THE THEORY OF HELIUM-III

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• Collection: General CIA Records
• Document Number (FOIA) /ESDN (CREST): CIA-RDP82-00039R000100110031-5
• Release Decision: RIPPUB
• Original Classification: C
• Document Page Count: 11
• Document Creation Date: December 22, 2016
• Document Release Date: June 8, 2012
• Sequence Number: 31
• Publication Date: March 13, 1951
• Content Type: REPORT

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Title: T ~' 'CCC ~'O~Y 0~' CC~L~CU~C -III by I ~ z'omorcuichuk (USS~~)
So~rcas zhurnal Lkn erimontal~no i 'r~~orotich~dko ~i2iki, Vt~l 2Q, No ~.4
oc 9 , ~~~ q
CONf~IDEWY~AI
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T~ T~IORY Or ~LIVM-III
I ~ Fomeraaohuk
Abrtraatt to 8aotion 1 we determine the temperature dependenoe of thermal
oapaaity, 4ieoority~ and thermal ooaduotiKty in helitur.~, to ~eatioa ^ we olar-
STy the influeuoe of eaohaage effeata duo to the ~olear rpinr of helium. atomr
upon the phare tranrition of liquid helium.3 to the rolid rtate~ The heat of i"a~.
rion o! heliu~.~ at low temperaturer mart bo negative and equal to -R~log 2.
Thoorotioal porribilitiea of obtaining temperaturoe of the order of 10'6 to
10'7 degreo duties adiabatio freering of liquid helium., are indioatod~ Certain
peouliaritier oi' the nuolear mrlgnetio ruroeptib3lity are olarified~
1. Thermal Oapaoity~ Viraority~ and Thermal Conduotivity of Liquid Hel:ium.3
~eoently it has been ertabliehed that liquid helium.3 in oantraet to li-
quid helium-4 doer not po~rere ruper~uidity down to the te~rperature 105?R ~1'~~
Thir result maker probable the abrenoe of runerfluidity is helium-~ for any tare.
perature~ In the oars of helium. the 8ore..Hinrtein rtatirtior favorr ruperflui-
dity ~2), If a ruffioiently rarefiod gar it oanridered which obeyr th? Ferrai-
Dirao atatirti,or, then the influenoe of the interaction of the atomr upon the
propertier of this gar Dan be explained by the methodr of the theory of pertur-
bationr~ The theory of pertUrbationr it appl3oable for euffioiently rma11 gas
denritier and in the Dees of foroer acting in short ranges, Oonriderationr and
actual oalaulationr ruoh as mentioned do cot indioate a~y- ruper~~d~t~~~i~
helium-3~ Under similar oonditionr a fore gsa revee~lr euperfluidity in oerte-in
eAeer~ 2) , These ,rte the bases fQr not Q~+nrideriag reli'o~-3 euperfluid. The enr
orgy of the exoited rtater of helium.3 for rma11 eaoitation energier it the rum
of the elementary earoitation energier of the Mquaripaxticlern ~3)~ It it errent-
ial to oonrider that there exoitationr obey the Fermi-~irao ~etatirtior~ rinse in fh~s
vase ruoh exoitationr of the entire gyrtem parr oontinuour~.y to the excited ate.
toe in the ranee of the for~rard motion of the helium.3 individual a~omr, when the
tranrition from the li quad to the gar ooaurr. The propertier of the exaitationr
~- CONFIpENiIAt
r Y
t
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~~ll~~
~~~
one to eimilax ouneideratione of aacoit-
oonduoti~ eleotronr is metaie lead
oT
the eleotxon thexa,al oapaoit~r oT
ao in liquid heliwe?3~ ae ie will known,
atio
See of Male oorrer~oud with the Fer~-i-
iale ~d a aumber o: other propert
mr
The $~,rteaoe oT eupe~~uQti~tY ie oon-
o etatietiae Tor e~coitationr ~ ~
Di ra
a into ooneideration is the sough Sermi?
