Preliminary results of a study of the propagation of the quartet of stable isotopes of hydrogen and helium are reported. A mean pathlength of 7.5 + or - 0.5 g/sq cms at approximately 300 MeV/nucleon is required to explain the low energy deuterium spectrum. This pathlength is consistent with pathlengths derived from the elements with Z  2, but is a (He-3/He-4) measurement of Jordan and P. Meyer (1984). The propagation calculations reported here incorporate the preliminary results of an updated nuclear interaction cross section survey covering the period since the review by J. P. Meyer (1972)

Beatty, J. J.

English

NASA Technical Reports Server

§ 6 OG4.2-1
INTERSTELLAR PROPAGATION AND THE ISOTOPIC COMPOSITION
OF HYDROGEN IN THE GALACTIC COSMIC RAYS
James J. Beatty
Enrico Fermi Institute and Department of Physics
University of Chicago, Chicago, Illinois, USA
Abstract Preliminary results of a study of the propagation of
the quartet of stable isotopes of hydrogen and heliumare
reported. A mean pathlength of 7.5_+0.5 g/cm 2 at %300
MeV/nucleon is required to explain the low-energy deuterium
spectrum. This pathlength is consistent with pathlengths
derived from the elements with Z>2, but is a factor _2 lower
than the value required to explain the (Re/_e) measurement
of Jordan and P. Meyer (1984). The propagation calculations
reported here incorporate the preliminary results of an up-
dated nuclear-interaction cross section survey covering the
period since the review by J.P. Meyer (1972).
Introduction. The quartet of isotopes of hydrogen and helium constitute
a closely-coupled set of nuclides which provide strong constraints on the
cosmic ray source spectra and on the escape pathlength of cosmic rays
from the galaxy. (See Simpson (1971) for a review.) The recent measure-
ments of (3He/4He) in the energy range 5-10 GeV/nucleon by Jordan and P.
Meyer (1984) and Jordan (1985) require a pathlength of _15 g/cm 2 to ac-
count for the experimental data, which is inconsistent with the value _6
g/cm 2 inferred from CNO and their secondaries. (e.g. Garcia-Munoz et. al.
(1981)) In this paper, the pathlength traversed by low-energy II and He
during interstellar propagation is studied using the high-resolution, low
energy spectra of IH,2H and 4}le determined using the University of
Chicago IMP-8 telescope under solar minimum (1976-1977) conditions
(Beatty et. al. 1985 and references therein). It is found that
the observed fluxes of these nuclei
at low-energy are consistent with b,,, i.... t.... i ,, _.........
the pathlength deduced from the _ I_H ,if!
elements with Z>2, hut not with the ii_i:i!_ _ , 2H
much longer pathlengths required by !_iiiii_!_:_
the high energy He isotopic ratio. _ 1o2 _ _:_
Measurements. The 2Dlmeasurements _ !i__ D4 Energy Deposit
used in this work were obtain ed _ ii!ii__,_1 105-,o9_MeV
June 1976 to April 1977, at solar z
minimum modulation. 2H is iden-
tified by the (dE/dx) vs. residual
E method. The measurement of 2H is 1o0
most reliable near the end-of- ,_ _i_!_ _!i_il
range, where the 2H energy deposit 0 5 10 15 20 25
in the Csl(Tl) residual E detector D2(-dE/dX) Chonnel Number
(D4) is _30% greater than the
largest enerBy deposited by the Figure 1
more abundant _H (Figure l,insert).
56 
IN STE LAR P GATION  T  ISO PI  POSITION 
 GEN IN  CTIC I  R  
Ja es . eatty 
Enrico Fermi Institute and Department of Physics 
niversity of hicago, hicago, Illinois, USA 
bstract Preli inary results of a study of the propagation of 
the quartet of stable isotopes of hydrogen and helium. are 
r orted.  ean ath1ength f . ±0.5 / 2 t ~ 0 
eV/nucleon is required to explain the lo -energy deuterium 
spectrum. This path1ength is consistent ith patQ1engths 
derived fro  the ele ents ith >2, but is a factor ~2 lo er 
t  t  lue r uired t  lain t  (3ae/ 'lie) easurement 
of Jordan and P. eyer (1984). he propagation calculations 
reported here incorporate the preli inary results of an up-
dated nuclear-interaction cross section survey covering the 
eri d si ce t e re ie  by J. . eyer ( 72). 
