The mechanism of particle evaporation was used to examine ablation effects in the fragmentation of 2.1 GeV/nucleon oxygen nuclei by lead targets. Following the initial abrasion process, the excited projectile prefragment is assumed to statistically decay in a manner analogous to that of a compound nucleus. The decay probabilities for the various particle emission channels are calculated by using the EVAP-4 Monte Carlo computer program. The input excitation energy spectrum for the prefragment is estimated from the geometric ""clean cut'' abrasion-ablation model. Isotope production cross sections are calculated and compared with experimental data and with the predictions from the standard geometric abrasion-ablation fragmentation model

Townsend, L. W.

English

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NASA-TM-85704 19840008909
NASA Technical Memorandum 85704
Ablation Effects in Oxygen-Lead
Fragmentation at 2.1 GeV/Nucleon
FOR _ _-_-_'-'r,,,,',,-
NOT TO |E T*_II:_ FROM _ ROOM
Lawrence W. Townsend
FEBRUARY 1984
LZ_RYCPY
LANGLEYRESEARCHCENTER
LIBRARY, NASA
HAMPTON, VIE(;.'.NIA
N/ A
https://ntrs.nasa.gov/search.jsp?R=19840008909 2020-03-20T23:43:04+00:00Z

NASA Technical Memorandum 85704
Ablation Effects in Oxygen-Lead
Fragmentation at 2.1 GeV/Nucleon
Lawrence W. Townsend
Langley Research Center
Hampton, Virginia
NI A
National Aeronautics
and Space Administration
Scientific and Technical
Information Office
1984

INTRODUCTION
With the advent of the Space Transportation System and the era of career astro-
nauts, who will spend appreciable portions of their careers in space, the problem of
providing radiation protection increases in importance (ref. I). For career astro-
nauts and long-duration missions, the high-energy heavy-ion (HZE) component of galac-
tic cosmic rays will become of major radiobiological significance, especially for
nonregenerative tissues (ref. 2). Since the range of these particles is large com-
pared with a typical spacecraft wall thickness, nuclear attenuation and fragmentation
appears to be a possible means of protection.
In this work, initial estimates of fragmentation cross sections for a typical
cosmic ray nucleus (160 at 2.1 GeV/nucleon) colliding with a heavier target nucleus
(208pb) are made and compared with experimental results (ref. 3). The fragmentation
process is analyzed by using an abrasion-ablation collision model. Tne abrasion
formalism utilized is described in detail in references 4 through 7. In order to
complete our initial efforts at describing the fragmentation process, we adopted a
simple ablation formalism where the excited projectile prefragment, which remains
after the abrasion step, is treated as a compound nucleus and allowed to statis-
tically decay by particle evaporation. The prefragment excitation energy is deter-
mined from the geometric "clean cut" abrasion-ablation model of Bowman, Swiatecki,
and Tsang (ref. 8). The compound nucleus particle evaporation probabilities are
calculated by using the Monte Carlo program EVAP-4, developed at Oak Ridge National
Laboratory (ref. 9). The resultant theoretical predictions are also compared with
the predictions obtained from the geometric clean-cut model (ref. 8).
PROJECTILE FRAGMENTATION
The HZE particle fragmentation is assumed to take place in a two-stage formalism
called the abrasion-ablation model. In this model, the projectile nuclei, moving at
relativistic speeds, collide with stationary target nuclei. Those portions of their
nuclear volumes which overlap are sheared away by the collision. This is the abra-
sion step. The remaining projectile piece, called a prefragment, continues its tra-
jectory with essentially its precollision velocity. As a result of the abrasion
process, the prefragment is in an excited state and decays by the emission of gamma
radiation and/or the evaporation of nuclear particles (ablation). The resultant
isotope is the nuclear fragment whose cross section is measured. The abrasion part
of the collision process is often analyzed from classical geometric considerations
(refs. 8 and 10) or by using formal quantum scattering theory (refs. 4 to 7 and 11).
The ablation part of the process may be analyzed by calculating the prefragment
deexcitation through geometric arguments (ref. 8) or more sophisticated methods based
upon Monte Carlo or intranuclear cascade techniques (refs. 10 through 13).
Abrasion Cross Sections
The cross sections _m for abrading m nucleons from the 160 projectile were
calculated by means of the quantum mechanical methods given in references 5 and 7.