aeoted with roar rmall ei~eotr not tame
TTeotr a~peax in the r~llneae aT the tem-
Dirr-o model The roaal'lnerr oT there e M
oaoure, is oomparie0n with the h~tural
eratuxer at whi oh rupexoo~aduotiwity
p
r the order off' m~nitu~de oT the te~aerature
eleotron temperaturer which porrer
the dei~er~Y of eleobroar ~ )
go~vera~
he exoibatiosr of the ryrtem of iatesaoting
i~e111a~own it tho oars where t
tier ~~') + Thar care ccrreaponde tb the rtater
electro~aa obey the ~0ie etatir
e "n~,1" rtater is whioh the eleotron rpiar are
that diTTer slightly Troca th
" ~~ rtate it a "ringalar point" ana therefore ex~
oriented t o oae ride ~ ~ null
to alto porrerr urturual propertler, xa the oaae
oitationr aioee to ruoh a rte
a the oars of noaTerromn~aetio meta~r 3n aoaruper-
of liquid heliu"~-3 duet as i
~~" ~~ mate it oharaoteriaed only by th? lowert
oonduating rtater the l~xert null
xo r~etio ones it it Tuthex ~araateri~ed
energ,Y end nothiaa rtore~ (Ia the f'er ~
oe the we,~velength a~' helium?3 atomr it of the
b a large magnetio moment.) Bin
~'
~~ m the intaraotioa between the heliura~3 e,tomr
order of the ~rtanoe between the ,
Lion oT the auolea~ spine ~ is hbli~a?3 the n~
~,epend~e upon th? mutual o ri ent a ed
is li 8 heliv.~a?3 the errential role it play
r is equals ~) t S) , Thur q~
sleet p
sot ed with the exaha~a6e o f two helivun?3
by the exahatige effeotr which are oona
re exohenge effeatr apparea'~lY lead to the
~toma~ tt it eae~ to show that the
of the neighboring nualee~r rpinr, ro that
riaoipal antiparallel o~entation
p le of ~- ex~
it sot a auolear ferromagaetio but is en e~calmp
liquid helSum?~ etio of
eti4 rimilar to an electron exoha~e paxam~'n
change auolear paxame~n w~,~ pore.
In the acre of two ~-elium-3 e~toma, is fact
the oolid oxygen tyPe~ tit
dinate part of the wa4e iunotioa mart be an
err parallel rpinr, the ooor rd,inate
interohaage between two atomr~ Therefore the aoo
etrical xelati4e to the of
tion~ Under there oonditionr the probability
part oae include the ~ mac e
tomr it very' night in com~ariaon with th
rn~all dirta~-cer between heli~am?3 a
~~NFIDENriei
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~ONFIDENTIAI.
~- ooordinate part of trio ware f~aotio~ of two ato~ae oaa be inol.
ogee where t e
he B ~uaotioa ~ bhat ie, when trio spine are aatiparallel- ~! t~ao r~
udod with t
in the ae ati4o ener~- of attraotion of two helium. atomr with
pid deoreaee d
inoree-eia dietaaaee between them ie takes into ooadid?xati?a, then one oaa eon..
that the eaer~r of the two atocae o! holiu~.3 will be lees in the oi~ee
olade
o be closer to ea~oh other; that ir+ iht~tho ogre of antiparallel
where they an
i n of the aoighbars~ epiae- Therefore onetakee into ooaeideration
orieatat o
distances between the atoms, but all greater than ro, which ie the
even email
t which intense repulsion sate in- Thie limitation it oarxied oat
d~ebanoe a
li uid helium-3, since trio avore~ge distance between the~.~atome it eev
well in q
~tex th~a r - l~a~oe~y there exietr a liquid helium-~ is which the
oral tim?s gre o
t of sash other oa the average- Thus there is no reason to ooarider
atomr at ra
li uid helium?~ it a nuclear ferromagnetic. Therefore one aaa afro aos~
that q
that close to the null rtate of helium.3 the excitation rtatirticr oo?