OG4.2-1 
I tr duction. e uartet f is t es f drogen a  eli  nstitute 
a closely-coupled set of nuclides hich provide strong constraints on the 
cosmic ray source spectra and on the escape path length of cos ic rays 
fr  t  alaxy. ( e i pson ( 71) f r  r i .)  r ent easure-
ments of (3He/ 4He) in the energy range 5-10 GeV/nuc1eon by Jordan and P. 
eyer (1984) and Jordan (1985) require a path1ength of ~15 g/cTJil to ac-
unt f r t  perimental ata, hich i  i onsistent ith t  alue ~ 
g/cm2 inferred from CNO and their secondaries. (e.g. Garcia- unoz et. a1. 
(1981» In this paper, the path1ength traversed by lo -energy H and e 
during interstellar propagation is studied using the high-resolution, low 
energy spectra of la,2H and .e determined using the University of 
hicago I P-8 telescope under s lar ini um (1976-1977) c nditions 
( eatty t. 1. 85 a d r ferences t erein). t i  f und t at 
 bserved es f se uclei 
at lo -energy are onsistent ith 
the path1ength deduced from the 
elements with Z>2, but not with the 
much longer path lengths required by 
the high energy He isotopic ratio. 
Measurements. The 2H measurements 
used in this work were obtained 0 
using the University of Chicago ~ 
IMP-8 telescope during the period E 
::J J ne 976 t  pril 9 7, t s lar z 
inimum odulation.  i  i en-
tified y t e /dx) s. r sidual 
 ethod. he easurement f 2JI is 
most reliable near the end-of-
range, here the 2  energy eposit 
i  t e sl(T1) r sidual  detector 
( 4) is ~30% reater t an t e 
largest eneryy deposited by the 
ore abundant  ( igure 1,insert). 
o 
Figure 1 
https://ntrs.nasa.gov/search.jsp?R=19850025708 2020-03-20T18:03:29+00:00Z
OG4.2-i
57
Plotting the number of counts per (-dE/dx) channel (D2), the 2H appears
as a peak superposed on a high energy interaction background. At solar
minimum, subtraction of this background leads to a correction of only
25%. The r.m.s, width of the 2H peak is 0.13 amu, corresponding to a FWHM
of 0.31 ainu. A more detailed discussion of the data analysis has been
presented in Beatty et. al. (1985).
Modelin_ of Cosmic Ray Propagation. The effects of interstellar propaga-
tion on an assumed cosmic ray source spectrum are computed using a
weighted-slab model (WSM), in which solutions of the equation describing
the passage of nuclei through interstellar matter
__J _ .dE . • .._
Sx= _-_(_Ji ) + Zk J" _,_i dE' - A±
are weighted by a pathlength weighting function (PLWF) to obtain the lo-
cal interstellar cosmic ray flux:
f
Jc.r.(E)= I dx P(E,X)Jslab(E,x)
For a leaky-box model (LBM) with energy-independent escape pathlength ,
it can be shown that the PLWF is an exponential: P(x)=exp(-x/%).
(Lezniak, 1979)
The calculation procedure used in this work includes the effect of
ionization energy loss at all energies, and includes kinematic energy-
changing effects in the reactions H(p,d w+ ) and He(p,d) He. Kinematic
effects in other reactions and energy losses due to elastic scattering
are small and have been neglected. Results of calculations including the
small effects neglected here will be published elsewhere (Beatty, 1985).
The nuclear interaction cross sections used here are the prelimi-
nary result of a survey in this laboratory of the experimental
cross section measurements performed since the i ....
compilation by J.P. Meyer (1972). The
remaining uncertainties in the cross sections
are largest for the production of deuterium by
the spallation of cosmic ray helium on the in- \ (T+200) -2'6
terstellar medium at energies above _500 MeV \_
per nucleon. _.