The appropriate oxygen and lead nuclear distribution parameters and nucleon-nucleon
scattering parameters were taken from reference 14. The results are displayed in
table I. (The symbols used in this paper are defined in a list after the refer-
ences.) If n of the abraded nucleons are neutrons and z are protons, the
TABLE I.- OPTICAL MODEL ABRASION CROSS SECTIONS FOR THE
REACTION 160 + 208pb . m + X
[Incident kinetic energy is 2.1GeV/nucleon]
Number of
abraded Abrasion cross section,
nucleons, _ , mb
m
m
I 404
2 226
3 166
4 136
5 118
6 108
7 102
8 98
9 98
10 100
11 105
12 115
13 133
14 172
15 284
16 964
resultant abrasion cross section, Onz can be obtained from _m by using a
hypergeometric distribution
<N) Z)nzo = o (1)
nz<:) m
where N is the total neutron number, Z is the total proton number, and the mass
number is
A =N + Z (2)
It should be noted that the assumption of a hypergeometric distribution could result
in inaccuracies, since it assumes there is no correlation at all between neutron and
2
proton distributions,and hence could lead to such unphysicalresultsas abradingall
neutronsor protonsfrom a nucleuswhile leavingthe remainingfragmentintact.
Prefragment Excitation Energies
The excitation energy of the projectile prefragment following abrasion of m
nucleons is calculated from the clean cut abrasion formalism of references 8
and 10. For this model, the colliding nuclei are assumed to be uniform spheres of
radii Ri (i = P,T). In the collision, the overlapping volumes shear off so that
the resultant projectile prefragment is a sphere with a cylindrical hole gouged out
of it. The excitation energy is then determined by calculating the difference in
surface area between the misshapen sphere and a perfect sphere of equal volume. This
excess surface area A is given by (ref. 10)
A 4 211+P-(i (3)
where for 160 (Rp = 3.32 fm) and 208pb (RT = 7.04 fm), we have (ref. 10) i
= - - 0.125 .5(_v) - + (4)
and
= - - 0.1 2513(1 - V)1/2 _ 1 (5)
with
R
P
v - Rp + RT (6)
b
P-R +R (7)
P T
and
I RT
_=--- 1=--v R (8)
P
Equations (4) and (5) are valid when the collision is peripheral (i.e., the two
nuclear volumes do not completely overlap). For this case, the impact parameter b
is restricted such that
R - R < b < R +R (9)
T P T P
If the collision is central, then the projectile nucleus volume completely over-
laps the target nucleus volume (b < RT - Rp), and all the projectile nucleons are
abraded. In this case, equations (4) and (5) are replaced by
P = -I (10)
and
F = I (11)
and there is no ablation of the projectile, since it was destroyed by the abrasion.
If the excess surface area is used from equation (3), the excitation energy is
E = A,E (I2)
exc s
where Es = 0.95 MeV/fm2 is the nuclear surface energy coefficient (refs. 8 and 10)
from the liquid drop model of the nucleus.
Ablation Factors
Depending upon the excitation energy, the excited prefragment may decay by
emitting one or more nucleons (protons or neutrons), composites (deuterons, tritons,
3He, or alpha particles), or gamma rays. The probability _ij for forming a par-
ticular fragment of type i as a result of the deexcitation of a prefragment of
type j is obtained from the EVAP-4 computer code (ref. 9) by treating the prefrag-
ment as a compound nucleus with an excitation energy given by equation (12). The
final fragmentation cross section for production of the type i isotope is then
given by
OF(Zi,Ai) =E eij _abr(ZJ'A')3 (13)
J
The _abr(Zj,Aj) values are obtained from equation (I) by setting
aObr (Z''A') = o (14)3 3 nz
4
where
zj= z - z (15)
and
Aj = A - m (16)
FRAGMENTATION RESULTS
Table II displays the cross section results obtained from equations (1) and (13)
for 160 projectiles at 2.1GeV/nucleon colliding with a 208pb target. Also displayed
are the experimental isotope production cross sections from the fragmentation experi-
ments described in reference 3. Despite the crude and unsophisticated nature of
TABLE II.- ABRASION AND FRAGMENTATION CROSS SECTIONS FOR THE REACTION
160 + 208pb . AZ + X
[Incident kinetic energy is 2.1 GeV/nucleon]
Species, AZ _abr(Z,A), mb _F(Z,A), mb %xp (ref. 3), mb
150 202 202 135 _+22
140 53 0 2.8 _+1.5
130 17 17
120 5 0
110 1.5 0
15N 202 202 202 + 26
14N 120 120 71 _+22.5
13N 66 53 17 _+3
12N 33 0
11N 15 .6
14C 53 53 12.3 ± 2.2
13C 66 0 45.4 +_8.3
12c 58 132 126 + 25
11C 43 33 36.9 + 5.7
10C 26 4.3 7.21 + 1.40
13B 17 0 0.7 + 0.4
12B 33 17 3.98 + 0.75
11B 43 33 52.8 _+5.9
10B 42 85 35.2 _+11.3
9B 35 3
these fragmentation calculations, the overall agreement between theory and experiment
is quite good. Two main sources of error are the input excitation energy estimate
and the assumption of a hypergeometric distribution. The excitation energy calcula-
tion assumed that the excitation energy was independent of the charge or quantum
states of the abraded nucleons and also ignored the surface diffuseness of the
nuclei. The latter probably accounts for the overestimates of the 150 and 14N cross
sections, since the excitation energies of these species were too small for any par-
ticle evaporation to occur. The most apparent example of the error due to the hyper-
geometric distribution assumption is the overestimate of the 130 cross section. The
use of this assumption resulted in a clearly unphysical 10-percent probability that
the three abraded nucleons were all neutrons. This is also the likely source for the
13N overestimate, since 13N is produced by evaporation of a proton from 140, which
has a substantial cross section for removal of only two neutrons. The errors in the
13C and 14C cross sections are attributable to the input excitation energy for 14C.