rider
iaoide with atom rtatietice-
8 e to a~ tine ~'err~i-~irac dirtribution for the excited states one ocua
Y ~ ~
umber of oon~olusions ooncerni~ certain praportiee of liquid
easily derive a n
~i suxface in the oanridered case reprerente a sphere of radius
helium.3- The ~'er~ 1
2 1~~- ~1Q f 3 + where N it the
whick~ in order of magnitude will equal (3 n ~
Po
er 1 om~ (bore it was learned that nuclear spin of heliwn-3
number of stoma p
~'or to eraturer ema11 in comparison with temperatures of degene-
ec~ale ~)
xoitatioa will have momente- (impulses) close in magnitude to po -
racy the e
ener a e~.lon E in a power series in (p ? po) we het
Axpauding the excitation ~ p
~,- . P (1)
E _ Ip o~
n role at tea~perature T ie pla~Yed by excitations ~brti~,~ahibh~~~e
Since the mai
of such excitations per l om3) equals the quantity
huge ~ ^~ T and the number
2 ~ 2 ~ r?+ ~ ~~4 then the energy per 1 om~ of heliwa-3 depends
p Qp~~ ~ ~ po ?Ch v po ~ +
0
upon tearperature in the following manner
-~, ax2 ~ z)
u ~, ~ ~
a ~ po~h v ,where
bons are true for temperatures euffioiently small is comparison with the
Aqua
CON~IDENI IAl
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bemperabure of de~eaoseoy of ~)ae e~oitabioaa To ~ is order o~ a~nitudo To is
zo poi (3 ~ 1
Aooordiag to e~tatioa (~} the theraai oapaaity o~ holiwa?3 turns out to be pro-
portio~aal to the t~e~erl~~pr~t~ae~TOl~a
o ? rs (T> 2,
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CONFIDENTIAL
t it ea to show bhab tbA 'Abase br~aitioa~ squid heliwa.~ ?.~ solid
b ~
met reveal oertain a~ueual peou3~iaritiea due to bhe a~obanae eff-
heiiu~.~
~ helit~? stoma in tbo liquid ebate~ To olari~y bboae peouliaribiva
sobs o 3
re the vatropy ~ oi' bhe liquid and rol~d 'pbarea off' beliu~3~ Sa
let ur oompa
state the eabxop~ 0 bends bo aero ae bhe teaaperatn-xe calla t0 0~
tip.,, liquid
-nirao diatribubion !or the esoibabione is oorreot, then 6 mush
~~ the fermi
t T ~ 10) ~ it ie neoeraary to note, ho~reoor~ bhab it ie not
be proportional o
her what kind of f~tnation ~ is of T iu bhe liq~d
vaaentia~ bo kno~r furb
im rtant it the tall in ~ with deorearis~ T. It it i~ortant
phare, Solely ~
aims thab here what fallr ie the part of g bhat is duo to the ~olear
to er~ha
the abaeeoe of eaohan~e effeotr due to nuclear rein the spine of
epinr. In
oould be freel~- oriented in a~~aoe down to temporaturoe eo low that
the nuolei
etia interaotion of the nuolear rpinr with snob other would beoome
the mean
ri ifiaarit~ There temperat~tirer in the order of magnitude equal
8n
n~ 2 kb3 ti ZO'7 degree, where N 14-2~ ~ ~ 11)
T~ I ~
er one gram--ato~a) would enter tho esc-
Thue apart equal to R lag 2 ( p
~ r ~ in the abrenao of exchange effeotr for T >?TM ~ The e~obange
preesion o
earanoe of oorralation between the orientations of the
effeotr lead to the app
borin nuolei of b-eliumr~ even far temperaturer of the order of
Apinr of neigh g
rder of ~~nutural~~ helium tompere~turee, Thir oonolue~ans
degre ee ; that i r, of the o
r ~a the feat ths~t the differenoe in the energy of interaotion of two
follows ~ o
mr in the aase of pe,rallel and antiparallel orientation of spins
helium 3 ato
rder ae the energy of interaotion itself free Section 1).
