zotero/storage/7FRM5WLA/.zotero-ft-cache

LE TTE RS TQ THE E D I TOR

of the same kind, the method of calculating matrix ele-

ments developed in reference 1 is applicable. The calcula-

tions are tedious, however, and the resulting expression

for the energy in terms of cx, P, and c is rather complicated. Minimization of the energy leads to an optimum value for
the binding energy of roughly 0.135 ev, when O. =P = (0.5)& an/ c = 0.052, approximately.

In previous calculations considerable improvement could

be obtained by a slight improvement in the function. The fact that this is no longer true suggests that we might

be near the convergence limit.

If we let Pp approximate the quadrielectron wave func-

tion, the mean distance between the various particles

' constituting
=4.SX10

this cluster is found to cm and r~~=r2g ——rj.t, =r2~

b3e.0rXou1g0hly'

r»
cm,

= r,&
that

is, fp gives reasonable relative values of the "repulsive"

and the "attractive" distances. Furthermore, using the

same function we find the value 1.16 for the ratio of the

root mean square value of r» to the mean value of this quantity. For the bielectron in the ground state, on the

other hand, the corresponding ratio for the separation of

the two particles has the value 1.15.

The values of the various mean distances reveal that the

quadrielectron has a considerable size and, consequently,

a large even of

bsrmeaakllupdenpsriotyb.ab' ility

when passing through

matter

*The work here reported forms part of a dissertation presented for

J. the'

Ede.gAre.eHoyflleDraoacstoranodf

Philosophy in A. Ore, Phys.

Yale Rev.

University. 71, 493 (1947).

2 S. Weinbaum, Chem. Phys. 1, 593 {1933).

J. e For more details regarding the probability of breakup vs. annihila-
tion of light polyelectrons see: A. Wheeler, Ann. New York Acad.

Sci. 48, 219 (1946).

The Hyperfine Structure of Atomic Hydrogen
and Deutexiumt
J. E. NAFE, E, B. NELSON, AND I. I. RABl
Columbia University, Rem York, New York May 19, 1947

&HE hyperfine structure separation, ~H and yp, of

atomic hydrogen and deuterium were measured di-

mreectthlyod.by' 'meFaonrs

of the atomic beam magnetic resonance each atom two resonance lines were

measured, each at the same value of the magnetic field,

and the vH and vD were evaluated entirely from differences

in the frequencies. Neither the value of the magnetic field

nor the g values of the atomic and nuclear systems enter

into the final result.

I In H, where the value of the nuclear spin = 1/2 and the

J a(t1o,m0i)c~(1,=—11/2),

the were

~-transitions
measured at

the

(1, 1)~(0, 0) and
same value of the

magnet current. The difference between these two fre-

I=i quencies gives r H directly (see Eqs. 9—12 of reference 3).

For (1/2,

D—, 1w/2h)e,re

(3/2,

and J=1/2, —1/2)+-+(1/2,

the line (3/2, 1/2)~
1/2), an unresolved

doublet, and the line (3/2, 3/2)~(1/2, 1/2) were meas-

ured in quite weak fields of the order of one gauss. The
~ first line gives almost directly, and the difference in

frequency of the two lines gives a small correction of less

than 0.01 percent.

~, The measured values of vH and

in megacycles per

second, are

vI=1421.3 &0.2 yp= 327.37&0.03.

The method is inherently capable of greater precision with the improvement of our frequency meter.
Since the theory of the H and D atoms is considered to be complete and exact, these values can be compared directly with calculations. The formula for the hyperfine
structure separation of S states was given by Fermi4 and is

The nuclear spin is denoted by I, p~ is the magnetic mo-
ment of the nucleus in question, po is the Bohr magneton,
and P(0) is the value of the Schroedinger wave function
evaluated at r =0. P(0) is propor'tional to (1/a)', the cube
of the reciprocal of the radius of the first Bohr orbit.
Since a is inversely proportional to the reduced mass, the
appropriate value of the reduced mass, m„has to be in-
serted. If the values of the quantities in Eq. (1) are expressed in terms of the fundamental constants, Eq. (1)
becomes

(2)

R is the Rydberg constant for infinite mass, n is the fine
structure constant, and p~ is the nuclear moment in terms
of the nuclear magneton, po/1836. 6. For pp and pD ave have
the accurate values of Millman and Kusch'

p,p =2.7896 &0.0008 pD = 0.85648 +0.00037,

R„, for n',

and C we have the values given by Birge'

a'= (5.3256&0.0013)&&10 5
R =109737.303&0.017 cm ' C= (2.99776+0.00004) &&10"cm sec. '

With these values and the value of the ratio pp/pD given
by Kellogg, Rabi, Ramsey, and Zacharias' and by Arnold
and Roberts' as 3.2571+0.001, we obtain the results given
in Table I.

TABLE I. The hyperfine structure separation of H and D.

