Date: Wed, 27 Sep 2000 14:46:35 +0200     ahw96b

    Dear Georges,
    Here my APAC talk revised for printing - and without figures.
    Greetings,
    Aaldert

              Memories of Mass Determinations

                     A.H.Wapstra

  I will make a few observations, that I hope will be of some general
use.

The first physicist who did a good job in measuring masses was Aston
1). He used a combination of electric and magnetic fields and took
good care to build a reasonably focussing mass spectrometer. My
experience, in the course of 55 years in evaluating data, has been
that precision measurements with non focussing instruments should
be considered with a healthy distrust. This is true both for
measurements of atomic masses and for measurements, in electric
or magnetic spectrometers, of energies of particles involved in
nuclear reactions or decays.

Aston's spectrometer focussed in one direction. Later improvements,
around 1935, by groups around Mattauch 2), Bainbridge 3), Nier 4)
and some others introduced focussing not only in two space directions,
but also in momentum space, taking care that variations in velocity
did not result in objectionable shifts in spectral line positions.
This resulted in socalled double-focussing mass spectrometers.

Their measurements led to accurate ratios of atomic masses. In order
to convert them to absolute values, it was decided to define an
atomic mass unit; the mass of oxygen was taken to be 16 units.

I use here an element name, not a specific isotope, this because
a confusion arose. Chemist took as standard the average atomic
mass of the three stable oxygen isotopes in the "naturally occurring
mixture", physicists that of the isotope 16O. Only when it was
discovered, that the ratio in which the three isotopes occur is not
unique, chemists agreed to change their definition. But they
furiously objected to using 16O. That would have meant a decrease
of 278(
 ppm in all atomic weights. This would imply a change of
many millions of dollars in the price of all chemicals sold yearly.
Mattauch, the chemist Kohman and I 5) then found out, that the
change would almost precisely 10 times less (in the other direction)
if 12C was taken to be 12 units. And this proposal, as you will know,
was accepted.

A discussion arose about a name for that unit. I proposed the name
"aston", but especially the English did not want this. I have the
feeling that, for one reason or another, the person Aston was not
popular among them. So the name "unified unit" was adopted, symbol
u. I remember that some time later a new discussion was started.
I then defended the symbol u; in fact I said "let us be firm in
retaining the u, let us even make it a double u! " And I was rather
amazed that nobody seemed to understand my little joke!
         (Or, may be, they were trying to be polite...)

The new techniques of measuring masses in Penning traps and storage
rings are so new that I suppose I cannot say anything about it that
you do not yet know. But I must say that I am very impressed by the
results and very pleased with them.

The other source of data on atomic masses are measurements of
energies of particles and/or gamma rays involved in nuclear
reactions and decays. And it has been quite interesting to follow
the relative importance of the two. The first evaluation of data
obtained by such means was the famous collection of papers by Bethe,
Bacher and Livingston 6). They found a disagreement between the data
from the two sources of information. They decided that the reaction
data were then more dependable than the mass spectroscopic ones.

This was the beginning of a curious competition between the groups
involved in these measurements. I think it happened three times,
in the course of time, that it appeared that the results from the
other field were better. And only after some 3 decades some
harmony was established.

I have been involved in one of the changes. Around 1955, spectrom-
eters used in reaction energy measurements were calibrated with
the alpha particle energy in the decay of 210Po. This energy was
accurately measured by Rytz, a person who did much in the field of
precision measurements of particle energies. But the spectrometer
he used was not a focussing one. I 7) decided to investigate the
situation, together with Mattauch and his collaborators in Mainz.
We did this by making a least squares evaluation in which those
reaction energies were treated as ratios with this calibration
energy. The outcome for 210Po was one part in a thousand smaller
than Rytzes value, some four times larger than his reported error.
I am quite pleased to remember that Rytz then repeated his
measurements with steadily improving accuracy; it is now about
10 ppm. Also, he even recently took care 16) to give recalibrated
values for many alpha-particle measurements with precisions of
5 keV or better.