Solar modulation has been taken into ac- _ ",,,',,_,'\
count using the model of Evenson et. al.
(1983). For the solar minimum data discussed _ \\
here, the adiabatic deceleration parameter _ #x-\",,\
is 440 MV. -_ p-2._ "'Q',,\.,,,Q,,,
The Primary Energy Spectra. In the leaky box _ ,,\
propagation model, the local interstellar _ _A",\
spectra of IH and _ _He are simply related to _ 26 _,_,the source spectrum and to the functional form (T+400)-
- of %(E). The pathlength for nuclear inelas-
tic interaction with the interstellar medium
is long compared with the expected escape .....
pathlength. Secondary production of these io2 1o3
species can be neglected because of their Energy(MeV/nucleon)
large source abundances. Energy loss effects
are less important than for heavier elements: Figure 2
the lowest energy local interstellar particles
4. 1 
 
lotti g the nu ber of counts per (~dE!dx) channel ( 2), the 2H appears 
s   s r s    i  r  i t r ction ckground. t l r 
1n1mum, s btraction f t is background leads t  a c rrecti  f only 
25 . The r. .s. idth of the 2H peak is 0.13 a u, corresponding to a FWHM 
f .  amu.  ore etailed is ssion f t e ata a al sis ha~ been 
t  i  eatt  t. 1. ). 
odeling f s i   r agation.  t  f i t r t ll r r a-
ti  on an assu ed cos ic ra  source spectru  are co puted si g a 
eighted-slab odel ( ), i  hic  l ti s f t  ati  s ri i  
 e  clei t  t ll r a ter 
_Q.J.= L(  J .) + 2:: f ~ dE I _ ti. 
dX dE dx 1 k A ' A 
ki i 
 
l 
eighted   t l gt  eighti  f ti  (PL ) t  t i  th  10-
i t r t ll r c s ic ra  flu : 
J (E)= ( dx P(E,x)J 1 b(E,x) 
C.T. J S a 
For a leaky-box odel 
it   s n t t 
zniak, ) 
(LB ) ith energy-independent escape pathlength , 
t  F i  a  po ential: (x)=exp(-x!A). 
he calc lati n r ce ure used i  t is ork i cl es t e ff ct f 
i ization er y l  t ll ergies,  i l  i atic r -
changing effects in the reactions (p,d rr+ ) and e(p,d) e. ine atic 
ffects i  t er r cti ns a  e er  l sses due t  l sti  s tt ri  
are s all and have been neglected. esults of calculations including the 
s all effects neglected here ill be published else here ( eatt , 1985). 
The nuclear interaction cross sections used here are the reli i-
nary result of a survey in this laboratory of the experi ental 
 ti  easure ents r ed i  t  
mpilation  . . eyer ( 972). e 
aini g certainties i  t  ss cti ns 
are l r st f r t e r ducti n f e teri  by 
t  all ti  f i  r  li   t  i
terstellar medium at energies above '\,500 MeV 
r ucleon. 
Solar modulation has been taken into ac-
unt si g t  odel f venson t. l. 
(1983). For the solar minimum data discussed 
here, the adiabatic deceleration parameter 
is 440 MV. 
The Primary Energy Spectra. In the leaky box 
propagation model, the local interstellar 
spectra of lH and 4He are simply related to 
t e s rce s ectr  and t  t e f cti nal for  
f A(E). he t l gth  clear elas-
 t raction ith  t rstell r edi  
is long co pared ith the expected escape 
pathlength. Secondary production of these 
ecies n e eglected ecause f eir 
l r e s urce a undances. nergy l ss ff cts 
r  l  i portant t  r eavier l ents: 
t e lo est energy l cal i t rstellar articles 
(T+200)-2.6 
"-/ 
\ 
\ 
p-2.2 
\ 
\ 
\ 
\ 
(T+400)-2.6 
\ 
'~ 
, 
1~ 1~ 
Energy( eV /nucleon) 
Figure 2 
5 8 OG4.2-I
which are seen at Earth
(i.e., which have local _ 1oI- . .......j _ :_-T-. ......i ........ 1oO
interstellar energies _ (a) _ (b) 5"
_U
greater than the energy _,.
