beam
motion.
Table I
Accel. Pot. [keV]
coinc, rate [sec -1]
decay loss e -At/r
loss in mylar [%]
beam rate [e+ sec -l]
grid transmission
coinc, efficiency
backscatter loss [%]
from Si detector
f-- [lO-Sl
a)
b)
22.5 33.75 45
o._o25(6) o.541(3) 0.385(2)
0.113 0.135 0.140
14(_) 6.5 (_) 3.5 (a)
2.5 X 105
0.45 +0.1
0.4 ±0.I
lS (b)
6.1 +2 7.1 +2 7.5 +2
R. D. Evans, The Atomic Nucleus
V. E. Cosslett & R. N. Thomas, Brit. J. Appl. Phys.
_e, 77o (,06.s)
, 217
Y. K. Ho: You showed a slide with a
laser interacting with the Ps- beam; can you
measurethe photoionization crosssection and
the electron affinity?
Mills: Yes, Marv Leventhal and I are
working on it, and Lewis Rothberg has given
us a laser. We'll have the answer for you in
ten years.
Y. K. Ho: So you can measure the
binding energyof Ps-?
Mills: Maybe, but its pretty hard to find
the binding energy from the photoionization
threshold because the cross section vanishes
at threshold.
Marv LeVenthah We can find the
binding energy quite accurately from the
location of the Feshbach resonances.
Alex Weissi What are the wigglers that
you showed? [See Fig 23 of Ref 16]
Mills: The wigglers are to excite the
triplet-singlet hyperfine resonance in a fast
monoenergetic positronium beam. By moving
two ]dentlcal wigglers one can obtain R:amsey
fringes in the triplet positronium abundafice,
and so measure the hyperfine interval
accurately.
Richard Drachman: Is there a
preliminary Hfetime result from the new
data?
Mills: Unfortunately, no.
Alex Weiss: Have you thought about
making a tuneable gamma-ray source?
Mills: Not very hard. The gamma rays
are emitted isotropically in the center of
mass, so its not like having a laser. If you
had a very intense relativistic beam of Ps-,
tri-e¥l_otons:would be foreward directed, and
it would be a good idea.
6. POSTSCRIPT
In a subsequent experiment using a Ge
detector in a geometry similar to that of Ref
7, we found that the Ps- yield of the 0.3
220
I_gcrn -2 foil (15 ._ thick) is in fact about an
order of magnitude less than a 0.6 pgcrn -2
foil, and the yield of the latter is in
agreement with the measurements of 1981
and 1983. The stripping foil was observed to
be damaged over a significant portion of its
area. We conclude that
1) very thin carbon films are perhaps
multiply connected like lace;
2) more care is required to prevent high
voltage damage to the stripper foil;
and 3) there is no evidence to suggest that
energetic positroninm has a particularly long
mean free path.
REFERENCES
[1] J. A. Wheeler, Annals of The New
York Academy of Sciences XLVIII,
219 (1946).
[2] Y. K, Ho,"Positronium Ions and
Molecules", eontribut|on to this
volume. See also M. A. Abdel-Raouf,
Fortschr. Phys. 36, 521 (1988).
[3] D.W. Gidley, P. W. Zltzewitz, K. A.
Marko, and A. Rich, Phys. Rev. Lett.
37, 729 (1976); C. I. Westbrook, D. WI
Gidley, R. S. Conti, and A. Rich, Phys.
Rev. Lett. 58, 1328 (1987).
[:t] A.P. Mills, Jr., in Positron Solid State
Physics, edited by \V. Brandt and A.
' Dupasquier : (Nor/h-Holland,
Amsterdam, 1983) p. 432; P. J. Schultz
and K. G. Lynn, Rev. Mod. Phys. 60,
701 (1988).
[51 A. P' Mills, Jr. and E. M. GullikSon,
Appl. Phys. Lett. 49, 1121 (1986).
[6] A. P. Mills, Jr., Phys. Rev. Lett. 48,
717 (1981),
[7] A. P. Mills, Jr-, Physl Rev. Left. 50,
671 (1983).
[8] Y.K. Ho, J. Phys. B: At. Mol. Phys.
18, 1503(1983).
[9] V.E. Cosslett and R. N. Thomas, Brit.
J. Appl. Phys. 16, 779 (1965).
[10] R. D. Evans, The Atomic Nucleus,
(McGraw-Hill, New York, 1955) chap.
21.
[11] H. A. Bethe and E. E. Salpeter,
Quantum Mechanics of One- and
Two-Electron Atoms (Springer-Verlag,
Berlin, 1957), p. 264.
[12] V. L. Highland, Nucl. Instrum. Meth.
161, 171 (1979); 128, 497 (1975);
Particle Data Group, C. G. Wohl, et
al., Rev. Mod. Phys. 56, No. 2, Part
II, pp. 951-$53.
[13] S. Mrbwczy_ski, Phys. Rev. A 33, 1549
(1986); Phys. Rev. D 36, 1520,1529
(1987).
[14] L. L. Nemenov Yad. Fiz. 34, 1306
(1981); V. L. Lyuboshits and M. I.
Podgoretsky, ZETF, 81, 1556 (1977).
[15] Jack Stratton, "Positronium
Formation in e + H- Collisions",
contribution to this volume.
[16] A.P. Mills, Jr., Hyperfine Interactions
44, 107 (1988).
221



Decay rate and other properties of the positronium negative ion

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