 Now I want to say something about an important matter for general
physics: the error assigned to a measured value. It is really
disturbing how often papers do not state estimated precisions
(errors). Audi and I have some experience in doing experiments in
the field, and we can then make reasonable guesses; still, it
must be considered a serious defect. And then, if they do give
errors, they do not always say what is meant: standard errors
(as defined in least squares estimates), so-called limits of error
or even something different. A special case is the way mass
spectroscopists used to give errors. They repeated their measur-
ements many times, and calculated errors from the spread of the
data. This is a good method; but it neglects the possibility of
systematic errors. Now, the several mass ratios they published in
one paper mostly form an over-determined set. Thus, one may make
a least squares evaluation of this set. We 8), and sometimes the
experimenters themselves, did so, and the result was that the
errors mostly had to be multiplied by about 2.5 in order to get
consistency.

Of course, it is not certain in itself that making this correction
to the errors takes full care of the influence of systematic errors.
But in combining mass spectroscopic data, thus corrected, with
data from reactions and decays in a least squares calculation,
the total collection always came out sufficiently consistent.

I was of course curious to see, how the Penning trap precision
measurements of the last decades behave in such tests. I was quite
pleased to note, that these analyses did not indicate a necessity
for changing the errors assigned to them.

Another quantity entering these least squares evaluations we
also had to treat with some care. Mass spectroscopic measurements
are expressed in the mass units I mentioned, but reaction energy
measurements in electronvolts. Thus, we have to include the ratio
of the two units. The precision in this quantity, in the beginning
of the evaluation work, was not much better than that in the other
data. So we also used it as a variable in our calculation. The
results were not of much use for evaluators of physical constants.
Reversely, their work has been of much use to us. I will therefore
mention with pleasure those evaluators: DuMond 9), Cohen 10) and
at present Mohr and Taylor 11). And in this respect,
the following is of interest. The ratio electronvolt to mass unit
can be expressed using the internationally accepted volt unit, but
for a long time it could be done more precisely in standard volt
defined by accepting a standard value for the constant in the
Josephson relation between voltage and frequency. In 1987 10) , the
mass-energy ratio expressed in the first had a precision of 300 ppb,
in the latter of only 89 ppb. Thus, we expressed the results of our
mass evaluation in standard electronvolts. In the recent evaluation
of Mohr and Taylor 11) , the situation is improved by not less than
an order of magnitude: the precisions are now 40 ppb and 8 ppb
respectively. Only for very few of our output data, using standard
electronvolts has still an advantage over using international
electronvolts. But since the ratio of the two volts now differs from
1 by only as little as 4 ppb, I think we will still use "standard"
electronvolts.

As said, we put the data obtained in a least squares calculation,
that automatically gives best values, So, you may ask: what is your
real contribution? Well, I will give two examples.

In the 1983 atomic mass adjustment 12) it was shown, that direct
measurements of masses of mercury isotopes 13) did not agree with
directly measured masses of isotopes of several other elements
combined with results of nuclear reaction measurements. The
difference is more than 15 keV compared with errors, on both sides,
of 3 keV or less (see ref. 13) fig. 1.) Whom do we trust? Well, it
appears that the mass spectroscopic values for odd mass Hg isotopes
differ about 5 keV more than those for even mass ones. This is
explained by the fact, that they are compared with molecules
containing the rare 13C isotopes, the other ones not. There seems
to be a dependance of the result on the intensity of the ion beams.
Since we feared that such an effect may have influenced all their
data, we decided not to use any of them. Of course, we then tried
to convince people to make new Hg mass measurements - but this did
not lead to new results in the 20 years that we did so.