Er_
lost during solar _
+. 10-I_'
modulation) have lost ? I0° - ++<20% of their initial _
energy during inter- ? _ +_.+_[_
stellar propagation. _ _ +
Under these conditions, _
the leaky box model -6 l°-I Deuterons 10-2 _._ t_
solution can be ap-_
proximated by the _
X
simple algebraic result _
J(E) = _(E) Q(E). In _ 10-2 _-U_ULU_I__U _J__UUI____LLLLU lO-3g101 102 103 101 10z I0 3
this paper, momentum Kinetic Energy (MeV/n)
power law source
spectra of the form FiKure 3 Computed 1 A.U. H, H, and He
dN = dJ -y spectra for a 7.5 g/cm pathlength under 1976-
dP dT _ p have 1977 solar minimum conditions. Panel (a): open
been used. Figure 2 circles, protons; filled circles, helium;
compares the chosen Garcia-Munoz et. el. (1977). Panel (b),
source spectrum deuterium: filled circles, Beatty et. al.
p-2.2 with the spectra (1985); crosses, Webber and Yushak (1983); up-
(T+200MeV) -2"6 used by per limits, Leech and O'Gallagher (1978).
J.P. Meyer (1974), and (T+400MeV) "2.6 used by Garcia-Munoz et. al.
(1981). The latter two spectra lead to a spectrum which is too steep when
the energy dependence of % (E) at high energies is taken into account, but
are similar to the momentum power-law spectrum above at energies below
several GeV/nucleon.
The source abundances used in this work are those of J.P. Meyer
(1985), except that the ratio IH/_He at constant energy/nucleon is deter-
mined to be _12.2 at low energy.
Deuterium Production. The pathlength is determined by the requirement
that the modulated deuterium flux at 1 A.U. match the value measured un-
der solar minimum conditions by the University of Chicago telescope on
IMP-8. Figure 3 shows the computed 1 H, 2 H, and _ He spectra together with
experimental data from this period. (See caption) The pathlength required
is 7.5 g/cm 2 , using the model of Evenson et. el. (1983) to describe the
effects of modulation during the 1976-1977 solar minimum. The error in
this pathlength due to the experimental uncertainties in the measured
fluxes is 0.5 g/cm2 .
Figure 4 illustrates the relative importance of contributions from
cosmic ray IH, _He, and CNO. The local interstellar spectrum has been
divided by the momentum power law source spectrum used in the
calculations. Because the contribution from cosmic ray IH is entirely due
to energy-changing kinematic processes, the importance of these reactions
is strongly dependent on the source spectral form and on the low-energy
behavior of I(E).
 
OG4.2-1 
hich re en t ~th 
(i.e., which have local c 
interstellar energies ~ 
greater than the energy 1 
lost during solar ~ 
modulation) have lost f 
 f t eir itial ~ 
energy during inter- f 
stellar propagation. S 
Under these conditions, ~ 
the leaky ox odel] 
solution can be ap- ~ 
roximated y t e e;.. 
si ple al ebraic r sult ~ 
J(E)== A(E) (E). In ~ 
this paper, momentum 
power la  source 
spectra of the form igure 3 omputed 1 .U. , , and He 
s ectra f r a .  g/c  athlength nder 976-
1977 solar ini um conditions. Panel (a): open 
d  = dJ a: p- Y dP dT have 
been used. Figure 2 circles, protons; filled circles helium' 
. " compares the chosen Garc1a-Munoz et. a1. (1977). Panel (b), 
source spectrum deuterium: filled circles, eatty et. a1. 
p-2.2 with the spectra (1985); crosses, Webber and Yushak (1983); up-
(T+200MeV)-2.6 used by per limits, Leech and O'Gallagher (1978). 