porresree the erne o
It is not essential here whether heliwo-~ is a liquid exoheage nuclear pare
etia or a ferromagnetio~ The neture of the oorrelation in these two carer
t the existenoe itself of correlation meet be noted in sash of these
differr, bu
< 1?~ ~ Renee followr the fall Tan that part of S due to nucle>rr apinr
oae8e for T ~
leer lees than R'log 2, even for '~ ~ lob ~ 6inae the entropy whiab ie
to va
nuolear a in also faller bhen even for T ~ loR the er>r-
not oonneat?d with the p
re entro of liquid helium-3 rr~et Fall to valu?r lees than R' log 2 ~ Let
ti p'Y
ue now oocarpar? Thir entropy with the entropy of valid helium~~~ The e~io.tenae
of a as~yetal lattioe in which the an>plitude of the zero osoillationg are oon~.
cc~r~i~ENria~
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CONFIDENY~AI
riderably lase than the distance botwoen stoma loadr either to the diea~aear?
anoe oi' the oTi'eota oonneoted r~th the exo~bonge of two atoms or to their ooa~
aiderable dooroaee~ Sa solid holium~3, therefore, tie nuclear spine moat be
t'reely oriented down to temperatures T ~+T~ ~ 4oneequently the entropy of salad
heliwe?~ has a part equal to R~ log ~, if T >? 10'7 a R ~ ainoe tho part oT 8
due to osoillationa is proportional to T3 and in the order of ma~nitvde equals
(12~ 5~ ~' 4R(T~9) 3, there ~ 7i 30? (note: The theta a of li d heliuca.~ a vela
~ 4
30? (lly and that ~ r s l h
o o id elium.3 moat be of the came order of mognitude~y,
then the entire dntropy of solid heliu~.~ for T 1o turns out to be a ooastant
equal to R~ log Z ~ Oaly for T < TM doer the a~etio interaotion of tho nuolear
spies in a orystal quiokly decrease the eatro~ 8 down to sero for '='~TM ~ An
example of dependence off' ~ upon T in the two nharer of hel,iu~.~ ie shown in i'i~
gore 1. Ira we note, T1 ie of the order off' magrsitude l?, We ree that for temps.
ratures snob that 10"7 0 ~ TM K T ~ T1 ~ 1? ,the entropy of solid helium=3
turns out to be greater than in liquid phase; that is! there lsiets a relatioa
that is reverse to the ordir~ry oae~ Therefore for en isothermal transition
of solid helivm.3 to liquid helium?3 heat must not be absorbed, but released,
and aoaverrely heat must be absorbed during isothermal eolidifioation, We have
here negative heat of fl~sion Q whioh for TrtC~T KT1 equals
Q= T(Sliq ~. ~eol~ = - RT~log 2 ~ (12)
~t the same temperatures we obtain an unusual dependence for the pressure at
whioh the phase txaneition of the temperature oaaurs, According to the Clausius
.Clapeyron relation dp~dT = (saol ' ~liq~~~veol - vliq~
(sol refers to the solid phase, and liq refers to the liquid phase, we have
dp~dT : R log 2f ~vaol- vliq~ - .. R log 2~~Qliq "'asol~ ~ 0 . (13~
It is taken into oansideratioa here that the liquid possesses a volume that is
greater than the eryet~l~s volutt~~
beginning with certain temperatures of the order of degrees the entropy
~~q wi11 be greater than Beol . Therefore p duet ae function T will bane the
form shown in figure 2, The eaistenoe of ~~f~~~ a reotilinear sect-
ion ~,th a negative slope for small temperatures qualitatively di~Pferentiates
helium. From helium.-~, in which the dependence of p upon T hs,s a aomplete~r
'- CONFIDENTIAL
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CONFIDE Ni~AI,
ter ~12y tees figure ~)~
dil~arent aharao
teAdo to~ardr eero is haw o~ the
to that for T~ S~ the entropy grol
we ao
e t a1 ~ Aexe ~~ f dT t ends toward eero
f oorrelation between rp~ae to the ory
onset o then as ~ r reen from
tabatio rolidilioatioa of holia~3~
i ~' one oonridere the ad rolid he'liv~
eeibi'lty~ ~a prinaipia~ off' obtaining
~igura ~ one dieaovera the po ?7 o tie it it
order ~,d'6 to l0 =. To do
x e~ctr,ee~- low tempArat~rer o~ the
~ ~o
d heliu~?3 havi~ a t e~vesature lower
to oomprerr adiabatioally ligni
~aeoeeaa~'
1e for wnioh eoliditioation retr in.