The 14C excitation energy (6 MeV) obtained from equation (I2) is too small to ini-
tiate particle evaporation. If it is increased, however, to =9 MeV, then neutron
evaporation to 13C can occur. This possibility is further supported by noting that
the calculated _ for 14C is nearly equal to the sum of the experimental production
cross sections foF both 14C and 13C.
Comparisons of the predictions of this work with those of the geometric
abrasion-ablation model of reference 8 and the experimental results of reference 3
are shown in table III, where the cross sections for production of nitrogen, carbon,
TABLE III.- ISOTOPE PRODUCTION CROSS SECTIONS FOR THE REACTION
160 + 208pb . Z + X
[Incident kinetic energy is 2.1GeV/nucleon]
Isotope production cross sections, mb
Process
Geometric model (ref. 8) This work Experiment (ref. 3)
0 . N 419 375 290 ± 35
O . C 286 223 228 ± 27
0 . B 239 138 93 ± 13
and boron isotopes from oxygen projectile nuclei are given. The production cross
sections for a particular nuclear species (e.g., boron) were obtained by summing the
contributions from all isotopes for that given species
oF(Z,A) (IV)
A
As can be seen from table III, when the predictions of this work were compared with
the experimental values of reference 3, closer agreement was obtained than by com-
parison with predictions of the geometric model (ref. 8).
Future efforts at improving these and similar fragmentation calculations will
center upon improving the method for estimating the prefragment excitation energy
following the abrasion process. A more sophisticated quantum mechanical calculation
using a weighted sum-rule method (ref. 11) is a possible improvement to this aspect
of the theory. In addition, much of the neglected physics, including partitioning of
the input excitation energy into rotational and internal degrees of freedom and cor-
relations between neutron and proton distributions, needs to be incorporated.
CONCLUDING REMARKS
Predictions for the production of secondary nuclear species through the frag-
menting of 160 projectile nuclei by 208pb target nuclei are presented and compared
with experimental results. Although the theoretical calculations utilize very simple
methods to treat the ablation effects, reasonable agreement with experimental data is
noted. Tne major sources of disagreement appear to be attributable to the simple
geometric model used to estimate the excitation energies of the projectile prefrag-
ments and to the assumption of a hypergeometric distribution, which neglects correla-
tion effects between the neutrons and protons in the nucleus. Clearly, much work
remains to be done.
Langley Research Center
National Aeronautics and Space Administration
Hampton, VA 23665
December 12, 1983
REFERENCES
1. Nicogossian, Arnauld E.; and Parker, James F., Jr.: Space Physiology and
Medicine. NASA SP-447, 1982.
2. Grahn, Douglas, ed.: HZE-Particle Effects in Manned Spaceflight. National
Academy of Sciences, 1973.
3. Lindstrom, P. J.; Greiner, D. E.; Heckman, H. H.; Cork, Bruce; and Bieser,
F.S.: Isotope Production Cross Sections From the Fragmentation of 160 and 12C
at Relativistic Energies. LBL-3650 (NGR-05-003-513), Lawrence Berkeley Lab.,
Univ. of California, June 1975.
4. Townsend, Lawrence W.: Optical-Model Abrasion Cross Sections for High-Energy
Heavy Ions. NASA TP-1893, 1981.
5. Townsend, Lawrence W.: Harmonic Well Matter Densities and Pauli Correlation
Effects in Heavy-Ion Collisions. NASA TP-2003, 1982.
6. Townsend, Lawrence W.; and Bidasaria, Hari B.: Improvements to the Langley HZE
Abrasion Model. NASA TM-84542, 1982.
7. Townsend, L. W.: Abrasion Cross Sections for 20Ne Projectiles at
2.1GeV/Nucleon. Canadian J. Phys., vol. 61, no. I, Jan. 1983, pp. 93-98.
8. Bowman, J. D.; Swiatecki, W. J.; and Tsang, C. F.: Abrasion and Ablation of
Heavy Ions. LBL-2908, Univ. of California, July 1973.