. . eyer ( 974), a d ( 4 0MeV)- .  sed y arcia-Munoz t. !. 
(1981). The latter t o spectra lead to a spectrum hich is too steep hen 
the energy dependence of A( ) at high energies is taken into account, but 
re i ilar t  t e omentum ower-law s ectr m a ve t ergies el  
several eV/nucleon. 
he s urce a undances sed i  t is ork r  t se f J. . eyer 
(1985), except that the ratio 1HtHe at constant energy/nucleon is deter-
ined t  e ~ 2.2 t l  e ergy. 
euterium roduction. he athlength is etermined by t e re uirement 
at e odulated uterium  t  . . atch  alue easured n-
der solar ini um conditions by the niversity of hicago telescope on 
I P-8. Figure 3 shows the computed 1 H, 2 H, and 4 He spectra together with 
experimental data fro  this period. (See caption) The path1ength required 
is 7.5 g/c~, using the model of Evenson et. al. (1983) to describe the 
ff cts f odulation uring t  76-19 7 lar inimum. he rror i  
t is pathlength due to the experimental uncertainties in the easured 
fl es is .  g/CJD. 2 • 
Figure 4 illustrates the relative i portance of contributions fro  
cosmic ray 1H, 4He, and CNO. The local interstellar spectrum has been 
divided by the omentum power la  source spectrum used in the 
alculations. ecause t e c ntribution fro  cos ic ra  1  is tirely due 
to energy-changing kinematic processes, the i portance of these reactions 
is strongly dependent on the source spectral form and on the lo -energy 
ehavior f A( ). 
5 9 OG4.2-1
Difficulties in the inter-
pretation of weighted-slab models Contributionsto
arise when energy-changing _stellar 2H
processes become important. Lezniak c_ -
(1979) has compared the LBM to the _ ._____f/_WSM, and has noted cases in which Total
the mean of the WSM exponential X _ C.R 4H
PLWF and the value of the LBM es-
cape pathlength are not equivalent.
We have investigated the importance 00 _.C.R.IH
of these effects on the quartet. "_ J \J //_._ CNOFor the case where %(E) increases
with increasing energy as E°°5 --o9
(Garcia-Munoz et. al. 1981; Ormes
and Protheroe 1983), the effect of
ionization energy loss will in- ] ,\__j....I . . ,,....
crease 2H production by _5%, and 02 103 1°4
the effect of energy-changing Energy(MeV/nucleon)
processes involving cosmic ray 1 H
will increase 2H by _i0-20%. It Figure 4
should be noted that in both cases
the WSM
underestimates the production of 2H relative to the corresponding LBM,
and therefore overestimates the pathlength traversed in the case where
%(E) increases with increasing energy. The quantitative analysis of the
case of energy-dependent PLWFs will be published elsewhere (Beatty,
1985).
Acknowledgements. Discussions with M. Garcia-Munoz, T.G. Guzik, R.A.
Kroeger, K.R. Pyle, and J.A. Simpson are greatly appreciated. This re-
search was supported in part by NASA Grant NGL 14-001-006 and NASA
Contract NAS 5-28442.
References.
Beatty, J.J., 1985, Thesis, University of Chicago, in preparation.
Beatty, J.J., Garcia-Munoz,M., and Simpson, 3.A., 1985, Ap.J. 294, 455.
Evenson, P., Garcia-Munoz, M., Meyer, P., Pyle, K.R., and Simpson,
J.A., 1983, A._A__., 275, LI5.
Jordan, S.P., 1985, _ 291, 207.
Jordan, S.P., and Meyer, P., 1984, Phys. Rev. Left. 53, 505.
Leech,H.W., and O'Gallagher, J.J., 1978, _ 221, 1110.
Lezniak, J.A., 1979, AP. Space Sci. 63, 279.
Garcia-Munoz, M., Guzik, T.G., Simpson, J.A., and Wefel, J.P., 1981,
Proc. 17th Internatl. Cosmic Ray Conf.(Paris)9, 195.