VH VQ VH/VD

Measured
142 .1. 3 &0.2 Mc.
327.37 &0.03 Mc
4.3416 +0.0007

Computed from
Eq. (2)

1416.90&0.54 Mc

326.53 4.3393

&~00..01061M4 c

There is clearly an important difference between the
~ measured and calculated values of vH and of about
0.26 percent compared with the probable error of the calculated value of 0.05 percent. The difference is five times
greater than the claimed probable error in the natural constants. Khether the failure of theory and experiment to agree is because of some unknown factor in the theory of the hydrogen atom or simply an error in the estimate of

LE TTE RS TO THE E D I TOR

one of the natural constants, such as cE', only further ex-
periment can decide. The comparison of the experimental ratio to the cal-
culated ratio is particularly important, since most of the natural constants cancel out. The agreement is much better than for the absolute value but still not exact. The experimental value is about 0.06 percent greater than the calculated value. The error of the calculated ratio arises chiefly from the measured ratio of pp/po which is claimed to be accurate to about 0.03 percent. Clearly this interesting deviation is worthy of further study.

t Publication assisted by the Ernest Kempton Adams Fund for

¹ Phyi sJi.caMl .RBes.eKareclhlogogf, CIo.luIm. bRiaabi,UnainvdersJit.y.R. Zacharias, Phys. Rev. 50,

472
~

J(.1M93.6B)..

Kellogg,

I. I. Rabi,

F. Ramsey, Jr.. and J. R. Zacharias,

Phys. Rev. 56, 728 (1939). s P. Kusch, S. Millman, and

I. I. Rabi,

Phys.

Rev. 57, 765 (1940).

4 E. Fermi, Zeits. f. Physik 60, 320 (1930),

S S. Millman and P. Kusch, Phys. Rev. 60, 91 (1941).

E R. T. Birge, Rev. Mod. Phys. 13, 233 (1941).

T W. R. Arnold and A. Roberts, Phys. Rev. 70, 320 (1946).

Phase of Scattering of Thermal Neutrons

by Aluminum and Strontium*

Argonne

E. FERMI AND L. MARSHALL
National Laboratory and Uni ersity of Chicago, Chicago, Illinois May 15, 1947

N a previous paper' we have described a method for determining whether neutrons scattered by an atom have the same phase as the primary neutron wave or opposite phase. The method has now been applied to two more elements, Al and Sr. The crystals investigated were A1203 (corundum) and SrSO4 (celestite). The measured intensities of various orders of Bragg reflections of rnonochromatic neutrons are given in the following table, which is arranged like Table I of reference 1.

TABLE I. Intensities of reflection of thermal neutrons
by A1202 and SrSOq.

Crystal A1203
SrSOE

Plane Order
001 210 101

Form factor

2A1 2A1

——11..4344

2A1+2.09

000

0.44 0.62 0.98 0.24

SSrr+-00..7179
Sr+0.48 Sr+0.93

SSSS++—+0011....06817112

0000

0.78 0.21 0.44

SSrr+—00..6164 Sr+0.84

S —0.01 SS++01..3096

000

0.46 0.55 1.94

Sr Sr

——01..6156

Sr+0.83

S S

——02..5544

S+0.50

000

Intensity 480 700
5940 4351 3576 2182 1682 6021 413 1493
702 3182 5759

Attempts to fit these data with actual values of the
scattering length for aluminum and strontium have not
been satisfactory. It seems unambiguous, however, that
the sign of the scattering of aluminum is the same as that of oxygen, namely, positive according to our convention. This is proven by the low intensity of first and second order compared with that of the third order.

A similar behavior of the reflection from the (101) plane of celestite indicates that the scattering length of strontium
is also positive. From the scattering cross sections of these
" two elements, 1.4&&10 s' cm for Al and 9.5 &&10 for Sr, " one can calculate the scattering lengths 0.35 0&10 cm for
Al and 0.88&(10 '2 cm for Sr.

+ This document is based on work performed under Manhattan

Proi jEec.tFesrpmonisoarnshdipL.aMt atrhsehaAll,rgoPnhneys.

National Laboratory. Rev. 71, 666 (1947).

Pressure and Temperature of the Atmosphere to 120 km
N. BEsT, R. HAvENs, AND H. LAGow Naval Research Laboratory, Washington, D. C.
May 9, 1947
"PRESSURES and temperatures of the atmosphere up
to 120 km were determined from data taken on the V-2 rocket fired at White Sands, New Mexico on March 7, 1947. The methods used in obtaining these data were
similar to those used in a previous flight. ' The pressure
measurements were made with bellows gauges for pres-
' sures between 1000 mm Hg and 10 mm Hg. For pressures
between 2 mm Hg and 10 mrn Hg, tungsten and platinum wire Pirani gauges were used. A Philips gauge was used for
pressures between 10 ' and 10 ~ mm Hg.
Ambient pressures (Fig. 1) were measured up to about

AMBIENT PRESSURE Ol
—— ia 01
~ V-2 DATA .~ BALLOON DATA

RAM PRESSURE

10

20

30 40 SO 60 70 . BO SO

100 110

120

— ALTITUDE KM ABOVE 'SEA LEVEL

FIG. 1. Ambient and ram pressures as a function of altitude,

80 km with gauges mounted on the side of the V-2, just

forward of the tail section. Pirani gauges, mounted in

similar positions on opposite sides of the rocket, gave

readings which agree swithin experimental errors, indicating

that no appreciable error was introduced by yaw of the

missle up to this altitude. A single Philips gauge was
mounted on the 15' cone of the warhead. The readings of

this gauge theories of

Twaeyrelorreadnu/cedMatcocoallm. 'biPehnot togprraepsshusresofbtyhe

use of earth

made from the missile and gyroscope data indicated a yaw
of about 15' at 110 km and a roll period of 40 seconds.