The other one concerns the alpha decay of 176Au. Measurements were
made by two groups. The first one 14) reported branches with
energies 6260 and 6290 keV withe intensities 80% and 20%. The second
one 15) found 6228 and 6282 keV, no intensities given. All estimated
errors are 10 keV. The difference between the energies is a bit
large, but not disturbingly so. The second group reported the low
energy line to be in coincidence with a 138 keV gamma ray. It was
assumed that this combination feeds the ground-state in the daughter
172Ir, and the other a known isomer; the energy difference then
agrees with the known excitation energy of the latter.
 This seems satisfactory! But my very recent analysis of the new
GSI mass measurements indicated that the resulting energy
difference between the 196Au and 192Ir groundstates is probably too
high. Thus, I felt forced too look at the published alpha particle
spectra. This showed, that the intensity ratio of the reported alpha
branches were found drastically different!
 This can be explained in two ways. It may be that the strong branch
in 14) is due to a contamination. This, though, is made improbable
by the fact that its excitation curve agrees well with that of the
other branch. Or, there may be two 176Au isomers produced in quite
different ratio's in the two experiments. In 14) the activity is made
in a bombardment of 141Pr with 40Ca, in 15) with the rather different
reaction between 92Mo and 88Zr. It is therefore not impossible that
15) mainly observes the upper 176Au isomer, whereas the 6260 keV of
14) one occurs between the ground-states. This assumption would solve
the mentioned problem!

Finally, I want to add a remark about the application of the least
squares method. It is often said to be valid only for Gaussian
probability distributions; but this is not true. The only
condition is, that the probability distribution gives an average for
the measured value and for its square: the standard error is the
square root of the difference between the square of the average
and the average of the square.
 A case in point is the following. In modern mass measurements on
radio-active substances, both in Penning traps and in storage rings,
one often cannot separate isomers. And often the ratio, in which a
ground-state and its upper isomer occur, is not known. The only
fair way to derive a value for the mass of the ground-state is
then to assume that the probability distribution of that ratio is
flat between 0 and 1. This allows calculating both its average and
its standard error. Thus, one can derive a value for the mass of
the ground-state - that is, if the excitation energy of the upper
isomer is known.

And I want to add a warning. The least squares distribution gives
the "best" value for average and error if, of the distribution, only
the two conditions outlined above are known. And for Gaussian
distributions, they are indeed the best ones. But this is not
necessarily true for other distributions. For Poisson distributions,
one can derive a best value different from the least squares one,
and with a smaller error!

References.
 1) F. W. Aston, Phil. Mag. 39(1920)611
 2) J. Mattauch and R. Herzog, Z. Physik 89(1934)786
 3) A. O. Nier, Phys. Rev. 50(1936)1041
 4) K. T. Bainbridge and E. B. Jordan, Phys. Rev. 50(1936)282
 5) T.P.Kohman, J. H. E. Mattauch and A.H.Wapstra, Science
    127(1958)1431
 6) H. A. Bethe, R. F. Bacher and M. S. Livingston Rev. Mod. Phys.
    8(1936)82; 9(1937)245
 7) A.H.Wapstra, Nucl. Phys. 18(1960)587
 8) F. Everling, L. A. Koenig, J. H. E. Mattauch and A. H. Wapstra,
    Nucl. Phys. 25(1961)177
 9) J. M. W. DuMond and E. R. Cohen, Rev. Mod. Phys. 90(1953)691
10) E. R. Cohen and B. N. Taylor, Rev. Mod. Phys. 59(1987)1121
11) P. J. Mohr and B. N. Taylor, J. Phys. Chem. Ref. Data 28(1999)1713
12) A. H. Wapstra, G. Audi and R. Hoekstra, Nucl. Phys. A432(1983)185
13) K. S. Kozier, K. S. Sharma, R. C. Barber, J. W. Barnard,
    R. J. Ellis, V. P. Derenchuk and H. E. Duckworth, Can J. Phys.
    58,1311
14) C. Cabot, C. Deprun, H. Gauvin, B. Lagarde, Y. Le Beyec and
    M. Lefort, Nucl. Phys. 241(1975)341
15) J. Schneider, Thesis (GSI 84-3)
16) A. Rytz, At. Data Nucl.Data Tables 47(1991)205