than Tl down to prereur
~ eotropY in tho solid and lic~id
The oonditiou goterni~ the egy,ality o
1 being obtained o~ the order o!
tr in the te~era~ure of the oryrta
stater sera/
thr dotted line in ~ignre 1)~
~ the tranoitio n it oo~1etod along li-
M ~ the are transition off'
~' thermodyn~io rolatsonr to '~
The app1iaation o
teat all ao r rorpo~i~ timer oi' the
uid heliua3 to the solid mate arrumew rer
q
~ the ~earibility of this assumption re
relaxatsou are ra~all~ ~xple~ation o
rpeoial aoneideratiouei ro to the nuolear
e in liquid he~i~~ must be due ~
The exo~ge e~~eot
entation off' the spins o~ naolei ooare1
m of helsu~-3~ rinOe the free on
,magnet i s e o rtho?
es exoluding oo~po~dr o~ the typ
,r T as in al~aost all boas ~
not for T M
o th there ternperat~:~rer the nualee~r
o en ,but for Tel ~ 8eginnit~g ~
or pareihydr g ~ ld need not be pro-
elium- in an externe~l ~gnetia fie
m etio moment of liquid h 3 net as
agn
~1~~ but mu~rt depend upon the temperature
portional to the temperature ' r~lid hY~ogen
e el a at xon pare~a+~rie ti or o f the type
the raeoeptibility o~ exahang ecuosed in Sea
the model of liquid heliua3 di
de ends upon the tearpere~ture, xn u n the
p need not depend '~
etia euroeptibility o~ helium~3
Lion 1 the naalear
exature for T ~ to ~ hir
temp
thank l~aademiaian Z ~ ~ ~ Lande~u for
In acnalurion the author wishes to
also q ~ V, Vladimirekiy for hir
ertions end iartruationr , r-na
important r'
rionr in oonneotion nth this work
interertin,~ dieour
gubmitted 22 Meacoh 1950.
~ibliogra~'
breth~. 1~,Yr rev, 75~9~a+ l9~'
1~ D~ Orborng~ ~. Weinetook, 0? ~
rti a !~ SSSR, Ser ~'iz, 11, ~7~ 197
2. ~~~~'~~ 8ogolyubov~ lrve Y
g_ CONFIDENT-A~
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i'ONADENriai
3, L. Landau Joy o! ~e~ S~ 7~r 19~~~
W, ~', a to ah ~ Z~~ye ~ 6~, 20 b, lg ~0
S, R, ~ndereon~ pb,Yr Rey, 76, 2460, ~9~9~
6, ~, ~~~u ,add i , PomexanohvJc~ Zhur Rke~es i T eore~ ~'i e, 7, 3?9 ~ 1937
7. W. d. 8abor~ yroa aoy Boa ~-, 1~8, 38~, 19371
8, s ~ Tomona~a~ Z~ fir Phyr, Z10, X73 ~ 1938
M eoxn and M. Sep~ert.Mayer, Theory o! the Bolid ~Teoriya Tterdo~o Tela~,
9?
ONTI, 1~~8,
10. L. 8xillouis, Qaan~v~ Btatittico ~Ktan~oveya 5~ati~~ika), aNTtV, 1934,
11, Y, ~e'emom~ Reliuaa ~Oeliy), IIL, Pie 393 194'9
12. " " " " " ~33~ "~
13~ ~', 81ooh, !1~-e Re4, 70, 460, 1946,
~ 3 liguxee lollow~
-~ - CONFIDE~~!
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?S
F~~~ ~~ /
4P
~CONFIDENiIAI
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