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Fig. 2.- Plot of the cosine of the angle between the electron direction and a radius vector from the sun. One obtains a clear peak from the solar neutrinos. The solid line shows the best fit to the data. (In this original figure we added the ordinates mentioned in our text regarding the division in 97, 37 and 26 degrees, and in intervals of 10 degrees.) |
They say clearly: one obtains a clear peak from the solar neutrinos. We will also show clearly that the curve as it is plotted in Fig. 2 is misleading to the reader or observer. We will show this in a series of steps.
First, we will analyze a wide angular interval at two different positions.
We will suppose that 37 degrees (cos 37
0.8) is the interval
where the signal event is coming from the sun. This is not technically true,
but we want to clearly show that even taking a wide theta angle there is
more signal events when this same angle (37o), or interval, is
taken close to 90o.
Counting, the events from theta = 0 to theta
37 degrees (cos
= .8) we have the following sum: 0.24 + 0.179 + 0.163 + 0.134 + 0.132 +
0.118 + 0.112 + 0.105 = 1.183 event/day.
Taking the same interval of 37 degrees from theta = 60 degrees to theta = 97 degrees we count 27 events. The average of the values is 0.095 and 27 x 0.095 = 2.565, that is, 2.565/1.183 = 2.17 times the value in the first interval, that "correspond to the sun direction." That is to say, the interval between theta = 60 degrees and theta = 97 degrees contains 2.17 times more events than the interval between theta = 0 degrees (cos theta = 1) and theta = 37 degrees (cos theta = 0.8). We mention the last interval as the "sun direction," evidently a very wide interval!
Looking at Fig. 3, we cannot see the peak favoring the sun direction! It is the contrary. In ONE day there are more events in many other directions than from the sun direction!
What the sun direction mean? What is the angle "defined" for the sun direction: 37 degrees, 26 degrees or less? Technically, it is at theta = 0 but there, there are no events, and consequently our argument above makes sense.
As shown in Fig. 3, if we take the first interval of 10 degrees (0-10 degrees) as the sun direction, that is closer to fact, there are 0.24 event/day while in the second interval (10-20 degrees), there are 0.2625 event/day that is larger than in the first interval and it is not in the sun direction.
In the third interval there are 0.4405 events and in the fourth interval 0.44 events, etc.
It is easy to see that all intervals that follow the first, contain more events than the first one. Simply put, there are more events in each interval than in the sun direction.
Fig. 2 tries to mislead us and will mislead many Physicists. At least, it is accepted by 126 paper's authors.
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Fig. 3.- The 180o has been divided into 18 intervals of 10o. In each interval the total quantity of event/day is shown. Clearly, the "peak from the solar neutrinos" disappears. The figure clearly shows that there are more events at any other interval (except between 160o-180o) than at 10o, this is especially true around 90o. |
It is not true that 0.24 event/day have their origin from the sun. Contained in the 0.24, is the summation of all the neutrino-like reaction produced by rock (R), cosmic rays (C) and the spallation (Sp) (Fig. 5), as remaining contamination after the application of all special techniques to suppress them.(3) The cosine function was chosen because the cosine compresses the first interval of 10o that "correspond" to the "sun direction" showing this as a peak. Clearly this peak doesn't exist as it is shown in Fig. 3 and Fig. 4 after expanding cosine of 10o and 20o.
Fig. 4 - Expanding the cos, and taking the same quantity of events at the different angle the "peak" disappears. |
To show the fallacy involving the use of cos theta we ask the following: why is not used sin of theta? This will of course show the "peak" at 90oand the neutrinos are coming from 90o with respect to the sun direction regarding the argument used in the original paper with respect to the cos theta!! Of course, this is what Fig. 3 shows without neutrinos!
The neutrino changes direction according to the trigonometric function used!
Want neutrinos from the sun? Use cos theta. Want neutrinos at 90 degrees? Use sin theta.
Even though the largest systematic error comes from the uncertainty of the angular resolution, between 70 and 110 degrees, there are 4 intervals of 10 degrees with 7 dots in each interval. This means that each dot is separated from its neighbor by 1.43 degrees. There is no technical reason to suppose that this same angular separation of 1.43 degrees between dots is not the same for all other intervals. The event in the first interval and in all other intervals were measured with at least the same 1.43 degrees of angular resolution, [or the values used in Fig. 4, for example] All 0.24 events do not have the same angle (3).
If we take the total 7.6 event/day between 0 and 180 degrees and divide this by the 0.24 event/day at the 10 degrees interval, this supposedly represents the events coming from the sun direction, the ratio is overwhelmingly inverse. 0.24 event/day is only 3.16% of all events detected, and this as "background,"(4) represents 96.84%. In other words, if we divide 7.6 event/day by 0.24 event/day accepted from the sun direction, we get 31.6 times more signal events than in the sun direction. If we accept (3) 0.6, then the percentages are 8 and 92 respectively.

Looking alternatively at Fig. 3 and Fig.
5 we see in Fig. 5 that the sun direction coincides
with the larger contamination R from the rock at
= 90o,
= 180o and
= 270o.
We pointed out three notable positions but, really, this happen continuously
between
= 0o and
=360o.
That is to say, many event/day at theta = 0 degrees are similar to neutrino
reactions, but are not coming from solar neutrinos. Also, cosmic ray contamination
increases the signal events at
= 0 degrees. This contamination
could be estimated looking the interval between 170 and 180 degrees, where
the cosmic rays produce 0.09 events as neutrino-like reactions at
= 180 degrees (cos
= -1). Of course, we pointed out
that this position as an illustrative example, but as we said before, this
happen at all positions.
If we subtract the number of events at position
= 0 degrees, 0.09
(with
= 0o) from 0.24, the value of 0.24 is reduced
to 0.15 event/day. The contamination between
= 0o
and 360o (R, Sp) mentioned above increases the apparent signal
events from the sun. Supposing that this introduces a total of only 0.05
neutrino-like event/day in the 0.15 remaining mentioned above, we obtain
the final value of 0.1 event/day, subtracting 0.05 from 0.15. This represents
a signal of only 6%, not the reported 38%.
If we take 0.6 events as the value, we need to look the interval between 160o-180o where there is 0.266 events that subtracted from 0.6 giving 0.334. This only represents a signal of 21%, not 38% as