Garcia-Munoz, M., Mason, G.M., and Simpson, J.A., 1977,
. Proc. 15th Internatl. Cosmic Ray Conf.(Plovdiv) 3, 209.
Meyer, J.P., 1972, Astron. Astrophys. Suppl., 7, 417.
...... , 1974, Thesis, University of Paris.
......, 1985, Ap. J. Suppl. 57, 173.
Ormes, J.F., and Protheroe, R.J., 1983, _ 27_.__2,756.
Simpson, J.A., 1971, Proc. 12th Int. Conf. on Cosmic Rays (Hobart),
Invited and Rapporteur Papers, 324-356.
Webber, W.R., and Yushak, S.M., 1983, _ 275, 391.
.. 
59 
ifficulties i  t e i ter-
pretation of weighted-slab models 
arise when energy-changing 
processes become important. Lezniak N 
(1979) has compared the LBM to the N~ 
WSM, and has noted cases in which 
the mean of the WSM exponential 
PLWF and the value of the LBM es-
cape pathlength are not equivalent. 
We have investigated the importance 
of these effects on the quartet. 
For th  cas  where A(E) inc eases 
ith increasing energy as EO.s 
( arcia- unoz et. al. 1981; Ormes 
and Protheroe 1983), the effect of 
ionization energy loss ill in-
creaSe 2H production by ~%, and 
the effect of energy-changing 
processes invo lving cosmic ray 1 H 
will increase 2H by ~10-20%. It 
s ul  e oted t t i  oth ses 
t e SM 
Q) 
:> 
..... 
....., 
ro 
-Q) 
0:: 
Contri uti  t  
Loc l Interstellar 2li 
, 
C.R. O 
G4.2-1 
~--~~~~~~~--~~~~~~ 1~ 1~ 1~ 
nergy( eV /nucleon) 
i ure  
underesti ates the production of 2  relative to the corresponding LB , 
a  t refore erestimates t  at 1ength tra erse  i  t e case here 
A(E) increases with increasing energy. The quantitative analysis of the 
. case of energy-dependent PL Fs ill be published else here (Beatty, 
1985). 
Acknowledgements. Discussions with M. Garcia- unoz, T.G. Guzik, R.A. 
Kroeger, K.R. Pyle, and J.A. Simpson are greatly appreciated. This re-
search as supported i  art by S  rant NGL 14-001-006 and S  
ontract S - 2. 
eferences. 
Beatty, J.J., 1985, Thesis, University of Chicago, in preparation. 
Beatty, J.J., Garcia- unoz, ., and Si pson, J. ., 1985, p.J. 294, 455. 
Evenson, P., Garcia- unoz, ., eyer, P., Pyle, K.R., and Si pson, 
J. ., 1983, p. J., 275, LIS. 
Jordan, S.P., 1985, Ap. J. 291, 207. 
Jordan, S.P., and eyer, P., 1984, Phys. Rev. Lett. 53, 505. 
Leech,H. ., and O'Gallagher, J.J., 1978, Ap.J. 221, 1110. 
Lezniak, J. ., 1979, Ap. Space Sci. 63,279. 
arcia- unoz, ., uzik, . ., Si pson, J. ., and efel, J. ., 1981, 
r c. t  I t r atl. os ic ay nf.( aris) ~, 195. 
arcia- unoz, ., ason, . ., and Simpson, J.A., 1977, 
r c. t  I t r atl. os ic ay nf.( l div) 1, 209. 
Meyer, J.P., 1972, Astron. Astrophys. Suppl., 1, 417. 
------, 1974, Thesis, University of Paris. 
------, 1985, Ap. J. Supple 57, 173 • 
Ormes, J.F., and Protheroe, R.J., 1983, Ap. J. 272, 756. 
Simpson, J.A., 1971, Proc. 12th Int. Conf. on Cosmic Rays (Hobart), 
Invited and Rapporteur Papers, 324-356. 
Webber, W.R., and Yushak, S.M., 1983, Ap. J. 275, 391. 


Interstellar propagation and the isotopic composition of hydrogen in the galactic cosmic rays

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