9. Guthrie, Miriam P.: EVAP-4: Another Modification of a Code to Calculate
Particle Evaporation From Excited Compound Nuclei. ORNL-TM-3119, U.S. At.
Energy Comm., Sept. 10, 1970.
10. Gosset, J.; Gutbrod, H. H.; Meyer, W. G.; Poskanzer, A. M.; Sandoval, A.;
Stock, R.; and Westfall, G. D.: Central Collisions of Relativistic Heavy
Ions. Phys. Rev., ser. C, vol. 16, no. 2, Aug. 1977, pp. 629-657.
11. Hufner, J.; Schafer, K.; and Schurmann, B.: Abrasion-Ablation in Reactions
Between Relativistic Heavy Ions. Phys. Rev., ser. C, vol. 12, no. 6,
Dec. 1975, pp. 1888-1898.
12. Oliveira, Luiz F.; Donangelo, Raul; and Rasmussen, John 0.: Abrasion-Ablation
Calculations of Large Fragment Yields From Relativistic Heavy Ion Reactions.
Phys. Rev., ser. C, vol. 19, no. 3, Mar. 1979, pp. 826-833.
13. Morrissey, D. J.; Oliveira, L. F.; Rasmussen, J. O.; Seaborg, G. T.; Yariv, Y.;
and Fraenkel, Z.: Microscopic and Macroscopic Model Calculations of
Relativistic Heavy-Ion Fragmentation Reactions. Phys. Rev. Lett., vol. 43,
no. 16, Oct. 15, 1979, pp. 1139-1142.
14. Townsend, Lawrence W.; Wilson, John W.; and Bidasaria, Hari B.: Heavy-Ion Total
and Absorption Cross Sections Above 25 MeV/Nucleon. NASA TP-2138, 1983.
8
SYMBOLS
A nuclear mass number
b projectile impact parameter, fm
Eexc projectile prefragment excitation energy, MeV
Es nuclear surface energy coefficient, MeV
F defined in equations (5) and (11)
m number of abraded nucleons
N total number of nuclear neutrons
n number of abraded neutrons
P defined in equations (4) and (10)
Rp uniform nuclear radius of projectile, fm
RT uniform nuclear radius of target, fm
Z total number of nuclear protons
z number of abraded protons
(_> binomial coefficient
_ij probability of formation of type i fragment as a result of deexcitation
of type j prefragment
defined in equation (7)
A excess nuclear surface area, fm2
defined in equation (8)
v defined in equation (6)
_abr(Z,A) cross section for production of nucleus of type (Z,A) by abrasion, mb
o experimental cross section
exp
oF fragmentation cross section, mb
o cross section for abrading m nucleons, mbm
o cross section for abrading n neutrons and z protons, mbnz
1. Report No. 2. GovernmentAccessionNo. 3. Recipient'sCatalogNo.
NASA TM-85704
4. Title and Subtitle 5. Report Date
ABLATION EFFECTS IN OXYGEN-LEAD FRAGMENTATION AT February 1984
2.1 GeV/NUCLEON 6. PerformingOrganizationCode
199-20-76-01
7. Author(s) 8. Performing Organization Report No.
Lawrence W. Townsend L-I5716
10. Work Unit No.
9. Performing Organization Name and Address
NASA Langley Research Center 11 ContractorGrantNo
Hampton, VA 23665
13. Type of Report and PeriodCovered
12. Sponsoring Agency Name and Address Technical Memorandum
National Aeronautics and Space Administration 14. Sponsoring Agency Code
Washington, DC 20546
15. Supplementary Notes
16. Abstract
Ablation effects in the fragmentation of 2.1 GeV/nucleon oxygen nuclei by lead tar-
gets are examined by using the mechanism of particle evaporation. Following the
initial abrasion process, the excited projectile prefragment is assumed to statis-
tically decay in a manner analogous to that of a compound nucleus. The decay proba-
bilities for the various particle emission channels are calculated by using the
EVAP-4 Monte Carlo computer program. The input excitation energy spectrum for the
prefragment is estimated from the geometric "clean cut" abrasion-ablation model.
Isotope production cross sections are calculated and compared with experimental data
and with the predictions from the standard geometric abrasion-ablation fragmentation
model.
17. Key Words (Sugg_ted by Author(s)) 18. Distribution Statement
Heavy ions Unclassified - Unlimited
Projectile fragmentation
Abrasion-ablation model
Subject Category 73
19. Security Classif. (of this report) 20. Security Classif. (of this page) 21. No. of Pages 22. Price
Unclassified Unclassified I0 A02
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Ablation effects in oxygen-lead fragmentation at 2.1 GeV/nucleon

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